CN110516282A - A Bayesian Statistics-Based Modeling Method for Indium Phosphide Transistors - Google Patents

Abstract

The invention discloses an indium phosphide transistor modeling method based on Bayesian statistics. Based on Bayesian statistical technology, without knowing the internal characteristics of the transistor, according to the change rule of the input and output state of the transistor, the characteristics of the transistor can be predicted, and the high-precision transistor model can be established. The model established by the circuit method reduces the complexity of the model and improves the modeling efficiency and modeling accuracy. The invention breaks through the existing InPDHBT device modeling technology, can solve the problem of low prediction accuracy of the existing strong nonlinear device model, and the developed device behavior model has good feasibility and accuracy.

Description

A Bayesian Statistics-Based Modeling Method for Indium Phosphide Transistors

technical field

The invention relates to the field of microelectronic device modeling, in particular to a modeling method of an indium phosphide (InP) double heterojunction bipolar transistor (DHBT) small signal behavior model based on a Bayesian statistical technique.

Background technique

InP is an important III-V compound semiconductor material, which has the advantages of extremely high mobility and good radiation resistance. InPDHBT devices have the characteristics of high frequency, low noise, high power, high efficiency and radiation resistance. They are one of the strategic commanding heights of international high-tech technology development. They can be widely used in various amplifiers, oscillators and digital circuits. , communication, remote sensing, detection, security imaging and biomedicine and other fields that urgently need high power, low noise and high frequency characteristics have important application value.

However, as the basis of circuit computer-aided design, accurate models of InPDHBT devices suitable for large-scale electronic design automation (EDA) simulation applications are still lacking, and the development of modeling technology is relatively lagging behind. Model accuracy and feasibility of modeling technology are the keys to the success of integrated circuit computer-aided design. As the structure of InPDHBT devices becomes more complex, the power increases, the frequency increases, and the nonlinearity increases, new requirements for circuit design are constantly put forward, which brings new problems and challenges to the accurate development of the model. The development of an accurate model of the small-signal behavior of InPDHBT has become one of the difficult problems recognized by the industry and academia, and is an area in which breakthroughs are urgently needed.

The existing InPDHBT small-signal models mainly include physical base model and equivalent circuit model, such as MEXTRAM model, HICUM model, UCSD model, Agilent HBT model, etc. Most of the models are developed for Si/SiGe HBT process. HBT is not particularly targeted, so the model fit is not high. In comparison, the UCSD and Agilent HBT models are more suitable for the model development of InP HBTs, which correct the time transfer function, but do not perform well in terms of current blocking effects. With the development of measurement equipment and measurement technology, behavioral models have received extensive attention due to their special advantages. Because of its simple principle, extremely high precision, and suitability for all types of transistors of different materials, behavioral models have been extensively studied in the field of high-frequency, strongly nonlinear transistor operation.

Therefore, if we want to give full play to the technological advantages of InP DHBT devices and improve the level of circuit CAD design, it is necessary to have a high-precision modeling method to describe the behavior characteristics of transistors.

SUMMARY OF THE INVENTION

The invention overcomes the deficiencies of the prior art, and proposes a modeling method for the small signal behavior model of the InPDHBT device based on the Bayesian statistical algorithm, solves the problem of low modeling accuracy of the existing InPDHBT device behavior model, and establishes a model that can accurately predict Modeling of the nonlinear behavior of InPDHBT devices.

The technical scheme of the present invention is as follows:

A Bayesian statistics-based modeling method for a small-signal behavior model of an InPDHBT device, which specifically includes the following steps:

Step 1. Initial steps of fitting function:

In the ultra-wideband frequency range, the bias state of the InP transistor and the corresponding S-parameter characteristic sample are actually measured, and the linear function of the bias state and the S-parameter sample is obtained by fitting as follows:

y=f(x)=w ^T x+b (1)

where w is the weight coefficient, x is the bias state, b is the bias term, y is the S parameter sample, and T is the transpose;

The above set of bias states and S-parameter samples is n represents the total number of samples, i represents the sample number; x _i ∈ R ^d , represents the bias state, including bias voltage state, bias current state and frequency y _i ∈ R, represents the transistor S parameter; R represents the set of real numbers, and d represents the dimension of the set of real numbers;

Step 2, Bayesian inference derivation steps:

In Bayesian inference, p(w) represents the prior probability, and w here refers specifically to the weight coefficient of the model. The formula for Bayesian inference is as follows:

In the formula, p(w) represents the prior probability, representing the probability that the weight coefficient w is the weight coefficient required by the model; p(w|D) represents the probability that the weight coefficient is w under the condition of a given event D; p( D|w) is the likelihood probability, that is, the probability that event D is determined under the condition of given model weight coefficient w; p(D) is a certain item, which remains unchanged for different weight coefficients w.

Based on Bayesian inference, in order to obtain the optimal model equation, the maximum a posteriori probability technique (MAP) will be used, and the optimal model weight coefficients obtained are as follows:

w _MAP = arg max _w p(D|w)p(w) (3)

is the required model weight coefficient.

The specific acquisition process of the calculation process of the optimal model weight coefficient w _MAP is as follows:

Under the condition of real numbers, based on the equation of the Gaussian kernel function, the log-likelihood function equation can be obtained:

where β represents the inverse of the variance of the Gaussian distribution, w ^T =(w ₁ , w ₂ , w ₃ ,...w _k ) ^T is the transpose of the weight coefficients, Φ( _xi )=(Φ ₁ , Φ ₂ , Φ ₃ ,...Φ _k ) is the basis function, and k represents the serial number of the coefficient. For example, for a one-dimensional polynomial model, the basis function is: Φ _l (x _i )=x _i ^l , 1 is any value between 1 and k number.

The Gaussian distribution with mean 0 and variance reciprocal α is selected as the prior probability, as follows:

After negative log transformation we get:

Thus, based on equations (2), (4), (6), the maximum posterior probability is the minimized equation:

The model coefficient obtained by minimizing (7) is the required optimal model equation coefficient w _MAP .

Step 3. Steps for fitting the nonlinear behavior of InP DHBT transistors:

The relationship between the small-signal S-parameter characteristics of the InP DHBT transistor and the bias state and frequency can be expressed by the characteristic description equation:

Among them, S _xx represents four S parameters corresponding to the transistor, S ₁₁ , S ₁₂ , S ₂₁ , and S ₂₂ . I _b is the bias current of the base, V _ce is the bias voltage of the collector and emitter, and f is the corresponding operating frequency.

The input part is a real number, but the output end is a complex number. In order to adapt to the Bayesian inference equation, the complex number of equation (8) is divided. The divided equation is as follows:

in, and are the real part equation and imaginary part equation of the Bayesian S-parameter model, and w represents the corresponding weight coefficient of the Bayesian model.

Taking the real part of _S11 as an example, based on Bayesian theory, the equations of the model can be obtained such as:

where w=(w ₁ , w ₂ ,..., w _k ) is the model equation coefficient, k represents the weight coefficient serial number, Φ(I _b , V _ce , f)=(Φ, Φ ₂ ,..., Φ _k ) represents the basis function equation.

Given a training set, the relationship between bias states and S-parameters can be expressed as: D={I _b , V _ce , f; Real(S ₁₁ )}.

The prior probability p(w) represents is the probability of the target optimal model; p(D|w), as the likelihood probability, represents the The probability of obtaining the training data set under the equation condition of .

Based on equation (7), substituting the variables corresponding to the real part of S ₁₁ , we get:

By minimizing equation (12), the real part corresponds to the coefficient w _{MAP_real} of the optimal model.

In the same way, the modeling process for the imaginary part is the same as that for the real part. Based on equation (7), the variables corresponding to the imaginary part of S ₁₁ are substituted to obtain:

By minimizing equation (13), the imaginary part corresponds to the coefficient w _{MAP_imag} of the optimal model.

According to the formula (14), the behavior model of the S ₁₁ parameter is obtained, and the formulas (11)-(14) are repeated to obtain other S parameters S ₁₂ , S ₂₁ , and S ₂₂ .

S ₁₁ =Real(S ₁₁ )+Imag(S ₁₁ )×j (14)

where j represents the unit quantity of the imaginary part.

Further, ultra-wideband small-signal behavior characteristics with bandwidths from 200MHz to 325GHz.

Further, the actual measurement includes S ₁₁ , S ₁₂ , S ₂₁ and S ₂₂ ultra-broadband characteristic curves of the InPDHBT device under different bias state conditions.

Compared with the prior art, the present invention has the following advantages:

The invention breaks through the existing InPDHBT device modeling technology, can solve the problem of low prediction accuracy of the existing strong nonlinear device model, and the developed device behavior model has good feasibility and accuracy.

The invention is based on Bayesian statistical technology, without knowing the internal characteristics of the transistor, according to the change rule of the input and output states of the transistor, to realize the prediction of the characteristics of the transistor, and to realize the establishment of a high-precision transistor model. The model established by the equivalent circuit method reduces the complexity of the model and improves the modeling efficiency and modeling accuracy.

Based on Bayesian statistics, the present invention develops a model that can be used for behavior prediction of InPDHBT devices in a strong nonlinear and ultra-wideband state, and obtains high precision. The model obtained by the Bayesian statistical method has a good fit with the measured data.

Description of drawings

Fig. 1 is the topological structure diagram of the model of the present invention;

Fig. 2 is the broadband characteristic diagram of the real part of the test small signal S ₁₁ parameter of the present invention; wherein (a) is a characteristic curve; (b) is an error;

Fig. 3 is the broadband characteristic diagram of the imaginary part of the test small signal _S11 parameter of the present invention; wherein (a) is the characteristic curve; (b) is the error;

Fig. 4 is the real part and imaginary part characteristic curves of all four S-parameters of the test InP DHBT transistor in the bias state Ib=400uA, Vce=1.0V; wherein (a) is S ₁₁ , (b) is S ₁₂ , ( c) is S ₂₁ , (d) is S ₂₂ ;

Fig. 5 is the Smith original map characteristic of test small signal _S11 and _S22 of the present invention;

Fig. 6 is the Smith original map characteristic of the test small signal S ₁₂ and S ₂₁ of the present invention.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

As shown in Figures 1 to 5, a Bayesian statistics-based modeling method for a small-signal behavior model of an InPDHBT device includes the following steps:

A Bayesian statistics-based modeling method for a small-signal behavior model of an InPDHBT device, which specifically includes the following steps:

Step 1. Initial steps of fitting function:

In the ultra-wideband frequency range, the InP transistor bias state and S-parameter characteristic samples are actually measured, representing the bias voltage, current state and frequency, and the linear function of the bias state and S-parameter samples obtained by fitting is as follows:

y=f(x)=w ^T x+b (1)

where w is the weight coefficient, x is the bias state, b is the bias term, y is the S parameter sample, and T is the transpose;

The above set of bias states and S-parameter samples is n represents the total number of samples, i represents the sample number; x _i ∈ R ^d , represents the bias state, including bias voltage state, bias current state and frequency y _i ∈ R, represents the S parameter of the transistor, R represents the real number set, and d represents the dimension of the real number set;

Step 2, Bayesian inference derivation steps:

In Bayesian inference, p(w) represents the prior probability, and w here refers specifically to the weight coefficient of the model. The formula for Bayesian inference is as follows:

In the formula, p(w) represents the prior probability, representing the probability that the weight coefficient w is the weight coefficient required by the model; p(w|D) represents the probability that the weight coefficient is w under the condition of a given event D; p( D|w) is the likelihood probability, that is, the probability that event D is determined under the condition of given model weight coefficient w; p(D) is a certain item, which remains unchanged for different weight coefficients w. Based on Bayesian inference, in order to obtain the optimal model equation, the maximum a posteriori probability technique (MAP) will be used, and the optimal model weight coefficients obtained are as follows:

w _MAP = arg max _w p(D|w)p(w) (3)

is the required model weight coefficient.

The specific acquisition process of the calculation process of the optimal model weight coefficient w _MAP is as follows:

Under the condition of real numbers, based on the equation of the Gaussian kernel function, the log-likelihood function equation can be obtained:

where β represents the inverse of the variance of the Gaussian distribution, w ^T =(w ₁ , w ₂ , w ₃ ,...w _k ) ^T is the transpose of the weight coefficients, Φ( _xi )=(Φ ₁ , Φ ₂ , Φ ₃ ,...Φ _k ) is the basis function, and k represents the serial number of the coefficient. For example, for a one-dimensional polynomial model, the basis function is: Φ _l (x _i )=x _i ^l , 1 is any value between 1 and k number.

The Gaussian distribution with mean 0 and variance reciprocal α is selected as the prior probability, as follows:

After negative log transformation we get:

Thus, based on equations (2), (4), (6), the maximum posterior probability is the minimized equation:

The model coefficient obtained by minimizing (7) is the required optimal model equation coefficient w _MAP .

Step 3. Steps for fitting the nonlinear behavior of InPDHBT transistors:

The relationship between the small-signal S-parameter characteristics of the InP DHBT transistor and the bias state and frequency can be expressed by the characteristic description equation:

Among them, S _xx represents four S parameters corresponding to the transistor, S ₁₁ , S ₁₂ , S ₂₁ , and S ₂₂ . I _b is the bias current of the base, V _ce is the bias voltage of the collector and emitter, and f is the corresponding operating frequency.

The input part is a real number, but the output end is a complex number. In order to adapt to the Bayesian inference equation, the complex number of equation (8) is divided. The divided equation is as follows:

in, and are the real part equation and imaginary part equation of the Bayesian S-parameter model, and w represents the corresponding weight coefficient of the Bayesian model.

Taking the real part of _S11 as an example, based on Bayesian theory, the equations of the model can be obtained such as:

where w=(w ₁ , w ₂ ,..., w _k ) is the model equation coefficient, k represents the weight coefficient serial number, Φ(I _b , V _ce , f)=(Φ, Φ ₂ ,..., Φ _k ) represents the basis function equation.

Given a training set, the relationship between bias states and S-parameters can be expressed as: D={I _b , V _ce , f; Real(S ₁₁ )}.

The prior probability p(w) represents is the probability of the target optimal model; p(D|w), as the likelihood probability, represents the The probability of obtaining the training data set under the equation condition of .

Based on equation (7), substituting the variables corresponding to the real part of S ₁₁ , we get:

By minimizing equation (12), the real part corresponds to the coefficient w _{MAP_real} of the optimal model.

In the same way, the modeling process for the imaginary part is the same as that for the real part. Based on equation (7), the variables corresponding to the imaginary part of S ₁₁ are substituted to obtain:

By minimizing equation (13), the imaginary part corresponds to the coefficient w _{MAP_imag} of the optimal model.

Finally, the behavioral model of the complete S-parameter is obtained according to the following formula.

S _xx =Real(S _xx )+Imag(S _xx )×j (14)

where j represents the unit quantity of the imaginary part.

In summary, the actual InPDHBT transistor was tested to obtain the S-parameter characteristics of the device in the ultra-wideband frequency band, including the characteristic curves of S11 _{, S12} , S21 and _{S22 under} different biases; The data is extracted according to the modeling method of the present invention, and the model parameters of the test transistor are obtained.

The test data and the model simulation data are fitted and compared, as shown in Figure 2 to Figure 6 for the comparison results of characteristic curves with operating frequencies from 200MHz to 325GHz. Figures 2(a), 2(b), 3(a) and 3(b) show the real and imaginary characteristics of the _S11 parameter of the transistor in the bias state I _b =200uA and V _ce =1.0V Curves and errors, Figures 2 and 3 respectively include the measured data, the traditional equivalent circuit prediction data and the Bayesian model proposed in the patent. It can be seen from the results that the proposed model can perform better than the traditional equivalent circuit function. To predict the characteristics of the transistor, even if the transistor works in a strong nonlinear region (the curve has obvious curvature), the proposed model still gives a high prediction accuracy, which reflects the output characteristics of the test piece well, and verifies this The superiority and effectiveness of the proposed device behavior modeling technology. Figure 4 presents the real and imaginary characteristic curves of all four S-parameters of the tested InP DHBT transistor at bias state I _b = 400uA, V _ce =1.0V, the proposed model is also used in the prediction of UWB characteristic curves gives high accuracy results. At the same time, Fig. 5 shows the characterization characteristics of the S-parameters of the transistor at I _b =400uA, V _ce =1.5V on the original Smith chart. Similarly, the proposed model based on the Bayesian statistical method still gives good modeling accuracy.

The above are only the preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, without departing from the concept of the present invention, several improvements and modifications can also be made, and these improvements and modifications should also be regarded as are within the protection scope of the present invention.

Claims (2)

1. An indium phosphide transistor modeling method based on Bayesian statistics is characterized by comprising the following steps:

step one, initializing a fitting function:

actually measuring the bias state of the InP transistor and the corresponding S parameter characteristic sample in the ultra-wideband frequency band range, wherein the bias state comprises a bias voltage state, a bias current state and a frequencyThe S parameter includes S₁₁、S₁₂、S₂₁And S₂₂Fitting to obtain a linear function of the bias state x and the S parameter y as follows:

y＝f(x)＝w^Tx+b (1)

wherein w is a weight coefficient, b represents a bias term, and T represents transposition;

the set of bias states and S parameter samples isn represents the total number of samples, i represents the sample number; x is the number of_i∈R^d，y_iE is an element R, R represents a real number set, and d represents the dimensionality of the real number set;

step two, Bayesian inference derivation step:

in Bayesian inference, p (w) represents the prior probability, where w is referred to herein as the weight coefficient of the model; bayesian inference formula notation is as follows:

p (w) in the formula represents prior probability, and represents the probability that the weight coefficient w is the weight coefficient required by the model; p (w | D) represents the probability of a weight coefficient of w given event D; p (D | w) is the likelihood probability, i.e., the probability that event D is determined given the model weight coefficient w; p (D) is a definite term which is kept unchanged for different weight coefficients w;

based on bayesian inference, in order to obtain an optimal model equation, a Maximum A Posteriori (MAP) technique is used, and the obtained optimal model weight coefficients are as follows:

w_MAP＝arg max_wp(D|w)p(w) (3)

the model weight coefficient is the required model weight coefficient;

the optimal model weight coefficient w_MAPThe specific acquisition process of the calculation flow is as follows:

under the real number condition, based on the equation of the gaussian kernel function, the log-likelihood function equation can be obtained:

where β represents the inverse of the variance of the Gaussian distribution, w^T＝(w₁，w₂，w₃，...w_k)^TIs the transposition of the weight coefficients, Φ (x)_i)＝(Φ₁，Φ₂，Φ₃，...Φ_k) Is a basis function, k represents the number of coefficients, where_l(x_i)＝x_i ^lL is any number between 1 and k;

selecting Gaussian distribution with the mean value of 0 and the inverse variance of alpha as prior probability, and adopting the following formula:

after negative logarithmic transformation we obtain:

thus, based on equations (2), (4), (6), the maximum a posteriori probability is the minimization equation:

the model coefficient obtained by the minimization (7) is the required optimal model equation coefficient w_MAP；

Step three, fitting the nonlinear behavior of the InP DHBT transistor:

for the relationship between the InP DHBT transistor small signal S-parameter and the bias state, the characterization equation can be used to represent:

wherein S is_xxRepresenting four S parameters S corresponding to the transistor₁₁、S₁₂、S₂₁And S₂₂；I_bIs the bias current, V, of the corresponding base of the transistor_ceIs the bias voltage of the corresponding collector and emitter of the transistor, f is the corresponding working frequency of the transistor;

since the input part is real number but the output end is complex number, in order to adapt to the bayesian inference equation, the complex number of equation (8) is divided, and the divided equation is as follows:

wherein,andthe real part equation and the imaginary part equation of the Bayes S parameter model are adopted, and w represents a corresponding weight coefficient of the Bayes model;

wherein S₁₁For example, based on bayes theory, the equation of the model can be obtained as follows:

wherein w ═ w₁，w₂，...，w_k) For the model equation coefficients, k represents the weight coefficient index, Φ (I)_b，V_ce，f)＝(Φ₁，Φ₂，...，Φ_k) Representing a basis function equation;

given a training set, the relationship between bias state and S-parameter can be expressed as: d ═ I_b，V_ce，f；Real(S₁₁)}；

The prior probability p (w) representsIs the probability of the target optimum model; p (D | w) as likelihood probability, represented inObtaining the probability of the training data set under the equation condition of (3);

based on equation (7), S₁₁And substituting variables corresponding to the real part to obtain:

obtaining the coefficient w of the real part corresponding to the optimal model by minimizing equation (12)_{MAP_real}；

Similarly, the modeling procedure for the imaginary part is the same as for the real part, and based on equation (7), S is set₁₁And substituting variables corresponding to the imaginary part to obtain:

obtaining the coefficient w of the optimal model corresponding to the imaginary part by minimizing equation (13)_{MAP_imag}；

Obtaining S according to formula (14)₁₁Rows of parametersFor the model, repeating the equations (11) - (14) and further obtaining other S parameters S₁₂、S₂₁、S₂₂；

S₁₁＝Real(S₁₁)+Imag(S₁₁)×j (14)

Where j represents the imaginary unit quantity.

2. The modeling method for the InP transistor based on the Bayesian statistics as recited in claim 1, wherein the ultra-wideband frequency range in the step (1) is 200MHz to 325 GHz.