WO2008054846A2 - Photomixer for generation of coherent terahertz radiation and radiation detection - Google Patents

Abstract

A photomixer for generating terahertz and microwave radiation or for use in a optical detector has an active volume including a semiconductor absorbing layer having a top and a bottom, an antireflective cap layer abutting the top of the absorbing layer, a free space disposed above the cap layer, a buried mirror abutting the bottom of the absorbing layer, and a plurality of interdigitated electrodes embedded in the absorbing layer at different positions along a z-axis, where each electrode has a lead for connection to other electrodes of the plurality. The electrodes are formed during epitaxial growth of the semiconductor absorbing layer.

Description

PHOTOMIXER FOR GENERATION OF COHERENT TERAHERTZ RADIATION AND RADIATION DETECTION

RELATED APPLICATIONS This application claims the priority of U.S. Provisional Application No.

60/787,115, filed March 29, 2006, which is incorporated herein by reference in its entirety.

FIELD OF THE INVENTION The present invention relates to a device for generation of continuous, coherent microwave and terahertz (T-Ray) radiation.

BACKGROUND OF THE INVENTION Over the past decade, several groups have demonstrated compact, narrow- linewidth, tunable, microwave to THz radiation sources for spectroscopy and local oscillator applications. With the advent of reliable and affordable diode lasers and fiber optic systems, similar techniques are explored to generate and distribute microwave signals for cellular broad-band mobile communications networks as well. The generation and distribution of microwave signals by optical means is of considerable interest for future WDM communication systems operating at rf modulation frequencies > 60 GHz to better utilize the available optical bandwidth. The basic approach for the generation of millimeter and submillimeter waves is to first generate optical millimeter wave signals using standard optical heterodyne techniques. The frequency spacing of the two fundamental optical lines corresponds to the desired millimeter and sub-millimeter frequency. Optical to electrical down conversion is achieved by mixing the optical radiation in a suitable photoconductive medium such as a photo diode or a planar MSM device also known as an Auston switch. Thus, there are three major components in this optical down conversion approach to electrical millimeter wave (0.1 to 10 THz) generation. These are: 1) tunable optical radiation source using heterodyne techniques, with two fundamental optical lines whose beat frequency (or difference frequency) is in 0.1-10 THz range; 2) high efficiency photomixer with subpicosecond carrier recombination time to convert the optical difference frequency signal to a corresponding electrical signal; and 3) a well optimized antenna or waveguide coupled to the photomixer to emit T- rays generated from the down-converted optical radiation to emit the microwaves into the free space or to couple to other electronic subsystems. The photomixer is formed from a single layer of metal-semiconductor-metal

(MSM) device consisting of interdigitated electrodes and planar antenna fabricated on a semiconductor with ultrashort photocarrier relaxation time such as low temperature- grown GaAs (LT-GaAs) layer on a high-resistivity GaAs substrate. Optical radiation with difference frequencies from few MHz to THz are generated based on well known optical heterodyne techniques, by using highly coherent, tunable, and affordable external cavity stabilized diode lasers (at infrared and optical wavelengths), with output power up to 150 mW. Sub-Hertz relative frequency stabilization of two lasers has been demonstrated in 1992, using Pound-Drever-Hall technique where, the two lasers are coupled to different axial modes of an external high finesse (~22 000) Fabry-Perot ("FP") cavity to produce the discriminator signal for servo control. This optical radiation is mixed in the above photomixer to generate the desired electrical signal at the difference frequency in the interdigitated region. A well designed planar antenna coupled to the interdigitated electrodes allows T-rays to be released into the free space. Planar antenna designs used for emitting the THz radiation are also well characterized and optimized.

FIGs. Ia- Id illustrate a prior art conventional Metal-Semiconductor-Metal (MSM) photomixer design for T-ray generation. As shown in FIGs. Ia-Ib, the active volume 102 of the device comprises of a 1.5 μm thick LT-GaAs layer deposited on a high-resistivity GaAs substrate 104 using MBE techniques. This layer is covered by interdigitated electrodes 106 fabricated using submicron e-beam lithography. When this region is illuminated by radiation with photon energy larger than the semiconductor's band gap, electron-hole pairs 108 are generated for each incident photon absorbed in the photoconductor, shown in FIG. Ic. Immediately after pair creation, the electrons and holes are accelerated away in the opposite directions by the strong electric fields 110 generated by the DC biased interdigitated electrodes. Due to these high electric fields, the carriers attain drift velocity in a relatively short time when compared to their average transit time, i.e., the time required for a carrier to reach an electrode and contribute to the external current. As the incident optical radiation intensity varies at the beat frequency, the pair density also varies at the same rate provided the carrier recombination time is short when compared to the inverse of the difference frequency.

Typical dimensions of the active device are 10 ^χ 10 x l.5 μm. The devices optimized for THz generation have 100 nm thick metal lines that are typically 200 nm wide, < 10 μm long, with a pitch of 0.8 to 1 μm. The capacitance C calculated for this complex structure using conformal mapping is given by Equation (1) C = ₀O ₊ O ά ₍₁₎

K(k') finger period where ε_r is the relative dielectric constant of the photoconductor, A is the area of the interdigitated region, and

π finger width the complete elliptic integral of first kind, with k = tan and

4 finger period

For LT-GaAs, ε_r = 12.8 resulting in C = 2.7 to 3 fF for the above dimensions of the interdigitated region. FIG. Id provides the equivalent circuit diagram of the prior art photomixer.

For two single mode CW laser beams with frequencies V₁, V₂ having average powers P₁, P₂ and the difference frequency /= (V₁ - V₂) stabilized with the help of external cavity, the instantaneous optical power incident on the photomixer active region is given by Equation 2:

P₁ = P₀ + 2^mP₁P₂ [cos 2π(v_x - v₂)t + cos 2π(v_x + V₂ )t] (2) where Po = Pi + P₂ is the total incident power averaged over time, and m is the mixing efficiency with a value between 0 and 1. In the above expression, the last term with -A-

sum frequency varies at a much shorter time scale than the carrier recombination time τ therefore its contribution to the photoconductance can be ignored. If this incident optical power generates a photocurrent i_v in the external circuit, the millimeter wave output power is then given by

In this equation, R_L, Rs are the load resistance and small internal resistance of the photomixer respectively. In general, for well designed antenna or waveguide coupled to the photomixer, R_L is in 72-200 Ω range and Rs « R_L-

Based on photomixer theory, it can be shown that for the prior art design illustrated in FIGS. Ia- Id, i_v is given in Equation 4.

where η is the efficiency of the photomixer and v = (V₁ - v₂)/2. Qualitatively, the parameter η is a product of carrier generation factor which is a measure of the fraction of incident power absorbed in the active volume and a collection factor which is a measure of the fraction of carriers generated that contribute to current in external circuit. Hence, large increase in output power should result from modest increases in η if τ and C are minimized with the better choice of photoconductor material and electrode design. When the Auston switch designs were first explored for optical down conversion, ion damaged (O⁺ ions) Si on sapphire (SOS) was used for photomixer fabrication. It was later found by several groups that As⁺ implanted in GaAs substrate is a better suited for photomixer application owing to its higher electrical breakdown characteristics, direct band gap, and higher carrier mobilities. In the past decade, MBE grown LTGaAs was proved to be the best material of choice for photomixer design over a wide frequency range. The main advantages of LT-GaAs over other materials is easy tunability of its material properties during low temperature MBE growth, subpicosecond (-0.25 ps) carrier life time, high mobility (> 200 cm²/Vs), and high electric breakdown field (> 5^χ10⁵ V/m). However, due to its band gap in the 800 to 860 nm region, LT-GaAs is not suitable for optical communications applications where the spectrum of choice is at 1.55 μm. Fueled by growing demands from the fiberoptic telecommunications industry, this area has produced a wide range of commercially available products, such as lasers, detectors, modulators, and optical amplifiers. Many of these components are based on the compound semiconductor material system Ino.53Gao.47As/Ino.52Alo.4gAs on InP substrates. Only recently LT-InGaAs as well as ErAs/InGaAs materials are being explored for THz photomixer applications at 1.55 μm. Much work is still desired in improving the crystalline quality and other photoconductor properties of these materials to match the success of LTGaAs in THz photomixer applications.

Efforts to increase the THz down conversion efficiency have been focused on the material issues such as decreasing the carrier recombination time τ rather than on improving the efficiency of photocarrier generation and collection in the external circuit with better design of the interdigitated electrodes. At a first glance, it is clear that the incident optical radiation penetrates the photoconductor to a depth well over 1.5 μm from the surface while the electrostatic field lines originating from the interdigitated lines decay rapidly with depth. Thus, most of the carriers generated deep within the active volume are not collected in the external circuit while the absorbed radiation produces undesired heat in the system. In addition, increasing path length of the photocarriers with depth results in some of these carriers not reaching the electrodes before the beat cycle reverses thus leading to unwanted side effects including increased phase noise in the THz output. One method to improve the photomixer performance (i.e., increase Go ) is to form an optical cavity by depositing a mirror layer at a depth D = nX/2 from the surface ( X = X₀ where XQ is the wavelength of the incident radiation in air and n ~ 3.11 is the refractive index of LT- GaAs) and an antireflective (AR) coating on the surface so that standing wave pattern is generated in the active medium with an antinode near the electrodes. The increased intensity, thereby photocarrier density near the top surface, should increase the photomixer efficiency while lowering the noise with decrease in effective path length of the carriers. The estimated THz output power for a cavity device with 5.2 x 5.2 x 1.5 μm active volume is estimated to be ~ 6.5 and 2 μW respectively at 0.65 and 1.5 THz. This is ~7.2x improvement in the output power when compared to a noncavity device. However, even within this cavity there are multiple resonances corresponding to 1 > n , so that all the optical power is not fully utilized. In addition, a fundamental drawback of all MSM designs using optically thick electrodes is that the metal lines act as optical stop barriers thereby limiting the amount of incident optical power that is effectively used in photocarrier generation. In the above case an estimated -25% of the incident power is blocked by metal lines if they are treated as geometrical stops. As the line width of 200 nm is comparable to the wavelength of the incident radiation inside the photomixer (225.4 nm), the system must be treated as a near field diffraction grating. This leads to further reduction in the optical power coupled into the cavity device.

In view of the foregoing, existing photomixer designs are critically deficient in their optical conversion efficiency and long time stability. The present invention is directed to increasing the efficiency and long time stability of this most crucial component of terahertz generators.

BRIEF SUMMARY OF THE INVENTION

The present invention is directed to the enhancement of the photomixer performance in generating higher THz power for a given incident optical power and DC bias voltage across the device. A similar device when used as an optical detector, offers unprecedented speed with high gain. The physical basis for the inventive photomixer is electron-hole pair generation by photon absorption in LT-GaAs, InGaAs or GaN. The LT-GaAs has recently displayed the remarkable photoconductive properties of subpicosecond electron-hole recombination time (τ) and high DC breakdown field (E_B > 4 X IO⁷ V/m). In addition, it displays high photocarrier mobility (μ ~ 200 Cm²V ¹S ¹) relative to semiconductors having a comparable recombination time.

In one aspect of the invention, a photomixer includes a Fabry-Perot cavity comprising a top distributed Bragg reflector, a bottom distributed Bragg reflector and a semiconductor absorbing layer disposed between the top distributed Bragg reflector and the bottom distributed Bragg reflector; and a plurality of layers of interdigitated conductive lines embedded at different heights within the absorbing layer, each of the plurality of layers having a pair of leads extending therefrom for connecting to a DC bias source and/or to other layers of lines. The electrodes are formed during epitaxial growth of the semiconductor absorbing layer. In another aspect, the photomixer of the present invention has an active volume comprising a semiconductor absorbing layer having a top and a bottom; an antireflective cap layer abutting the top of the absorbing layer; a free space disposed above the cap layer; a buried mirror abutting the bottom of the absorbing layer; and a plurality of interdigitated electrodes embedded in the absorbing layer at different positions along a z-axis, each electrode having a lead for connection to a DC bias source and/or to other electrodes of the plurality. The electrodes are formed during epitaxial growth of the semiconductor absorbing layer.

The improvement provided by the invention is increased output power (~2.8 mW at 1 THz and 31.8 μW at 5 THz) of the coherent, CW, T-ray source in the 0.1 to 10 THz frequency range. Present research in this area is focused on increasing the output power of the source to > 10 μW to be useful for practical applications. The maximum power available from the present continuously tunable CW sources is < 10 μW at ITHz. The present invention offers tunability in the entire spectral range and very low linewidth of the emitted radiation. The inventive photomixer offers high quantum efficiency, low noise, and high speed when used as an optical detector. Present day detectors used in applications ranging from long haul high bit-rate fiber optic communication systems, microscopy and astronomy offer up to 500 GHz gain-bandwidth product. The present invention offers close to unity quantum efficiency and detection rate > 5 THz at unity gain.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGs. Ia- Id are diagrammatic views of a prior art photomixer, where FIG. Ia is a cross-sectional view of the photomixer, FIG. Ib is a schematic drawing of the interdigitated metal lines, FIG. Ic illustrates the photo generated carriers accelerated along the electrostatic field lines, and FIG. Id is a schematic view of the equivalent circuit diagram of the photomixer. FIG. 2a illustrates the FP cavity and FIG. 2b illustrates the stacked inter digitated metal line.

FIG. 3 is a contour plot of the electric field amplitude.

FIG. 4a is a contour plot of field strength and FIG. 4b is a plot of the static electric field strength distribution.

FIG. 5 is a plot of the carrier transit time distribution.

FIG. 6 is a plot of the calculated THz output power Pf.

FIG. 7 is a schematic drawing of the modified interdigitated electrode structure. FIG. 8a illustrates the photomixer design and FIG. 8b is a contour plot of the electric field amplitude.

FIG. 9a is a contour plot of field strength and FIG. 9b is a plot of the static electric field strength distribution.

FIG. 10a illustrates the photomixer design and FIG. 10b is a contour plot of the electric field amplitude.

FIG. 1 Ia is a contour plot of field strength and FIG. 1 Ib is a plot of the static electric field strength distribution.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention is directed to the enhancement of the photomixer performance in generating higher THz power for a given incident optical power and DC bias voltage across the device. A similar device when used as an optical detector, offers unprecedented speed with high gain. The physical basis for the proposed photomixer is electron-hole pair generation by photon absorption in LT-GaAs, InGaAs or GaN. The LT-GaAs has recently displayed the remarkable photoconductive properties of subpicosecond electron-hole recombination time (τ) and high DC breakdown field (E_B > 4 X IO⁷ V/m). In addition, it displays high photocarrier mobility (μ ~ 200 Cm²V ¹S ¹) relative to semiconductors having a comparable recombination time. The optical microwave signals are generated by heterodyning the optical spectral lines of a mode locked laser or of two or more semiconductor diode lasers whose difference frequency is stabilized using external high finesse (~22 000) Fabry- Perot (FP) cavity. The existing art in generating the optical microwaves is well developed over a wide range of optical frequencies including far infrared, infrared, and visible spectrum. Depending on the photoconductive medium used for the down conversion, a suitable commercially available. For the present invention, either Ti- Sapphire or DBR lasers operating at 800 to 860 nm spectral range are most appropriate as the photoconductive medium used for the photomixer described next is Low Temperature grown GaAs (LT-GaAs). For this material, photon energies in this spectral range are just above the semiconductor band gap in the 77 to 300 K range to allow efficient absorption of the incident radiation.

If the semiconductor used for photomixer is InP, Ini__xGa_x As_yPi__y lattice matched to InP substrate, Ini__xGa_x As, InAs, GaN, AlGaN, or InGaN, DBR lasers operating in different spectral regions suitable for each material in the 340 to 1600 nm spectral range are also commercially available. The inventive multilayer photomixer design increases the carrier collection efficiency by decreasing the carrier transit time t_Xv, increases the average electrostatic field throughout active volume at lower bias voltage Vb , and increases the carrier generation efficiency by effectively absorbing most of the incident optical radiation. Thin interdigitated metal lines are embedded in the host semiconductor matrix grown by suitable epitaxial techniques such as MBE, LPE (Liquid Phase Epitaxy), and

MOCVD. In the past, several groups have demonstrated lateral overgrowth of device quality semiconductors such as GaAs, InGaAs, and GaN on thin tungsten metal lines. As the dimensions of the metal lines of the inventive photomixer are much smaller than those used in the prior art, growing excellent quality epitaxial layers to completely embed the metal lines will not be a problem. Due to the decrease in t_Xv to less than 1 ps in this design, the carrier recombination time τ can be as large as 4 ps. This is a significant advancement because present designs requiring τ ~ 0.1 ps set severe constraints on the material choice and its growth conditions. In general the low temperature growth conditions required for obtaining low τ degrade the material conductivity and breakdown field limit. Until now only in LT-GaAs all the photomixer requirements were sufficiently met but the present design allows most of the semiconductors to be suitable for THz power generation.

Recent experimental discovery of the enhanced optical transmission through thin, normal metal films with periodic subwavelength holes has given rise to their numerous applications in subwavelength optics, data storage, and microscopy. In the infrared to far-infrared spectral region, the electrical permittivity of normal metals has a negative real component. This results in material response that is 180° out of phase with respect to the electric field incident on the medium. Under right conditions this property can be exploited to enhance the electric field in the vicinity of thin metal structures with subwavelength features. Previously, such enhancement was demonstrated using traveling electromagnetic waves only but the physics is equally applicable to standing waves. In the prior art MSM device of FIG. Ia, no carriers are generated directly below the metal lines 106 because most of the incident light is reflected away. However, if carriers could be generated in this region they will have the shortest transit time (for electrons generated below +ve electrodes and holes generated below -ve electrodes), thereby increasing the collection efficiency. Therefore, it is desirable to have thin (in comparison to the skin depth of the metal) metal lines with subwavelength features distributed throughout the active volume, as illustrated in FIG. 2a, in a manner that would collectively enhance the optical field intensity in the vicinity of the metal lines. This must, however, be accomplished without significantly increasing the device capacitance and internal resistance of the electrodes.

FIGS. 2a and 2b illustrate the FP cavity and stacked interdigitated metal line parameters used in FDTD computation. As shown in FIG. 2a, the FP cavity 200 is formed by a three layer (TiO₂, Si₃N_x, CaF₂) top DBR 202, four pairs of (Al₂O_x, GaAs) layers forming the bottom DBR 204, and LT-GaAs absorbing layer 206 of thickness ~ λ for λo = 850 nm radiation. All lengths are in nm. The active volume is terminated by 15 cell Uniaxial Perfectly Matched (UPM) layers 208 in FDTD implementation to mimic real world structure. The parameters in brackets show the refractive index and thickness of each layer. FIG. 2b illustrates the geometry of the interdigitated metal lines 210 placed at various z locations within the LT-GaAs absorbing layer 206. The two 200 nm wide lines 212, placed along the x axis are connected to either signal transmission lines or planar antenna fabricated on top of the LT-GaAs layer (not shown). Through layer vias electrically connect the leads 214 of multiple layers of interdigitated lines 210. The overall dimensions of the active structure (excluding DBRs 202, 204 and via leads 214) are given by L_x, L_y, and D whereas the metal line thickness, z location (measured from the Air- TiO₂ interface), line pitch, width and lengths of the interdigitated lines 210 are given by d, Z₁, p, w, l\, and h as shown.

A convenient way to model such a complex structure is to solve the Maxwell's equations with appropriate boundary conditions using Finite Difference Time-Domain (FDTD) formulation first introduced by Yee in 1966. A 3D FDTD simulator with Uniaxial Perfectly Matched Layer (UPML) surrounding the active volume to mimic real world photomixer is developed for this purpose. Along the z-axis, the active volume consists of a few hundred nm of free space 201 followed by an antireflective cap layer 202 with two or three layer quarter wave stack, photomixer region 206 with complex structure of normal metal electrodes 210, and a four pair DBR (Distributed Bragg Reflector) stack 204 for the buried mirror (FIG. 2a). The top antireflective coating 202 along with the bottom DBR stack 204 thus forms the FP cavity for plane waves propagating along z-axis. To reduce the effect of UPML 208 terminations along x and y axes on the photomixer volume covered by metal electrodes, at least 1500 nm of computational space 220 is left between the UPML slabs 208 and photomixer volume. For example, if the photomixer cross sectional area is 7000 x 2500 nm (i.e., area covered by metal lines in x-y plane), the active area sandwiched between UPML slabs along x or y axis is at least 10000 x 5500 nm. The 15 cell UPML region is polynomially graded for optimal results. The DBR and antireflective layer parameters (i.e., index and thickness) are first optimized by calculating the reflection and transmission coefficients of the FP cavity using matrix methods for a given photomixer layer parameters.

In the FDTD computation, the FP cavity is excited by a monochromatic, linearly polarized, plane wave propagating along z + direction, with gaussian intensity profile in the x-y plane, where the source electric field is given by Equation 5. E_x(x,y,z₀) =

(5)

The source plane is located in the free space above the top antireflective layer at z = Zo. For this source field, total field/scattered field formulation is adopted. For an ideal cavity, the scattered field at the source plane goes to zero when the cavity is fully excited, therefore this source condition is adequate, provided the simulation is not run for too long. For an FP cavity with parameters shown in FIG. 2a, the matrix calculations show that the amplitude reflectance (into air) is 0.057 and transmittance (into the substrate) is 0.063 at λo = 850 nm when the metal lines are absent.

Therefore, under ideal conditions most of the incident power will be absorbed in the LT-GaAs layer. The standing wave thus formed will have antinodes at the interfaces of LT-GaAs with top and bottom DBRs as well as at the center of LT-GaAs layer. A direct comparison of the field amplitudes at these antinodes showed that the FDTD calculations for this cavity are in excellent agreement with the above matrix calculations. The noise resulting from reflections from the UPML slabs is observed to be < 0.5%.

To compute near field enhancement close to normal metal lines embedded in the host semiconductor matrix in FDTD scheme (FIG. 2a and 2b), a second-order material model such as a frequency-domain Lorentz dispersion model is adapted for metals with negative dielectric constant in the frequency of interest such as W or Pt. This model can be designed to give the correct refractive index for any material at a single frequency. The dielectric constant and refractive index of a metal in Lorentz model is given by Equation 6;

n_m ² _etal (ω = 2πv) = ε_r - Is₁ (6)

where (χ₀ ,ε_∞ , ω₀,T) are the four parameters that are adjusted to produce the desired refractive index at a given frequency. For tungsten (W), n = 3.29 - 2.96/ at 1.4 eV (887 nm) resulting in the Lorentz model parameters (χ₀ , ε_∞ , ω₀ , F) = (5.6, 7.38, 2.06 x 10¹⁵, 5.0 x 10¹⁴). At this frequency, the dielectric constant is though not -ve, is very small (2.06) when compared to the host semiconductor matrix (14.2). In general, for thin metal films, the material parameters can be very sensitive to impurities and film's morphology resulting in variation of the dielectric constant from +ve to -ve or vice versa (note: the tabulated values are for pure bulk metal and its dielectric constant changes sign in the vicinity of 1.4 eV), therefore, the Lorentz model parameters were varied over a wide range in the FDTD computation. Surprisingly, the near field enhancement is insensitive to such model parameter variations indicating that enhancement results as long as the material response is not instantaneous (as in a perfect metal), and the host matrix dielectric constant is large when compared to the normal metal used.

FIG. 3 shows the FDTD results of a three layer stack of interdigitated W lines embedded in LT-GaAs absorbing layer of a photomixer design of FIG. 2a and 2b. The metal lines are 10 nm thick with the same interdigitated pattern of FIG. 2b in each layer of the stack. The plot clearly shows the near field enhancement resulting from the thin normal metal electrodes. In the absence of the W electrodes, amplitude maxima at z = 440 to 450, 550 to 560, and 660 to 670 nm, corresponding to three antinodes in the standing wave formed between top and bottom DBRs. Instead of thin, periodic, stacked electrodes if there is a single layer of thick W lines at z = 440 nm, similar to the prior art photomixer design (FIG. Ia - Id), the calculations showed diffraction effects significantly reducing the incident power coupled into the photomixer. Similar FDTD calculations were performed for different photomixer parameters in an effort to optimize the THz power output from the photomixer (discussed below) and the above plot shows the field profile inside one of the well optimized device structures.

To compute the THz power output from the above photomixer, one needs to calculate the static electric field distribution resulting from DC biased interdigitated metal lines as well. For this purpose, a general purpose 3D Finite Difference (FD) simulator was developed to solve either Laplace's or Poisson's equation with appropriate boundary conditions. As the computation volume does not extend over multiple length scales and all electrode geometries can be broken into smaller rectangular regions, a simple FD Cartesian grid is adequate for this purpose. To test the simulator, the internal electric fields generated by a parallel plate capacitor enclosing the LT-GaAs layer as well as a single layer of interdigitated metal lines covering the photomixer (similar to FIG. Ia- Id) were first computed. The FD results were cross checked with analytical formulae for capacitances in each case (such as Equation 1). The FD computed values are in excellent agreement with the theoretical values in each case. The internal electric fields and capacitances were then computed for the stacked electrode geometry of FIG. 2a and 2b for different L_x, L_y, d, Z₁, p, w, l\, h parameter values. In each case, the FD volume included the DBRs with the appropriate static dielectric constant values for each layer available in literature and sufficient buffer volume between outermost computational boundaries and the active volume to mimic real world device.

Illustrated in FIG. 3, the electric field amplitude inside the D = 230 nm LT- GaAs absorbing layer of the photomixer design of FIGS. 2a and 2b computed using FDTD technique for 850 nm incident radiation with field amplitude E_x° = 1 V/m. For clarity, field amplitude in only the x = ± 600 nm region along the y = 0 plane is plotted (x = 0, y = 0 is located at the center of interdigitated pattern in FIG. 2b). The grey rectangular regions in the plot show the positions of the interdigitated W lines with L_x = 7000, Ly = 2500, d = 10, Z₁ = 475, z₂ = 555, z₃ = 635, p = 300, w = 100, 1₁ = 1500, and h = 1400 respectively.

FIGS. 4a and 4b illustrates the contour plot and distribution of the static electric filed strength as a volume fraction within the D = 230 nm LT-GaAs absorbing layer of a photomixer with parameters same as that of FIG. 3. The metal electrodes are DC biased ±1.0 V. The plots show that unlike the traditional MSM structure of FIG. 1 , the field strength in this design is well above the critical field (~5 kV/cm) required to accelerate the photocarriers generated throughout the absorbing layer volume. For the structure illustrated in FIGS. Ia- Id, bias voltage Vb > 40 V is required to accelerate carriers generated deep inside the photomixer. At these high bias voltages, the field close to the electrodes exceeds the breakdown field for

LTGaAs (-500 kV/cm) leading to device failure. In the present design, the results show that in the photomixer volume the field strength is mostly -90 kV/cm between neighboring electrodes, in particular at the center of the device where most of the carriers are generated due to gaussian intensity profile of the incident laser beams. In the rest of the volume the field has a broad peak at 18 kV/cm (FIG 4b). In addition, optical near field enhancement regions observed in FIG. 3a coincide very well with the high static field regions in FIG. 4a leading to enhanced contribution from ballistic and quasiballistic transport of carriers discussed below. The capacitance for the photomixer design of FIG. 3, 4 calculated from the above FD results is 4.90 fF. The internal resistance of the electrodes is estimated to be 2.4 Ω based on the resistivity of thin annealed or epitaxial W films (~5 μ Ω -cm). The highest electric field inside the device is about four times lower than the breakdown voltage; therefore device failure due to electric breakdown is unlikely at this V_b.

FIGS. 4a and 4b illustrate the static electric field strength inside the D = 230 nm LT-GaAs absorbing layer of the photomixer design of FIG. 2 computed using FD method when the electrodes are biased ±1.0 V. The length of the +ve electrodes Z₁ = 1500 nm, and -ve electrodes /₂ = 1400 nm. FIG. 4a illustrates the contour plot of field strength (kV/cm) in the x = ± 600 nm region along the y = 0 plane (x = 0, y = 0 is located at the center of interdigitated pattern in FIG. 2b). The grey rectangular regions in the plot show the positions of 10 nm thick interdigitated W lines with/? = 300, w = 100, and d = IOnm respectively. FIG 4b illustrates the static electric field strength distribution in the D = 230 nm LT-GaAs absorbing layer of FIG. 4a plotted as a volume fraction. The two peaks indicate that in a significant portion of the absorbing volume the field strength is either -18 kV/cm or -90 kV/cm.

Based on the above 3D FDTD and FD calculations of the optical field, and static field inside the photomixer, one can calculate the carrier collection efficiency and photo current /p by first computing the carrier transit time distribution for the entire absorbing volume. This distribution is obtained by dividing the total volume into smaller volume elements and then calculating the number of carriers generated in each volume element as well as their transit time to the nearest electrodes. In the traditional design of FIG. 1 for the photomixer, the transit time ( ttr» 1 ps) of the carriers is on an average » τ and the carriers travel at equilibrium drift velocity. In the present case however, one can exploit the nonequilibrium effects such as velocity overshoot and ballistic transport of carriers that takes place when the electric field is uniformly high along the carrier's trajectory. THz photomixer based on qasiballistic transport in LT-GaAs and GaAs nano-pin-diodes has been recently proposed to take advantage of the nonequilibrium transport in semiconductors. For GaAs and LT- GaAs with ultrafast carrier recombination, the field dependent, transient velocity of electrons and holes has been studied extensively using Monte-Carlo techniques. From these studies, it is now well known that under high fields, electrons can achieve peak velocities 8 to 10 times their equilibrium saturation drift velocity in these materials. However, the overshoot effects can only be exploited over a limited range of transit distances before polar optical emission and intervalley scattering lead to negative differential mobility of the carriers. From the data available in literature for GaAs and LT-GaAs, for t_b < t_onSet = 100 fs, the carrier motion can be approximated by ballistic transport with electron effective mass m_e = 0.088 mo, where mo is electron rest mass. This value is consistent with the slope of the linear portion of transient drift velocity curve obtained from Monte-Carlo calculations. The corresponding effective mass for holes is mu = 0.106 mo. Effective masses larger than the accepted values for GaAs (0.063, 0.076 mo for electron and light holes respectively) are considered so that longer transit times, thereby lower estimate of /p results from these calculations. In the photomixer design of FIGS. 3a and 3b and 4a and 4b, ballistic transport is mostly applicable to electrons generated close to the +ve electrodes and holes generated close to -ve electrodes. These carriers generated predominantly in the near field enhancement region, transit through non-uniform DC fields in the 5 to 90 kV/cm range. It should be noted that t_onset = 100 fs is considerably lower than the theoretical limit of ballistic motion in GaAs for this field strength range. For t_tr ≥ t_onset, electron motion is approximated by qasiballistic transport with time dependent velocity distribution up to 4 = 3 ps, and equilibrium drift velocity (~1 x 10⁷ cm/s) for t_Xv > 3 ps. In the absence of reliable velocity data for holes, hole motion is approximated by one third of the electron velocity at any given t_tr ≥ t_onset value. FIG. 5 shows the carrier transit time distribution «tr(/tr) for electrons and holes in the photomixer design of FIG. 2 obtained with the above approximations for carrier velocities. The integral of n_tr(ttr) curves in this figure give the carriers ( N_β, Nh for electrons and holes respectively) generated per period (T -2.83 fs) of the 850 nm source with P₁ = PQ = 60 mW. The data shows that n_tr has peaks at t_tr ~ 65 and 70 fs for electrons and holes respectively (solid and dotted curves) for the device parameters of FIG. 3 and FIG. 4. Such a sharp peak followed by several satellite peaks and a long tail of the n_Xx distribution can be understood from the fact that most of the carriers are generated close to the electrodes in the near field enhancement regions where the static fields are also strong. The satellite peaks result from periodicity of the electrode structure and specific choice of the velocity distribution. It is important to note that in the above distribution, number of carriers with t_Xx > 1 ps is very small therefore, for this device structure τ is not the critical factor in determining the photomixer performance at THz frequencies. A sharp drop in n_b by a factor of 2 for electrons and a factor of 3 for holes at t_b ~ t_onSet is due to the lower estimate of carrier velocities resulting from the uniform field qasiballistic distribution function applied to a case where fields are inherently inhomogeneous. Although, the above choice of velocity distribution for quasiballistic motion is consistent with the fact that over a large volume fraction (FIG. 4b) of the absorbing layer the static field is -18 kV/cm, a rigorous calculation should include quasiballistic velocity distribution appropriate for inhomogeneous fields. This would require ensemble Monte Carlo and carrier trajectory calculations carried out in parallel throughout the absorbing layer volume. However, above calculations are adequate for obtaining the lower limit of the THz power output because a rigorous calculation would probably produce a more uniform distribution around 4 ~ Unset without altering the distribution for t_b < Unset or the integral of n_Xv{t_Xv). This will further reduce the number of carriers in the long tail of the n_Xv distribution.

FIG. 5 illustrates the carrier transit time distribution røtr(ttr) for electrons (e) and holes (h) in the photomixer design of FIG. 2. The parameters for the solid and dotted curves are same as in FIG. 3 and 4 with w = 100 nm where as for the dash-dotted curve, only polarization is changed to E_y. For the dashed and short dashed curves (L_x, p, w) are changed to (7560, 300, 60) and (7480, 320, 120) nm respectively while rest of the parameters remaining unaltered from those of FIGS. 3 and 4. The photomixer is excited by an 850 nm source at P₁ = PQ = 60 mW for all structures. For clarity, the curves are shifted along y-axis and the relative shift can be easily obtained from the values at t_ti = 0 fs.

In an effort to optimize the THz output power, similar calculations were peformed for over 70 photomixer configurations by systematically varying L_x, L_y, d, Z₁, p, w, h, h, number of interdigitated layers ( i ), polarization (E_x or E_y), orientation of interdigitated lines in different layers, LT-GaAs absorbing layer thickness, and other DBR parameters. Although the number of configurations explored is small when compared to the parameter space, most of the general features of the inventive photomixer can be summarized from this effort. It is observed that increasing the number of interdigitated layers along with LT-GaAs layer thickness increases the device capacitance well above 5 fF negating any performance gain one may obtain such as reduced internal resistance, reduced carrier density, and better thermal transport. The device capacitance is lowest when the metal lines in all layers lineup perfectly along the z axis with the same orientation angle in all layers as shown in FIG. 2a. Although carrier transit time decreases with/?, significant reduction in carrier generation efficiency is observed when (p - w) is much smaller than λ, irrespective of the line width w and their relative orientations. For λo = 850 nm, p — w ~ 200 nm is observed to be optimal. Similar reduction in carrier generation efficiency is observed when Z₁ of the two outermost interdigitated layers are close to the two antinodes formed at the LT-GaAs layer - DBR interfaces. This is due to increased reflectance from the structure resulting from the fact that significant portion of the near field enhancement regions now lie in the two DBR layers. For example, calculations show that for the parameters of FIGS. 3 and 4, -98% of the incident radiation is absorbed in the LTGaAs layer where Z₁ and zi are 475 and 635 nm for this structure. When they are changed to 455 and 655 nm respectively, only 63% of the incident radiation is absorbed. Likewise, when zi alone is changed from 635 to 645 nm, up to 97% of the radiation is still absorbed in the LT-GaAs layer. Once/? and Z₁ are optimized, line width w (in the 60 to 150 nm range studied) did not have much affect on the absorption efficiency, but it strongly influenced the near field enhancement in the photomixer.

The dashed and short dashed curves in FIG. 5 show the effect of w on n_ti distribution. For w = 120 nm, a small decrease in number of carriers occurs with t_b < I Onset- For w > 120 nm this decrease is more pronounced (not shown). This is partly due to reduction of static field strength in the space between vertically stacked metal lines (FIG. 4a) with increasing line width. The calculations also show that with increasing line width, the near field enhancement close to the electrodes in the top two interdigitated layers decreases while it increases below the 3^rd layer. For w = 60 nm, the plot shows (FIG. 5) significant reduction in the number of carriers with t_ti < t_onset along with a broad peak at t_tr ~ 400 fs. Based on these calculations, line width in the 90 to 120 nm range appears to be optimal for the above photomixer design.

Calculations showed that -5 % reduction in capacitance can be achieved without affecting røtr(ttr) distribution, if the line length h of-ve electrodes is -100 nm shorter than the +ve electrodes. It is well known that polarization of the incident radiation plays a vital role in the transmissivity of rectangular apertures. To observe its effect on absorption efficiency and THz output power, the laser polarization was changed to E_y in the FDTD simulation of a well optimized photomixer design of FIGS. 3 and 4. The dash-dotted curve in FIG. 5 shows the n^ distribution in a photomixer excited by E_y polarized 850 nm radiation. Although, -81% of the incident power is absorbed in the LT-GaAs layer for this case, due to significant reduction in near field enhancement, fewer carriers have 4 < t_onset.

Due to the smaller photomixer dimensions and high (-98%) absorption efficiency, even at modest laser power of Po ⁼ 60 mW, the number of carrier pairs generated in the above photomixer in 1 THz cycle will be -6 x 10¹⁶ cm³. For the conventional photomixer of FIG. 1, space charge effects begin to degrade the device performance at this carrier density because the devices are transit time limited. In order to reduce the steady state carrier density, the conventional designs require ultra short carrier recombination time , τ typically in sub picosecond range. In the present invention however, due to very short transit time 4 of carriers, the steady state carrier density will be not high even when τ is of the order of a few ps. For photomixer design of FIG. 2, the number of electrons captured in the metal electrodes at time t is given by Equation 7.

n:_ap (t) = ]n_gen {t_c)nA^e t - t_c)e-^(t-^t<)"'dt_c (V)

where n_g ^e _en (t) =

+ cos(2;r / 1)] is the number of electrons generated in LT-GaAs layer per second by incident laser power P₁ modulated at a THz frequency ,/and t_c , n_t ^e _r , τ_e are the carrier creation time, electron transit time distribution (see FIG. 5), and electron recombination time. Similar expressions can be written for number of holes captured n_c ^h _ap (t) and the carriers available for conduction in the photomixer n_a ^e _vl it) and n_m ^h _l (t) . From this expression, it is clear that the photocurrent i_p (t) = e{n_c ^e _ap (t) + n_c ^h _ap (t)) ( e is electron charge) is also modulated at a frequency/ generating power at the desired THz frequencies. Based on the transit time distributions «_tr(/_tr) of FIG. 5 and other photomixer designs, «_cap, «_avl, i_p, and pi were calculated for/in the 0.1 tolO THz range (see FIG. 6). In these calculations, antenna load resistance R_L = 72Ω, τ = 2τ_e = 2iV3 with varied τ in the 0.5 to 6 ps range. For the well optimized photomixer parameters of FIGS. 3 and 4, the steady state electron density obtained from the DC value n_a ^e _vl (t) for τ = 4 ps is ~6 x 10¹⁵ cm^"3 (at P₀ = 60 mW) with holes 1.5 times more numerous than electrons. Dipole fields arising from this space charge are negligible (-2.5%) in comparison to strong electric fields (FIG. 4) present in the photomixer.

The output power (P/) data of FIG. 6 in the 0.1 to 10 THz frequency range obtained from Equations 3 and 7 show that for a well optimized photomixer, Pf ^f ^{2 77} in the 0.5 to 6.5 THz range. For the prior art photomixer design of FIG. 1, Equations 3 and 4 result in/⁴ roll-off of THz power. A recent n-i-p-n-i-p photomixer concept is shown to have/² roll-off for/< 1.5 THz. Therefore, the design of FIG. 2 offers significant improvement over the existing photomixer designs. Table 1 lists Pf of FIG. 6 at a few representative frequencies. The design parameters of FIGS. 3 and 4 (Sl in FIG. 6) results in highest THz power throughout the 0.1 to 10 THz range. As expected, lowering τ to 1 ps (S7 in FIG. 6), does not significantly affect P/for/> 1 THz. Moving the interdigitated layers at (Z₁ , z₃) closer to the two outermost antinodes (S2, S6 in FIG. 6) decreases P/ by -55% throughout the THz frequency range. A similar decrease (S3 in FIG. 6) can be seen when the incident radiation is E_y polarized. For w = 60 and 120 nm (S4, S5 in FIG. 6), P/ is -10 to 20% lower than the output power for w = 100 nm with the decrease more pronounced at higher frequencies. While computing Pf , the time required to fully excite the FP cavity which is -20 fs obtained from FDTD calculations was not taken into account, resulting in > 20% error in the estimates at/~ 10 THz.

FIG. 6 is a plot of the calculated THz output power Pf from the photomixer design of FIG. 2 excited by 850 nm radiation with Po = 60 mW. Recombination time τ is 4 ps for designs Sl to S6 where as for S7 τ is 1 ps. Parameters for Sl are same as in FIGS. 3 and 4 where as for S2 z^ = 645 nm, for S3 z^ = 645 nm and incident radiation is E_y polarized, for S4 (p, w) are (320, 120) nm respectively, for S5 ) , (L_x, w) are (7560, 60) nm respectively, and for S6 (Z₁ , z₃) are (455, 655) nm respectively. The remaining unlisted parameters are the same in all cases.

Table 1

Although, the incident laser power used above ( Po ⁼ 60 mW) is lower than the maximum power at which the conventional photomixers of FIG. 1 begin to fail, due to increased absorption efficiency and smaller dimensions of the proposed photomixer, device heating is a problem even at significantly lower V_b (2 V instead of 40 V). The internal temperature of the photomixer of FIG. 2 is estimated to rise by as much as -200 K above the fixed substrate temperature To for V# = 2 V, and Po = 60 mW. This estimate is based on 3D FD computation of steady state heat equation with appropriate thermal boundary conditions for the photomixer of FIG. 2. In this computation, room temperature thermal conductivity (k) of various DBR layers and that of LT-GaAs are approximated by assigning £"^"GaAs = 46 Wm^-1K^"1 and

^LT-GaAs ₌ J.DBR ₌ ^DBR ₌ J Q ψ^ ^-^ _wherg £_{||>k± arg mg} J_{n plan}g _{and Qut Q}f _pl_ane

conductivities. For most of the optical films that constitute DBRs k is in the 10 to 18 Wm^"1 K^"1 range, therefore above values are adequate for obtaining approximate change in temperature of the photomixer. The small contribution from thin metal lines as well as interface impedances were ignored and it was assumed that heat is uniformly generated throughout the D = 230 nm thick LT-GaAs layer. Based on this estimate, the substrate may need to be cooled to liquid nitrogen temperature (77°K) when the laser power Po is high. FIG. 7 is a schematic drawing of the modified interdigitated electrode structure of FIG. 2b for doubling THz output power. Two interdigitated patterns 704, 706 similar to that shown in FIG. 2b are connected in series with the center electrode 710 grounded. Through layer vias electrically connect the leads 708 of multiple layers of interdigitated lines. The resulting structure is excited by a laser beam with two quasielliptical spots 712 as shown. Such a radiation pattern is achievable by choosing the proper laser propagation mode (such as TEMlO mode). The spacing between the two metal patterns 704, 706 is adjusted to match the beam pattern of the specific laser system being used.

Further increase in output power P/ can be obtained by fabricating two interdigitated metal structures of FIG. 2b next to each other along the y-axis as shown in FIG. 7. When the resulting structure is biased as shown, it is equivalent to two capacitors in series coupled to the antenna or transmission line. The incident radiation will now have two elliptic intensity profiles as shown with the total power of Po =120 mW. If this power is focused on one half of the photomixer, a fourfold increase in P/ should result because P/ ∞ P₀ ² (from Equations 3 and 4). However, in the design of FIG. 7, the increase in Pf results from the decrease in device capacitance rather than from twofold increase in Po- FD calculations show that device capacitance C decreases to 3.17 fF from 4.9 fF if each half of the inter digitated structure has the parameters of FIGS. 3 and 4 and center electrode in FIG. 7 is grounded. From Equation 3, this decrease in C results in twofold increase in Pf . Grounding center electrode 710 is necessary due to unequal electron and hole contributions at any given time in most of the photoconductors; otherwise this electrode will also be a radiative element complicating the THz output radiation pattern. It is believed that the output power of this photomixer (2 Pf) is equal to the algebraic sum of the output power of two independent sources each generating Pf output.

From the data presented thus far it appears that photoconductor properties such as recombination time τ are not that important for the inventive photomixer. As long as the absorbing layer has τ = 4 ps with large nonequilibrium, high field carrier mobility (velocity overshoot) and low effective mass of carriers, the photomixer design offers excellent THz power generation and detector capabilities.

Photoconductors such as InP, Ini__xGa_xAs_yPi__y, Ini__xGa_xAs, InAs lattice matched to InP substrate, GaN, AlGaN, and InGaN grown on sapphire, SiC, CVD diamond, or Si are other alternatives for the proposed photomixer. All these materials can readily offer τ ~ 4 ps with excellent high field, nonequilibrium carrier mobilities (> 10⁷ cm/s) however, due to the difficulty in lowering τ to subpicosecond level while retaining high crystalline quality and breakdown field limits in these materials similar to LT- GaAs; they were not previously considered for THz power generation using conventional design of FIG. 1.

Ini__xGa_xAs, and to some extent Ini__xGa_xAs_yPi__y and InP are the materials of choice for optical communication devices and components because fiber-optic communication frequencies match material's band gap at λ < 1550 nm. The band gap of LT-GaAs at λo = 850 nm is rather too large to be useful for optical communications applications. On the other hand, Ini__xGa_xAs based photomixer can exploit low cost lasers, fiber amplifiers and other devices already available at λ₀ = 1550 nm. Local oscillators in the 0.1 to 5 THz range, with small form factor and output power > 10 μW will be in great demand in near future as the RF modulation frequency of the WDM channels increases beyond 100 GHz. Larger L - F valley separation energy and lower effective electron mass are some of the advantages of InGaAs over GaAs. However, Ini__xGa_xAs is much more challenging for photomixing than LT-GaAs because smaller band gap tends to make breakdown field and resistivity low. Undoped, normally grown material is usually n-type due to the large background electron donors. Recently, Low Temperature (LT) grown, Be modulation doped (~4xl O¹⁹ cm^"3) Ino_.53Gao_.47As (λ₀ = 1550 nm), Fe-implanted Ino_.53Gao_.47As, and ErAs layers embedded in Be doped Ino_.53Gao_.47As, LT grown Ino_.3Gao_.7As (λo = 1060 nm), LT grown Ini__xGa_xAs on GaAs have all been demonstrated to have short recombination time and acceptable resistivity for photomixing applications. Heavy ion doping or very low temperature growth required for achieving τ in subpicosecond range also reduce the carrier mobility, thereby device performance. As the recombination time requirement for the present invention is only 4 ps, any LT-grown Be doped Ini__xGa_xAs is a natural choice for the photomixer operating at λo = 1550 nm. For this stacked MSM photomixer, having a thin layer (< 2nm) of InAlAs to raise the effective Schottky barrier height on InGaAs is also possible for reducing the dark current of the device.

FIGs. 8a and 8b illustrate the photomixer design based on Be doped LT- Ino.53Gao.47As absorbing layer and the corresponding electric field amplitude inside the D = 220 nm absorbing layer. FIG. 8a illustrates that the FP cavity 800 is formed by three layer (TiO₂, CaF₂, InP) top DBR 802, 25 nm of InP buffer layer plus 11 pairs of (oxidized InAlAs, InP) layers forming the bottom DBR 804, and LT-InGaAs absorbing layer 806 of thickness ~ λ/2 for λo = 1550 nm radiation. The active volume is terminated by 15 cell UPML layers 808 in FDTD implementation to mimic real world structure. Interdigitated lines 810 of tungsten (W) are embedded within the absorbing layer 806. The parameters in brackets show the refractive index and thickness of each layer. FIG. 8b is a plot of the electric field amplitude computed using FDTD technique for 1550 nm incident radiation with field amplitude E° = 1

V/m. For clarity, field amplitude in only the x = ± 1000 nm region along the y = 0 plane is plotted (x = 0, y = 0 is located at the center of interdigitated pattern similar to FIG. 2b). The grey rectangular regions in the plot show the positions of the interdigitated W lines with L_x = 7600, L_y = 2500, d = lθ, zι = 765, z₂ = 835,/? = 500, w = 100, /i = 1500, h = 1400 respectively. All lengths are in nm.

FIG. 8a shows the layer structure and optical near field enhancement in a photomixer based on Be doped Ini__xGa_xAs grown on InP substrate optimized for operation at λo = 1550 nm. With small changes in the thickness of various layers, this structure can also be optimized for Ini__xGa_xAs_yPi__y, LT grown Ino.3Gao.7As (λ₀ = 1060 nm), or LT grown Ini__xGa_xAs on GaAs. Due to longer wavelength, the line pitch p needs to be higher than in the case of A₀ = 850 nm. To reduce the device capacitance and carrier transit length, the absorbing layer thickness is reduced to λ/2 ~ D = 220 nm resulting in two antinodes near the DBR-absorbing layer interfaces. In the presence of W lines, strong near field enhancement can be observed in FIG. 8b, similar to LT-GaAs photomixer discussed earlier. The vertical positions Z₁, z₂ of the interdigitated layers are optimized to produce maximum (> 96%) absorption efficiency. FIGS. 9a and 9b illustrate the static electric field strength inside the D = 220 nm Be doped LT-Ino_.53Gao_.47As absorbing layer of the photomixer design of FIG. 8a computed using FD method when the electrodes are biased ±1.0 V. The length of the +ve electrodes I₁ = 1500 nm, and -ve electrodes I₂ = 1400 nm. High electric fields suitable for achieving velocity overshoot in InGaAs are generated throughout the absorbing volume for V_b = ± 1.15 V. For InGaAs, the breakdown field is roughly 5 times lower than LT-GaAs but fortuitously the strong overshoot effects also manifest at relatively lower fields. Therefore, obtaining uniformly strong fields < 100 kV/cm is all the more important in this case. FIG. 9a is a contour plot of field strength (kV/cm) in the x = ± 1000 nm region along the y = 0 plane (x = 0, y = 0 is located at the center of interdigitated pattern in FIG. 2b. The grey rectangular regions in the plot show the positions of 10 nm thick interdigitated W lines with/? = 500, w = 100, J = IO nm respectively.

FIG. 9b illustrates the static electric field strength distribution in the 220 nm LT-InGaAs absorbing layer of FIG. 9a plotted as a volume fraction. A broad distribution with a peak at -42 kV/cm shows that throughout the absorbing volume the field is well below the breakdown field, yet strong enough for exploiting ballistic and quasiballistic carrier motion. The volume fraction plot of FIG. 9b demonstrates that the above electrode design satisfies this requirement fairly well. Increasing the bias voltage moves the distribution in FIG. 9b to higher field values without significantly altering its shape, therefore the design allows sufficient bias voltage tuning suitable for different absorbing materials in the 1060 to 1550 nm range.

Due to the limited data available on the field dependent velocity of carriers in LT-InGaAs and related materials, it is difficult to correctly estimate the THz output from the above device. However, due to the strong similarity of overshoot phenomena in InGaAs and GaAs, a few conclusions can be drawn from the above FD and FDTD calculations. Doubling the gap between metal lines (200 nm in LT-GaAs device versus 400 nm in the present case) results in longer carrier transit time t_ti. However, stronger near field enhancement in FIG. 8b than in FIG. 3 coupled with lower effective mass and larger F - L valley separation energy in InGaAs, may reduce its effect on the «tr(/tr) distribution (FIG. 5) for t_tI < 0.5 ps. The device capacitance C and internal resistance R_s for the structure of FIG. 8a are -3.01 fF and 5.31 Ω respectively. Increase in R_s (from 2.4 Ω in the case of LT-GaAs device) is due to the decrease in number of metal fingers and layers to 8 pairs and 2 layers respectively. To reduce the effect of R_s, the load resistance R_L now needs to be increased. Due to lower C value (4.9 fF for LT-GaAs device) the RC factor in Equation 3 does not increase significantly above the value obtained for LT-GaAs device up to R_L = 150Ω. Based on these results, even in the unlikely scenario where Pf in this case is only 10 to 20% of the power obtained from LT-GaAs device, the present invention would still offer 25 to 50 times better performance than all CW THz emitters of its class in the 0.1 to 5 THz range. From the results presented so far on LT-GaAs and LT-InGaAs based devices it is clear that carrier transit time t_ti can be reduced if lower wavelength radiation is used, provided ballistic and quasiballistic transport of carriers can still be exploited. A photoconducting material that works well at elevated temperatures and has better thermal conductivity than GaAs is desirable for cryogen free operation at high THz power generation. GaN, a wide direct band gap semiconductor (λ₀ = 363 nm), has received much attention for its ability to operate at high power levels and at high temperature. In addition, GaN 's large peak velocity in the overshoot regime makes it an important candidate for high frequency applications such as photomixing. In a recent comparative study of GaN versus GaAs, it was shown that for t_ti < 200 fs, the transit distance in GaN and GaAs are approximately equal (-120 nm) when the accelerating fields are 300 and 30 kV/cm in GaN and GaAs respectively. For t_b > 200 fs, the distance traversed in GaN is significantly higher than in GaAs due to larger peak velocity (> 8^χ10⁷ cm/s) in GaN. Also, the breakdown field in GaN (2MV/cm) is about 4 times lager than in GaAs. Various types of GaN devices have been demonstrated including Schottky barriers detectors, p-n junctions, p-i-n structures, MSM photodetectors, and AlGaN/GaN heterostructure field effect transistors (HFETS). Recently, the carrier recombination time τ as low as 720 fs was demonstrated in LT grown GaN with 200 kV/cm breakdown field. However, GaN has not been used to date for THz photomixing applications mainly due to the difficulty in lowering τ to subpicosecond level while having large breakdown field limit. If near field enhancement can be achieved in GaN similar to LT-GaAs photomixer, one only needs τ > 4 ps thereby providing a material with high breakdown field limit and good crystalline quality.

FIGS. 10a and 10b illustrate a photomixer design based on GaN absorbing layer and the corresponding electric field amplitude inside the D = 144 nm absorbing layer. FIG. 10a shows the FP cavity 900 is formed by three layer (CaF₂, Si₃N_x, Al_xGai__xN) top DBR 902, 10 pairs of (Al_xGai__xN, AlN) layers forming the bottom DBR 904, and GaN absorbing layer 906 of thickness ~ λ for λo = 363 nm radiation. All lengths are in nm. Interdigitated lines 910 of platinum (Pt) are embedded in GaN absorbing layer 906. The active volume is terminated by 15 cell UPML layers in FDTD implementation to mimic real world structure. The parameters in brackets show the refractive index and thickness of each layer. The desired refractive index of Al_xGai__xN is obtained by varying Al concentration (x). FIG. 10b illustrates the electric field amplitude computed using FDTD technique for 363 nm incident radiation with field amplitude E° = 1 V/m. For clarity, field amplitude in only the x = ± 600 nm region along the y = 0 plane is plotted (x = 0, y = 0 is located at the center of interdigitated pattern similar to FIG. 2b). The grey rectangular regions in the plot show the positions of the interdigitated Pt lines with L_x = 7000, L_y = 2500, d = S, z\ = 236, Z₂ = 284, Z₃ = 324 p = 300, w = 100, 1₁ = 1500, 1₂ = 1400 respectively.

FIG. 10a shows the FP cavity parameters of a photomixer based on GaN absorbing layer optimized for maximum absorption efficiency (> 97%) with strong near field enhancement when the cavity is illuminated with 363 nm radiation. Similar to LT-GaAs device, the absorbing layer thickness 906 is =λ ~ D = 144 nm (instead of λ/2 as in LT-InGaAs device) resulting in three antinodes near the DBR-GaN interfaces as well as at the center of GaN layer. Standard epitaxial growth techniques with GaN growth temperature -650 to 750 ⁰C are adequate to produce a GaN film with τ > 4 ps and high breakdown field limit. Due to its large +ve real part of the dielectric constant, W is not suitable for near field enhancement at λo = 363 nm. Pt with a -ve real part of the dielectric constant is more suitable in the UV region. W is typically the material of choice for lateral growth of GaAs, InGaAs as well as GaN. Lately, Pt-GaN and Pt/Pd-GaN systems are widely studied for metallization of GaN based devices. However, lateral overgrowth of GaN on Pt has not been reported so far. It is shown that Pt does not form an alloy with GaN similar to Pt on GaAs when annealed in an inert atmosphere but balls up when the anneal temperature is well above 600 ⁰C. In these studies, 80 nm thick Pt on GaN was annealed for 30 min at temperatures > 600 ⁰C in dry N₂ flow. It is observed that prior to balling up of metal, pinhole formation occurs. Although, annealing severely degrades the metal contact, epitaxial overgrowth even at normal growth temperature of 750 ⁰C should not degrade the metal mainly because growth of ~8 nm thick GaN requires only a few seconds provided rapid heating of the substrate can be accomplished. Moreover, epitaxial overgrowth prevents dislocation of metal during further processing of the substrate. It is believed that epitaxial overgrowth proceeds via pinhole formation. Therefore, under right growth conditions, pinhole and island formation in Pt on GaN observed during annealing may in fact facilitate lateral overgrowth of GaN on Pt.

FIG. 10b shows the near field enhancement in the GaN photomixer with the DBR parameters of FIG. 10a. For platinum (Pt), n = 1.62 - 2.62/ at 3.4 eV (367 nm) resulting in the Lorentz model parameters (χ₀, ε∞, ω₀, T) = (1.2, 7.7, 4.99 x 10¹⁵, 2.08 x 10 \14 ). Similar to LT-GaAs and LT-InGaAs devices, interdigitated Pt line width w, pitch/? , vertical positions Z₁, and thickness d are varied in the FDTD computation to optimize the near field enhancement and absorption efficiency. For w > 100 nm the low static field region between the layers (FIG. 1 Ia) becomes large in addition to increased capacitance. For w < 80 nm the two lobes indicated by arrows in FIG. 10b begin to merge resulting in more power being concentrated directly below the metal lines where static field is weak. For/? < 300 nm (the gap between lines < 200 nm) increased enhancement at the top layer (Z₁ = 236 nm) was observed along with dramatic drop in field amplitude near the bottom layer (z₃ = 324 nm). Finally, vertical positions Z₁ shown in FIG. 10 produced optimal near field enhancement and absorption efficiency > 97%. To exploit velocity overshoot effects in GaN, static fields > 30 kV/cm were required.

FIGS. 11a and 1 Ib show the static electric field strength inside the D = 144 nm GaN absorbing layer of the photomixer design of FIG. 10a computed using FD method when the electrodes are biased ±3.0 V. FIG. 1 Ia is a contour plot of field strength (kV/cm) in the x = ± 600 nm region along the y = 0 plane (x = 0, y = 0 is located at the center of interdigitated pattern in FIG. 2b. The grey rectangular regions in the plot show the positions of 8 nm thick interdigitated Pt lines with/? = 300, w = 100, d = 8nm respectively. FIG. 1 Ib plots the static electric field strength distribution in the 144 nm GaN absorbing layer as a volume fraction when the electrodes are biased ±3.0 (solid) and ±5.0 V(dashed). A broad distribution with a peaks at -61 and 268 kV/cm shows that in -56% of the volume field is between 12 and 200 kV/cm, in 36.6% of the volume field is > 200 kV/cm while in the remaining 7.4% of the volume it is < 12 kV/cm when the electrodes are biased ±3.0 V. Length of the ±ve electrodes /i = 1500 nm, and -ve electrodes I₂ = 1400 nm. FIG. 11a shows the static fields generated inside the photomixer when V_b = ±

3 V. Due to the close proximity of metal layers, the field is weak directly below and in between adjacent layers. However, the fractional volume in which the field is < 12 kV/cm is only 7.4%. The volume fraction plot FIG. 1 Ib shows the electric field distribution inside the photomixer for V_b = ± 3 and ±5 V. The data shows that in -56% of the volume field strength is between 12 and 200 kV/cm (peak at -61 kV/cm) for Vb = ± 3 V whereas in the same volume fraction the field is between 12 and 300 kV/cm (peak at 87 kV/cm) for V_b = ± 5 V. In the remaining 36.6% of the volume the field has a peak at 268 and 430 kV/cm for Vb = ± V 3 and ± 5 V respectively. Very high breakdown field in GaN (-2 MV/cm) allows wide range of bias voltages Vb for transit time t_b optimization. GaN is a relatively new material for device applications and many of its properties are not yet fully explored. From the field dependent velocity of carriers in GaN available at a few static field values, it is difficult to correctly estimate the THz output from the above device where the fields vary over a wide range. Accurate estimate is feasible if ensemble Monte Carlo calculations are carried out along with the transit time calculations to correctly account for field dependent velocity of carriers. However, similar to LT-InGaAs photomixer, a few conclusions can be drawn by comparing the above GaN based photomixer with LT-GaAs based device. By comparing FIGS. 10 and 11 with FIGS. 2, 3, and 4 it appears that in GaN (Zincblende) based photomixer, the transit distance of the carriers is reduced by 20 to 35% while the equilibrium electron velocity is 2 to 4 times higher than in LT-GaAs. Due to higher electron peak velocity (-6.2 x 10⁷ cm/s) in GaN (Zincblende) at 200 kV/cm, the time t_ti required to transit a distance (p - w) = 200 nm is reduced by -50% when compared to t_ti in LT-GaAs device. The steady-state drift velocity of holes in GaN (Zincblende) for applied electric field > 130 kV/cm is also considerably higher than the value used for LT-GaAs (-3.4 x 10⁶ cm/s). However, hole velocity overshoot phenomena in GaN similar to GaAs is not yet explored. Due to closer spacing of the Pt interdigitated layers (FIG. 1 Ia) and lower dielectric constants of GaN and AlGaN (ε_r ~ 10.3), the capacitance C of the above photomixer obtained from FD calculations is only 3.79 fF. This lower capacitance leads to 1.5 times increase in Pf (from Equation 3) when compared to LT-GaAs device (FIG. 2a) with C = 4.9 fF. Based on the above information, the THz output power from GaN based device should be either comparable or higher than the power generated by a LT-GaAs photomixer. GaN, with higher thermal conductivity and higher operating temperature capability should therefore be a better choice for THz power generation if other material's issues discussed earlier are resolved. In addition to CW THz generation using the above LT-GaAs, LT-InGaAs, or GaN based photomixers, the same device structure with little modification can be used for wideband, ultrafast optical signal detection as well. Due to the excellent signal-to-noise ratio offered by these photoconductors, the invention offers near unity quantum efficiency at detection rates exceeding 5 THz. Simultaneous generation of continuous spectrum of THz signals from an MSM photomixer excited by a femtosecond optical pulse is a well known technique in coherent time domain THz spectroscopy. These high power optical pulses can generate THz waves with several mW of peak power. However, the power in higher frequency (> ITHz) spectral components is very weak due to long t_ti in single layer MSM photomixer discussed earlier. The present invention can significantly improve the power in the high frequency spectral components similar to FIG. 6 due to significantly reduced t_b.

The present invention is directed to increasing the efficiency and long time stability of this most crucial component in generating T-rays as summarized in Table 2.

Potential commercial applications of the photomixer of the present invention include: 1) All solid state, semiconductor based 0.1 to > 5THz local oscillator for use in optical communications. The local oscillator is one of the most crucial components in modulating and demodulating rf signals carried by WDM channels of the present day long haul fiber optic communications systems. The current state-of-the-art local oscillators used in these applications do not have the capability to go beyond -190 GHz. 2) Local oscillator for space based and astronomical applications. Monolithic, vibration proof, light weight, preferably solid state oscillators with low power consumption are in great demand for satellite communications and spectrometry. Due to the lack of photomixers with sufficient output power, presently bulky frequency multipliers with relatively high power consumption are used in space based applications. In addition, there are no known multipliers for frequencies > 1.9 THz. 3) Continuously tunable, narrow linewidth, high power THz source for R&D applications such as THz imaging and spectroscopy. THz imaging in physical, chemical and biological sciences is an emerging field with potential applications in chemical analysis and identification such as trace explosive detection, water and oil content analysis; noninvasive imaging of metal objects hidden in baggage; biological tissue analysis such as identification bad fat tissue from good tissue, cancer detection. Recently, skin cancer was detected using THz imaging. Semiconductor chip inspection, industrial process control, environmental monitoring, food inspection are few other important applications based on THz spectroscopy.

It will be evident that there are additional embodiments that are not illustrated and/or described in the specification and drawings but that are clearly within the scope and spirit of the present invention. The foregoing description and accompanying drawings are, therefore, intended to be exemplary only, and the scope of the invention is to be limited solely by the appended claims.

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Claims

What is claimed is:

1. A photomixer comprising: a Fabry-Perot cavity comprising a top distributed Bragg reflector, a bottom distributed Bragg reflector and a semiconductor absorbing layer disposed between the top distributed Bragg reflector and the bottom distributed Bragg reflector; and a plurality of layers of interdigitated conductive lines embedded at different heights within the absorbing layer, each of the plurality of layers having a pair of leads extending therefrom for connecting to other layers of conductive lines.

2. The photomixer of claim 1, wherein the top distributed Bragg reflector comprises a multi-layer anti-reflective coating.

3. The photomixer of claim 2, wherein the multi-layer anti-reflective coating comprises materials selected from the group consisting of TiO₂, CaF₂, InP, and Si₃N_x.

4. The photomixer of claim 1, wherein the bottom distributed Bragg reflector comprises a buried mirror.

5. The photomixer of claim 4, wherein the buried mirror comprises a plurality of repeating multiple layers formed from materials selected from the group consisting OfAl₂O_x, GaAs, InP, InAlAs oxide, AlN and Al_x,Gai__xN.

6. The photomixer of claim 1, wherein the absorbing layer comprises a low- temperature epitaxially-grown semiconductor.

7. The photomixer of claim 6, wherein the interdigitated conductive lines are formed during epitaxial growth of the semiconductor.

8. The photomixer of claim 6, wherein the semiconductor is selected from the group consisting of GaAs, InGaAs and GaN.

9. The photomixer of claim 1 , wherein the pair of leads of each of the plurality of layers is connected to corresponding leads of other layers through vias.

10. The photomixer of claim 1 , wherein each layer of interdigitated conductive lines is aligned along a z-axis.

11. The photomixer of claim 1 , wherein each layer of interdigitated conductive lines comprises two sets of interdigitated structures connected in series and having a grounded center electrode.

12. The photomixer of claim 1, wherein the absorbing layer is GaAs or InGaAs and each layer of interdigitated conductive lines is formed from tungsten.

13. The photomixer of claim 1 , wherein the absorbing layer is GaN and each layer of interdigitated conductive lines is formed from platinum.

14. A photomixer comprising: an active volume comprising a semiconductor absorbing layer having a top and a bottom; an antireflective cap layer abutting the top of the absorbing layer; a free space disposed above the cap layer; a buried mirror abutting the bottom of the absorbing layer; and a plurality of interdigitated electrodes embedded in the absorbing layer at different positions along a z-axis, each electrode having a lead for connection other electrodes of the plurality.

15. The photomixer of claim 14, wherein the anti-reflective cap layer is a distributed Bragg reflector.

16. The photomixer of claim 15, wherein the anti-reflective cap layer comprises a multi-layer structure formed a combination of from materials selected from the group consisting of TiO₂, CaF₂, InP, and Si₃N_x.

17. The photomixer of claim 14, wherein the buried mirror comprises a distributed Bragg reflector.

18. The photomixer of claim 14, wherein the buried mirror comprises a plurality of repeating multiple layers formed from materials selected from the group consisting OfAl₂O_x, GaAs, InP, InAlAs oxide, AlN and Al_x,Gai__xN.

19. The photomixer of claim 14, wherein the absorbing layer comprises a low-temperature epitaxially-grown semiconductor.

20. The photomixer of claim 19, wherein the interdigitated electrodes are formed during epitaxial growth of the semiconductor.

21. The photomixer of claim 19, wherein the semiconductor is selected from the group consisting of GaAs, InGaAs and GaN.

22. The photomixer of claim 14, wherein leads of each of the electrodes is connected to corresponding leads of other electrodes through vias.

23. The photomixer of claim 14, wherein each interdigitated electrode is aligned along a z-axis.

24. The photomixer of claim 14, wherein each interdigitated electrode comprises two sets of interdigitated structures connected in series and having a grounded center electrode.

25. The photomixer of claim 14, wherein the absorbing layer is GaAs or InGaAs and each interdigitated electrode lines is formed from tungsten.

26. The photomixer of claim 14, wherein the absorbing layer is GaN and each layer of interdigitated electrode is formed from platinum.