GaN HEMT small signal modeling method based on GRU

Abstract

This invention discloses a GRU-based small-signal modeling method for GaN HEMTs. The method includes fitting and predicting behavioral characteristics under different bias states, operating frequency conditions, and temperatures. This transistor behavioral characteristic modeling method utilizes gated recurrent unit technology. Based on the input and output variation patterns of transistors, through optimization of model parameters and data processing, it further improves the accuracy of the output behavioral characteristics of the base GaN transistor, establishing a highly accurate transistor model that effectively characterizes small-signal behavior.

Description

Technical Field

[0001] The present invention relates to the field of microelectronic device modeling, and in particular to a modeling method for a small-signal behavior model of a GaN transistor based on a gated cyclic unit network. Background Art

[0002] Gallium nitride (GaN) is a direct-gap semiconductor. It is an extremely stable compound with a high degree of ionization, the highest among Group III-V compounds. The research and application of GaN materials is currently at the forefront and hot topic of global semiconductor research. It is a new semiconductor material for the development of microelectronic and optoelectronic devices. Along with other semiconductor materials such as SiC and diamond, it is hailed as the third generation of semiconductor materials, following first-generation Ge and Si semiconductor materials and second-generation GaAs and InP compound semiconductor materials. Wide-bandgap semiconductor GaN materials possess excellent properties such as a large bandgap, high electron saturation velocity, high breakdown field strength, and high electron mobility.

[0003] A GaN high electron mobility transistor (HEMT) is a heterojunction field-effect transistor that utilizes a highly mobile two-dimensional electron gas. Its high electron mobility, high saturation velocity, and low dielectric constant make it a preferred material for microwave devices. This device is well-suited for ultra-high frequency (millimeter wave) and ultra-high speed applications. Significant progress has been made in the GaN microwave and radio frequency field, making it a promising device for power amplifiers in wireless base stations and military applications. Its development and application significance continues to be demonstrated in fields such as radar, 5G communications, and aerospace.

[0004] While GaN devices offer superior performance, their complex electrical characteristics can reduce circuit design efficiency and hinder device performance. Furthermore, due to the relatively short history of research on GaN-based devices, relatively few studies have been conducted on both small and large signal modeling of GaN HEMTs, which hold great potential for microwave applications. Currently, the majority of applications rely on MESFET-related models. However, due to the differences in operating principles between HEMTs and MESFETs, coupled with the unique properties of GaN HEMTs, errors are inevitable when applying MESFET-related models. Model accuracy and the feasibility of modeling techniques are crucial to meeting the performance requirements of power devices and ensuring their industrialization. Establishing and developing accurate small-signal behavioral models of GaN HEMTs is crucial to improving GaN device design efficiency and has long garnered attention from the semiconductor industry, representing a critical area in urgent need of breakthroughs.

[0005] Most existing GaN HEMT small-signal models are based on analyzing the device's operating principle to construct a simple device model, followed by relevant simulation, analysis, and optimization design. However, most of these behavioral models still have large errors and cannot meet the extremely high accuracy requirements of the device model. Therefore, if the superior performance of GaN HEMT devices is to be fully utilized, a high-precision modeling method that describes the transistor's behavioral characteristics is required. Summary of the Invention

[0006] The present invention overcomes the shortcomings of the existing technology and proposes a modeling method for the small-signal behavior model of a GaN HEMT device based on a gated recurrent unit network. This method solves the problem of low modeling accuracy of the existing GaN HEMT device behavior model and establishes a model that can accurately fit the nonlinear behavior of the GaN HEMT device and has excellent generalization capabilities.

[0007] The technical solutions of the present invention are as follows:

[0008] A modeling method for a small-signal behavior model of a GaN HEMT device based on a gated recurrent unit network specifically comprises the following steps:

[0009] 101) Model establishment steps: Under the broadband state, the S parameter characteristic sample set obtained by measuring the GaN HEMT device is n represents the total number of samples, t represents the current frequency point, where x t ∈R d ,y t ∈R,y t The real or imaginary part of the S parameter at the current frequency point is represented by R, which represents a set of real numbers, and d, which represents the dimension of the set of real numbers. The network processes input data through two gates: the reset gate and the update gate. All operations can be described by the following formula:

[0010] Reset Gate:

[0011] r t =σ(W r ·[x t ,h t-1 ]+b r ) Formula (1)

[0012]

[0013]

[0014] Update Gate:

[0015] z t =σ(W z ·[x t ,h t-1 ]+bz ) Formula (4)

[0016] Status Update:

[0017]

[0018] Where σ(·) represents the activation function, W r ,W,and W z Represents the corresponding weight matrix in each gate. b r ,b,andb z is the corresponding bias term in each gate. is vector multiplication, where h t Output the value for the current moment.

[0019] 102) Loss function step: The output h of the current frequency obtained in formula (5) t Compared with the actual measurement data y t The error between them is measured using the mean square error function:

[0020]

[0021] 103) Model training step: The weights and biases in step 101) need to be continuously optimized based on the MSE to achieve the best fit. The most commonly used parameter learning methods for the Gated Recurrent Unit (GRU) network are as follows:

[0022] 1. Stochastic Gradient Descent:

[0023] Let f(x;θ) be a neural network to be trained, θ be the network parameter to be optimized, L() be a differentiable loss function, select K training samples, and the partial derivative of the loss function with respect to the parameter θ at the tth iteration is:

[0024]

[0025] The difference Δθ of the parameter update at each iteration t for:

[0026] Δθ t =-αg t Formula (8)

[0027] The update direction of the parameters at each iteration is Δθ t And with the gradient g t Exactly the same; t represents the number of iterations as above;

[0028] 2.RMSprop (Root Mean Square prop) algorithm:

[0029] The algorithm first calculates the square of the gradient at each iteration The exponentially decaying moving average of :

[0030]

[0031] Where β is the decay rate, the default value is 0.9; t represents the number of iterations,

[0032] The difference Δθ of the parameter update at each iteration t for:

[0033]

[0034] Where α is the initial learning rate, the default value is 0.001.

[0035] 3. Adam (Adaptive Moment Estimation) algorithm:

[0036] The algorithm also calculates the square of the gradient The exponentially weighted average of g t The exponentially weighted average of:

[0037] M t =β1M t-1 +(1-β1)g t Formula (11)

[0038]

[0039] The default values ​​of decay rates β1 and β2 are 0.9 and 0.999; is vector multiplication, t represents the number of iterations, M t and G t They are regarded as the mean of the gradient and the variance before subtracting the mean;

[0040] To avoid large deviations, corrections need to be made at the beginning of the iteration:

[0041]

[0042]

[0043]

[0044] The initial learning rate α defaults to 0.001 and ε is set to 10 -8 .

[0045] 3. Nadam (Nesterov Adam) algorithm:

[0046] The basic principle is the same as the Adam algorithm, and the difference mainly lies in the following deviation correction formula:

[0047]

[0048] The deviation correction not only updates the current time step Also update the next time step Update:

[0049]

[0050]

[0051] The default values ​​of parameters α, β1, β2, and ε are: 0.001, 0.9, 0.999, and 10 -8 .

[0052] 104) By selecting appropriate hyperparameters and applying the optimizer, the optimal model parameters are finally selected to fit the test data to predict the small signal behavior of the device.

[0053] Furthermore, the device has a wide bandwidth from 1 GHz to 65 GHz and small signal behavior characteristics at temperatures from 35°C to 200°C.

[0054] Furthermore, actual measurements include the S11, S12, S21, and S22 broadband characteristic curves of GaN HEMT devices under different operating conditions.

[0055] The present invention offers advantages over existing technologies in that it breaks through existing GaN HEMT device modeling techniques, resolving the low prediction accuracy of existing models for strongly nonlinear devices. By incorporating information such as temperature and bias, it generates a highly generalizable device behavioral model with excellent feasibility and accuracy. Based on a gated recurrent unit network, the present invention develops a model for fitting and predicting GaN HEMT device behavior in strongly nonlinear, broadband, and high-temperature states, achieving high accuracy. The resulting behavioral model closely matches measured data. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 A topological structure diagram of the model of the present invention;

[0057] Figure 2 The test operating conditions of the present invention are Vgs = -3.5V, Vds = 10V, and the temperature is 145°C. The small signal S11, S12, and S22 Smith original graph characteristics;

[0058] Figure 3 This is a wide-band characteristic diagram of the small signal S21 parameter when the test bias conditions of the present invention are Vgs = -3.5V, Vds = 10V and the temperature is 145°C;

[0059] Figure 4The test operating conditions of the present invention are Vgs = -3.1V, Vds = 20V, and the temperature is 200°C. The small signal S11, S12, and S22 Smith original graph characteristics;

[0060] Figure 5 This is a wide-band characteristic diagram of the small signal S21 parameter when the test bias conditions of the present invention are Vgs = -3.1V, Vds = 20V and the temperature is 200°C;

[0061] Figure 6 The test bias conditions for the present invention are local (participating in model training): Vgs = -3.5V, Vds = 20V, temperature is 145°C, interpolation (not participating in model training): Vgs = -3.09V, Vds = 30V, temperature is 35°C, extrapolation (not participating in model training): Vgs = -3.1V, Vds = 10V, small signal S22 Smith original graph characteristics at temperature of 200°C.

[0062] Figure 7 The test operating conditions are Vgs = -3.1V, Vds 10V, 20V and 30V, and temperature 35℃. The small signal S22 Smith original graph characteristics;

[0063] Figure 8 The test operating conditions are Vgs = -3.5V, Vds 10V, 20V and 30V, and temperature 35℃. The small signal S22 Smith original graph characteristics;

[0064] Figure 9 for Figure 7 and Figure 8 The kink effect of S22 under various biases is characterized by parameters obtained based on the gated neural network. DETAILED DESCRIPTION

[0065] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0066] like Figures 1 to 9 As shown, a modeling method for a small-signal behavior model of a GaN HEMT device based on a gated recurrent unit network specifically includes the following steps:

[0067] 101) Fitting function step: Under broadband signal excitation, the GaN transistor is modeled, and the small signal behavior bandwidth of the transistor starts at 1GHz and ends at 65GHz. The model topology of the GaN HEMT device is as follows: Figure 1 shown.

[0068] The S-parameter characteristic sample of the device measured under specific bias conditions, n represents the total number of samples, t represents the current frequency point, where x t ∈R d ,y t ∈R,y t Indicates the real or imaginary part of the S parameter at the current frequency point, R represents the real number set, and d represents the dimension of the real number set. t is a vector of operating condition information containing the bias point, frequency, and temperature. The output is the real and imaginary parts of the GaN HEMT device's S-parameters under these operating conditions. The network processes the input data through two gates: the reset gate and the update gate. All operations can be described by the following formula:

[0069] Reset Gate:

[0070] r t =σ(W r ·[x t ,h t-1 ]+b r ) Formula (1)

[0071]

[0072]

[0073] Update Gate:

[0074] z t =σ(Q z ·[x t ,h t-1 ]+b z ) Formula (4)

[0075] Status Update:

[0076]

[0077] Where σ(·) represents the activation function, W r ,W,and W z Represents the corresponding weight matrix in each gate. b r ,b,andb z is the corresponding bias term in each gate. is vector multiplication, where h t Output the value for the current moment.

[0078] 102) Loss function step: The output h of the current frequency obtained in formula (5) t Compared with the actual measurement data y t The error between them is measured using the mean square error function:

[0079]

[0080] 103) Model training step: The weights and biases in step 101) need to be continuously optimized based on the MSE to achieve the best fit. The most commonly used parameter learning methods for the Gated Recurrent Unit (GRU) network are as follows:

[0081] 1. Stochastic Gradient Descent:

[0082] Let f(x;θ) be a neural network to be trained, θ be the network parameter to be optimized, L() be a differentiable loss function, select K training samples, and the partial derivative of the loss function with respect to the parameter θ at the tth iteration is:

[0083]

[0084] The difference Δθ of the parameter update at each iteration t for:

[0085] Δθ t =-αg t Formula (8)

[0086] The update direction of the parameters at each iteration is Δθ t And with the gradient g t Exactly the same; t represents the number of iterations as above;

[0087] 2.RMSprop (Root Mean Square prop) algorithm:

[0088] The algorithm first calculates the square of the gradient at each iteration The exponentially decaying moving average of :

[0089]

[0090] Where β is the decay rate, the default value is 0.9; t represents the number of iterations,

[0091] The difference Δθ of the parameter update at each iteration t for:

[0092]

[0093] Where α is the initial learning rate, the default value is 0.001.

[0094] 3. Adam (Adaptive Moment Estimation) algorithm:

[0095] The algorithm also calculates the square of the gradient The exponentially weighted average of g t The exponentially weighted average of:

[0096] Mt =β1M t-1 +(1-β1)g t Formula (11)

[0097]

[0098] The default values ​​of decay rates β1 and β2 are 0.9 and 0.999; is vector multiplication, t represents the number of iterations, M t and G t They are regarded as the mean of the gradient and the variance before subtracting the mean;

[0099] To avoid large deviations, corrections need to be made at the beginning of the iteration:

[0100]

[0101]

[0102]

[0103] The initial learning rate α defaults to 0.001 and ε is set to 10 -8 .

[0104] 3. Nadam (Nesterov Adam) algorithm:

[0105] The basic principle is the same as the Adam algorithm, and the difference mainly lies in the following deviation correction formula:

[0106]

[0107] The deviation correction not only updates the current time step Also update the next time step Update:

[0108]

[0109]

[0110] The default values ​​of parameters α, β1, β2, and ε are: 0.001, 0.9, 0.999, and 10 -8 .

[0111] 104) By selecting appropriate hyperparameters and applying the optimizer, the optimal model parameters are finally selected to fit the test data to achieve the purpose of fitting and predicting the small signal behavior of the device.

[0112] In summary, actual GaN HEMT devices were tested to obtain the S-parameter characteristics of the device over a wide bandwidth, including characteristic curves of S11, S12, S21, and S22 under different test conditions. The modeling method of the present invention was used to extract model parameters from the test data to obtain a small-signal behavior model of the gated recurrent unit network of the test transistor under the operating conditions.

[0113] Compare the test data with the model simulation data, such as Figures 2 to 8 The comparison results of characteristic curves with operating frequencies from 1GHz to 65GHz are shown in Figure 2. Figures 2 to 8 The characterization characteristics of S11, S12, and S22 of the transistor under different bias conditions on the Smith chart and the wide-band S21 real and imaginary part characteristic curves are shown. From the results, we can see that the proposed model can fit the characteristics of the transistor very well. Even if the transistor works in a strong nonlinear region under different bias conditions, the proposed model still gives a high fitting accuracy and well reflects the output characteristics of the test piece, verifying the effectiveness of the device behavior modeling technology proposed in this scheme. At the same time, Figure 6 The generalization ability of the transistor is verified by showing the S parameters under different test conditions on the Smith chart. It can be seen that the model can fit the test data well under the three conditions, which proves the excellent generalization ability of the model. Figure 7 and Figure 8 As can be seen from the figure, the obtained model can also accurately fit the warping part of the curve on S22. Figure 9 As shown, accurate parameter values ​​for quantifying the warping effect can be obtained through the model.

[0114] The above is only a preferred embodiment of the present invention. It should be pointed out that ordinary technicians in this technical field can make several improvements and modifications without departing from the concept of the present invention. These improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A GaN HEMT small signal modeling method based on GRU, characterized by: The specific steps include: 101) Model establishment steps: Under the broadband state, the S parameter characteristic sample set obtained by measuring the GaN HEMT device is n represents the total number of samples, t represents the current frequency point, where x t ∈R d ,y t ∈r,y t Represents the real or imaginary part of the S parameter at the current frequency point, R represents the real number set, and d represents the dimension of the real number set; the network processes input data through two gates of the unit: reset gate and update gate; all operations are described by the following formula: Reset Gate: r t = σ(W r · [x t , h t-1 + b r ) Equation (1) Update Gate: z t =σ(W z ·[x t ,h t-1 ]+b z ) Formula (4) Status Update: Where σ(·) represents the activation function, W r ,WW z Represents the corresponding weight matrix in each gate; b r ,b, and b z is the corresponding bias term in each gate; is vector multiplication, where h t Output value for the current moment; 102) Loss function step: The output h of the current frequency obtained in formula (5) t Compared with the actual measurement data y t The error between them is measured using the mean square error function: 103) Model training step: The weights and biases in step 101) need to be continuously optimized based on the MSE to achieve the best fit effect; 104) By selecting appropriate hyperparameters and applying the optimizer, the optimal model parameters are finally selected to fit the test data to predict the small signal behavior of the device.

2. The GRU-based GaN HEMT small signal modeling method according to claim 1, characterized in that: The wide frequency band is from 1 GHz to 65 GHz, and the temperature is from 35° C. to 200° C.

3. The GRU-based GaN HEMT small signal modeling method according to claim 1, characterized in that: The actual measurements include four nonlinear S-parameter characteristics of the GaN HEMT device under different operating conditions.

4. The GRU-based GaN HEMT small signal modeling method according to claim 1, characterized in that: The gated recurrent unit network parameter learning method is the stochastic gradient descent method; specifically: Let f(x;θ) be a neural network to be trained, θ be the network parameter to be optimized, L() be a differentiable loss function, and K training samples be selected. The partial derivative of the loss function with respect to the parameter θ at the tth iteration is: The difference Δθ of the parameter update at each iteration t for: Δθ t = -αg t Formula (8) Where α is the initial learning rate, and the update direction of the parameter at each iteration is Δθ t And with the gradient g t Exactly the same.

5. The GRU-based GaN HEMT small signal modeling method according to claim 1, characterized in that: The gated recurrent unit network parameter learning method is the RMSprop algorithm; Specifically: First calculate the square of the gradient at each iteration The exponentially decaying moving average of : Where β is the decay rate, the default value is 0.9; is vector multiplication, t represents the number of iterations; The difference Δθ of the parameter update at each iteration t for: The initial learning rate α defaults to 0.001 and ε is set to 10 -8 , ensuring that no division by zero errors are encountered.

6. The GRU-based GaN HEMT small signal modeling method according to claim 1, characterized in that: The gated recurrent unit network parameter learning method is the Adam algorithm; specifically: The algorithm also calculates the square of the gradient The exponentially weighted average of g t The exponentially weighted average of: M t =β1M t-1 +(1-β1)g t Formula (11) The default values ​​of decay rates β1 and β2 are 0.9 and 0.

999. is vector multiplication, t represents the number of iterations, M t and G t They are regarded as the mean of the gradient and the variance before subtracting the mean; To avoid large deviations, corrections need to be made at the beginning of the iteration: The initial learning rate α defaults to 0.001 and ε is set to 10 -8 .

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