WO1989001615A1 - Improved method and apparatus for monitoring and/or controlling gaseous processes including processes where thermal transpiration effects are present and improved gauging for use therewith - Google Patents

Abstract

Improved apparatus and method for monitoring and/or controlling gaseous processes including processes where thermal transpiration effects are present and improved gauging for use therewith. A generalized gauge interpreter (304) is disclosed together with a reaction site interpreter (380) to thus facilitate accurate monitoring and/or control of the process. Devices (320, 334) for introducing measurable thermal transpiration effects between the reaction site (322) and gauge (324) facilitate accurate measurement of reaction site pressure to thus further facilitate accurate measurement and/or control of the process.

Description

IMPROVED METHOD AND APPARATUS FOR MONITORING

AND/OR CONTROLLING GASEOUS PROCESSES INCLUDING

PROCESSES WHERE THERMAL TRANSPIRATION EFFECTS

ARE PRESENT AND IMPROVED GAUGING FOR USE

THEREWITH Related Applications

This application is a continuation-in-part of U.S. application serial no. 165,290 filed March 8, 1988 and U.S. application serial no. 087,409 filed August 20, 1987.

Background and Objects of the Invention

This invention relates to (a) a method and apparatus for monitoring and/or controlling gaseous processes including processes where thermal transpiration effects are present and (b) improved gauging for use therewith.

Vacuum processes are notoriously nonreproducible. In spite of great care in the control of parameters such as the gas pressure and sometimes the reaction site temperature, the results most often suffer serious run to run and day to day variability. The results are sufficiently poor that the situation is one of frustration and distrust of the measured parameters and the assumed reaction mechanisms.

There are different measurement errors that cause these problems. For example, quality process control requires knowledge of the parameters at the reaction site. Measurements are made off-site to avoid placing delicate transducers in the reaction site. However, there is a failure to understand and develop the required translations and make the required auxiliary measurements that would make it possible for the Transducers to provide realistic values for the reaction site situation. Especially at very low pressures, transducers do not sense the parameters ascribed to them. In many cases the processes do not respond to the parameters that are assumed, and often the reaction site is not so designed that it can establish or maintain a uniform parameter such that the measurement can have validity.

Present equipment typically does not measure the correct parameters at the low pressure reaction site or control them such that the process is accurately managed. It is one object of this invention to provide a method and apparatus by which meaningful reaction site parameters can be measured, and how by these, and other inputs, the processes can be accurately controlled.

Gaseous processes are typically controlled by maintaining what is thought to be constant or controlled pressure. The gas temperature is sometimes ignored or crudely controlled in many cases. It is another object of this invention to bring together the effects of the thermal response of the pressure transducing operation, the effects of assuming that reaction site "pressures" are the same as the gauge "pressures", and the effects of the pressure and gas temperature on the process reactions.

It is only as this entire family is considered together that it is possible to provide the instrumentation by which gaseous processes can be accurately controlled to provide quality product. There are many steps involved in providing such instrumentation, some of which have been disclosed, but primarily at the gauge site, in the above-mentioned patent applications (density/pressure and transpiration corrections) and which are also disclosed in detail hereinafter.

For process control to be meaningful and accurate all factors as they affect the process rate must be controlled. It is thus a further object of the invention to determine or measure and mathematically compensate for, or control most, if not all, of the factors that enter the kinetics of the process. To fail to do so is leaving the process rate to chance--even though some factors may be controlled very carefully. It is not necessary to directly control all of the factors, but all of them should be known and taken into the correct relationship so that the parameters that are controlled actually control the reaction as desired. As an example of this aspect of the invention, consider a process where rate is given by Eq. A.

Rate = CPT² (A)

Pressure (P) can be controlled and temperature (T) measured. If a constant rate is desired while T varies, the value of P must be computed which will provide the desired rate at any given time, and then control to provide that moment by moment pressure. Rearranging Eq. A gives Eq. B. P = Rate/CT² (B)

If Rate = 100 at P = 1 x 10^-3 Torr and T = 400°K, C will equal .625. If the temperature increases to 450°K, the new pressure control value needed to maintain the rate of 100 can be calculated. P = 100/(.625 x 450²) = 7.90 x 10^-4 Torr (C)

If control of the pressure were continued at 1 x 10^-3 Torr, the reaction rate would be m error by 26%.

Many factors can be involved such as gas flows of different gases, pressures and/or partial pressures of gases, densities or partial densities, impact rates or partial impact rates and a host of less well defined thermal coefficients depending upon chemical reactivity and other functions. The present application describes a few cases in detail as examples of the much broader concepts involved.

In the example given, the kinetic equation was known. For accurate rate control in accordance with the present invention such an equation must be obtained. The altemavtive is that all parameters must be maintained constant in order to achieve the desired control. However, such levels of parameter control are seldom practical or financially feasible.

Thermal control of the reactor elements is often slow, especially when trying to cool them. Thus, thermal control of a reaction is seldom adequate by itself. The primary control should, if possible, be one with a very fast response in both directions. Fortunately, the gas pressure, for example, can often be adjusted very rapidly to maintain the desired reaction rate--but, in accordance with the present invention, only if the thermal status is correctly involved in the control equation can the correct value of this control parameter be selected. In addition to these kinetic relationships, the equipment that is employed is finite in its response characteristics. It thus becomes necessary to also consider the differential, integral and proportional functions as appropriate in control technology (DIP).

It will be demonstrated hereinafter that pressure gauges often measure other relationships than pure pressure. Also, the reaction rates are seldom a direct function of pressure. The question then arises as why, in accordance with the present invention, pressure is a desired gas parameter to control a gaseous process. In few cases, it is possible to measure the gas parameter of choice directly at the reaction site. However, in most cases, reliance must be made upon a remote measurement for the desired information and control. Where temperatures differ between gauge interior and reaction site, pressure, in may cases, is the only parameter that is the same at the two locations. Thus pressure in these cases is the only communication between the two regions. Pressure then provides communicability. However, there are complications in that the outputs of gauges that do not sense pressure have been labeled "pressure", and these complications can lead to understanding of some of the above principles. Moreover, pressure is not always fully the same between gauges and reaction site.

The more conventional gas gauge relationships are described below. It will then be shown many reaction site processes can be described in the same manner. It is thus a further object of this invention to relate the gauges to the processes for communication and control.

A new approach to understanding and correcting transpiration is also described which leads to a further object of the invention whereby a predetermined transpiration effect can be introduced between the reaction site, for example, and the gauge to thus eliminate other transpiration effects which might otherwise be present to thus provide a more accurate measurement of site gas pressure.

A further object of the invention is to provide improved control and information systems which interact with the more complex reactions and process systems to provide the process accuracy that is absent with conventional pressure measurement and pressure control systems.

A further aspect of the present invention relates to a method for automatic temperature compensation of gas density gauges, as disclosed, in particular, in above-mentioned U.S. patent application Serial No. 087,409. Such gauges include cold and hot cathode type ionization gauges. Such automatic temperature correction in the aforesaid gauges permits them to be more accurately used in the measurement of pressure. The concepts of the present invention can be applied to ionization gauges and some other types of gauges. The ionization type of gauge is discussed in greater detail hereunder.

Pressure measurement can result from the collision of gas molecules with a sensing surface. The pressure effect is a product of the number of molecules striking a unit surface per unit time and their average energy transfer. The same pressure reading at a higher gas temperature where there is greater average energy transfer per molecule, must thus have proportionately fewer gas molecules contacting the sensor per unit time.

A gas density gauge, however, measures only the relative number of molecules present - without concern for their average molecular energy. Thus, the density is an incomplete measure of the pressure, and those "pressure" gauges which measure only the density will be in error from this effect.

The universal gas law is shown in Eq. 1 where P is pressure, V is volume, n is moles of gas,

PV = nRT (Eq. 1) R is a constant, and T is the absolute temperature. Gas density is in units of moles of gas/volume. Solving for density gives Equation 2. density = n/V = (1/R) (P/T) = P/RT (Eq. 2)

The density is therefore proportional to the measured pressure divided by the measured temperature. Thus, the local density is inverse to the local absolute gas temperature. A density gauge can thus indicate a wide range of values at a fixed pressure, depending upon the absolute temperature of the gas in the sensitive part of the gauge at the time of making the measurement. Devices are well-known in the prior art for use as temperature compensating pressure transducers, which transduce pressure directly. Such pressure transducers transduce pressure directly into another variable such as displacement change or frequency change. This transduced variable may then be transduced into a second variable such as capacitance change, change in strain, and possibly even into several other variables before being transduced to an electrical voltage which is processed and displayed as the measured pressure. Each of these variables may be influenced by transducer temperatures and cause the measured pressure to be inaccurate by a fraction of a percent to several percent of the reading if the transducer temperature changes sufficiently. Therefore, for accurate pressure measurement, compensation must be provided for temperature induced changes in the physical dimensions of the transducer or changes in first, second or higher order variables. See for example, U.S. Patent 4,607,530 to Chow wherein frequency changes are compensated.

The recent patent literature contains references to such aforementioned temperature compensated pressure gauges. The foregoing patents, which are discussed further hereunder, all seem to correct for the errors of the transducer only when it is operated at specified temperatures. Although the transducers measure pressure, they give incorrect indications at some temperatures.

The pressure is an independent variable - it should be possible to correctly measure pressure independently of the transducer temperature. Note that the situation under discussion is somewhat different from that of a gas trapped, as by a valve, in the transducer. The pressure of such a gas in a fixed volume does indeed respond to the absolute temperature of the gas, but that is not the case of concern here, though in Smalarz et al., U.S. Patent No. 3,905,237, that principle is used to create compensating mechanisms for the range and zero of a pressure gauge, but not to make the fundamental measurement itself.

The U.S. Patent 4,468,968 to Kee teaches that the temperature is that of the transducer assembly and also teaches of adjusting the voltage supply so that the electrical value of the output equals the assigned electrical value corresponding to the combination of parameter values. The patent to Kee does not consider gas density, per se, but rather refers broadly to this concept along with all other types of measurement.

U.S. Patent No. 4,464,725 to Briefer works only with force systems, so the temperature correction is for the non-linearity of the transducer with temperature changes of the transducer.

Gross, in U.S. Patent No. 4,399,515, also works with force systems, including those with multiple transducers. Thus, such corrections are also usable for transducer corrections with changing transducer temperature.

In the U.S. Patent to Meyers, No. 4,392,382, there are taught direct pressure sensing capacitance manometers. The temperature related corrections are for transducer temperature correction.

Kurtz, in U.S. Patent No. 4,192,005 teaches use of strain gauges and pertains to measurement of pressures. The temperature correction removes the sensitivity and zero shifts caused by changes in transducer temperature.

Pearson in U.S. Patent No. 4,000,643 also uses strain gauges, and also pertains to pressure, and corrections taught therein-are for transducer temperature problems.

Heise in U.S. Patent No. 3.004,434 works with Bourdon tube gauges which sense pressure directly. This patent appears to be limited very specifically to such technology.

Cucci in U.S. Patent No. 4,598,381 covers a differential pressure sensor (or set of sensors) and applies corrections to these only.

Yamada et al., U.S. Patent No. 4,556,807, teaches a semiconductor diaphragm which responds to pressure. Located on the diaphragm is also a temperature sensor to correct the transducer response for changes in the diaphragm temperature.

Chow in U.S. Patent No. 4,607,530, teaches a fast acting thermal sensor to determine the temperature at one point on a quartz crystal resonator gauge. The gauge senses pressure, and the thermal data is used in conjunction with a computer model to establish its effect on the pressure reading.

Scott, in U.S. Patent No. 4,084,248, also teaches a general method for correcting errors from any transducer due to an independent error source, such as temperature. However, the technology employed is a specific type of look-up table that is outside the field of the present invention.

Juanarena, in U.S. Patent No. 4,644,482, is a vibrating cylinder pressure gauge with a means for detecting the temperature of the transducer.

In the foregoing references a number of pressure gauges are taught, i.e., gauges that respond to force on a given area. These gauges have no fundamental temperature errors caused by the pressure changing with temperature. Their mechanisms are responsive to temperature changes by changing of the zero point of the gauge itself and by any changes in the response of the transducer used therewith. These changes can result from temperature changes occurring in various parts of the device, and have no direct relationship to the temperature of the gas. The situation regarding density sensitive gauge elements, however, is just the reverse. The indication of such a gauge does not respond to the temperature of the gauge assembly by any measurable extent, but only to the temperature of the gas itself. The various electrodes in these density gauges can be at widely different temperatures - from white hot to near room temperature. Most often these gauges are of a very open format such that gas is not retained by any of the elements in any sense. If the temperature of one element of such a gauge is chosen as being representative of the gas temperature, this can generate an inconsistency if that element is not heated almost solely by the gas, or unless it restricts gas motion such that it totally determines the temperature of the contained gas. Such situations will usually occur only if intended by careful design.

Direct pressure transducers are rarely used for sensing pressures below pressures of about 1 x 10^-3 Torr, and are rarely used for directly transducing pressure to another physical variable such as displacement. The force per unit area exerted by the rarified gas at low pressures is too small to be simply and conveniently transduced into an easily measurable displacement (of an indicator needle, for example) or other similar variables, using presently available technology.

To measure pressures below about 1 x 10^-3 Torr conveniently and simply, gauges such as hot and cold cathode ionization gauges are commonly used. The output of ionization and discharge gauges depends not on the gas pressure but rather on the gas density in the transducer. The output of these types of gauges depends on the number of atoms or molecules of gas present in the transducer and thus on the gas density. The very name "ionization gauge" implies action on individual molecules of gas. Such gauges are herein termed "gas density dependent pressure transducers" to distinguish them from direct pressure transducers such as strain gauges.

It is well-known that gas density varies inversely with the absolute temperature of the gas in different parts of the system. When the gas temperature rises in one portion of the system relative to another, the gas density in the hotter portion decreases relative to that in the cooler portion. To provide an accurate pressure measurement using a gas density dependent transducer, the gas density in the transducers must be corrected for the effects of gas temperature. This is to be contrasted with temperature compensation for direct pressure transducers wherein the correction is applied because of temperature induced changes in the properties of the transducer itself - not because of changes in the medium being measured.

Existing gas density dependent transducers are commonly calibrated against a pressure standard and serve to measure gas pressure reasonably well only so long as the gas temperature in the transducer remains the same as was the gas temperature in the transducer during calibration. If the gas temperature changes, significant errors will exis in the pressure measurement. For example, a gas temperature change of 30°C from calibration to actual use will produce approximately an 8% error in the pressure measurement in a typical ionization gauge. At a typical bakeout temperature of 450°C, the pressure measurement error using an ionization gauge is approximately 50% due to gas density change. Proportional errors exist for temperature changes intermediate to those cited above. Such errors cannot be ignored for many applications.

It has been well-known for almost two centuries that gas density varies inversely with absolute temperature. Thus, it has been known for many years that such errors exist in gas density dependent transducers. Heretofore, there has not previously been made a serious effort to correct for such errors. Indeed, it appears that such errors have sometimes been treated as inconsequential when they are indeed not inconsequential.

In National Bureau of Standards Note 298, dated February 3, 1967, page 27, in analyzing errors in ionization vacuum gauges, the author states "...It is generally assumed, at least to a first approximation, that the rate of ionization in the gauge is proportional to the gas density. Safely, minor changes in envelope temperatures will not appreciably affect the rate of ionization, and therefore not affect the gauge indication. Two assumptions will be made: first that the gas and envelope temperatures are the same, arid second, that equilibrium conditions exist in the gauge and vacuum system. If the temperature of the envelope is changing, adsorption and desorption and degassing in the gauge are far more significant on the indication of the ionization gauge than the direct effect of changes in gas temperatures."

The author of the above quote further states that if "the envelope temperature differs from that at which the gauge was calibrated, the pressure P will equal P_i (T_o/T), where P_i is the indicated pressure, T_o is the envelope temperature at which the gauge was calibrated, and T is the envelop

temperature". The author further states "Ordinarily this

rrection is not applied, first because the additional accuracy obtained is usually insignificant, and second, because envelope and gas temperatures are not necessarily related, particularly in a hot cathode gauge. It is impractical to measure the gas temperatures." Ionization gauges are commonly calibrated in air conditioned laboratories such as exist at the National Bureau of Standards. They are often then placed in use deep within a complex vacuum system next to large horsepower mechanical pumps or next to high wattage diffusion pumps where the prevailing temperature is often at least 60° to 70°C. Thus, the temperature change is often about 40°C from calibration to actual use. This change will cause an error in a typical gauge of about 10%. Such errors are significant for many applications.

In addition to changes in gas temperature induced by changes in ambient temperatures, there are larger changes induced by changes in cathode heater power. When the cathode (the electron emitter) is clean and new, the power required to produce a constant electron emission is minimal. When the cathode is contaminated or near the end of its life, the required power may increase several times. Thus, the gas temperature may change significantly because of changes in the power required to maintain a constant electron emission. When such temperature changes are added to typical ambient temperature changes, pressure measurement errors of 20 to 30% can easily exist in gas density dependent gauges.

A possible reason such errors have been ignored is that for many vacuum process applications it is not strictly necessary to know the exact value of the pressure. It is only necessary to be assured that the gas pressure, whatever it may be, is the same in the process from run to run. Thus, it may have been erroneously assumed that as long as the gauge indication was the same run to run that the gas pressure remained the same run to run. This assumption is incorrect, as discussed hereunder. Clearly there is a need for a convenient and reliable method for the temperature compensating of gas density dependent pressure transducers.

It is thus a further object of the present invention to provide a method for compensating density dependent pressure gauges for temperature changes.

A further object of the present invention is to provide a method for automatically and accurately providing a pressure measurement that is temperature compensated.

Another aspect of the present invention relates to an apparatus and a method for transpiration compensation of gas pressure gauges and gas density gauges, and in particular to automatic correction of pressure and density measurements for errors due to transpiration effects, as disclosed, in particular, in above-mentioned U.S. patent application Serial No. 165,290. Transpiration effects can occur when the aperture of a conduit or orifice connecting the gauge to a system which is to be measured, has an opening into the system vessel of a size which is of roughly the same order as or smaller than the mean free path of the gas in the system. Such effects then occur due to any differences in temperature between the system gas to be measured and the temperature of the gas in the gauge which is performing the measurement.

Vacuum gauges are known in the prior art, as are other types of pressure gauges, wherein temperature compensation, in general, is disclosed. For example, in above-mentioned U.S. Patent No. 4,464,725 to Briefer, a temperature compensated measuring system is disclosed wherein an internal signal-processor has a calibration mode and a measurement mode, and includes a microprocessor, a RAM device, a ROM device, and a display for obtaining a temperature-compensated pressure value. However,this reference does not address the problem of transpiration correction for measurement of pressure or density in a system under vacuum. It addresses only the sensitivity of the measurement system based upon the temperature of the transducer. Neither system gas temperature nor transducer gas temperature are measured, per se, nor are these temperatures used in the computation of the system pressure.

The above-mentioned U.S. Patents, having Numbers 4,192,005 issued to Kurtz, 4,399,515 to Gross, 4,607,530 to Chow, and 4,644,482 to Juanarena, are also representative of the prior art. Each of these patents compensates pressur transducers for temperature differences of some part of the transducer system by storing various compensation functions or constants in a memory. None of these references teach correction for pressure measurement errors due to transpiration effects.

Thermal transpiration is a serious problem because in many pressure measurement operations, the gas in the pressure transducer is at a different temperature from that in the chamber where the pressure measurement pertains. If the opening between the chamber and active portion of the transducer is sufficiently large, at some given pressures the pressures are the same in the gauge as in the chamber regardless of the temperature differences. Thus, if the transducer senses "pressure", as such, the reading may be correct for the chamber pressure. However, when the active portion of the gauge is separated from the chamber by any form of tube or orifice whose diameter approximates or is less than the mean free path of the gas (about 5 cm at 10 Torr at 20°C for nitrogen, for example, and inverse to pressure), a pressure phenomenon is introduced by the temperature difference. This phenomenon is referred to as thermal transpiration. Thermal transpiration has been studied since before the turn of the century, but is not totally understood nor fully appreciated even at this date. A well determined mechanism has not been established for the transition, and there is no fundamental equation defining it. It is not accounted for by prior art pressure or density measuring devices, and no manual correction is typically made therefor.

Thus, a typical reference to the thermal transpiration problem may be found in "A Survey of Ionization Vacuum Gauges and Their Performance Characteristics", NBS Technical Note 298, February 3, 1967 by Brombacher which discloses the ratio of the pressure in the vacuum chamber to the pressure in the gauge is equal to the square root of the gauge temperature. However, the reference suggests compensation of the problem is facilitated by use of a large conductance such as a nude gauge, which, as indicated above, results in the gauge pressure being the same as the chamber pressure regardless of temperature differences between them. Hence, there is no suggestion to provide a means in a pressure or density measuring device to compensate for transpiration when, in fact, there are pressure differences between the gauge and chamber due to thermal transpiration.

In order to more fully appreciate the solutions to this problem provided by the present invention, a more detailed discussion of the thermal transpiration phenomenon follows. It appears that under some situations a pressure difference occurs from location to location in a system related to the absolute temperature at these locations. Normally, it is anticipated that even with different local temperatures, the pressures would be the same throughout a system. Otherwise, it seems that gas would flow from the higher to lower pressure areas to equalize these pressures. However, thermal transpiration causes the pressure in the hotter side to be greater than the pressure on the cooler side of the orifice or tube. The most elementary explanation is that the hotter molecules have a poorer chance to escape than do the cooler ones to find their way in. Thus, there is a pressure difference across the opening that remains even at equilibrium. When the passage is small enough, or the pressure low enough, the limiting relationship reasonably fits Eq. 3., this limiting relationship of full transpiration being mentioned in the above-mentioned NBS Technical note and illustrated on the left side of Fig. 4,

P_c/P_g = (T_c/T_g)^1/2 (Eq. 3) where:

P_c = pressure in the chamber P_g = pressure in the gauge

T_c = absolute temperature of gas in the chamber T_g = absolute temperature of gas in the gauge One aspect that does not appear to be fully or clearly addressed in much of the prior technical literature is that at equilibrium at high system (or chamber) pressure, the pressures are uniform, i.e., P_c = P_g, regardless of T_c and T_g and thus Eq. 3 does not pertain here. As the system pressure is decreased the situation will be eventually reached where transpiration effects will reach their full value, which usually relates to the temperature in accordance with Eq. 3. Transition effects remain in full effect at all lower pressures. See left side of Fig. 4. In measuring the pressure ratio as the orifice or tube is enlarged, or as the pressure is increased, it is found that the pressure ratio moves back toward unity, i.e., the pressure becomes the same on both sides of the opening. This is the situation on the right side of Fig. 4.

This situation can be expressed by Eq. 4 which is like Eq. 3, except that the exponent on the temperature ratio has changed to zero.

P_c/P_g = (T_c/T_g)^o = 1.0 (Eq. 4)

Thus, as seen in Eq. 3, the classical transpiration equation only pertains in the lower pressure cases. From there, over about three decades of rising pressure to the Eq. 4 case, the pressure ratio can be expressed as shown by Eq. 5.

P_c/P_g = (T_c/T_g) ^q (Eq. 5)

Here q is between zero and 1/2, depending upon pressure and geometry.

With full transpiration, a 10°C difference between the temperatures of the gauge gas and the chamber gas causes a 2% measurement error. If the gauge is heated to a temperature of 180° above the chamber, the error is 21%. That is, the gauge reading will increase 21% due to this effect from the time of initial turn-on at chamber temperature until reaching thermal equilibrium, assuming full transpiration where the transition occurring along the pressure function depends upon the geometry of the interconnection.

As more stable and more repeatable gauges become available, this correction becomes more and more important. Where measurements are desired to within even a few percent accuracy, corrections are needed for this transpiration effect. As process perfection becomes more dependent upon accurate low pressure measurement, this correction will play an increasingly vital role.

The apparatus and method of the present invention compensates for variations in gauge gas pressure or density readings which may occur during measurement due to transpiration effects. An ionization gauge, for example, may be calibrated under known conditions to optionally provide a table of ionization current versus system pressure at known values of system gas temperature and gauge tube gas temperature and gas type. This table may be stored in a memory device. The ionization gauge current output is measured for a known gas corresponding to an unknown pressure at a measured absolute temperature of gas in the gauge and a measured absolute temperature of the gas in the chamber. From the entry in the stored table, which relates to the values of these data, an output pressure value is obtained where this pressure value corresponds to the transpiration compensated, unknown pressure for the given gas type. Alternatively, curve fitting, and/or mathematical equations may be used in place of the look-up table to determine the value of the unknown pressure.

It is thus another object of the present invention to provide a method and apparatus for compensating pressure and density gauges for measurement errors due to transpiration effects.

It is a further object of this invention to provide improved gauges for effecting transpiration and/or density corrections.

These and other objects and advantages of this invention will be apparent from a reading of the following specification and claims taken with the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a schematic view of an ionization gauge and vacuum system as used in the present invention;

Figure 2 is a schematic diagram of the elements usable in the present invention; and Figure 3 is a flow chart diagram illustrating the steps used in obtaining the system pressure compensated for temperature.

Fig. 4 graphically represents thermal transpiration effects when the gauge gas temperature is hotter than the vacuum chamber gas temperature;

Fig. 5 schematically represents an apparatus for automatically correcting for transpiration effects according to the present invention;

Fig. 6 represents a graph of gauge sensitivity as a function of pressure;

Fig. 7 represents a sensitivity curve as a function of pressure, wherein thermal transpiration effects are present;

Fig. 8 shows a graph of defining additional functions used in adapting equations;

Fig. 9 shows a graph of similar shape from an electrochemical technology;

Fig. 10 graphically represents a curve fit of the transpiration transition to a linear transition;

Fig. 11 shows another curve representing a pressure transition range versus a function of a temperature ratio; and

Fig. 12 schematically illustrates a method according to the present invention; and

Fig. 13 is a diagrammatic illustration of an ionization gauge having internal and external temperature sensors in accordance with a further aspect of the invention.

Fig. 14 is a block diagram of an illustrative, generalized pressure gauge system in accordance with the invention. Fig. 15 is a block diagram of a gauge system of the type illustrated in Fig. 14 including a transpiration correction capability.

Figs. 16 - 16D are diagrammatic illustrations of various embodiments of tubes for introducing a measureable transpiration amount between a reaction site and a pressure gauge.

Fig. 17 is a diagrammatic illustration of an embodiment of means for maintaining a region of the connection between a reaction site and a pressure gauge at a constant temperature to eliminate transpiration effects therein.

Fig. 18 is a block diagram of an illustrative reaction site parameter measurement system.

Fig. 19 is a block diagram of an illustrative reaction site process control system.

Fig. 20 is combined block diagram and flow chart illustrating in further detail an illustrative implementation of the system of Fig. 19.

Detailed Description of Preferred Embodiments of the Invention

The relationships between the three basic types of gauges used to measure pressure. are first discussed, these gauges being respectively responsive to pressure, density, and impact rate. All three of these gauge types are proportional to pressure and differ primarily in the temperature coefficient of their response. It is only in the response to temperature that one gauge type can be distinguished from another. This concept has not been well understood. With the foregoing in mind, typical pressure responsive gauges for measuring gas pressure will first be discussed. A manometer responds to the force per unit area in its fundamental mechanism. It is thus considered to be a pressure gauge. It is only, however, if its mechanisum is immune to temperature effects that it can be a pure pressure sensor. It is only the temperature effect on the pressure that should be seen, not other temperature phenomena related to expanded metal and changing modulus of elasticity, etc.

These other thermal effects may serve as a mechanical thermometer which contributes some unwanted or unknown thermal function to the gauge output. As a result, the operation of the manometer at other than calibration temperature may not prove to be pressure measurement, per se. It could become dependent upon density, impact rate or some other temperature relationship between or outside of these easily identified ones.

As described in detail in above-mentioned application Serial No. 087,049, in a density responsive gauge, the reading thereof can be combined with the measured temperature of the gauge gas to obtain a pressure signal. In similar manner, the reading of an impact rate sensing gauge can be combined with temperature information to become a pressure gauge. Thus, the output of a thermally imperfect pressure gauge of the type discussed above, if its thermal characteristics are known, can be combined with temperature information to provide accurate pressure signals.

Turning now to density sensitive gauges, the ionization gauge is one of the best density responsive gauges at high vacuum. Because of the very high velocity of the ionizing electrons, the velocity of the gas molecules has almost no effect on the gauge sensitivity. This makes the gauge density sensitive rather than pressure sensitive, for it is only the number of molecules pressent, not their pressure that counts.

Density signals can be generated from pressure sensitive or impact rate sensitive meters by properly combining their signals with temperature information.

With respect to impact rate sensitive gauges, impact rate data are obtained from some pirani and thermocouple type gauges. If the sensor element is very hot relative to the gas temperature, the gas temperature plays no significant role in the output. Thus, the gauge measure the rate of molecular impact upon the sensor element.

Less highly heated sensor elements lose sensitivity rather markedly as gas temperature increases, for hotter molecules remove less heat from the sensor than do cooler ones. This gives a very different response than pressure, and one which changes with pressure. Again, if the thermal response is known, and so is the gas temperature, the device can be made to indicate pressure quite accurately using electronic treatment of the data. If it were necessary, an impact rate gauge could be made to read density, or pure impact rate, depending upon how the gauge sensitivity and gas temperature functions were combined.

In summary with respect to the three types of gauges, pressure may be generated from the gauges as follows. If off-site pressure is being measured by a pressure sensitive gauge the measurement should generally be adequate as is, unless there are gas flow or transpiration errors involved.

If density is the parameter of measure (that is, if a density sensitive gauge is being used), the density measurement should be converted to a pressure measurement as discussed above. This should then be adequate unless there are gas flow or transpiration errors involved. If impact rate is the parameter of measure, this can be converted to pressure as discussed below where the gauge gas temperature would be measured and be used in the computation.

If the output indication of the gauge as a function of pressure and temperature is a more complex function than these three simple gas law gauge cases, the knowledge of the function and the values of the measured parameters should be sufficient to make possible the determination of the pressure. Again, gas flow or transpiration can cause errors. Depending upon the mechanisms of these gauges, the composition of the gas that reaches them may also provide a reading error, which can also be taken into account.

With respect to the measurement of reaction site pressure, pressure is chosen as the preferential parameter for off-site measurement, because it alone is directly related to the reaction site condition. If the system design places no gas flow or thermal transpiration error in the path to the reaction site from the pressure transducer, the pressures will be the same in both places.

It should be noted that the pressure at the reaction site may not be the needed parameter there. However, it is the one that can be measured without being in the reaction site with the transducer (or gauge). It can be subsequently modified, if necessary.

Assuming a pressure responsive gauge is used to make this measurement, it is critical that pressure is truly being measured at the off-site location. This means that the gauge output must have the correct temperature coefficient. This can be achieved as discussed above by knowing the temperature characteristic of the transducer and sensing a known function of the temperature of the gas as well as its gas property transduced effect. The measurement system must then use these data as required to provide the pressure signal. At present, applicant knows of no gas property transducer that can provide a pressure signal without in some way correcting its response for temperature effects.

The mechanism of the transducer does not establish its pressure sensitivity, per se. Any device that provides a correct pressure reading at only a single fixed temperature is only a pressure gauge if it also controls the temperature of the gas that it senses to that value. The transducer mechanism can sense any pressure related parameter provided that its output is temperature corrected to provide a pressure signal.

It is possible to accurately measure reaction site density when the reaction site gas temperature in addition to the pressure there are known. Once these two parameters are known, Eq. (6) can be used to establish the value there, utilization of this equation having been discussed in the above-mentioned applications. D = P/RT (6)

Note that the gauge pressure need not be computed from the transducer to be used. Eq. (7) shows the relationship between the gauge density

P = D_gRT_g = D_sRT_s (7) and the reaction site density where D_g and T_g are the density and absolute temperature of the gas in the gauge, D_s and T_s are the density and absolute temperature of the gas in the system (or the reaction site), and R is the universal gas constant. Rearranging gives Eq. (8). D_s = D_gT_g/T_s (8)

This is dependent upon the pressure in the gauge being the same as that in the reaction site, but it is not necessary to calculate the pressure value to use the data from which D_s can be determined. If the data comes from a pure impact rate meter and its gauge gas temperature sensor, Eq. 9 can be used for establishing pressure.

P = N_gRT_g ^1/2/J (9)

The density could then be computed from Eq. (6) where T is the reaction site temperature. If there is no need to display the pressure, the reaction site density can be computed from N_g via Eq. (10).

D_s = N_gT_g ^1/2/JT_s (10) Where N_g = the number of molecular impacts against the gauge wall per unit area per unit time, J is a constant of the gauge, and D_s, T_g, and T_s are as defined above for Equation (7).

This same philosophy is used if the transducer has a more complex relationship between its signal, H, temperature, T_g, and pressure.

P = f(H,T_g) (11)

D_s = (f(H,T_g))/RT_s (12)

N_s = (f(H,T_g))J/RT_s ^1/2 (13)

Thus, whatever the pressure related gas sensor relationships, reaction site pressure, density or impact rate can be determined from them.

Reaction site immpact rates also require a knowledge of the pressure and the reaction site temperature. See Eq. (14).

N_s = PJT_s ^-1/2/R (14)

Eq. (6) is expressed in terms of P and substituted for (a) P to express Eq. (14) in gauge density and gauge temperature, and (b) Eq. (11) for P to give the general expression. Eq. (15) shows the N_s, N_g relationship.

N_s = N_g(T_g/T_s)^1/2 (15)

Assuming a generalized situation at the reaction site for reaction rate, Eq. 16 obtains. rate = f(S₁, S₂, ---S_x,) (16)

S_n is a system or reaction site parameter. The pressure is established as before, if it is one of the parameters, and the reaction site gas temperature is measured if it is needed. Each of the parameters must be known, measured or controlled.

With respect to thermal parameters of the various vacuum pumps associated with many gaseous processes, these processes will most often behave in ways similar to those discussed for above gauges. The pumpdown of a vacuum system is typically a density phenomenon. The mechanical roughing pump tends to remove a volume of system gas per stroke, independent of pressure or temperature over much of its operating range. The diffusion and turbo pumps also are primarily density dependent, but will have some temperature effects (inverse) as temperature becomes too high. The ion pump is also density related.

Cryo and sorbtion pumps are impact rate dependent over their normal operational temperature ranges. The cryo trap over the diffusion pump is also impact rate dependent.

With respect to the thermal parameters associated with the gas processes per se, pressure plays a critical role in gas/gas chemical reactions, for the number of collisions is of importance and also the probability of reaction increases with the energy of the molecules. The rate is typically proportional to the product of the partial pressures raised to powers related to the stoichiometry. When the gases react on the surface of a catalyst, the temperature, as well as area and quality of the catalyst enter the equation. Gas reactions with a solid also tend to be pressure related.

Where multiple steps are involved in a reaction, the kinetics deal only with the rate limiting step. This step is not usually intuitively obvious. Often the temperature effect is not this simple, for activation energy of the rate controlling step is involved. Once the charactertistic is known, however, a suitably programmed process interpreter can apply it to control the reaction.

Density related operations include gas discharges, sputtering, and gas interference with ion, atom or electron beams. It has been proposed that because the bombarding entities move so fast, they are not influenced by the speed of the gas molecules, but rather by how many of the gas molecules are in the paths of the bombarding entities. Even evaporation, where the atoms move relatively slowly will be influenced in the same manner. Thus it is related to density and unrelated to relative velocity.

Impact rate relates to gas chemical reactions with very hot solids, or very reactive ones, like getters. If nearly every contacting molecule reacts, momentum is to no advantage, and only T^1/2 applies, see Eq. (9), for example.

Gauge calibration is an important factor, for here each gauge type will interpret differently the gas to which it is exposed. Density responsive and impact rate responsive gauges will only fully reflect their calibration in use if they see the same gas temperature with which they were calibrated.

A detailed description will now be given as to how a density sensitive gauge such as an ionization gauge, when utilized to measure pressure, can be thermally compensated when the gauge gas temperature is different from the gauge gas calibration temperature. This description corresponds to that given in U.S. application Serial No. 087,409.

In order to illustrate this method, it is helpful to consider an ionization gauge transducer, such as that described in U.S. Patent No. 4,636,680, which is to be used to measure the pressure of gas in a vacuum system. The transducer is used with an ionization gauge controller, such as is available as Granville-Phillips Cat. No. 307 001, which serves to supply controlled voltages to the electrodes, power the electron emitter, control the emission and measure the ion current as is well-known in the art.

The transducer is fitted with a temperature sensor such as a tungsten ribbon or coil which is in good thermal contact with the gas in the transducer. A second electron emitter may be used for this purpose as well as an auxiliary heater which serves to heat the IG (ionization gauge) to outgassing temperature as is well known in the art. The temperature sensor material is selected to have a suitable temperature coefficient of resistance so that by measuring the resistance of the sensor, the temperature of the sensor may be ascertained. Such means of measuring temperature are well-known. Other means such as a thermocouple may also be used.

It is not necessary that the temperature sensor be at exactly the gas temperature but only that it move up and down in temperature in step with the gas temperatures. The closer the temperature of the sensor is to the actual gas temperature and the smaller its thermal mass, the more accurate will be the temperature measurement of the gas.

Prior to use in measurement of vacuum system pressure, the above described assembly of transducer, temperature sensors and controllers is calibrated by any of a number of well-known measurements. The National Bureau of Standards offers such a calibration service as do a number of commercial laboratories. As an example of this general method we will provide a detailed description of the treatment of a density transducer, which is somewhat non-linear in density response, but responds to changes in temperature in a manner proportional to the ratio of absolute gas temperature to absolute calibration temperature. During calibration of the assembly, the calibration system pressure is scanned over a suitable range and the corresponding calibration pressures and indicated pressures are recorded in a table as is well-known in the art. In addition, the gas temperature in the transducer is recorded.

This table of known pressure values, P_o, indicated pressure values, P_i, and indicated gas temperatures T_o, is stored for future use in the memory of the ionization gauge controller. Such storage can be accomplished using a number of microprocessor electronic techniques which are well-known in the art.

It is observed experimentally that the indicated pressure tends to vary smoothly and predictably point to point with changes in the calibration pressure and that indicated pressure varies smoothly and predictably point to point with the gas temperature. Therefore, a preferred method of storage of the table of calibration information is by means of one or more mathematical equations which relate one variable to another variable to accurately describe the three dimensional mathematical surface defined by the calibration pressures and temperatures.

Generating mathematical equations from such data is called curve fitting and is a technique well-known in the art.

The resulting mathematical equations relating P_o to P_i, and P_i to T_i may be used to calculate the value of P_o corresponding to any P_i and T_i simply by substituting the values of T_i and P_i into the equations and evaluating the equations as is well-known in the art. Storage of such equations is much more convenient and more useful than is a table of values of P_o, P_i, and T_i. However, either means of storage, or any other storage means, can be used so long as the required information is available for subsequent use in the ionization gauge controller memory.

Figure 1 illustrates the system 10 having a system temperature T_s and a system pressure P_s. The system 10 is evacuated to a very low pressure through conduit 14 by a high vacuum pump 12, which pump may be any type of pump suitable for this application.

The system pressure is measured by an ionization gauge 18 which senses the pressure of the system 10 via a conduit 16. The ionization gauge 18 has a collector 20, a filament 22, and leads 24 and 26. The ionization gauge 18 is connected to a collector measuring circuit 30 by line 28. The ionization gauge 18 serves as a transducer. Output line 32 is used to transmit the output of the collector measuring circuit 30 to a downstream device such as a controller for further processing and display.

In use, the ionization gauge transducer is attached to the vacuum system whose gas pressure is to be measured. Attachment is by means of a Conflat flange or other well-known means. Gauge gas temperature is measured by transducer 5.

In use, the ionization gauge 18 measures an unknown pressure in the vacuum system in terms of an indicated pressure, P_x, and a gas temperature T_x. These measured values are output as representative electrical current values, which then are continuously output to the ionization gauge controller (not shown in Fig. 1) for processing.

The microprocessor in the ionization gauge controller is programmed by software methods well-known in the art to periodically carry out the following steps in order: 1. Identify a specific value of indicated pressure, P_x, corresponding to a specific value of unknown gas pressure in the system. 2. Identify the gas temperature, T_x, that prevails in the transducer at the indicated pressure, P_x. 3. Insert the identified values of P_x and T_x into the stored equation for gas temperature and gauge reading to obtain the temperature corrected gauge reading.

4. This temperature corrected reading is then inserted into the equation for gauge reading and pressure to calculate the pressure in the gauge, P_oc.

5. Output the value, P_oc, as the corrected measured value of the unknown system pressure.

By repeating the above steps on a sufficiently frequent time schedule a continuous measurement of the corrected pressure in the system can be displayed independently of changes in temperature of the gas in the transducer 18.

The foregoing steps are further illustrated with reference to Figures 2 and 3. In Figure 2, the circuit elements and system elements of the present invention are illustrated schematically. A vacuum system 10 communicates with an ionization gauge 18 and a temperature gauge 40 by a conduit 16. The temperature gauge 40 sends an output signal indicated as signal 42 to an A/D converter 46. Similarly, the ionization gauge 18 transmits an output signal indicated as signal 44 to the A/D converter 46. The processed output signals from the converter 46 are supplied to a microprocessor 48.

The microprocessor 48 as shown in Fig. 2 preferably contains a memory such as a RAM memory, disk memory, tape memory, or any other available memory means. The microprocessor 48 itself can be any commercially available microprocessor capable of accessing stored information and of conducting the types of calculations used in the lookup table or in a curve-fit algorithm. The microprocessor 48 preferably contains a RAM memory 82 such as is seen in Fig. 3. The microprocessor 48 then communicates with a downstream device such as a display device 50 or a controller 60. If a controller 60 is used, it then produces an output signal to control a controlled device 70. Such a controller 60 might be, for example, a safety shutdown device to shut down a process of the system if the pressure exceeds a predetermined level. In such a case, the controlled device 70 might be, for example, a system control device which controls ongoing processes in the system whose pressure is being measured.

The procedure whereby the actual system pressure is calculated is shown schematically in Fig. 3. First, the ionization gauge (IG) is calibrated. The calibration of the ionization gauge is necessary in order to define a curve or series of curves, or alternatively to define a lookup table, for the ionization gauge output current I_c versus the actual system pressure P_c during the calibration procedure. During the calibration procedure, the ionization gauge is maintained under controlled conditions, as is the vacuum calibration system, such that the temperature of the gas being measured is at a measured temperature in the gauge of T_c, the temperature T_c being in absolute degrees Kelvin or Rankine.

As shown schematically in Figure 3, a calibration step 81 is used to provide the calibration data described above. The calibration information is supplied, in either algorithm form or lookup form, to a memory device 82 (such as a RAM) which can be part of a microprocessor 48, or which alternatively can be an accessory to the microprocessor 48. Thus, the microprocessor 48 as seen in Figure 3 can access the calibration data in the memory device 82 when called upon to do so. An ionization gauge such as the gauge 18 of Fig. 1 is used to measure the actual ionization current I_A1 and a temperature gauge such as gauge 40 is used to measure the absolute temperature of the gas in the vacuum gauge 18 and is indicated as temperature T_A1. This step is indicated schematically at block 83 of Fig. 3.

The measured values are then stored in the memory 82 by the microprocessor 48 as indicated by block 88 of Fig. 3. As seen in the foregoing discussion, the calibration data does not take into account the variation with temperature of the gas in the vacuum gauge 18.

While Fig. 3 shows a schematic procedure for determining pressure of a gas in a vacuum system 10, it is contemplated that information relating to a variety of different gases can also be stored including their calibration curves, and that the particular gas being used can be input in the method step shown in Fig. 3 so that the microprocessor 48 can select the appropriate calibration curve information for the particular gas being measured. All such embellishments and modifications are contemplated as being within the scope of the present invention. At the next step in Fig. 3, the values of relevant parameters are called up from the memory 82 via the microprocessor 48. In particular, the temperature of the gas measured during calibration T_c is called up, as is the aforementioned ionization gauge output current I_A1 and the measured temperature of the gas in the gauge T_A1.

As seen at block 86 in Fig. 3, the aforementioned information is used to calculate a new ionization current value I_N which can be used to determine the temperature-corrected gas system pressure from the calibration information. The equation used is as follows.

I_N = I_A1 (T_A1/TC) (17)

The new ionization current is calculated as I_N, and is then supplied to the microprocessor for lookup in the calibration data to determine a temperature-compensated value of pressure of the gas in the vacuum system 10 as

P_ACT'L. The temperature-compensated value of the pressure is then output as seen at block 89 of Fig. 3 as P_ACT'L.

Where accurate curve fitting requires that more than one equation be used to represent the dependent variable over the entire span of the independent variables, referring to the enumerated steps listed hereinabove, an additional step is required between steps 2 and 3 and steps 3 and 4. Each such additional step consists of identifying which of the several stored equations to use. Such identification is readily accomplished using suitable IF-THEN statements by those skilled in the software art.

The family of interrelated requirements accorditng to the present invention are:

1. A gas density gauge providing a reading of K times D, where K is relatively constant, and D is gas density. 2. A thermal sensor providing a reading of j times T at an appropriate location in gauge, where j is a constant and T is the temperature, or alternatively providing a reading from which jT can be computed. 3. A computer related controller which is able to store critical data and perform appropriate look-up, calculation and display, as well as operate the gauge functions. 4. Software for automatic operation in at least one of the following modes:

a. Gauge which is linear in D, and has directly calculable temperature effects

Calibration - direct or by class, etc., one pressure point, P_o, data = D_oK, jT_o.

Compute and store calibration factor C .

Calibration factor = P_o/D_ok = C (18)

Multiplication of gauge reading by calibration factor gives correct pressure reading at the calibration temperature.

However, when the gauge is used at a temperature which gives a reading jT, Equation 18a provides the temperature corrected pressure reading as follows.

P = DKCjT/jT_o (18a) Thus, C and jT_o are placed in memory and used in the computation of Equation 18a for every incoming data set of DK and jT. Such storage and computation are possible by many well-known techniques.

Computed values of P are then displayed and used for control purposes in ways well- known in the art. b. Gauge non-linear in D, and which has directly calculable temperature effects. Calibration - directly or by class, of multiple pressure points, P_i, over a full range at a measured temperature of the gauge, jT_o. Data is represented by D_ik vs. P_i, jT_o.

Data representing P_i and D_ik are stored in tabular form or preferably have a smooth curve fit through them by well-known curve fitting techniques, and only the algorithm and a few required constants are stored.

When the gauge is used at a temperature which gives a reading jT_i and Dk, Equation 19 provides the temperature corrected reading.

D_ik = DkjT/jT_o (Eq. 19)

Then P_i is estabished by entering D_ik in the stored algorithm or iterating to obtain it from the data stored in a table, whichever storage technology is employed. Values of P_i are then displayed and can be used for control purposes in ways well-known in the art.

Some prior art thermal gauges have relatively crude temperature corrections, but they fail to meet the requirements that the present approach provides. On the other hand, the ionization gauges and discharge gauges do not seem to have any reported systems for measuring the gas temperature. As indicated earlier, there are possibilities of generating crude temperature measurements using the electrodes in some existing gauges. In some cases even the envelope temperature may provide some level of correction. However, this is typically a poor correction, especially if the conductance into the gauge is significant. If the gauge involves a rather closed structure at a fixed or measured temperature and with a small conductance to the system being measured, the closed structure controls the temperature of the gas being measured. This appears to be the most effective system for measuring the gas temperature. Measurement of the temperature of such a closed structure is possible by many known temperature sensing techniques.

An alternate density correction approach is discussed hereunder. This approach can be used in the foregoing embodiment to correct for temperature effects upon measured pressures.

There is another type of question which can arise, namely whether the pressure, P, is the same in all locations of the vacuum system, including the gauge. There are two cases where a pressure difference can occur:

1. gas flow effects due to flowing gas

2. thermal transpiration If the gauge is clean and has operated for a few hours continuously under reasonably constant conditions, the gas flow problems from pumping and/or outgassing are very small. Thermal transpiration is involved only when the mean free path is larger than the entry. The following discussion assumes the gauge is used under conditions that avoid both of these effects.

In an ionization gauge the ion current, i₊, is proportional to the product of the emission current, i-, and the number of gas molecules present n_gauge, where

i_c is proportional to (i-) (n_gauge) (20)

i_c = (K) (i-) (n_gauge) (21)

The fundamental gas law can also be used to define the number of gas molecules present in the gauge.

P = (n_gauge) (k) (T_gauge) (22)

Solving for n_gauge gives:

n_gauge - p/(k T_gauge) (23)

Substituting Equation 23 into Equation 21 gives:

i_c = (K i- P)/(k T_gauge) (24)

The classical equation for the ion gauge is Eq. 25.

i_c = S i- P (25) Placing Eq. 24 in this same form gives Eq. 26.

i_c = (K/(k T_gauge)) i- P (26)

Thus,

S = K/(k T_gauge) (27)

Thus, S is temperature dependent, and not a constant as has been assumed in the previously known literature.

Previous explanations for this laxity may have been made on the basis that the gauge was calibrated to obtain S at a temperature very similar to that of its use. Thus, S involves an absolute temperature very similar to the

T_gauge used here.

S_cal = K/(k T_gauge/cal) (28)

S_use = K/(k T_gauge/use) (29)

S_use/S_cal = T_gauge/cal/T_gauge/use (30)

Thus, the ratio of use sensitivity to calibration sensitivity is simply the ratio of the absolute temperatures inverted.

If the gauge temperature of calibration was 100°C = 373°K, and the use temperature is 110°C = 383°K, then the ratio of use sensitivity to calibration sensitivity is:

S_use/S_cal = 373/383 = .9739

Thus, there is a nearly 3% error per 10 degrees difference from the calibration, or 1/3% per degree C difference. Corrections for this fundamental error form a basis of certain novel features of the present application.

In Fig. 14 there is shown a generalized pressure gauge 310 in which some function or parameter (Par) of the pressure P of a gas is sensed by a gauge mechanism 300 where P will equal the pressure in the gauge, P_g, if P_g = P_s, the reaction site or system pressure and where P = P_s if P_g = P_s. A function of the gauge gas temperature, T_g, may also be sensed by mechanism 300 or other appropriate means. A gauge controller 302 is connected to gauge mechanism 300. The controller provides the current, voltages, controls, etc., required to operate gauge mechanism 300 and extract signals of some type from it such as Par and T_g.

A gauge interpreter 304, in accordance with an important aspect of the invention, receives these signals and processes and interprets them into a format that provides direct relation to the gauge pressure. As discussed hereinbefore, a wide variety of process and interpretive operations may be needed in order to extract from the controller output signals that relate directly to pressure. These can include calibration equations, mathematic manipulations, comparison with selected tables, interpolation, smoothing, digitizing, display and outputting, etc. The greatest flexibility is provided when computerized technologies are employed. However, conventional circuitry can serve when the ranges are limited or the functions are sufficiently simple.

Thus, for example, gauge interpreter 304 may have incorporated therein or inputted thereto Eq. 18a to provide a thermally corrected, pressure measurement, as provided by an ionization gauge. Alternatively, the type of gauge mechanism 300 (that is, pressure gauge, density gauge, or impact rate gauge, for example) may be inputted to interpreter 304 whereby if an impact rate gauge were being employed, the interpreter 304 would select Eq. (9) for determining the pressure in response to an input signal indicating the impact rate meter was being utilized.

As shown by dotted line 306, the interpreter 304 may provide control operations for the temperature sensor so that the gauge controller can be one of the presently existing types which does not provide temperature measurement, regardless of the parameter that it senses. It is also possible that the gauge interpreter be a component of the gauge controller. It may also be a component of the process interpreter or control equipment to be described below. If the interpreter is sufficiently flexible, it can be adapted to process the signals from any of the available, or to be invented, transducers to provide system pressure related signals.

There has been described hereinbefore the situation at low pressures, and generally it has been assumed that the situation of low pressures pertains at high and ultra-high vacua. However, when temperature differences are present at very low pressures this classical P₁ = P₂ picture can not be applied throughout the vacuum system, for it is not true. The error, if treated at all, is called thermal transpiration. A lack of understanding of the phenomenon has apparently deterred many people from correcting their data for this error.

A further approach to understanding and correcting transpiration will now be discussed.

Consider an orifice at a thermal junction in the equipment where the temperature of the gas on one side is T₁ and that on the other side is T₂. If the pressure is very low, the gas molecules seldom stike each other, most collisions are with the walls. The flow of gas through the orifice depends upon how many molecules strike the orifice per unit area. A slow molecule passes through as easily as does a fast one, for there is no interference from other molecules. Thus, the flow per unit area is dependent only upon the impact rate, N. This, as stated in Eq. (14) is a function of pressure and temperature. At equilibrium the flows in both directions through the orifice are the same. Eq. (31) shows this equal flow and its implications.

N₁ = N₂ (31)

JP₁/RT₁ ^1/2 = JP₂/RT₂ ^1/2 (31b)

P₁/P₂ = (T₁/T₂)^1/2 (31c)

The pressures are not the same on both sides of the orifice when temperatures are different. Eq. 12c is also the experimentally determined equation for the full transpiration condition. It is obtained here as the result of pure molecular flow at equilibrium. Pressure is not the basis for equality because only the impact rate factor of the pressure is involved. The momentum transferred at each impact plays no role in the flow. Thus, transpiration is caused by the change in gas flow mechanism from pressure to impact rate. The equal-pressure-everywhere situation of higher pressures is so established that we have difficulty envisioning the true phenomena in high and ultra high vacua. Some have been misled here by the innocent statement "all at the same temperature", for this prevents one from having to face the situation where pressure can no longer be treated as the controlling parameter.

When the pressure is sufficiently low that gas moves only from hitting an opening, with no interference from the gas molecules, what may be termed the "molecular flow mode" obtains where pressure will not be the same on both sides of the opening if temperatures are different. Between this mode where there is no reflection of molecules back from the opening due to the presence of other molecules and the "viscous flow mode", where reflection is almost total, are nearly 3 decades of pressure in which both effects are present. If pressures are measured at equilibrium across an orifice separating gas of different temperatures, temperature will play a role from none to T^1/2.

It will now be demonstrated how to mathematically divide the gas into two fractions, one of which will act like high pressure gas and the other of which will act like molecular flow gas.

The equilibrium situation will be considered where the total flow through the orifice from one direction equals that from the other.

F₁ = F₂ (32)

In each direction the net flow consists of a quant ity that passes by impact minus the quantity that is reflected. q_i1 - q_r1 = S_i2 - q_r2 (33)

There can be defined the fraction of the flow across the opening from a to b that is reflected = f_ar. f_ar = q_r1/q_r2 (34)

The fraction that crosses as if nothing was in the way is f_ai. f_ai = (q_i1 - q_ri)/q_il (35) f_ar + f_ai = 1.0 (36)

The reflected fraction, f_ar, is interacting like pressure, the remainder, f_ai is interacting like free impact rate. f_arKP₁ + f_aiJP₁/T₁ ^1/2 = f_brKP₂ + f_biJP₂ + f_biJP₂/T₂ ^1/2 (37)

At high pressure all of the gas is reflected, i.e., f_ar = 1 = f_br or equal rates leak past the orifice in both directions and f_ai = f_bj = 0. Thus P₁ = P₂. When f_ar = f_br = 0, P₁/P₂ = (T₁/T₂)^1/2 This general equation thus meets the extreme cases. When neither fraction is zero it provides a mixture of the two cases. A fraction acts like pressure was there and the remainder acts like it was free of the rest of the gas, and in the molecular flow mode. The standard single direction flow equations are used, multiplied by the applicable fractions.

The fraction reflected back through the orifice is related to the ratio of the orifice radius to the mean free path of the gas.

L = hT₁ ^1/2/P₂ (38)

L is the mean free path and h is a constant for a given gas. T₁ ^1/2 relates to the velocity of the moving molecule and the P₂ to the gas into which it is traveling. The fraction reflected in this case is shown as an example to be r/L, where r is the radius of the orifice. f_ar = rP_B/nT_A ^1/2 (39) f_ai = 1 - rP_B/hT_A ^1/2 (40)

F_A = (rP_B/hT_A ^1/2)Kp_A + (1 - rP_B/hT_A ^1/2)JP_A/T_A ^1/2 (41)

F_B = (rP_A/hT_B ^1/2)KP_B + (1 - rP_A/hT_B ^1/2)JP_B/T_B ^1/2 (42)

When the constants are all known, plus measured values for P_A, T_A and T_B, the equations can be solved for P_B when F_A = F_B, i.e., at equilibrium.

This simple treatment becomes ineffective when L approaches r as higher pressures are approached. A slightly different mathematical model can be used at these higher pressures to shape the bottom of the curve. Additional models for shaping the curve are discussed below.

In the above example the orifice is a great distance from walls facing it from either side. When a portion of system hardware is parallel to the orifice at a distance of, for example, 2r from the orifice, some fraction of the impact rate gas will be redirected back through the orifice, independent of the pressure, but acting like a pressure effect. Because there will be this pressure-like effect remaining when there should be only impact rate effects present, the fraction will reach a limit before it gets to 1.0 x P/T^1/2. That is, if the fractions were expressed in terms of the temperature exponent, x, the value would not reach 0.5. It could stop at 0.35, for example:

P₁/P₂ = (T₁/T₂)^x (43)

The geometry of the thermal transition thus determines how far the transition toward the "molecular flow" equation can go. Information of this kind may be required for the programming of the transpiration correction equipment utilized in conjunction with the gauge controller.

This very elementary treatment involves many simplifications of model, but provides a general format that could permit the utilization of one equilibrium equation in the viscous flow regime, through the transition, and in the molecular flow regime at one thermal transition (that is, orifice or tube).

It is only if an appropriate relationship following this general concept or a selected set of relationships is applied across each thermal transition between the gauge and the reaction site that an off-site pressure gauge can provide a pressure reading that can be translated into the reaction site pressure value. It is possible if the orifice radius is the same at each thermal transition that only the reaction site temperature and the gauge temperature would be needed to determine the transpiration correction over the entire series of transitions. That is, identical series transitions can be treated as a single transition bearing the sum of the temperature differences. If the orifice radii are different, however, the transitions will occur at different pressures, providing a complex shaped transition from direct pressure reading to impact-rate-determined pressure values. To accurately determine the entire transition, all of the temperatures and radii are then needed.

Once a correct gauge pressure signal is provided at the gauge, transpiration errors all the way to the process site will have to be corrected, if they exist. The thermal transpiration problem and some answers are further discussed below.

A detailed description will now be given with respect to the correcting of transpiration errors, this description corresponding to that given in U.S. application Serial No. 165,290.

The following is a theoretical discussion which is useful in understanding the nature and purpose of this aspect of the invention, and in performing calculating steps according to the present invention.

If the gauge is a pressure gauge, that is, one which is directly responsive to pressure such as a manometer, diaphragm gauge, or a force gauge, the variables measured would include chamber gas temperature T_c, gauge gas temperature T_g, and H (the gauge's pressure indication signal for each reading). In the following equation, the symbols q and j represent the calibration constants for the gauge at the pressure involved, and would come from a previous calibration.

P_c = (H/_j) (T_c/T_g)^q (44)

Eq. 44 would be used for the computation. If the pressure gauge is linear in pressure, j is a constant and can be easily determined at pressures where q = o. If the gauge is non-linear, distribution of effect between j and q becomes arbitrary in regions where q is not a known constant.

If the gauge senses gas density, impact rate or a function thereof, such as an ionization gauge, a Pirani gauge, or a thermocouple gauge, the pressure reading will be in error due to temperature differences, independent of transpiration. Many vacuum gauges are of this type. The full treatment of gas density correction where transpiration is not involved is provided in U.S. Patent Application No. 07/087,409, filed August 20, 1987, mentioned hereinabove.

As can be seen from Eq. 44, the temperature of the gauge gas should be measured; however it has not been well-understood how to measure accurately this temperature, especially when gauges were either heat loss devices or contained heated filaments for electron emission. Outside wall temperatures of the gauge have been used, for example, even though not an accurate measure of the internal gas temperature. More accurate means for determining internal gas temperatures are described below with respect to Figure 13.

When a density gauge is used in a transpiration situation, it is possible to return to Eq. 5. In Eq. 45, the pressure reading, G, of the gauge is related to the gas density in the gauge, where k is a constant for a linear gauge, and is a changing value for a non-linear one.

G=k (P_g/T_g) (45)

Solving Eq. 45 for P_g gives Eq. 46:

P_g = G T_g/k (46)

Substituting Eq. 46 into Eq. 5 and solving for P_c gives Eq. 47.

P_c = 1/k[G (T_C ^q) · (T_g (1-q) _)] (47 ) Without transpiration, i.e., q = o, Eq. 47 becomes Eq. 46.

Under maximum transpiration q will equal 1/2, thus Eq. 47 becomes Eq. 48.

P_c = (1/k)[G(T_c · T_q)^1/2 _] (48)

If such a gauge reads correctly when both temperatures are 20°C, a 10°C change in one temperature only will cause 1.7% error.

To correctly apply such a prior art density gauge, it appears that the following must be measured:

1. T_c, the temperature of the gas in the chamber.

2. T_g, the temperature of the gas in the gauge.

3. G, the measured gas density signal from the gauge.

4. k, the calibration constant for the gauge at the density involved.

5. q, the exponent related to the transpiration level.

Measurements listed above at points 1, 2 and 3 are needed for each reading. Measurements listed above as points 4 and 5 can come from a previous calibration.

6. Compute P_c using the data of the above-noted points 1-5 above in Eq. 42.

Note that in this system correction is made for (a) the transpiration caused differences, and (b) the density to pressure difference (Or the above-mentioned gas density correction) simultaneously in the case of a density gauge. The pressure gauge equation where the gas density correction is not applicable is as stated in Eq. 44:

P_c=(H/j)(T_c/T_g)^q.

The density gauge equation is as stated in Eq. 47:

P_c = (G/k) (T_c ^q · T_g ^(1-q)). To automate the reading of the pressure gauge to a very high degree of accuracy would seem to require the determination and storage of q and j as a function of H,

T_c and T_g. Such a complete block of knowledge requires the multi-condition calibration of the gauge and much storage room. Such a complete calibration would remove any question of the gauge sensitivity under its range of operating conditions. However, it is not possible to determine both j and q at all pressures. The symbol j can, however, be combined with the symbol q such that q has some arbitrary fixed value at all pressures and j compensates for the true value of q under all circumstances. This cuts the required storage in half.

An alternative approach is to store the calibraation values of P_c in a three-dimensional array where H, T_g and T_c ar the dimensions. The simultaneous H, T_g and T_c readings then direct the look-up system to the correct calibrated value of P_c for the actual measurement which occurs.

An alternative approach to this high resolution three-dimensional calibration is as much coarser point by point calibration with significant differences between the temperature points and the pressure points. A computer system can be employed to use curve fits to provide accurate three-dimensional information where the actual measurements occur. The curve transpiration functions are relatively smooth, and make such interpolations highly effective for the corrections.

How complete the calibration data needs to be in order to provide adequate computation over the full range of pressure and the temperatures depends upon the specific gauge designs. Fig. 5 shows a schematic view of a preferred embodiment of the system, having a gauge 120 having an output signal G (or H), with full calibration data being in recorded form in a read only memory system (ROM) 110 or any other appropriate memory. The entire system shown in Fig. 5 as system 100 automatically provides the chamber pressure reading corrected for thermal transpiration, density and gauge linearity and sensitivity.

The system 100 can incorporate a density reading gauge or a pressure gauge as the gauge 120 with no modification of the system, since using the gauge gas temperature as one of the variables for transpiration covers the effects of density as well. Recording the entire data set also fully covers gauge linearity and sensitivity. Thus, the general method shown in Fig. 5, discussed further hereunder, covers all aspects of the pressure or density gauge other than errors due to drifting zeros, drifting sensitivities, and in some devices changing gas composition. In most critical processes, the gas composition is controlled. However, gauges with drifting parameters become difficult to operate at the accuracy level involved herein. Attempting to automate such processes is more difficult, for it should involve periodic zero adjustments and local calibrations. These aspects are not considered directly herein, since these functions exceed those normally associated with the gauge and gauge controller.

Prior to use of the Fig. 5 system, a table of known pressure values, P_c, indicated pressure values, H, indicated gauge gas temperature T_g, and indicated chamber gas temperature, T_c, are obtained by calibration as described above, for example, and stored for future use in memory 110 or the memory of, for example, an ionization gauge controller as discussed in co-pending U.S. Application Serial No. 07/087,409, referred to hereinabove or in gauge interpreter 304 of Fig. 14. Such storage can be accomplished using a number of microprocessor electronic techniques which are well-known in the art, e.g. storage on a RAM device, a ROM device, etc.

The following discussion is with respect to calibration of pressure with temperature, however a similar procedure would also apply to the determination of j and q. It is observed experimentally that the indicated pressure tends to vary smoothly and predictably point to point with changes in the calibration pressure and that indicated pressure varies smoothly and predictably point to point with the gas temperature. Therefore, a preferred method of storage of the table of calibration information is by means of one or more mathematical equations which relate one variable to another variable to accurately describe the three dimensional mathematical surface defined by the calibration pressures and temperatures.

Generating mathematical equations from such data is called curve fitting and is a technique well-known in the art. The resulting mathematical equations relating P_c to H, and P_c to T_g, and P_c to T_c may be used to calculate the value of P_c corresponding to any H, T_g and T_c simply by substituting the values of T_c, T_g and H into the equations and evaluating the equations as is well-known in the art.

Storage of such equations is much more convenient and more useful than is a table of values of P_c, H, T_c and T_g. However, either means of storage, or any other storage means, can be used so long as the required information is available for subsequent use in, for example, an ionization gauge controller memory. Figure 5 illustrates a chamber 118 having a chamber gas temperature T_c and a chamber pressure P_c. The chamber 118 communicates with a pressure gauge or density gauge 120 via a conduit 119. The chamber 118 is evacuated to a very low pressure via a separate conduit using a vacuum pump (neither shown), which pump may be any type of pump suitable for this application. A gauge controller 116 is preferably provided to control the gauge 120. The gauge 120, in a preferred embodiment, may be a density responsive gauge of the ionization type although, as discussed above other gauges such as thermocouple gauges and Pirani gauges may be used. Moreover, pressure, per se, sensitive gauges such as manometers, diaphragm gauges and force gauges may also be used.

The microprocessor determines the corrected chamber pressure P_c as either a function f₁ of a pressure gauge sensor output signal H, or as a function f₂ of a density gauge sensor output signal G.

A microprocessor 114 associated with the gauge 120, such as an ionization gauge controller in the case of a density gauge, can be programmed by software methods which would be within the imbed of one having skill in the art, to periodically carry out the following steps in order:

1. Identify a specific value (124) of indicated chamber pressure, H (or G for a density gauge), corresponding to a specific value of unknown gas pressure in the chamber 118.

2. Identify the chamber gas temperature (126), T_c, and the gas temperature 122, T_g, that prevails in the pressure (or density) gauge 120 at the indicated pressure, H.

3. Insert the identified values of H (or G), T_g , and T_c into the stored equation for indicated pressure reading (or indicated density reading), using the memory 110 and the microprocessor 114, as necessary, to obtain a transpiration (and density) corrected gauge reading.

4. Output the value, P_c, as the corrected measured value of the unknown chamber pressure. This value can be output to a display 112 if desired.

The microprocessor 114 as shown in Fig. 5 preferably contains or communicates with a memory 110 such as a RAM memory, ROM memory, bubble memory, disk memory, tape memory, or any other available memory means. The microprocessor 114 itself can be any commercially available microprocessor, preferably on a single circuit chip, capable of accessing stored calibration information and capable of conducting the types of calculation used in the lookup table or in a curve-fit algorithm. The microprocessor 114 preferably contains a ROM memory 110 such as is seen in Fig. 5, or this can be provided as a separate component complete with calibration data for a given gauge. The microprocessor 114 then communicates with a downstream device such as a display device 112 or a system controller (not shown). If a controller is used, the controller would be used to then produce an output signal to control a controlled device (not shown). Such a controller might be, for example, a safety shutdown device to shut down a process of the system if the pressure exceeds a predetermined level. In such a case, the controlled device might be, for example, a system control device which controls ongoing processes in the system whose pressure is being measured.

The procedure whereby the actual system pressure is calculated is discussed briefly hereunder. First, a pressure gauge or a density gauge, such as an ionization gauge (IG), is calibrated. The calibration of the pressure or density gauge is necessary in order to define a curve or series of curves, or alternatively to define a lookup table, for the gauge output current signals versus the actual system pressure P_c during the calibration procedure. During the calibration procedure, the gauge is maintained under controlled conditions, as is the vacuum calibration system, such that the temperature of the gas in the calibration system is at a measured temperature, T_c, and the gas being measured is at a measured temperature in the gauge of T_g, the temperatures T_c and T_g being in absolute degrees Kelvin or Rankine.

The calibration information is supplied, in either algorithm form or lookup form, to a memory device 110 (such as a RAM or a ROM device) which can be part of a microprocessor 114, or which alternatively can be an accessory to the microprocessor 114. Thus, once the information is obtained and stored, the microprocessor 114 as seen in Figure 5 can access the calibration data in the memory device when called upon to do so.

While Fig. 5 shows a schematic procedure for determining pressure of a particular gas in a vacuum system 118, it is contemplated that information relating to a variety of different gases can also be stored including their calibration curves, and that the particular gas being used can be input into the system shown in Fig. 5 so that the microprocessor 114 can select the appropriate calibration curve information for the particular gas being measured. All such embellishments and modifications are contemplated as being within the scope of the present invention.

When accurate curve fitting requires that more than one equation be used to represent the dependent variable over the entire span of the independent variables, referring to the enumerated steps listed hereinabove, an additional step is required. Each such additional step includes identifying which of the several stored equations to use. Such identification is readily accomplished using suitable IF-THEN statements by those skilled in the software art.

Above there has been discussed both thermal transpiration corrections and gas density corrections (assuming a density gauge is employed) for gas density or pressure readings. The relationship between these two corrections will now be further discussed.

In the previously noted co-pending application, U.S. Serial No. 07/087,409, filed on August 20, 1987, gas density corrections with gas temperature were described, as also discussed above. Thus, gas density in a density gauge is equal to a constant times P/T_g , where P is the pressure in the gauge, and T„ is the absolute temperature of this gas in the gauge.

If T_g is constant, the sensitivity of the gauge is offset by the ratio of T_g and T_cal, the gauge temperature during the calibration of the gauge.

A graph of sensitivity, S vs. Log P is shown in Fig. 6. The lower dotted line is a case where T_g is greater than T_cal while the upper phantom line curve is for T_g < T_cal. Thus, the dotted line and phantom line curves represent density corrections which should be made when the gauge gas temperature differs from that occurring during calibration. The point to be appreciated here is that any temperature difference in the gauge from the temperature during calibration causes a calibration error at all pressures. Such is not the case with thermal transpiration errors which do not arise at all pressures. In particular, transpiration relates the gauge behavior to the ratio of absolute gas temperatures inside and outside the gauge, and depends upon the size and design of the gauge opening to the chamber whose pressure is to be measured.

Fig. 7 shows the sensitivity curve in which both the thermal transpiration effect and the density effect of Fig. 6 (T_g > T_cal) are present. Over a transition region wherein the mean free path of the gas is approximately the same magnitude as the opening between the gauge and the chamber, there is a change in the sensitivity correction which varies from lower pressures to high pressures. Note at the higher pressures where there is no transpiration effect, the correction is a density correction only. Thus, the need for density correction arises because of the difference, in a density gauge, between the gauge gas temperature during measurement of an unknown temperature and the gauge gas temperature during calibration and applies at all pressure while the need for transpiration correction arises because differences in the gauge gas temperature and the chamber gas temperature and applies only at lower pressure when the conductance between gauge and chamber is relatively small. Since gauge gas temperature requires measurement for both corrections, both corrections may be simultaneously effected, when needed, in accordance with an aspect of the invention.

As also mentioned above, gauge sensitivity and linearity corrections may also be made in accordance with the present invention where sensitivity and linearity as used in the above sense are functions of physical characteristics of the gauge such as the geometry thereof. Typically, sensitivity and linearity decrease at the high end of the pressure range, this being illustrated for sensitivity in Figs. 6 and 7, for example. The linearity and sensitivity corrections will be effected as a result of the above described calibration procedure where, for given gauge and chamber absolute gas temperatures, gauge readings H or G are respectively correlated with a sequence of known chamber pressures or where the gauge and chamber gas temperatures are also correlated with the sequence of known pressures.

To make the transpiration, density (if a density gauge), linearity and sensitivity corrections, it is necessary to obtain a table of the calibration data or an equation that adequately defines them. Moreover, with the transpiration correction, the correction procedure should also account not only for the full transpiration and no transpiration regions of Fig. 4 but also for the transition region thereof. Thus, a table of transition values or an equation which adequately defines them is also needed.

Following is an example of how the transpiration transition phenomenon can be matched to an equation and solved. The shape of these transpiration transition curves as measured by T. Edmonds and J. Hobbson (JVST 2 182 [1965]) shows good symmetry about a central pressure that will be defined as P_1/2g. See Fig. 8. The shape is very much like that of a current-voltage curve from Polarography as defined by J. Heyrovsky and D. Ilkovic (Col. Czech, Chem. Communs, 7 198 [1935]). See Fig. 9. In the following, the transpiration transition will be fitted to the format of the equation used for polarography. This is shown as Eq. 49, where j is a constant. The current i_d is the maximum current, zero the least.

E = E_1/2 - j log(i/(i_d - i )) (49)

The shape of these two curves matches very well, however, for direct substitution into Eq. 50 the full transpiration region must conform to a value of zero. To establish a zero value for the full transpiration situation, (T_c/T_g) ^{1 /2} is subtracted from the pressure ratio at every point on the curve. This gives the following statements of equivalence that we can now substitute into Eq. 49 to obtain Eq. 50. E = Log P_g E_1/2 = Log P_1/2g j = j i = P_c/P_g - (T_c/T_g)^1/2 i_d = 1.0 - (T_c/T_g)^1/2

We are assuming in this case that the gauge gas temperature, T_g is greater than the chamber gas temperature, T_c.

Log P_g = Log P_1/2g - jLog (50)

Solving for P_c as a function of P_g gives Eq. 51. P_c = P_g (51)

Calibration of a gauge over the transition range provides data from which j and P _1/2g can be established, as can the value S, the sensitivity of the gauge, as a function of P_g.

In use, the temperatures T_c and T_g are measured. This provides a maximum pressure ratio, by application of Eq. 3, that could exist between the gauge and chamber. If the measured P_g is within a factor of a constant K corresponding to the width of the transition reading (K being 30, for example, and which may vary depending upon the physical characteristics of the particular gauge and/or the conductance of the passageway between the gauge and chamber) in either direction of P_1/2g, it will be necessary to compute a correction via the full method using Eq. 51. If the factor P_g/P_1/2g is more than 30, then the gauge reads correctly with regard to transpiration effects, at that pressure. If density correction and non-temperature related calibration factors such as S are needed for providing correct pressure readings, these can then be applied. This sequence assumes that this S correction was not made on p_1/2g and p_g in Eq. 50 and Eq. 51.

If P_1/2g/p_g is greater than 30, the full transpiration correction can be made by application of Eq. 3. After this, density correction and non-temperature related calibration factors are needed for providing a correct pressure reading, and these can then be applied. This also assumes that the S correction was not made on the

P_1/2g value.

Between the above-noted ratios it will be appropriate to apply a computed correction as follows.

1. If T_g is greater than T_c, use 51.

2. Measure P_g, i.e., read the gauge.

3. Compute P_c from Eq. 51 using P_{1 /2g} and j from calibration.

4. This transpiration-corrected value of the pressure reading is then corrected for any density and nonthermal calibration factors as required.

If T_g is less than T_c, the format of Eq. 51 changes to Eq. 52. P_c = P_g (52)

/ The procedure is the same as before.

This method establishes for the gauge and its interconnection to the system a central pressure, P_{1 /2g ,} about which the transpiration transition occurs. This is established in the calibration of the gauge. The j factor involved in defining the slope of the transition curve is also established in the calibration. It is sought to fit to the phenomenon an equation which matches at least as welal as the quality of the data available to define it. This approach is well adapted to computer solution. It requires only calibration data and signals from the gauge and the temperature sensors. Thus, it can be applied by a micro-processor, such as micro-processor 114 of Fig. 5, which is designed to incorporate these inputs and generate from them the required higher accuracy pressure measurements.

In this treatment it has been implied that j is a constant from the calibration. This is only true for fixed temperature ratios. Because j is the slope of the transition curve, and the slope is dependent upon (T_c/T_g)^1/2, this must be corrected. The better approximation is that the transition pressure width is fixed. This makes j: / j = (53)

g

The linear approximation to the transition pressure width is Δ log P_g. This term is shown in detail in the following discussion detailing the relevant linear equation. The symbol k is a balancing constant. The ratio k/Δ log P_g thus becomes the calibration constant with reasonable stability over a range of temperature ratios. The symbol j can easily be calculated from Eq. 53 with the aid of the measured temperature values in each given case.

When less accuracy is required, but where it is still important to make a first order correction for transpiration, a linear approximation can be used. To do this, it is necessary to fit the transpiration transition to a linear equation. Such a case fits Eq. 54, and is illustrated by Fig. 10. y = ax+b (54)

The solid areas shown in the curve of Fig. 10 represent errors caused by the aforementioned oversimplification. These errors may represent a significant percent of the transpiration effect when the transpiration effect is very small. However, they become less significant as the transpiration becomes larger. For example: y = p_c/_pg x = log P_g a = j = [1.0-(T_c/T_g)^1/2]/[log P_gm - log P_go] (55)

See Fig. 10 for definition of P_gm and P_go.

It is assumed that log P_1/2g is known from calibration.

At log P_1/2g = X₁, P_c/P_g = ₁

Thus, the measurement of T_c and T_g and the calibration P_1/2g yields a set of values for y₁, X₁.

If the "pressure width" of the transpiration transition independent of the magnitude of T_c/T_g, then there can be determined from calibration the value of the Δ log P_g from th log P_g at which P_c/P_g is 1.0 and the log Ε at which it is (T_c/T_g)^1/2. This result gives the slope of the curve.

P_c/P_g (T_c/T_g)^1/2 at bottom of Δ log P_g

P_c/P_g = 1.0 at top of Δ log P_g a = slope = cTg (56)

Then fitting y₁ , X₁ into the linear equation there will be determined everything but b. y ₁ = ^X/2 = Log P_1/2g

(57)

Thus, we can solve this for b. b=1/2+1/2 (T_c/T_g) ^1/2 -Logp_1/2g (58)

Now, when P_g is in the transition region, the ratio P_c/P_g can be found by using:

P_c/P_g = Log P_g + 1/2 +1/2(T_C/T_g)^1/2

- Log P_1/2g (59)

To compensate for the transpiration effect by equation it is necessary to:

1. Measure the absolute temperature of the gas inside the gauge, i.e., inside the restrictive orifice or tube (T_g).

2. Measure the absolute temperature of the gas outside the gauge, i.e., outside the restrictive orifice or tube (T_c).

3. Establish the ratio of these absolute temperatures (T_c/T_g).

4. Extract the square root of this ratio as a maximum effect, (T_c/T_g)^1/2.

5. Establish via calibration of the gauge plus its restrictive orifice or tube the pressure indication which is central to the transpiration transition (P_1/2g).

6. Establish via calibration of the gauge plus its restrictive orifice or tube the length of the pressure indication curve in the transpiration transition (Δ P_g or

Δ log P_g).

7. Measure the pressure indication (P_g).

8. Establish the ratio of indicated pressure to a central transpiration transition pressure (P_g/P_1/2g).

9. From this ratio, R, establish the appropriate correction mode: a. When R = P_g/P_1/2g i s greater than 30, no correction needed, P_c = P_g . b. When R is less than 1/30, use a full transpiration correction P_c = P_g (T_c/T_g)^1/2 When P_g is within factor of 30 of

P_1/2g, use

1. Linear equation, or

2. Full curve fit equation.

10. When P_c is established, apply S.

P_A = P_c x S Where P_A and S are defined in item 11.

11. The gauge senses density rather than pressure:

P_AT = P_A x T_g/T_gcal, where

P_A is the transpiration corrected chamber pressure reading also corrected for the gauge sensitivity S. S has been reduced to a simple factor for this application.

P_AT then equals the P_A value as corrected for the absolute temperature, if it is a reading from a density sensing gauge.

T_gcal is the absolute temperature in the gauge gas at the time of its calibration.

The foregoing method steps are schematically depicted, in a highly simplified form, in Fig. 12. Steps 1 and 2 above can be interchanged, and it will be evident to those having skill in the art that other ones of the foregoing steps can be interchanged or reordered as well, without adversely affecting the advantageous resultant function of the present invention.

The present inventive method and apparatus lends itself to incorporation of any required temperature measuring means and circuitry in the gauge tube itself, such that replacement could be performed of an existing prior art gauge tube with a transpiration-compensating gauge tube according to the present invention.

As can be appreciated from the foregoing, the transpiration correction method and apparatus can be employed by itself or in conjunction with other corrections such as density correction, sensitivity correction, and linearity correction. Regardless of how employed, the transpiration correction requires measurement of the gauge gas temperature and the gas temperature in the system outside of the gauge.

In accordance with a further aspect of the invention, means are provided for accurately measuring the gauge (internal) gas temperature and/or the chamber (external) gas temperature. Referring to Fig. 13, there is schematically indicated an illustrative embodiment of an ionization gauge which may preferably be used in the invention to measure the above internal and external .gas temperature, this gauge being of the type described in U.S. Patents 4,636,680 and 4,714,891, both of which are assigned to the assignee of the subject application and both of which are incorporated herein by reference.

Referring to Figure 13, the gauge is similar to the Bayard-Alpert type and includes a filament 200, which acts as an electron source, a guard ring 202, an ion collector 204, and an anode 206, the foregoing elements being disposed with a container 208 having apertures 209 in the surface thereof to facilitate gas flow to the gauge from the chamber generally indicated at 216. Anode 206 defines a substantially enclosed cavity 207 which, in turn, defines a precise electron path length.

Because gas molecules for measurement are retained in cavity 207 for many collisions with the walls of the anode, the temperature of this gas is also the temperature of the anode. The anode temperature can easily be measured, providing an accurate measure of the gas temperature. The temperature measurement of the gauge gas thus may be effected by sensor 210 attached to anode 206 where sensor 210 may be any known device such as a thermocouple or temperature sensitive resistor. Thus sensor 210 constitutes an important addition to the gauges shown in U.S. Patents 4,636,680 and 4,714,891. Moreover, the gauge of U.S. Patent 4,714,891 employs a ceramic or the like support structure 213 upon which elements such as anode 206 may be coated. This support structure provides a more stable anode temperature and, accordingly, may preferably be used to measure gauge gas temperature.

In many cases the gauge tubulation or the gauge entry ports represent the only restriction across which a gas temperature difference will exist. Thus, a sensor 212 for measuring this external temperature, T_c, may be mounted with respect to the pressure or density gauge itself via a support 211 and extend beyond the gauge through the tubulation, if present, to sense gas temperature outside the tube or port, as illustrated by sensor 212. It is thus within the scope of this invention to include gas pressure and density gauges which also effect internal and/or external gas temperature measurements or the elements from which these could be achieved.

As indicated above, T_c is the gas temperature outside the gauge opening to the chamber. Because this gauge opening is typically inside the chamber with only very large and direct opening to the volume where pressure values are desired, T_c is also considered to be the temperature of the gas in that volume. If this is not the case, and there are temperature differences across other conductances between the volume of interest and the gauge, then transpiration across all must be considered for highest accuracy.

Because the geometries and temperature differences across each of these conductances can be unique, the P_1/2 and possibly Δlog P values will be also. This means that the pressure range where a given conductance influences the gauge will be different for each of the series of conductances. The effects are all additive, so as lower and lower pressures are encountered, more and more of the transpiration effects are included. To correct for these by equation the P_1/2, and Δ log P values must be known for each, and the temperature values measured on each side of each conductance. Only the temperature measurements must be included for a more complete table lookup system.

The techniques covered in the present invention are intended to include these more complex cases with more calibration constants and/or more temperature measurement points. No change in philosophy or general technique is required.

Thus, in general, there have been described, inter alia, gauge controllers and gauges for use therewith which provide corrected pressure measurements using:

(a) Absolute temperature of the gas measured in the gauge , V

(b) Absolute temperature of the gas measured in thee chamber, T_c

(c) Gauge reading, G or H, vs. chamber density or pressure calibration data; and

(d) Computer based control systems and data storage means.

Also described have been gauge controllers and gauges for use therewith which provide corrected pressure measurements using:

(a) Measured T_g;

(b) Measured T_c;

(c) Gauge reading, P_1/2g, at center of transpiration transition-from calibration;

(d) Transition width, k/ Δ log P_g, from calibration; and

(e) Computer based control systems for computation from:

(1) Linear equations;

(2) Adapted equations; and

(3) Fitted cubic or higher order equations. Moreover, there have been described gauge controllers which combine the above with linearity, sensitivity and density corrections to provide accurate pressure measurements at low pressures. Notice that linearity and sensitivity corrections are typically automatically made by the calibration. Moreover, the combined thermal corrections including the density correction and the transpiration correction would also be made by calibration in the multidimensional calibration, described above. If density and transpiration are corrected by equation, the linearity and sensitivity corrections are still typically determined by calibration and provide the calibration curve to which the density and/or transpiration corrections are applied.

The following discussion relates transpiration in general terms to all gauge types and extends treatment of this pheonomenon to the process site.

Because transpiration can prevent the gauge pressure from being a true measure of system pressure, it must be eliminated or measured and corrected. Fig. 15 shows a generalized pressure gauge 312 for transpiration measurement. Gauge 300 senses the the temperature T_t of the gas just outside the thermal junction 308, which may be an orifice or a tube, for example, and T_g the gauge temperature or temperature just inside a thermal junction.

The connections 306 and 314 of the thermal data to gauge interpreter 304 permit the use of gauge controllers that do not possess these thermal functions (no controllers presently have them). In accordance with an aspect of the invention, gauge controller 302 may be modified to incorporate such functions.

As discussed hereinbefore, low pressure process system design is also critical in providing meaningful measurements and control. The temperature of gases at the reaction site should be as uniform as possible in order that the correct parameter is consistent there. If the temperature consistency is not good, the gas measurement will be questionable even in the case of pressure. Consistency within each thermal segment (or transition) back to the gauge is needed for quality measurement involving transpiration corrections. This does not mean that temperature must be constant, just that it should be the same throughout each thermal segment at any time. Thus, for example, all of the gas in the reaction site should be at the same temperature although temperature distribution will likely occur even with the best designs.

Gas in the intermediate connection (orifice or tube) between the reaction site and the gauge becomes a concern. If there is a line of sight path from the gauge to the reaction site, some molecules will reach the gauge at reaction temperature, and some will have hit lower temperature hardware and be at intermediate temperatures. This will prevent an accurate transpiration correction for the pressure difference across this region. If only molecules directly from the reaction site reached the gauge, their temperature could be determined; however, this is not practical in most cases.

As discussed above, successive orifices of the same size can be summed in effect with only the total delta T involved. If the number of orifices becomes infinite, we have a tube. Transpiration across tubes follows similar rules--but is generally even less well understood than orifices. The tube mechanism is not as direct as that of a thin plate orifice because there are two mechanisms by which a molecule can get through. One is that of passing through without touching a wall, and the other occurs when a wall is contacted. The angle of incidence/angle of reflection rules do not apply, and half bounce forward and half bounce backward at each contact.

All of the molecules can be forced to use the second mechanism by providing sufficient bend to the tube, as shown in Fig. 16, where an intermediate transpiration system is illustrated including a transpiration tube 320 connected between a reaction site 322 and a pressure gauge 324. The reaction site may include an electrode 324', the electrode being surrounded by a tubular thermal reflector 326. The tubular thermal reflector may be disposed within a chamber diagrammatically indicated at 328. The reaction site temperature , T_s, is measured by a gauge 330 while the tube end temperature (or the temperature, T_g, of pressure gauge 324) is measured by gauge 332. Due to the loop 334 in the tube 320, the reaction site temperature can be the temperature of all molecules entering the inboard end 336 of tube 320, but none of these molecules reach the gauge without striking surfaces ox other molecules . Gauge 324 is sealed to the outboard tube end 338 which is also sealed to the wall of chamber 328. This novel tubing approach, in accordance with a further aspect of the invention, renders possible an accurate transpiration correction. A sufficiently long (exceeding L, the mean path length) tube without a bend would approximate this same simple performance.

The tube 320 introduces a known amount of transpiration between the reaction site (or other portion of the system) and the gauge. Thus by calibration, for example, the value of the exponent x in the transpiration equation P_s/P_g = (T_s/T_g)^x can be determined. Thus, in accordance with a further aspect of the invention, transpiration errors can be corrected whenever there is an uncertainty as to the source of a temperature difference between the gauge and the system. That is, in some systems, there may be a temperature difference between the gauge and system and yet no pressure difference . Of course, if there is no pressure difference, there is no transpiration effect to be corrected in spite of the pressure difference. In other systems, the pressure difference may be due entirely to the transpiration effect while yet, in further systems, the pressure difference may be due to a combination of transpiration effects and other effects not related to transpiration, which is the case quite often due to the complex nature of the gas path between the system and the gauge. In these latter instances, it becomes very difficult to precisely determine what part of the temperature difference causes transpiration and thus, of course, very difficult to correct the pressure for it. Hence, by providing the fixed transpiration by tube 320, any transpiration uncertainties inherent in the system are replaced by the fixed and known transpiration intoduced by the tube.

Accordingly, accurate transpiration corrections can be made to the gauge pressure measurement by utilizing the gauge and system gas temperature measurements to thus provide an accurate measurement of the reaction site (or system) pressure. Quite often, it is this latter parameter of the reaction site gas which is controlled to optimize a characteristic of the process such as the rate thereof. Hence, the accurate measurement of the reaction site gas pressure where quite often this cannot be done because of uncertain transpiration effects constitutes an important aspect of the invention.

Moreover, measurement of the reaction site gas pressure is important because this parameter can be corrected for transpiration effects in the system where a parameter such as the density or impact rate cannot be so corrected since they are essentially local phenomena. Accordingly, in accordance with a further aspect of the invention, regardless of what parameter of the gas the gauge is sensitive to, gauge interpreter 304 converts that measurement to a pressure measurement if the gauge is not already pressure sensitive. Moreover, even if the gauge is pressure sensitive, it will more than likely have a temperature dependence which will also be accounted for by interpreter 304, as discussed above, where the interpreter will be provided with the relationship that defines the temperature dependence.

The transpiration tube 320 of Fig. 16 includes loop 334 of tubing. There are other geometries that provide a non-see-through, consistent-repeating format having the above advantages with less complex mounting and higher conductivity than the Figure 16 embodiment. To seal the loop device 320 to a system flange--and introduce it into the chamber requires some unconventional technology. As an alternative, if the tube is rolled perpendicular to loop 334 and is then pulled to obtain a spiral shape as illustrated at 340 in Fig. 16A, the resulting tube 342 can be fed in the direction of the arrow into the chamber through a conventional flange 344 in the chamber wall (not shown) where the flange 346 at the outboard end of tube 342 can then be sealed to flange 344. If the spiral is quite flat, as illustrated in Fig. 16A, the tube will be much shorter than in the large loop embodiment of Fig. 16. The conductance will thus be greater for better operation of the gauge.

Alternatively, referring to Fig. 16B, tube 350 can be periodically half-blocked with half circle barriers 352. These can be connected to a center rod 354, and need not be sealed to tube 350. In Fig. 16B, the half circle barrier arrangement 356 is illustrated withdrawn from tube 350 for purpose of illustration.

Referring to Figure 16C, there is illustrated another embodiment where a tube 360 is half collapsed at portions 362 which are alternately disposed on opposite sides of the tube.

Other geometries are, of course, possible. A particularly preferred embodiment, illustrated in Fig. 16D, is a straight tube 370 with a spiral strip 372 inserted where the strip is shown withdrawn for purpose of illustration. The height of strip 372 is preferably approximately equal to the inside diameter of tube 370. Strip 372 can be twisted from a strip that is slightly longer than the tube. The strip divides the tube into two channels, both of which are open, but are non-see-through. There are virtually no reductions in cross-sectional opening, and the length is minimum.

The reaction site end of the tubes of Figs. 16 - 16D are exposed only to items at reaction site temperature, T_s, for example. Thus, gas entering the tubes from that end should be at T_s. The other end of the tube may be positioned such that it sees only gauge temperature, T_g. Thus, with T_s and T_g , transpiration from the reaction site can be corrected. The inboard end of the tube may not be at gauge temperature. For example, a thermal junction may be present in the gauge in addition to the thermal junction established by the tube. In this instance the transpiration effect introduced in the gauge would have to be determined and added to that introduced by the tube. These functions could be included in controller 302 or interpreter 304.

As discussed above, there are instances where complex mechanical intersections occur and thermal junctions would be difficult to measure and/or control. If the tubes of Figs. 16 - 16D are not used, the arrangement of Fig. 17 may be employed to prevent a temperature difference from occurring across that mechanical junction. Any irregular mechanical transition can thus be rendered transpiration-harmless by keeping that entire region at the same temperature. Force the thermal transitions to be where they can be measured.

Where electrical potentials prevent mechanical linking, it may prove necessary to measure the temperatures involved, and control one to match the other. Thus, in Fig. 17, where there would normally be a transpiration-caused pressure difference between T_t, the gas temperature within flange 382 and T_g, the temperature of the region between the gauge and flange can be controlled by controller 384 so that T_t is maintained substantially equal to T_g, this being effected by a heater coil disposed around transpiration tube 388.

Any mechanical regions where several diameters are present would involved several transpiration terms maturing at different pressures. The complexity of this measurement and correction can be avoided by forcing the entire mechanical region to be substantially at the same temperature. This thermally consistent region (from the flange to the gauge in Fig. 17) must be long enough relative to the cross-section that virtually all molecules moving into the critical mechanical region from either direction make at least three wall contacts with thermally consistent walls before striking the critical junction. This controls the gas temperature to be substantially at the wall temperature so that the transpiration effect will be very small.

Reference should now be made to Fig. 18, which is a further development of Figs. 14 and 15, where the Fig. 18 embodiment is directed to a reaction interpreter 380. Measurement of the reaction site temperature T_s may be effected by a sensor (not shown) and provided to the reaction interpreter. The reaction site pressure, P_s, is provided by gauge interpreter 304 of Fig. 14 or Fig. 15 so that the reaction interpreter can compute any desired parameter of the reaction site gas, which is a function of pressure and temperature. For example, using equations (12) or (13), the density, D_s, or the impact rate, IR_s, of the reaction site gas can be determined, as indicated in Fig. 18. Functions other than these such as that of Eq. (A) can also be computed, displayed and outputted as programmed into the reaction interpreter 380 of the system.

Although pressure-temperature functions are discussed above, a wider range of parameters can be involved in many processes. Accordingly, in addition to the reaction site gas temperature, T_s, n generalized parameters, H_n, are introduced in the reaction site process control system of Fig. 19, which, in addition to the Fig. 18 embodiment includes a process controller 390 and a control element 392, which may control reaction site gas pressure, for example, via a feedback loop. H_n may be surface temperatures, intermediate transitions temperatures, and/or or any other parameters related to the kinetics equation which defines the process at the reaction site where Eq. (A) is an example of such a kinetics equation where H_n are not parameters. Process controller 380 is provided with an input signal (DCP) that is indicative of a desired value of a process characteristic such as the rate thereof where the desired rate of Eq. (A), for example, might be 100, as discussed above. A situation signal (SCP) representative of the actual value of the process rate, for example, is also applied to controller 390. The process controller may also be adjusted to match the reaction system by setting the differential, integral and proportional (DIP) parameters, discussed hereinbefore, for smooth, fast control. Thus, process control is provided by measuring pressure P_s, temperature T_s, and other process site parameters, H_n, and controlling P_s and/or other process parameters to provide controlled rate via the process kinetics equation, as exemplified by Eq. (A), for example, the value of this equation being determined in reaction or process interpreter 380, in accordance with a further important aspect of the invention.

Heretofore R has been controlled by attempting to maintain P_s at a desired value thereof via a feedback loop. T_s has either been assumed to be substantially constant or attempts have also been made to at least maintain it within a limited range. However, since T_s is usually not substantially constant and since it is difficult to rapidly control T_s and, in particular to reduce it, process control in high vacuum systems, in particular, has not been adequate. This to a certain extent has been unavoidable due to the inadequate pressure measurements obtainable with prior art systems.

With the accuracy in pressure measurement now available with the present invention as described above with respect to the gauge interpreter of Figs. 14 and 15, accurate control of reaction site processes is now possible. Moreover, in accordance with invention, reaction site interpreter 380 is utilized in a novel manner to further enhance the accuracy of process control. That is, rather than controlling the rate, for example, of the process, by maintaining P_s at a desired value as is done in the prior art systems, the rate itself is maintained at a desired value. In particular, assuming the process R is defined by Eq. (A), this equation is inputted to reaction interpreter 380 via the Function Set input. Moreover, a desired value of the rate is applied to controller 390 as the signal DCP.

The actual value of the process rate is calculated from P_s and T_s (and possible H_n) utilizing Eq. (A), the actual value being applied to controller 390 as signal SCP. Control 390 may include a comparator or the like which produces an error signal in response to a deviation of the actual value of the process rate from the desired value thereof to drive control element 392, which controls P_s and thus the process rate R.

From the foregoing it can be seen the process rate R is not controlled in accordance with a desired value of P_s but rather in accordance with a desired value of R itself which is a function of both P_s and T_s. Thus, more accurate control of R is provided not only in the present inventon where P_s is accurately measured but also in those prior art systems where P_s is less accurately measured.

The control of T_s and H_n, if necessary, can be effected by auxiliary control systems (Fig. 20) optionally included in process controller 390 or process interpreter 380. If there are sufficient input/output channels and storage, i.e., adequate flexibility, process interpreter 380 or controller 390 can provide control or sub-controllers can be used on all of the process parameters that have constant or simple function control points. Because it is usually the fastest response parameter, the pressure would typically be given the primary control function to which the status and control of all other parameters is related. Other fast response parameters may, of course, also be used for the primary control function.

Reference should now be made to Fig. 20, which illustrates an expanded process control in accordance with the present invention whereby the foregoing reaction site technology may be applied. A measurement is made by gauge 300, which is f (P_g, T_g). The temperature of the gas in the gauge, T_g, may also be measured in gauge 300, to determine the gauge pressure, P_g, this step being effected by gauge interpreter 304. Next, transpiration must be corrected if operation occurs in a pressure range where it exists. The transpiration correction may require temperature measurements for each thermal sector from gauge temperature to process temperature. The complexity of this depends upon the mechanical junctions from gauge to process. The conventional gauge without a special mechanical junction such as those of Figs. 16 - 16D will fail to provide a correctable pressure reading for the process if the process temperature differs significantly from the gauge temperature. The transpiration correction(s) indicated at 394 can be computed by either gauge interpreter 304 or process interpreter 380. This provides the process pressure, P_s.

Next, the equation defining the gas function or process rate, for example, required for information and process control is inputted at 396 to reaction interpreter 380. At 400, Eq. (A) might be utilized to compute the actual value SCP of the process rate. The desired control value for the process rate or gas function is used as reference DCP, DCP and SCP being applied to primary function or process controller 390 which operates under the control of computer programs 398, which in turn calculate the current value SCP of the process site kinetics equation indicated 400. Other computations are also possible, such as control of the secondary functions as indicated at 390' and 398'. The primary and secondary control systems 402 and 402' typically operate by negative feedback to keep the reference (DCP) and control (SCP) signals substantially equal. DIP can be provided to the primary and secondary function controllers manually or by process interpreter 380.

The concept of controlling around the kinetic equation is the basis of much of chemical engineering. This has not been clearly applied in the low pressure industries, as discussed above. Much of this is because pressure readings are not really pressure, and there are often more parameters than understanding. In accordance with the present invention, enhanced measurement and control capability is provided by process interpreter 380 and generalized pressure gauges of Figs. 14 and 15, which incorporate gauge interpreter 304.

In general, the foregoing is effected as follows by control of a reaction parameter such as pressure P_s:

1. The desired situation (DS) is defined in terms of what is needed, rate = 100, (X) = 7 x 10^-5 Torr, etc. where DS = DCP. It is first assumed that rate, for example, cannot be measured directly.

2. Situation measurement (SM) is defined in terms of what can be measured and how it can be measured, for example, the measurement of P_s.

3. The mathematical equation defining relationship between SM and rate R is then determined. 4. For the process controller 390 and control element 392 the pressure P_s is the controlled parameter even though this is a continuously changing value if temperatures and other parameters are changing. 5. The Situation Control Parameter (SCP) or SM becomes the active input to process controller 390--that is, for example, the current value of the process rate R.6. The process controller drives primary control element 392 such as an input valve usually on the basis of a function of DCP minus SCP or SCP/DCP, attempting to generate SCP = DCP. 7. As the uncontrolled, semicontrolled or slow response controlled parameters such as T_s or H_n change value with time, P_s will also change in the present invention. However, in the prior art systems where it is attempted to control pressure rather than rate (where rate cannot be directly measured), there will be an error in the rate at least part of the time due to changes in T_s and H_n. 8. It is only if SM (which may be process rate, for example) can be measured in terms of P_s, for example, that the measurement is free of the effects of the secondary parameters that a simple/direct control system is effective. For example, if pressure is an absolute indicator of our reaction rate, pressure can be measured and controlled to a preset fixed or time related value and thus control the rate to a desired value. 9. If the rate or product level can be sensed directly, a simple control can be used without measuring the pressure, for example, that is being controlled. This is, of course, assuming a direct or continuous positive effect of the control element on the rate or product level. 10. However, if R = K X^m H_n, where rate R is measured and X (pressure, for example) is adjusted, this form of control is not always stable because of the m exponent and the changing H_n factors. Values for control DIP can vary from moment to moment. Hence, in this situation the approach of the present invention should be used whenever direct control of R, for example, leads to unstable control.

11. Moreover, continuous positive effect need not be an absolute requirement if reversal conditions are fully understood and allowed for. Large aircraft controls have many process reversals that they work with quite successfully, for example. Using DCP-SCP or SCP/DCP approach of the present invention will greatly reduce the instability. Computer continuous DIP analysis and auto adjustment may complete the control function.

The optimization of a process can come from many directions. For example: maximize yield versus the most expensive component, maximize yield versus the sum of all components, maximize yield versus the cost of the process, maximize yield versus time, maximize compatibility of the process with the total production line in which it is involved, etc.

Numerous control loops can be involved in such optimizations. Interacting slow control loops can be programmed to seek out the conditions which best meet the overall process optimization while the fast response control loop of the present invention provides assurance that the momentary fundamental needs are met at all times.

To automatically or manually optimize such processes, many parameters other than those involved in the immediate reaction must be measured. These could include the measure of downstream unreacted materials, total power, cooling water flow, flow of input materials, total production measure, etc.

The gas sensor with the greatest potential here is the residual gas analyzer (RGA). The ability to detect final gaseous product and the unreacted components make it unique. Because heretofore this mass spectrometer device has been a density sensitive sensor without related temperature measurement and at best, crude or accidential temperature control, the enhancement of an RGA in accordance with the present invention will substantially improve its detection flexibility in many of these applications. Because of this improvement in detection flexibility, an RGA can be used with great advantage in the present invention.

With respect to conventional RGA's, the temperature of the components of a pressure reduction system and a detector thereof may presently be ignored. Where some elements are pressure dependent and others density dependent a relatively few degrees difference from calibration can erode the high accuracy reported for these devices.

With respect to the employment of an RGA in the present invention, it should be noted a slow change product quantity loop from downstream coupled to a fast response local manufacture loop can provide a high efficiency without forcing extreme accuracy on the local detector. Moreover, the foregoing appraoch can be advantageously used in the present invention where a residual gas analyzer 410 (Fig. 20) is disposed downstream of the process 393 and measures the unreacted components, for example of the process and applies a signal indicative of the unreacted components to a comparator 414. A desired value of the unreacted components is also applied to the comparator which generates an error in response to differences between the signals applied thereto. The error or control signal may be applied to secondary control element 392' to control the temperature T_s of the reaction. Thus, control of the slow response T_s from the downstream loop including RGA 410 coupled with control of the fast response P_s can provide further optimization of the process control.

In summary, attempted accurate measurement and control of gaseous processes has not been very effective, especially in the low pressure regime. Part of the problem proves to be the temperature coefficient of the pressure measurement due to the nature of the gauges used. Part is the temperature relationships in the process, and part is the interrelating of the gauge output to the reaction site pressure.

The temperature coefficient of the gauge indicates whether the gauge responds to pressure, molecular density, or some other thermal relationship. It is only pressure that can be continuously related at gauges and reaction sites of changing and different temperatures. Finally, the reaction can be dependent upon a function of pressure, density, impact rate or some other thermal relationship. It is only when the measurement/control system is made to relate to the same gas and thermal relationships as does the reaction that accurate measurement/control can be achieved at other than a single preset fixed temperature.

If the gauge does not measure pressure directly, the gauge temperature will typically be required in order to generate pressure from the gauge output. That generated value should be converted to the process pressure, an action often requiring auxiliary temperature measurements and set up calibration and programming. If the process is not directly dependent on pressure, it will be necessary to also measure reaction site temperature in order to change the reaction site pressure into the correct reaction related function.

It is only when this reaction site measurement function is converted to the same thermal format and gas function as the reaction that most accurate feedback control can be applied to the process, over a range of gauge and/or reaction temperatures and other parameters.

Throughout the foregoing specification equations have been used to define relationships. It should be understood that in many instances such equations will not constitute an exact definition of the relationships but rather an approximate definition thereof due to the possible presence of other factors in the practical implementation of the relationships.

Claims

WHAT IS CLAIMED IS:

1. A gas pressure gauging system comprising: a gauge for sensing a first parameter of a gas where the pressure of the gas is a function of at least said first parameter; means for sensing in the gauge at least one further parameter of the gas where the pressure of the gas is also a function of at least said further parameter; and gauge interpreter means responsive to said first and further parameters for determining the pressure of the gas.

2. A system as in claim 1 where said first parameter is pressure.

3. A system as in claim 2 where said gauge is selected from the group consisting of manometers, diaphragm gauges, and force gauges.

4. A system as in claims 2 or 3 where said further parameter is temperature.

5. A system as in claim 1 where said first parameter is density.

6. A system as in claim 5 where said gauge is selected from the group consisting of hot and cold cathode ionization gauges.

7. A system as in claims 5 or 6 where said further parameter is temperature.

8. A system as in claim 1 where said first parameter is impact rate.

9. A system as in claim 8 where said gauge is selected from the group consisting of thermocouple gauges and Pirani gauges.

10. A system as in claims 8 or 9 where said further parameter is temperature.

11. A system as in claim 1 including means for inputting to said gauge interpreting means the function for determining said pressure as a function of said first and further parameters.

12. A system as in claim 1 including means for inputting to said gauge interpreter means the type of said gauge.

13. A system as in claim 1 where said gauge interpreter means determines the pressure of the gas within the gauge.

14. A system as in claim 1 where said gauge interpreter means determines the pressure of the gas within a chamber to which said gauge is connected.

15. A system as in claim 14 where the pressure in the chamber is the same as the pressure in the gauge.

16. A system as in claim 14 including means for maintaining the substantially the same temperature between first and second points disposed outside the gauge to prevent transpiration effects from arising between the points and thus insure that the pressure determined by the gauge interpreter means accurately corresponds to the pressure in the chamber.

17. A system as in claim 14 where said first and further parameters are pressure and temperature respectively and where the temperature outside the gauge is different from that inside the gauge, said system including means for determining the pressure in the chamber as a function of the pressure in the gauge and the temperatures inside and outside of the gauge.

18. A system as in claim 17 where the pressure difference between the chamber and gauge is caused at least in part by transpiration.

19. A system as in claim 17 where the pressure difference between the chamber and gauge is caused substantially only by transpiration.

20. A system as in claim 19 where said temperature outside the gauge is a temperature within the chamber.

21. A system as in claim 20 including a reaction site within the chamber and where said temperature outside the gauge is the temperature within the reaction site.

22. A system as in claim 19 including transpiration introducing means for effecting a substantially measurable transpiration effect.

23. A system as in claim 22 where said transpiration introducing means extends between said chamber and said gauge.

24. A system as in claim 22 where said transpiration introducing means extends between said gauge and a reaction site within the chamber.

25. A system as in claim 22 where said transpiration introducing means includes a tube extending at least between the chamber and the gauge.

26. A system as in claim 25 where the tube extends between a reaction site in the chamber and the gauge.

27. A system as in claims 25 or 26 where said tube is so shaped as to prevent direct passage of gas molecules through the tube from one end thereof to the other end thereof.

28. A system as in claim 27 where said tube includes a loop therein.

29. A system as in claim 27 where said tube includes at least a spiral-shaped portion.

30. A system as in claim 25 where said tube includes a plurality of indented portion alternately disposed on opposite sides of the tube.

31. A system as in claim 25 or 26 where said tube includes barrier means disposed therein.

32. A system as in claim 31 where said barrier means includes a rod disposed within the tube and a plurality of plates alternately disposed on opposite sides of the rod.

33. A system as in claim 31 where said barrier means includes a spiral strip disposed within the tube.

34. A system as in claim 14 including means for measuring the temperature within the chamber and determining a characteristic of the gas in the chamber in response to the pressure and temperature of the gas in the chamber.

35. A system as in claim 34 where said gas characteristic is the density thereof.

36. A system as in claim 34 where said gas characteristic is the impact rate thereof.

37. A system as in claim 14 where said chamber includes a reaction site where a process occurs, a characteristic of the process being a function of the pressure of the gas at the reaction site and at least one other parameter of the gas at the reaction site and where said system includes means for measuring the other parameter and reaction site interpreting means responsive to the pressure and the other parameter of the gas at the reaction site for determining said characteristic of the process at the reaction site.

38. A system as in claim 37 including means for displaying said determined characteristic of the reaction site process.

39. A system as in claim 37 where said other parameter is temperature.

40. A system as in claim 37 where said process characteristic is the rate thereof.

41. A system as in claims 37 or 39 including control means responsive to said determined characteristic of the process and a desired value of the process characteristic for controlling said pressure of the gas at the reaction site to thus maintain the determined characteristic of the process substantially equal to the desired value of the process characteristic.

42. A system as in claim 41 including secondary control means responsive to the other parameter of the gas and a desired value of the other parameter of the gas for maintaining the other parameter substantially at said desired value thereof to thus provide a further- control of said process characteristic.

43. A system as in claim 42 where said other parameter is the temperature of the gas at the reaction site.

44. A system as in claim 37 including means disposed downstream of the reaction site process for measuring a parameter of the output of the reaction site process and further control means responsive to the measured output parameter and a desired value of said output parameter to control the other parameter of the gas and thus provide a further control of said process characteristic.

45. A system as in claim 44 where said means for measuring said output parameter is a residual gas analyzer.

46. A system as in claim 45 where said other parameter is the temperature of the gas at the reaction site.

47. A gas pressure gauging system for measuring the pressure of a gas in a chamber comprising a gauge for measuring a parameter of the pressure of the gas at least within the gauge from which the pressure in the gauge may be determined; and temperature maintaining means for maintaining substantially the same temperature between first and second points disposed outside the gauge to prevent transpiration effects from arising between the points and thus insure that the pressure in the gauge is substantially correctable for transpiration all the way to the chamber so that the chamber gas pressure can be accurately determined from the gauge measurement.

48. A system as in claim 47 where said gauging system is selected from the group consisting of pressure sensitive gauges, density sensitive gauges, and impact rate sensitive gauges.

49. A system as in claims 47 or 48 where said temperature maintaining means includes means for sensing the temperatures at said points and means responsive to the sensing means for maintaining substantially the same temperature between the points.

50. A gas pressure gauging system for measuring the pressure of a gas in a chamber comprising a gauge for measuring a parameter of the pressure of the gas at least within the gauge from which the pressure of the gas in the gauge may be determined; and transpiration introducing means for effecting a substantially measurable transpiration effect so that the pressure in the chamber can be accurately measured as a function of the pressure in the gauge and the temperatures of the gas in the gauge and chamber.

51. A system as in claim 50 where said gauging system is selected from the group consisting of pressure sensitive gauges, density sensitive gauges, and impact rate sensitive gauges.

52. A system as in claim 50 or 51 where said transpiration introducing means extends between said chamber and said gauge.

53. A system as in claim 52 where said transpiration introducing means extends between said gauge and a reaction site within the chamber.

54. A system as in claim 50 or 51 where said transpiration introducing means includes a tube extending at least between the chamber and the gauge.

55. A system as in claim 54 where the tube extends between a reaction site in the chamber and the gauge.

56. A system as in claim 54 where said tube is so shaped as to prevent direct passage of gas molecules through the tube from one end thereof to the other end thereof.

57. A system as in claim 56 where said tube includes a loop therein.

58. A system as in claim 56 where said tube includes at least a spiral-shaped portion.

59. A system as in claim 54 where said tube includes a plurality of indented portion alternately disposed on opposite sides of the tube.

60. A system as in claim 54 where said tube includes barrier means disposed therein.

61. A system as in claim 60 where said barrier means includes a rod disposed within the tube and a plurality of plates alternately disposed on opposite sides of the rod.

62. A system as in claim 60 where said barrier means includes a spiral strip disposed within the tube.

63. A system for controlling a characteristic of a process occuring at a reaction site within a chamber where said characteristic of the process is a function of a first parameter of a gas at the reaction site and at least one other parameter of the gas at the reaction site, said system comprising means for measuring said first and other parameters of the reaction site gas; reaction site interpreting means responsive to said first and other parameters of the gas at the reaction site for determining said characteristic of the process at the reaction site; and control means responsive to said determined characteristic of the process and a desired value of the process characteristic for controlling said pressure of the gas at the reaction site to thus maintain the determined characteristic of the process substantially equal to the desired value of the process characteristic.

64. A system as in claim 63 where said first parameter is pressure.

65. A system as in claim 64 where said other parameter is temperature.

66. A system as in claim 63 where said process characteristic is the rate thereof.

67. A system as in claim 63 including secondary control means responsive to the other parameter of the gas and a desired value of the other parameter of the gas for maintaining the other parameter substantially at said desired value thereof to thus provide a further control of said process characteristic.

68. A system as in claim 67 where said other parameter is the temperature of the gas at the reaction site.

69. A system as in claim 63 including means disposed downstream of the reaction site process for measuring a parameter of the output of the reaction site process and further control means responsive to the measured output parameter and a desired value of said output parameter to control the other parameter of the gas and thus provide a further control of said process characteristic.

70. A system as in claim 69 where said means for measuring said output parameter is a residual gas analyzer.

71. A system as in claim 70 where said other parameter is the temperature of the gas at the reaction site.

72. An apparatus for determining a temperature-compensated value of a pressure measurement, comprising: a gauge means for connection to a system containing a gas; said gauge means producing an electrical output, signal in response to gas density measured; a means for storing calibration data of a gas, the calibration data being obtained at a measured calibration gas temperature in the gauge and including data relating said output current to measured values of pressure during calibration; a temperature measuring means for measuring temperature of gas in the gauge where pressure is to be determined; a computer means for temperature-compensating said output current value based upon actual measured system temperature as measured by said temperature measuring means; whereby said computer means can use said temperature-compensated output current value to determine a temperature-compensated pressure value.

73. An apparatus as claimed in claim 72, wherein said temperature-compensated current value is obtained by multiplying the actual current value measured by the actual absolute temperature of the gas in the gauge where pressure is to be measured, and dividing the product by the temperature of the gas during calibration, the temperature being expressed in absolute degrees.

74. An apparatus as claimed in claim 72, wherein said gauge means is an ionization gauge.

75. An apparatus as claimed in claim 72, wherein said computer means has a RAM memory for storage of calibration data.

76. An apparatus as claimed in claim 72, wherein said computer means employs at least one calibration algorithm for determining a nominal pressure at a given current value.

77. An apparatus as claimed in claim 72, wherein said computer means includes a storage means for storing the calibration data of nominal pressure versus output current in table form.

78. An apparatus as claimed in claim 72, further comprising an ionization gauge controller means for controlling said gauge means.

79. An apparatus as claimed in claim 72, wherein said temperature measuring means is a transducer having a tungsten element in thermal contact with the gas whose pressure is to be measured.

80. An apparatus as claimed in claim 79, further comprising a second electron emitter or an auxiliary heater.

81. An apparatus as claimed in claim 72, wherein said temperature measuring means is a thermocouple.

82. An apparatus as claimed in claim 72, wherein said gauge means is a Bayard-Alpert gauge.

83. A method for determining a temperature-compensated pressure value of a gas in a system, comprising the steps of:

(a) providing a gas density measuring means;

(b) providing a gas temperature measuring means;

(c) measuring a temperature and a density of a gas in a system;

(d) providing calibration data of the gas at a given temperature for converting output current from said density measuring means into calibrated pressure values;

(e) providing a computer means;

(f) using said computer means to calculate a temperature-compensated output current value based upon the measured gas temperature, the measured output current value, and said given calibration temperature value; and

(g) obtaining a temperature-compensated pressure value from said calibration data which corresponds to said temperature-compensated output current value.

84. A method as claimed in claim 83, wherein said pressure measuring means is an ionization gauge.

85. A method as claimed in claim 72, wherein the calibration data is stored as a calibration curve.

86. A method as claimed in claim 83, wherein said calibration data is stored as a lookup table.

87. A method as claimed in claim 83, wherein said computer means is a microprocessor, and said calibration data is stored in RAM memory.

88. Apparatus for providing a pressure measurement of a gas in a chamber corrected for at least transpiration effects, a pressure sensitive gauge being connected to said chamber by a passageway, the size of the passageway being such as to cause said transpiration when the temperature of the gas in the gauge is different than that in the chamber at certain pressures of the gas in the chamber, said apparatus comprising said pressure sensitive gauge for providing a reading, H, which is a function of an unknown pressure, P_c, of the chamber gas; means for measuring the temperature, T_g, of the gas in the gauge; means for measuring the temperature, T_c, of the gas in the chamber; and determining means responsive to at least H, T_g, and T_c for determining the unknown chamber pressure, P_c, to effect the transpiration correction.

89. Apparatus as in claim 88 where said pressure sensitive gauge is selected from the group consisting of manometers, diaphragm gauges, and force gauges.

90. Apparatus as in claim 88 where said determining means includes means for providing sensitivity and/or linearity corrections of P_c in addition to said transpiration correction.

91. Apparatus as in claim 88 where said determining means utilizes at least the equation:

P_c = (H/j)(T_c/T_g)^q

where q varies from one-half, where the transpiration effect is at a maximum, to zero, where there is no transpiration effect, and where j is at least one value which relates H to P_c and q and j are determined from at least one calibration of the pressure sensitive gauges previous to the gauge providing said reading H.

92. Apparatus as in claims 88 or 91 where said determining means includes a storage means having stored therein different values of P_c as function of at least H, T_g, and/or T_c obtained from at least one calibration of said gauge previous to the gauge providing the reading H.

93. Apparatus as in claim 92 where said storage means is a three dimensional array where H, T_g, and T_c are the variables of the array.

94. Apparatus as in claim 93 where said storage means is a ROM.

95. Apparatus as in claim 88 where said determining means includes calculation means for determining the transpiration corrected value of P_c from at least one mathematical equation where P_c is a function of at least

H, T_c, and T_g.

96. Apparatus for providing a measurement of a value of a parameter of a gas in a chamber corrected for at least transpiration effects, a density sensitive gauge being connected to said chamber by a passageway, the size of the passageway being such as to cause said transpiration when the temperature of the gas in the gauge is different than that in the chamber at certain pressures of the gas in the chamber, said apparatus comprising: said density sensitive gauge for providing a reading, G, which is a function of an unknown value of said parameter; means for measuring the temperature, T_g of the gas in the gauge; means for measuring the temperature, T_c, of the gas in the chamber; and determining means responsive to at least G, T_c, and T_g for determining the unknown value of said parameter to effect the transpiration correction.

97. Apparatus as in claim 96 where said density sensitive gauge is selected from the group consisting of ionization gauges, and discharge gauges.

98. Apparatus as in claim 96 where said parameter is the pressure, P_c of the gas in the chamber.

99. Apparatus as in claim 96 where said determining means includes means for providing density correction of

P_c in addition to said transpiration correction, the density correction compensating for any differences in the temperature of the gauge at the time it was calibrated and T_g, the temperature of the gauge at the time the reading G is provided.

100. Apparatus as in claim 99 where said determining means includes means for effecting the density correction simultaneously with the transpiration correction.

101. Apparatus as in claim 99 where said determining means includes means for providing sensitivity and/or linearity corrections of P_c in addition to said transpiration and density corrections thereof.

102. Apparatus as in claim 96 where said determining means utilizes the equation:

P_c = (G/k) (T_c ^q · T_g ^1-q)

whe)e q varies from one-half where the transpiration effect is at a maximum, to zero, where there is no transpiration effect, and where k is at least one value which relates G to P_c and where q and k are determined from at least one calibration of the density sensitive gauge previous to the gauge providing said reading, G.

103. Apparatus as in claim 96 where said parameter is density of the gas in the chamber.

104. Apparatus as in claim 96 where said determining means includes means for providing sensitivity and/or linearity corrections of P_c in addition to said transpiration correction.

105. Apparatus as in claim 96 where said determining means includes a storage means having stored therein different values of said parameter as a function of at least G, T_g, or T_c obtained from at least one calibration of said gauge previous to said gauge providing the reading G.

106. Apparatus as in claim 105 where said storage means is a three dimensional array where G, T_g, and T_c are the variables of the array.

107. Apparatus as in claim 106 where said storage means is a ROM.

108. Apparatus as in claim 96 where said determining means includes calculations means for determining the transpiration corrected value of said parameter from at least one mathematical equation where the transpiration corrected value of the parameter is a function of at least G, T_c, and T_g.

109. A method of at least transpiration correcting a measurement of an unknown value of a parameter of a gas in a chamber, the measurement being made by either a density sensitive or a pressure sensitive gauge, said method comprising the steps of obtaining and storing calibration data on said gauge, the calibration data at least including readings of said gauge respectively corresponding to a plurality of known values of said parameter of the gas in the chamber; providing a gauge reading H for a pressure sensitive gauge or G for a density sensitive gauge corresponding to said unknown value of said parameter; obtaining the absolute temperature, T_q, of the gas in the gauge at the time the reading H or G is provided; obtaining the absolute temperature, T_c, of the gas in the chamber at the time the reading H or G is provided; and determining the unknown value of the parameter as a function of (a) H, T_g, T_c, and the calibration data or (b) G, T_g, T_c, and the calibration data, the determined unknown value of the parameter being corrected at least for said transpiration.

110. A method as in claim 109 where said gauge is a pressure sensitive gauge and said parameter is pressure.

111. A method as in claim 109 where said gauge is a density sensitive gauge.

112. A method as in claim 111 where said parameter is density.

113. A method as in claim 111 where said parameter is pressure.

114. A method as in claim 113 where said determining step utilizes the equation:

P_c = (G/k) (T_c ^{q ·} T_g ^1-q)

wher)e k and q are determined from said calibration data.

115. A method as in claim 114 where said calibration data further includes (a) a plurality of absolute temperatures of said gauge gas respectively corresponding to said known pressures of said gas in said chamber and (b) a plurality of absolute temperatures of said chamber gas respectively corresponding to said known pressures and said latter calibration data is utilized to determine the unknown value of the chamber gas pressure.

116. A method as in claim 114 where said determining step includes calculating P_c utilizing said equation.

117. A method of determining whether at least a transpiration correction of a measurement of an unknown value of a parameter of a gas in a chamber is necessary and making said correction if necessary, where the measurement is made by either a density sensitive gauge or a pressure sensitive gauge, and, if necessary, effecting said correction, said parameter of the gas having a first range of values when said measurement is fully affected by said transpiration, a second range of values when it is not affected by said transpiration, and a transition range of values between first and second ranges when the measurement is partially affected by the transpiration, said gauge being connected to said chamber by a passageway, the size of which is such that said measurement will be transpiration affected when (a) said unknown value of the parameter is in either said first or said transition range of values of said parameter of the gas and (b) the absolute temperatures of the gas in the gauge and the chamber are different, said method comprising the steps of providing a reading of said gauge, said reading being a function of said unknown value of the parameter; and determining whether said reading is within either said first or transition ranges of values of said parameter of the gas; and correcting said reading for said transpiration effect if the reading is within at least said first range of values.

118. A method as in claim 117 where said determining step includes determining a central transition value of said parameter of the gas which is approximately in the cente of said transition range; obtaining the ratio, R, of said gauge reading to said central transition value; determining whether R is less than a predetermined constant, K, the value of which is related to the extent of said transition range; and said correcting step is effected if R < K.

119. A method as in claim 118 where said central transition value is established by calibration of said gauge and said passageway.

120. A method as in claim 118 including determining whether R < 1/K and, if so, correcting said gauge reading for said full transpiration effect and, if not, further determining whether R < K and, if so, correcting said gauge reading for said partial transpiration effect.

121. A method as in claim 120 where said parameter is the pressure P_c of said gas in the chamber, said gauge reading is P_g, said central transition value is P_1/2g and R = P_g/P_1/2g.

122. A method as in claim 121 where K = 30.

123. A method as in claim 121 where P_c = P_g if R

> K.

124. A method as in claim 121 including obtaining the absolute temperature, T_g, of the gas within the gauge and the absolute temperature, T_c, of the gas within the chamber, determining the square root of the ratio of T_c/T_g and where P_c = P_g (T_c/T_g)^1/2 if R < 1/K.

125. A method as in claim 121 where said transition range is represented by a mathematical equation which is solved for P_c in response to R < K and R > 1/K.

126. A method as in claim 125 including determining the extent of said transition range by calibration of said gauge and said passageway.

127. A method as in claim 126 where said mathematical equation is Eq. 13 stated in the foregoing specification when T_g > T_c.

128. A method as in claim 126 where said mathematical equation is Eq. 14 stated in the foregoing specification when T_c > T_g.

129. A method as in claims 127 or 128 where j is a constant.

130. A method as in claims 127 or 128 where j is defined by equation 15 stated in the foregoing specification.

131. A method as in claim 126 where said mathematical equation is linear.

132. A method as in claim 131 where said linear mathematical equation is of the form y = a x + b where, when y = P_c/P_g and x = log P_g, the linear equation is Eq. 21 stated in the foregoing specification.

133. A gauge for measuring the value of a parameter of a gas in a chamber, said gauge comprising sensing means mounted within said container for providing an output reading which is a function of said parameter of the gas in the chamber; first temperature sensing means mounted with respect to said container for sensing the temperature of said gas with within the gauge; second temperature sensing means mounted with respect to said container for measuring the temperature of the gas outside the gauge.

134. A gauge as in claim 133 where said parameter is the density of the gas.

135. A gauge as in claim 133 where said parameter is the pressure of the gas.

136. A gauge as in claim 135 where said sensing means for providing an output reading is sensitive to the pressure of the gas.

137. A gauge as in claim 135 where said sensing means for providing an output reading is sensitive to the density of the gas.

138. A gauge as in claim 137 where said sensing means is a Bayard-Alpert type ionization gauge.

139. A gauge as in claim 137 where said gauge includes a hollow anode disposed within said container, the hollow anode defining a substantially enclosed space in communication with said gas in the chamber, a cathode for emitting electrons into the enclosed space, and an ion collector in communication with the enclosed space and where said first temperature sensing means senses the temperature of said anode to thus sense the temperature of the gas in the gauge.

140. A gauge as in claim 142 including a heat insulating support member upon which at least a portion of said anode is coated.

141. A gauge as in claim 140 where said support member comprises a ceramic material.

142. A gauge as in claim 133 where said temperature of the gas outside the container is that of the gas within the chamber.

143. A gauge in claim 142 where said gauge is separated from the chamber by at least one passageway, the size of which introduces a transpiration effect at certain values of the parameter in the chamber whenever there is a difference between the temperature of the gas in the chamber and the temperature of the gas in the gauge, said sensed temperature of the gauge gas and chamber gas being available to effect correction of said output reading for said transpiration effect.

144. A gauge as in claim 143 including support means for said second temperature sensing means extending from said container through said passageway into said chamber, said second temperature sensing means being disposed within the chamber.

145. A gauge as in claim 139 including a plurality of said passageways disposed between the gauge and the chamber where the sizes of said passageways are different and are such as to introduce separate transpiration effects and where further temperature sensing means sense the temperature between each passageway.

146. A gauge as in claim 133 including a heat shield mounted between said first and second temperature sensing means.

147. A Bayard-Alpert type gauge comprising a hollow screen anode disposed within said container, the hollow anode defining a substantially enclosed space in communication with a gas whose density or pressure is to be measured; a cathode for emitting electrons into the enclosed space; an ion collector in communication with the enclosed space; and a first temperature sensing means for sensing the temperature of said anode to thus sense the temperature of the gas in the gauge.

148. A gauge as in claim 147 including a second temperature sensing means mounted with respect to said container for measuring the temperature of the gas outside the gauge.

149. A gauge as in claim 148 including a heat shield mounted with respect to said container disposed between said first and second temperature sensing means.