INTRODUCTION
The electronic information industry with semiconductor devices and circuits serving as the pillars has witnessed rapid development in recent decades, which has greatly promoted the prosperity of the personal consumer electronics industry, the aerospace field and the smart society. In turn, the boom on the demand side has also brought continuous iterative updates and diversified development of semiconductor devices. The material properties of some common semiconductor materials are listed in Table 11, 2-4, the wide bandgap and high saturation velocity make gallium nitride (GaN) a promising candidate in high power applications. And the satisfactory electron mobility and high frequency dielectric constant ensure a good high frequency performance of GaN. The material advantages of GaN were embodied clearly in Fig. 1, in which the curves of standard output power were plotted against working frequency of different semiconductor materials and different transistors5. It can be observed that the line of wide bandgap third-generation semiconductor materials, represented by GaN, covers both a high power and wide frequency range, indicating the huge potential of GaN in both high-power and high-frequency applications. Given the excellent high-power and high-frequency characteristics of high electron mobility transistor (HEMT), the GaN HEMT has greatly attracted many researchers’ interest since it was invented in 19936. Nowadays, GaN HEMT has been widely used in many key areas which are closely related to people's lives, including new mobile communications, radar systems and object detection, etc.
Table 1. Material properties of common microwave semiconductors1., 2., 3., 4.. |
| Property# | Bandgap (eV) | Electron mobility (cm2/V·s) | Saturation velocity (1e7 cm/s) | Critical breakdown field (MV/m) | Static dielectric constant | High frequency dielectric constant | Thermal conductivity (W/cm·K) | Melting point (K) | Power density |
|---|---|---|---|---|---|---|---|---|---|
| GaN | 3.39 | 1500 | 2.5 | 3.3 | 9.5 | 5.3 | 1.5 | 2791 | High |
| 4H-SiC | 3.26 | 950 | 2 | 2.2 | 9.7 | 6.7 | 3.8 | 2730 | Medium |
| InP | 1.34 | 5400 | 0.6 | 0.5 | 12.5 | 9.6 | 0.7 | 1062 | Low |
| GaAs | 1.42 | 8500 | 2 | 0.4 | 12.9 | 10.9 | 0.55 | 1238 | Low |
| Si | 1.12 | 1400 | 1 | 0.23 | 11.8 | 11.8 | 1.5 | 1415 | Low |
#At 300 K. |
Fig. 1. Saturated output power versus frequency for power amplifiers based on different transistor technologies5. The discrete points are used to represent the performance of designs in open literatures. The lines are used to represent the trend of performance limit of technologies. |
An accurate and reliable device model is necessary for the efficient and reliable delivery of the advances from GaN HEMT devices to GaN-HEMT-based circuits. In addition, the device model also needs to be featured with good simulation convergence and fast simulation time. Fig. 2 presents some landmarks of GaN HEMT large-signal models. In this timeline, the typical models to appear the earliest were empirical models, which is mainly ascribed to the fact that empirical models use relatively simple expressions to characterize HEMT performances. Some representative empirical models are the Statz7 and Crutice8 models, Angelov model9, 10, 11, and EEHEMT model12. These empirical models mainly appeared in the 1990s. However, the vitality of the empirical models did not vanish with the development of the times. Even in recent years, a large number of modified Angelov models13-21. have been appearing to meet the emerging needs of different new application scenarios. The empirical models exhibit the characteristics of being accurate, easy to be used and highly tunable, thus making them widely applied in many industrial scenarios so that the device model can be developed fast and flexibly. There are many machine-learning (ML)-based GaN HEMT models, in which the artificial neural network (ANN)-based GaN HEMT models are widely used. The ANN models first appearing in around early 2000s22., 23., is an interesting attempt by introducing machine learning methods to the GaN HEMT device modeling field. Due to the strong fitting ability and the low deployment cost of the ANN, the ANN-based models are naturally capable of accurately describing a device's nonlinearity with a low computational cost. One well-known example of the ANN-based models is the DynaFET model24,25 proposed by Keysight. Later on, in 2010s, people began to focus on building GaN HEMT models from the underlying physical properties of the device. For example, there are the Advanced SPICE Model (ASM) HEMT model26,27, the MIT Virtual Source (MVS) HEMT model28,29, the Hiroshima-University Starc Igfet Model for GaN HEMT30 (HiSIM GaN HEMT model), and the École Polytechnique Fédérale de Lausanne (EPFL) HEMT model31, Physical models are based on rigorous physical equations. Although some approximations of physical equations need to be done to make physical model robust and compact, the physical model still exhibits a much better scalability than empirical models. The physical models also can easily describe devices made by different materials. There have been attempts to merge different categories of models. For instance, the quasi-physical zone division (QPZD) model32 includes both empirical and physical parameters. One hybrid model33 proposed in 2022 integrates ANN with a classical physical model.
Fig. 2. Timeline of some typical GaN HEMT large-signal models. |
When it comes to the 2020s and beyond, the GaN HEMT large-signal models are also facing many challenges. Some of them come from the advancing of semiconductor technologies. The continuingly scaling of gate length leads to an increase of operating frequency, while the short-channel effects become more obvious28,34. The innovation on substrate materials35,36 brings about better device performance and different characteristics at the same time. It is worth looking forward to whether the rapid development of artificial intelligence and measurement technology can inspire novel device models. For existing large-signal models, the empirical models are usually lack of physical meaning, which leads to poor scalability. The training of ANN-based models requires a high computing resource, and it may have a non-convergence issue if the parameters are poorly obtained. The complexity and poor tunability of physical models may limit their wide applications.
In this article, the development of GaN HEMT large-signal models in recent decades have been reviewed, including the model classification, large-signal equivalent circuits and large-signal measurement, etc. The modeling methods for trapping effects and self-heating effects will be covered as well.
LARGE-SIGNAL MEASUREMENTS
The validity of large-signal models needs to be examined under large-signal conditions. Load-pull measurement is one common item among many validation metrics. A typical large-signal load-pull measurement setup in our lab is shown in Fig. 3a. Its core measuring instruments include the Rohde & Schwarz ZVA50, the Muary AM3200 pulsed IV system, the Muary automated source tuner and load tuner, the BONN Elektronik power amplifier, attenuator, isolator, 50-Ω terminator, couplers and high-power bias tees. In addition to the traditional continuous-wave load-pull measurement, this system also supports pulse mode measurement with the minimum pulse width of 200 ns. The pulsed power-added-efficiency (PAE) contours and pulsed output power contours measured by this system are shown in Fig. 3b and Fig. 3c. The system can also measure the current-voltage (IV) curves and S-parameters, as shown in Fig. 3d and Fig. 3e, respectively.
Fig. 3. Measurement equipment and results. a, Large-signal measurement setup. b, Measured pulsed power-added-efficiency contours. c, Measured pulsed output power contours. d, Measured pulsed IV curves. e, Measured multi-bias S-parameters (S21). |
LARGE-SIGNAL EQUIVALENT CIRCUITS
The equivalent circuit takes a very important and basic role in device modeling. As shown in Fig. 4, an equivalent can be divided into two parts: the intrinsic part and extrinsic one. The intrinsic part usually refers to an idea transistor, while the extrinsic part usually refers to the structures used to construct the HEMT. Usually, the modeling method of the intrinsic transistor determines the model type, for example, the empirical models, physical models, or the ML-based models.
Fig. 4. The micrograph of a GaN HEMT sample and its equivalent circuits. Different types of device model can be obtained by using different types of intrinsic models. |
Since the difference of the equivalent circuit will directly affect the performance of the model, the extraction of its parameters has always been one focus in device modeling. A wide variety of extraction methods have been reported, including the traditional cold-condition extraction and its improvements37-41, the extraction of resistances14,42,43, the algorithm improvements44,45, the structure-based extraction46, and the extraction method for novel devices47, etc. Mature and successful extraction methods can not only ensure modeling accuracy, but also naturally create favorable conditions for researches on scalability46-53.
EXAMPLES OF CLASSICAL LARGE-SIGNAL MODELS
In this section, several widely used large-signal models will be introduced in detail. We will elaborate the formulation method of one common model from the empirical models, physical models and the machine-learning based models, respectively.
Empirical Angelov model
The Angelov model is one widely used empirical model developed by Dr. Iltcho Angelov in 199210. This model was developed based on the Statz7 and Curtice8 models. Later, it went through two major improvements in 19969 and 199911. The validity of the Angelov model has been verified in many publications, including the high-frequency applications54, trapping effects modeling17, electrothermal effects modeling16,17,21,55 and its good applicability to machine-learning based modeling56.
The Angelov model adopts independent current source and capacitance source with flexible empirical equations, so that it has a strong tunability. The drain current is formulated as follows:
Ids=Ipk(1+tanh(sinh(ψ)))(1+λVds)tanh(αVds)
where, the Ipk is the maximum drain current at maximum transconductance point, λ is the channel length modulation parameter, α governs the transition from linear to saturation region. The ψ is the power series parameter, and it is defined as:
ψ=P1m(Vg−Vpk)+P2(Vg−Vpk)2+P3(Vg−Vpk)3
where, P1m is defined as:
P1m=P1(1+B1cosh(B2Vds))
The Angelov model uses nonlinear Cgs and Cgd models, and they are expressed as follows:
Cgs=Cgsp+αgsCgs0·(tanh(k'gs(Vds+V'sgs))+1)·(tanh(kgs(Vgs+Vsgs)+P111Vds)+1)
Cgd=Cgdp+αgdCgd0·((tanh(k'gd(Vds+V'sgd))+1−P111)·(tanh(kgd(Vgs+Vsgd)−P111Vds)+1)+2P111)
Physical MVS HEMT model
The MVS HEMT model28,29 is an industrial standard physical model developed based on the virtual source theory57. Different from another very popular physical model, which is the surface-potential based ASM model26,27, the MVS model is charge-based, i.e., it describes device property based on the 2DEG property. The physical models are significantly different from the empirical models, e.g. the Angelov model. The physical models do not have independent drain current sub-model and capacitance (charge) sub-model. Instead, the drain current equation and capacitance (charge) equation are depended on each other. In other words, the capacitance model is determined once the drain current equation is determined, vice versa. There are many recent studies based on the MVS-HEMT model, including the subthreshold swing improvement58, gate capacitance improvement59, circuit-level validation29, flicker noise improvement60 and the combination with ANN33,61, etc. In addition to the model based on MVS theory, there are the improved MVS-2 model62,63, self-consistent field effect transistor (FET) model64, carbon nanotube FET model65, etc.
The drain current equation of MVS HEMT model can be written as:
IDS=WngfQi(x)v(x)
Here, W is the width of each finger of the HEMT, ngf is the number of gate-fingers, Qi(x) means the channel charge density at a position x in the channel, and lastly the carrier velocity is the v(x). It is worthy to be emphasized that the unit of IDS is not A but A/mm.
Assuming µ is the carrier mobility and ψ(x) is the potential at the corresponding position, then v(x) = µEx = µdψ(x)/dx, so the IDS is:
IDS=WngfQi(x)μdψ(x)dx
Considering the influence of velocity saturation, Eq. (7) could be modified as:
IDS=WngfQi(x)μdψ(x)dx(1+(dψ(x)dxvsatμ)β)1/β
In order to get a charge-based formulation for current, the inversion capacitance Cinv is used to establish the connection between Qi(x) and ψ(x) as follows:
Cinv=dQi(x)dψ(x)
By using Eq. (7) and Eq. (9), the partial differential of channel distance x can be expressed as:
dx=WngfQi(x)μIDSCinvdQi(x)
Integrating Eq. (10) from x = 0 (drain) to x = L (source), and then substituting Qi(0) = Qid and Qi(L) = Qis, Eq. (8) can be written as:
IDS=WngfQi(x)μQis2−Qid2(1+(Qis−QidCinvvLμμ)β)1/β
To make the current expression look similar to the classical virtual source model, reformat Eq. (11) as:
IDS=WngfvQis+Qid2Fvsat
where,
v=vsat(1−Ff)+2ϕtμLFf
Fvsat=Qis−QidCinvVDSAT(1+(Qis−QidCinvVDSAT)β)1/β
The source-end and drain-end charge density is:
Qis=Cinv2nϕtln(1+exp(VGSi−(VT−αϕtFfs)2nϕt))
Qid=Cinv2nϕtln(1+exp(VGDi−(VT−αϕtFfd)2nϕt))
where, the Ffs and Ffd are the Fermi functions to realize a smooth transition between two states.
The charge density is linked to the charge by the following equations:
QS=WLngf(6Qis3+4Qid3+12Qis2Qid+8QisQid215(Qis+Qid)2)
QD=WLngf(4Qis3+6Qid3+8Qis2Qid+12QisQid215(Qis+Qid)2)
Then, the Cgs and Cgd can be obtained by taking the partial derivative of the charge with respect to voltage.
C=∂Q∂V
ML-Based DynaFET GaN HEMT model
The ANN-based HEMT model mostly adopts a feedforward neural network (FNN) with a simple architecture (usually one or two hidden layers) to construct the nonlinear current source and capacitance equations. One example of the widely used ANN-based models is the DynaFET model24,25 proposed by Keysight. Fig. 5 shows the DynaFET model topology, where three subcircuits are used to model the self-heating and trapping effects. In the DynaFET model, ANNs are used to model the bias- and temperature-dependent currents and charges. The equations are expressed as follows24,25,66:
IG(t)=IG(VGS(t),VDS(t),Tj(t),ϕ1(t),ϕ2(t))+ddtQG(VGS(t),VDS(t),Tj(t),ϕ1(t),ϕ2(t))
ID(t)=ID(VGS(t),VDS(t),Tj(t),ϕ1(t),ϕ2(t))+ddtQD(VGS(t),VDS(t),Tj(t),ϕ1(t),ϕ2(t))
where, VGS and VDS are the instantaneous voltages, ϕ1 and ϕ2 are the trap state voltages, and Tj is the junction temperature. The ANN-based large-signal model including electrothermal and trapping dynamics is trained and tested by the DC, S-parameters, and large-signal waveform measurements at different temperatures. In 2016, Zhang et al.67 introduced a parallel training technique for DynaFET modeling with large datasets, which adopted cluster systems to calculate the ANN feedforward and derivative in parallel to reduce model training time.
Fig. 5. DynaFET model with thermal and trapping subcircuits66. |
Traditionally, the current source sub-model and capacitance sub-model are independent, which are quite similar to the empirical models. Differently, the ANNs rather than the empirical equations are used to model the nonlinear components for better model accuracy. The drain current and capacitances can be modeled using similar ANN structures. For example, they can exhibit two inputs (Vgs and Vds), one output (Ids, Cgs or Cgd), and one or two hidden layers. The network configuration can be adjusted based on application scenarios. However, a trade-off between network complexity and its training costs should be considered. Usually, an ANN with more neurons and more hidden layers exhibit higher fitting ability (higher accuracy), while it is also easier to obtain local optimum training results.
ADVANCES IN EMPIRICAL MODELS
Although the idea of empirical models has been proposed for a long time, empirical models still play important roles in GaN HEMT modeling. Many new developments in the field of modeling are based on empirical models, such as the construction of dynamic68 and non-dynamic17,69 trapping model, self-heating effects16, thermal effects14,55, scalability13, circuit designs13,21, model simplification20 machine-learning based research56 and the innovation of extraction method40, etc.
In 2007, Jardel et al.68 proposed a widely used trapping sub-circuit to characterize the dynamic trapping effects and verified it based on an empirical drain current model. The RC-based trapping sub-circuit shown in Fig. 6a can be used to represent both drain-lag and gate-lag effects. With this RC-based sub-circuit, good performances were achieved by the device model in time-domain measurement and large-signal output current measurement, as shown in Fig. 6b and Fig. 6c, respectively.
Fig. 6. a, Schematic of the drain-lag model68. b, Measurement of a drain-lag related current transient68. Vgs is fixed at -6 V, Vds is pulsed from 30 to 20 V. c, Measured (crosses) and modeled average output current in different conditions68. d, Self-heating thermal subcircuit utilizing multiple time constants17. e, Long duration pulsed IV measurement pulsing from Vgsq = -2.64 V to Vgsq = -1.7 V for 5 ms at Vds = 28 V comparing single (X = 1) and three time constant (X = 3) thermal models17. f, Photograph of fabricated continuous class-F amplifier on PCB, designed with CREE CGH40010F transistor21. g, Continuous class-F PA measured and modeled results21. h, Large-signal measurement setup and photograph of GaN HPA MMIC13. i, Measured and modeled input power sweep of GaN MMIC HPA at 25°C and 6 GHz with 100-us pulse width and 10% duty cycle13. j, Measured and modeled frequency sweep of GaN MMIC HPA at 25°C and Pin = 23 dBm with 100-us pulse width and 10% duty cycle13. k, Measured and simulated gain, output power, and PAE versus the available power from the power source at -25°C55. l, Measured and simulated gain, output power, and PAE versus the available power from the power source at 150°C55. Reprinted with permission from refs.13., 17., 21., 55., 68.. © 2007, 2009, 2013, 2017, 2021 Institute of Electrical and Electronics Engineers Inc. |
In 2009, Yuk et al.17 proposed an improved Angelov model with the consideration of self-heating effects and trapping effects. In this paper, the authors proposed a novel self-heating equivalent circuit with three time constants, so that the time domain self-heating effects can be accurately modeled, as shown in Fig. 6d and Fig. 6e. Such a self-heating equivalent circuit is also used by King et al.21 Fig. 6f and g present the associated circuit along with the measured and modeled results. An additional contribution of the work by Yuk et al. is the proposal of a trapping modeling method based on quiescent voltage. This modeling method exhibits good accuracy in the pulsed Ids - Vds/Vgs test.
In 2011, Jarndal et al.40 proposed an improved large-signal modeling method of GaN on SiC devices. The buffer related parasitic conduction effect was taken into consideration in their work. The corresponding equivalent circuit and extraction method were also proposed. Jarndal et al. also developed the model of investigated GaN-on-SiC device and verified its performance in a class-AB power amplifier (PA) on plastic substrate.
In 2013, based on the improved Angelov model17, King et al.21 developed a GaN HEMT model and applied this GaN HEMT model into power amplifier design. This work also proposed a nonlinear thermal resistance, which is a function of dissipation power, as shown in Fig. 6e. Fig. 6f and g present the designed class-F PA on printed circuit board (PCB) and its corresponding modeling and measurement results, respectively.
In 2016, Chen et al.70,71 introduced a statistical model for GaN HEMT large-signal modeling. This method relied on extensive modeling of batches of devices and, which thereforeoffers valuable guidance for optimizing device processes and enhancing circuit yields. Later, in 2021, Mao et al.72 applied the statistical model to circuit designs and investigated the impact of process fluctuation in design procedure.
In 2017, Xu et al.13 investigated the scalability of GaN HEMT based on its Angelov model and applied the self-develop model into a GaN high power amplifier (HAP) microwave monolithic integrated circuit (MMIC) design. This proposed model exhibited scalable drain current source, scalable thermal resistance and scalable thermal capacitance. Fig. 6h, i, and j show the designed class-AB HPA MMIC and its two corresponding modeling and measurement results, respectively.
In 2021. Luo et al.55 improved the temperature dependence of nonlinear capacitances in Angelov model. The temperature dependence of subthreshold swing73 and threshold voltage74 was reflected in the temperature-dependent modeling of intrinsic capacitances (Cgs and Cgd). This work can be regarded as an extension of many previous studies regarding temperature dependence75., 76., 77., 78., 79., 80.. Fig. 6k and l are the large-signal performances at different temperatures simulated with original intrinsic capacitance models and improved intrinsic capacitance models.
ADVANCES IN PHYSICAL MODELS
Physical models are relatively new, however, they have witnessed rapid and remarkable development in the past decade. Their modeling methods are close to device physics, so that the built models are very reliable. Their excellent scalability can also well meet the needs of modeling large quantities of devices with different sizes. Therefore, in the past ten years, modeling methods or improvements of physical models have been continuously proposed, and the large-signal simulation capabilities of physical models have also been continuously improved. According to the different formulation methods of the physical model, the advances of the physical model can be divided into the advances in the charge-based models29,33,58-61,81, the advances in the surface-potential-based models82-92, and the other advances31,34,93-95.
Advances in the charge-based models
In 2018, Jia et al.81 proposed a scalable thermal resistance model for GaN HEMTs based on the MVS-GaN HEMT model. At continuous-wave (CW) condition, the device model presented satisfactory simulation results at different temperatures, which proves the accuracy of the developed thermal resistance model and the accuracy of MVS-GaN HEMT model in large-signal simulations.
In 2019, Radhakrishna et al.29 summarized the modeling method of the MVS-GaN HEMT model and reported its application in GaN-based RF- and HV-circuits. The dual-biased GaN PA MMIC96 shown in Fig. 7a and the common-source (CS) common-gate (CG) GaN PA MMIC97 shown in Fig. 7b are designed with the adoption of the MVS-HEMT model.
Fig. 7. a, Die micrograph of a dual-biased GaN PA MMIC96, designed using the MVS-GaN HEMT model. b, Die micrograph of a CS-CG GaN PA MMIC97, designed using the MVS-GaN HEMT model. c, An ANN model with 2 inputs, 2 hidden layers, and 1 output for terminal charges33. Reprinted with permission from refs.33., 96., 97.. © 2015, 2017, 2022 Institute of Electrical and Electronics Engineers Inc. |
Recently, in 2022, it was also pointed out that the machine-learning can be applied to physical models to reduce the difficulty of model development and enhance modeling accuracy33. The core idea of this work is to use ANN to fit the source-end and drain-end terminal charge densities (qis and qid), which are originally modeled by complex semi-physical equations. The configuration of the ANN model for qis and qid is given as Fig. 7c.
Advances in surface-potential-based models
In addition to the charge-based modeling method, the surface-potential-based modeling methods are also widely adopted to construct device models.
One famous representative of the surface-potential-based models is the ASM-HEMT model26,27. Avirup et al. refined the ASM model's flicker noise82 and thermal noise91 performances. Ahsan et al.88,89 studied the field-plate capacitance modeling of the ASM model. The modeling of DC, CV, and RF characteristics86, trapping effects90, and gate current87 within the framework of the ASM model were fully elaborated in the subsequent published articles.
There are also many other GaN HEMT models built with surface-potential theory. Some of them have been verified with excellent large-signal performance. Chen et al.85 proposed a model for intrinsic GaN HEMT, in which the Fermi-potential is obtained from charge-density-of-states function and Poisson equations. In 2018, Wu et al.84 studied the scalability of the surface-potential-based large-signal model.
Other advances
In addition to the well-known ASM model and MVS-GaN HEMT model, the emergence of some other physical models is also worthy to be noted. The HiSIM GaN HEMT model30 is developed based on the well-established industry-standard HiSIM model98. It is obtained by iteratively solving Poisson equation and can accurately predict current collapse effects. The QPZD model32, proposed by University of Electronic Science and Technology of China, combined the zone division method with the surface potential theory for model construction. It includes some empirical parameters in the drain current source model and shows excellent accuracy in various verifications. It has also been demonstrated to be capable of predicting the performance of the two-dimensional hole gas diamond MOSFET99. Another model worthy to be mentioned is the EPFL model31, which has undergone recent studies and improvements, including its transcapacitances94, short-channel effects34, high-temperature behavior93, non-quasi-static behavior95, etc. However, the large-signal properties of the EPFL model have not been studied yet. It is anticipated that the EPFL model has great potential for future research.
ADVANCES IN THE ML-BASED MODELS
Many investigations on ML-based modeling have been made, such as small-signal parameter extraction$1-100,101, nonlinear current and charge modeling102-107, spacing mapping techniques108-111, ML-based behavioral modeling112-114, network architecture optimization of ANN-based models115-117, extrapolation techniques118,119, new types of neural networks120, and model extraction from large-signal measurements5, 121,122.
In 2016, Huang et al.102 proposed an ANN-based large-signal model including self-heating, surface trapping and buffer trapping effects. The drain-source current and intrinsic capacitances were modeled by three-layer feedforward neural networks. The charge models are obtained by integrating the capacitance functions with respect to the terminal voltages. The large-signal model is trained and tested by the PIV measurements at different temperatures and quiescent biases and multi-bias S-parameter measurements at different temperatures. The modeled and simulated single-tone power sweeps are shown in Fig. 8a, where good agreement can be observed.
Fig. 8. a, Single-tone power sweep measurements (symbols) and simulations at Vdsq = 28 V at Idsq = 30 mA and f0 = 2.7 GHz, with 50-Ohm source and load impedance102. b, The measured and simulated pulsed IV104. c, Measured (solid lines) and simulated (dashed lines) load-pull contours of the output power and PAE at Vdsq = 30 V at Idsq = 44 mA and f0 = 3.5 GHz104. d, Outlier detection results of the extracted Cgs and Cds, including the normal points (circle symbols), outliers (diamond symbols), and decision boundary (dashed lines)105. e, Measured (symbols) and simulated (lines) CW S-parameters from 0.5 to 40 GHz with the reference plane at the probe tips. Biases are (from left to right) Vgs = −3 V and Vds = 0 V; Vgs = −2 V and Vds = 20 V; and Vgs = −1 V and Vds = 20 V105. f, Measured (solid lines) and simulated (dashed lines) load-pull contours of the output power and PAE at Vdsq = 20 V, Vgsq = -1.68 V, and f0 = 2.8 GHz105. Reprinted with permission from refs.102., 104., 105.. © 2016, 2020, 2021 Institute of Electrical and Electronics Engineers Inc. |
In 2017, Liu et al.120 proposed a Wiener-type dynamic neural network, which exhibited a better convergence performance compared with a time delay neural network.
In 2018, Na et al.118 proposed the nonuniform grid formulation and multidimensional cubic polynomial extrapolation to obtain the extrapolated data for ANN training and to improve the model predictions outside the measurement region.
In 2019, Jarndal103 adopted multilayer perceptrons (MLPs) to represent the bias- and temperature-dependent drain-source current, the bias-dependent power dissipation, and the bias-dependent incremental current due to trapping effects.
In 2020, Du et al.104 developed a large-signal model using an ANN to model the bias-dependent drain current and empirical equations to describe the breakdown issue, trapping effects, and self-heating effects. The combination of ANNs and empirical equations benefits from fewer measurement data and less training time. The modeling results of IV and load-pull contours are shown in Fig. 8b and Fig. 8c.
In 2020, Zhao et al.111 presented a space mapping technique for GaN HEMT modeling including trapping effects, where separate mapping modules were used to map different behaviors. The space mapping technique can make the existing equivalent circuit model match the new transistor behavior.
In 2021, Hu et al.105 proposed a consistent gate charge model for GaN HEMTs. The gate charge was calculated by integrating the extracted intrinsic capacitances, andan MLP was subsequently used to accurately model the bias and temperature dependence of the gate charge. The charge-conservative capacitance models are obtained by taking the partial derivatives of the gate charge model function with respect to voltages. An outlier detection method for capacitance extractions was proposed as well in this work, and the results can be found in Fig. 8d. The comparisons between measured and simulated S-parameters and load-pull contours are given in Fig. 8e and Fig. 8f.
MODELING OF NON-IDEAL EFFECTS
Trapping effects and self-heating effects are two well-known significant non-ideal effects in GaN HEMTs. For the completeness of the large-signal model, it is necessary to review some common modeling methods for them.
The modeling methods for trapping effects can be classified into the non-dynamic15,69 and dynamic methods68,123,124. These methods all modify gate voltage to reflect the influence of trapping effects on threshold voltage125. The non-dynamic methods focus more on the non-ideal IV performance caused by the trapping effects. For example, the quiescent voltage method uses gate and drain quiescent voltages to characterize the current collapse in the pulsed IV measurement. This modeling method for trapping effects is easy and direct. Subsequently, Zhao et al.14, Xu et al.13, and Hu et al.105 aopted this method or its improved version to model trapping effects. One problem of this method is that it is difficult to characterize the trapping effects in the time-domain. In other words, it is not dynamic. One example of the dynamic method was proposed by Jardel et al.68, who used a series RC subcircuit to model the trapping and de-trapping process, as shown in Fig. 7a and b. The voltage drops or rises caused by the RC circuit will directly change the effective gate voltage. This method is claimed to predict the average output current more accurately, as given in Fig. 7c. Later, Huang et al.102, Wu et al.84, and Luo et al.20,33 used this modeling method to model trapping effects. However, this method needs a lot of efforts to model the pulsed IV performance with non-zero quiescent voltages. Another dynamic trapping modeling method126 worthy to be mentioned is based on the Shockley-Read-Hall (SRH) model. This method has been widely used90,117,127,128 including the ASM-HEMT model.
The self-heating also influences GaN HEMT significantly, while its modeling methods are relatively consistent: a parallel RC network is commonly adopted to characterize the increase of channel temperature due to self-heating effects. The gap between different methods may lie in the difference in the time constants. For example, Yuk et al. and King et al. used three RC parallel networks (three time constants) to realize an accurate time-domain response, as shown in Fig. 7d and e.
CONCLUSION AND PROSPECT
This article comprehensively reviews the large-signal models for GaN HEMT, including their classical formulation methods and recent advances. The material properties of GaN, large-signal equivalent circuits, large-signal measurements, trapping effects and self-heating effects were introduced as well.
Empirical large-signal models exhibit excellent stability, satisfactory accuracy and low development difficulty. It can be seen, therefore, that they have played an important role in helping researchers verify various innovations related to trapping effects, electrothermal effects and scalability, etc. in the past years. In the future, it is foreseeable that the empirical models will still widely participate in various innovations related to models and circuits.
The physical large-signal models are currently developing at full speed: not only the application scenarios of the classical models are constantly being expanded, but also many new models are continuously being proposed. The physical model is endowed with many advantages, such as better scalability, being close to the physical nature of the device, high precision and so on. However, it cannot be ignored that there are still many difficulties limiting the application of physical models. For example, due to the complex expressions and high development difficulties of physical models, some of them have not been applied to the large-signal conditions yet. Therefore, in the future, for some physical models, how to apply them to actual circuit design is a problem which remains to be explored. In addition, some physical models only model the intrinsic transistor. The trapping effects and the self-heating effects, which significantly influence GaN HEMT performances, are necessary to be taken into consideration and modeled in the future.
The ML-based large-signal models show a diversified development trend with the continuous development of ML algorithms and the improvement of computing power. They participate in modeling in the way of ANN, space mapping based, support-vector-regression, etc. In the future, if the application of ML-based models in industry is to be increased, it is necessary to solve their scalability and extrapolability issues. In the ANN-based models, the overfitting issue is another topic that is worth working on in the future.
It is necessary to discuss the circuit design capabilities of different large-signal models. In circuit designs, the accuracy and convergence of a device model are two key considerations that may somewhat constrain each other and determine the predictive and application abilities of that model, respectively. In general, the empirical model is of good accuracy and convergence, and it has been widely used in circuit designs for a long time, with mainstream foundries continuing to use them. For a single device, when new technology or discovery appears, the original empirical model can be quickly adjusted by the model designers, therefore the accuracy of the new model can quickly meet the needs of circuit verification. However, the scalability of the empirical models is poor. As such, the accuracy of the empirical model is often unsatisfactory when modeling a batch of devices with different sizes. The convergence of the empirical model mainly lies in the problem of charge conservation, but the charge conservation problem can be solved by using the charge model rather than the capacitance model. Physical models have been used by more and more manufacturers recently, which also exhibit satisfactory accuracy and convergence. The accuracy of the physical models for single-size device modeling may not be as high as that of the empirical models, but owing to its excellent scalability, overall high-precision modeling can be well achieved by the physical modelfor a batch of devices with different sizes. At the same time, due to the direct modeling of channel charges, charge conservation issue of physical models is naturally assured. One problem for the physical models is that the initial verification is expensive. When new technologies appear, it is often necessary to make complex adjustments to the physical models for preliminary circuit verification. In addition, if the accuracy or convergence of the physical model is not good, it is also difficult to make adjustments. The accuracy of the ML-based models is excellent, but currently, there is no large-scale application of the ML-based model in circuit designs. One reason accounting for the phenomenon above is the convergence problem caused by charge conservation. Additionally, if the simulation range exceeds the modeling range, the accuracy of some ML-based models will drop significantly. Fortunately, solutions to these problems are being proposed continuously, as mentioned above.
To sum up, currently the large-signal GaN HEMT models are in a blooming era: the improvements of model equations are constantly refining existing models; the introduction of various subcircuits is greatly broadening the application scenarios of device models; and the successive application of different modeling methods are continuously increasing the model diversity and unveiling new possibilities. More importantly, the participation, passion and innovation of researchers from all over the world have been injecting a steady stream of impetus into the development of device modeling. As such, we can rightfully anticipate a more prosperous era of device modeling in the future.
MISCELLANEA
Funding This work was supported in part by the National Research Founda- tion (NRF) of Singapore under Grant NRF-CRP17-2017-08.
Declaration of Competing Interest The authors declare no competing interests.
