Improved modeling of GaN HEMTs for predicting thermal and trapping-induced-kink effects

Solid-State Electronics 123 (2016) 19–25

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Solid-State Electronics journal homepage: www.elsevier.com/locate/sse

Improved modeling of GaN HEMTs for predicting thermal and trapping-induced-kink effects Anwar Jarndal a,⇑, Fadhel M. Ghannouchi b a b

Department of Electrical and Computer Engineering, University of Sharjah, 27272 Sharjah, United Arab Emirates iRadio Lab, Department of Electrical and Computer Engineering, University of Calgary, T2N 1N4 Calgary, AB, Canada

a r t i c l e

i n f o

Article history: Received 14 September 2015 Received in revised form 8 May 2016 Accepted 26 May 2016

Keywords: GaN HEMT Large-signal modeling Thermal and trapping effects Genetic optimization Power amplifier design

a b s t r a c t In this paper, an improved modeling approach has been developed and validated for GaN high electron mobility transistors (HEMTs). The proposed analytical model accurately simulates the drain current and its inherent trapping and thermal effects. Genetic-algorithm-based procedure is developed to automatically find the fitting parameters of the model. The developed modeling technique is implemented on a packaged GaN-on-Si HEMT and validated by DC and small-/large-signal RF measurements. The model is also employed for designing and realizing a switch-mode inverse class-F power amplifier. The amplifier simulations showed a very good agreement with RF large-signal measurements. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Drain current is the key nonlinear element of the transistor model. The current nonlinearity is related to intrinsic nonlinearities (trans-conductance and output conductance bias dependency) and strong nonlinearities in Ohmic, breakdown, pinch-off and forward regions [1]. For high-power transistors, self-heating represents another regenerative process that strongly impacts the drain current [2]. The self-heating due to high power dissipation degrades the electrons saturation velocity and thus reduces the current. Further significant effects of the GaN transistor with respect to other technologies are surface and buffer trapping [3]. The surface trapping, which is related to polarization-induced surface states, can be reduced by proper surface passivation [4]. However, the buffer trapping cannot be ignored, especially for GaN on Si substrate [5]. The stronger lattice mismatch between GaN and Si results in free ions that behave as electron traps [6]. The kink effect in the DC characteristic (see Fig. 3) can be assumed as a signature of the buffer trapping. This effect is attributed to hot electrons being injected into the buffer traps under the influence of high drain voltage [7]. These trapped electrons deplete the 2DEG (Two Dimensional Electron Gas) channel and result in a reduction of the drain current for subsequent VDS traces [8].

⇑ Corresponding author. E-mail address: [email protected] (A. Jarndal). http://dx.doi.org/10.1016/j.sse.2016.05.015 0038-1101/Ó 2016 Elsevier Ltd. All rights reserved.

GaN HEMT transistors are becoming an attractive area of research, and there is a crucial need for device models to be used for design purposes. In the past few years, many modeling techniques for GaN HEMT devices have been developed [9–16]. Most of these models are based on table-based, analytical or artificial neural networks (ANN) modeling techniques. The first technique is based upon lookup tables developed from measured data of drain and gate currents. During simulation, the current, at any drain and gate voltages, is calculated using the interpolation or approximation technique [10]. This modeling approach is easy to implement; however, it cannot be used to predict out-of-range measurements and has limited nonlinearities simulation (lower convergence rate). ANN modeling has higher accuracy even under strong nonlinear operating conditions. This modeling technique, however, has limited prediction capability. The analytical modeling is more efficient in terms of rate of convergence and prediction capability; however, higher effort is required to formulate the model and optimize its fitting parameters. In this paper, a part of this problem will be solved by developing an automatic genetic algorithm optimization procedure to find the fitting parameters of a modified version of the reported model in [17]. The model formula is enhanced by adding extra fitting parameters to consider the thermal [18] and trapping-induced kink effects. The geneticalgorithm-based global optimization procedure is developed and programmed in the Matlab to find optimal values for the model fitting parameters. The adopted method improves the automaticity of the process and reduces the well-known local minima problem.

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The whole large-signal equivalent circuit model is implemented in ADS and validated by DC and RF (small- and large-signal) measurements. The paper is organized as follows. The physics behind the kink and thermal effects is explained in Section 2. The large-signal equivalent circuit model and the adopted models for the drain and gate currents are described in Section 2. The implemented genetic-algorithm-based optimization procedure is detailed in Section 4. Comparison of the model simulation with DC and RF small-/large-signal measurements of packaged GaN HEMT is presented in Section 5. In Section 6 the model is demonstrated by simulating the reported inverse class-F power amplifier in [11] based on the same considered packaged GaN HEMT on Si substrate. Finally, a conclusion is drawn in Section 7. 2. Thermal and trapping induced kink effect To reduce the cost and improve the circuit integration capability, GaN HEMT is currently fabricated on Si substrate. With respect to SiC substrate, there are some challenges including the lattice mismatch between GaN and Si (
17%) [6], which results in higher density of dislocations in the GaN-substrate interface. These dislocations manifest themselves as electrons or holes traps [19–22]. These traps are responsible for the last mentioned IV kink and DC-RF dispersion. The latter effect is attributed to the longer trapping time, which prevents electrons from following higher frequency stimulus and participating in the channel conduction. Furthermore, the negative charge due to the trapped electrons depletes the channel (backgating) and reduces the drain current under RF operation [8]. In the circuit level, this has been accounted for by adding series Crf and Rrf in the drain side (see Fig. 1) to simulate the channel conductance dispersion. The low thermal conductivity of silicon (1.3 W/cm/°C) and low thermal expansion coefficient (2.6  106/°C) present another challenge for GaN HEMT [18]. This could be observed clearly from the self-heating induced current collapse in the DC IV characteristics of the considered packaged GaN HEMT from Nitronex corporation at high-power dissipation region (see Fig. 8a). 3. Large-signal model The model is based on the equivalent circuit topology shown in Fig. 1, which includes both extrinsic and intrinsic elements. The same developed extraction method for the extrinsic and intrinsic elements of the model in [11] has been used. Table 1 lists the extracted extrinsic parameters of the considered 4-W packaged

Cgd

Rg

G Lg

Rd Crf

Cgs

D Ld

Rrf

Igs

Cdp Rs Cth 1Ω

Tch

IdsVds

Ls

S

Cdp [pF]

Lg [nH]

Ld [nH]

Ls [nH]

Rg [X]

Rd [X]

Rs [X]

1.39

1.65

1.58

1.30

0.14

0.77

0.91

0.38

GaN HEMT. The bias dependency of Cgd and Cgs has been modeled by simple polynomial and tangent functions, respectively [11]. The drain current Ids is modeled by the following formulas:

Idso ¼ b

V 2gs3 1þ

V plin gs3

!

 tan h

VL

a  ln ð1 þ V ds Þ V psat gs3

ð1Þ

where

  V gs2 V gs3 ¼ V ST  ln 1 þ e V ST  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 1 V gs1 þ V gs1  V K þ D2  V 2K þ D2 V gs2 ¼ V gs1 2 V gs1 ¼ V gs  V to b ¼ b0  b1  T ch

  T ch ¼ Rth ðV ds Ids Þ þ T A  T ref    Rth ¼ Rth0  1  K c tan h K x ðV gs  V c Þ    a ¼ ao  tan h p1 V gs  V c1 :

ð2Þ ð3Þ ð4Þ ð5Þ ð6Þ ð7Þ ð8Þ

In comparison with the model in [17], the term Vds in (1) is replaced by ln(1 + Vds) and a is represented as a tan h function of Vgs instead of the linear relation. It has been found that this description improves the model accuracy especially in the forward region. The fitting parameters VL and b are used to control the transition from the quadratic to the linear regions of the Ids  Vgs characteristics. The slope of the trans-conductance in the linear region is adjusted by plin, and the turn-on process is controlled by VST and Vto (the pinch-off voltage). To accurately simulate the typical smooth pinch-off of the GaN device, a second-order polynomial with VK and D fitting parameters is used. The transition from the triode region to the saturation region of the Ids  Vds characteristics is modeled by two hyperbolic functions with fitting parameters of psat, ao, p1 and Vc1 (the knee voltage at Vgs = 0 V). The first tan h function is to simulate the transition from triode to saturation, while the second tan h is to account for the dependency of the knee voltage on Vgs. The fitting parameter b has been modified to consider the complicated thermal behavior of such a high-power device. The dependence of thermal conductivity of the GaN HEMT on self-heating [23] is modeled indirectly by formulating the thermal resistance Rth in terms of the gate voltage. The trappinginduced kink effect has been accounted for by the additional term Ik in (9) to simulate the gate- and drain-pumping-induced kink effects [24]. Thus the complete formula of Ids is

Ids ¼ Idso þ Ik ð1 þ tan hðkr ðV ds  V c3 ÞÞÞ      Ik ¼ r  1  abs tan h s  V gs  V c2 :

Cds

Cgp

Cgp [pF]

ð9Þ

where

Ids Ri

Table 1 Extrinsic parameters of 4-W packaged GaN HEMT.

S

Fig. 1. Large-signal equivalent circuit model for GaN HEMTs including self-heating and output conductance dispersion effects.

ð10Þ

As illustrated in Fig. 2, the optimization process is carried out through three phases. Multi-region optimization is used to find optimal values for the influencing parameters at each region. As can be seen in Fig. 3, the entire IV characteristics are divided into three zones: zone 1, zone 2 and zone 3. The first zone (VDS < 4 V) is used to characterize the general IV without considering the kink or thermal effects. The second zone is an extension of the first one at higher VDS (<6 V) to characterize the inherent kink of the drain current. The last zone represents the whole IVs subjected to the kink and thermal effects. The IV measurements at zone 1 are used to optimize the related fitting parameters of ao, p1, Vc1, bo, Vto, D,

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The gate current Igs is modeled as

DC IV Measurements

Igs ¼ Igo  e

Opmize αo, p1, Vc1, βo, Vto, ∆, VK, VST, psat,, plin, and VL

Zone 2

Opmize r, s, Vc2, Kr and Vc3

Zone 3

Opmize β1, Rtho, Kc, Kx and Vc

1 Zone 3

Zone 2 0.6

I

DS

(A)

0.8

Zone 1

0.2

2

4

6

V

DS

8

ð12Þ

ag ¼ a3 V ds þ a4 :

ð13Þ

4. Genetic-algorithm-based optimization

1.2

0

V go ¼ a1 V ds þ a2

As can be seen in Fig. 4, increasing Vds will increase the turn-on voltage Vgo and reduce the decaying rate of ag. This effect has been considered simply by linear formulas for these parameters in terms of Vds. The same genetic algorithm optimization technique is used to determine optimal values for Igo, a1, a2, a3 and a4 fitting parameters of the gate current model.

Fig. 2. Flow chart of the drain current fitting parameters optimization process.

0

ð11Þ

Ig0

where

Zone 1

0.4

ag ðV gs V go Þ

In principle, a local optimization technique such as the simplex method can be used to find optimal values for the fitting parameters of the Ids and Igs models. However, with such a large number of variables, the optimization problem is nonlinear with multiple local minima and thus the quality of final optimized values depends on the initial guess. In this case, a local optimization technique is not efficient and in order to overcome this problem and find the global minimum, the genetic algorithm (GA) as a global optimization technique has been adopted. The GA is a widely used technique and well-matched to our problem because of its instinctiveness, ease of implementation, and the ability to efficiently solve highly nonlinear problems [25]. The optimization process has been applied to the fitting parameters of Ids and Igs. The steps of the implemented genetic optimization are illustrated in Fig. 5 and the whole procedure can be summarized as follows: 1. Generating of initial population of vectors. Each vector includes randomly assigned values for the considered model fitting parameters. These initial generation of vectors are the parents

10

(V)

Fig. 3. Measured drain current of 4-W GaN HEMT over three zones for fitting parameters optimization. VGS is from 8 V to 2 V in step of 0.2 V. VGS and VDS are the gate and drain extrinsic voltages.

DC IV Measurements

Generate an Initial Population of Vectors (Random Sets of Fitting Parameters)

0.3

Simulate and Calculate Error

0.2

Selection, Recombination and Mutation

I

GS

(A)

0.4

0.1 0

Simulate and Calculate Error 0

0.5

1

V

GS

1.5

2

(V)

Fig. 4. Measured gate current of 4-W GaN HEMT for VDS is from 0 V to 10 V. VGS and VDS are the gate and drain extrinsic voltages.

N=N+1 Reinsertion

N=Nmax or Error ≤ ε

No VK, VST, psat, plin, and VL. As can be seen, the kink effect is obvious in the IVs of zone 2 and thus optimized values for r, s, Vc2, Kr and Vc3 parameters are determined based on these measurements. The thermal fitting parameters of b1, Rtho, Kc, Kx and Vc are determined by optimizing the measurements at zone 3, which includes the high-power dissipation area.

Yes Select the Minimum Error Vector (Find Optimal Fitting Parameters) Fig. 5. Flowchart of the fitting parameters optimization using genetic algorithm.

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Table 2 Optimized fitting parameters of the models of the drain and gate currents. Model

Fitting parameters

Ids

plin = 2.36 VL = 2.28 [V] ao = 1.845 [1/V] p1 = 2.69 [1/V] Vc1 = 2.8 [V]

r = 0.041 [A] s = 0.903 [1/V] psat = 1.23 VST = 0.03315 [V] VK = 1.8277 [V]

D = 4.3 [V] Vto = 1.476 [V] Kr = 1.69 [1/V] bo = 1.464 [A/V2] b1 = 0.485 [A/KV2]

Igs

Igo = 0.04 [A] a1 = 0.1504

a2 = 0.51 [V]

a3 = 0.224 [A/V2] a4 = 1.34 [A/V]

0.03 8

Best = 0.0048444

0.025

Rtho = 0.0737 [K/W] Kc = 2.1685 Kx = 0.2734 [1/V] Vc = 2.2 [V] Vc2 = 0.7537 [V] Vc3 = 3.806 [V]

x 10 -3 Best = 0.0040155

7

Error

Error

0.02 0.015

6

0.01 0.005 0

5 0

20

40

60

80

100

4

Generation No.

0

20

40

(a)

80

100

(a)

0.8

0.8 Measurement Simulation

0.6

Ids (A)

0.6

Ids (A)

60

Generation No.

0.4 0.2

Measurement Simulation

0.4 0.2

0 0 -2

4 -4

Vgs (V)

-2

2

-6 -8

0

Vds (V)

Vgs (V)

4 -6

2 -8

0

Vds (V)

(b)

Fig. 6. (a) Variation of the error with the number of generation during fitting parameters optimization of the drain current model in zone 1. (b) Simulated and measured DC IV of a 4-W GaN HEMT in zone 1.

of the next-generation vectors that will undergo the optimization process until the maximum number of generation Nmax is reached. 2. Computing the error between simulated and measured DC IVs for each vector. Ids or Igs are calculated using the assigned model fitting parameters over the entire measured grid of voltages Vgs and Vds for the considered zone. The total error between the simulated Ids or Igs and the corresponding measured ones is determined by N  2 1X sim Imeas ds;gs  I ds;gs N m¼1

6 -4

(b)

Error ¼

0 0

ð14Þ

Fig. 7. (a) Variation of the error with the number of generation during fitting parameters optimization of the drain current model in zone 2. (b) Simulated and measured DC IV of a 4-W GaN HEMT in zone 2.

where N is the total number of measurements, Imeas ds;gs is the measured DC drain or gate current and Isim ds;gs is the corresponding simulated currents. 3. Sorting all vectors and their errors to reject some of the maximum error vectors in the population of the current generation. 4. Crossover reproduction of the selected vectors by using doublepoint crossover routine. The vectors are ordered such that vectors in odd numbered positions are crossed with the vectors in the adjacent even numbered positions. 5. Mutation reproduction by altering randomly the values of each vector to generate offspring from the previous crossover process.

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Fig. 10. Comparison between measured (symbols) and simulated (lines) output power, gain and efficiency for a class-C (VGS = 2.5 V and VDS = 28 V) operated packaged 4-W GaN HEMT in a 50 X source and load environment at 2.35 GHz.

Fig. 11. Comparison between measured (symbols) and simulated (lines) output power, gain and efficiency for a class-B (VGS = 1.6 V and VDS = 28 V) operated packaged 4-W GaN HEMT in a 50 X source and load environment at 2.35 GHz.

Fig. 8. Simulated (lines) and measured (cross) DC IVs of a 4-W GaN HEMT. The drain current (a) and gate current (b) versus the extrinsic voltages.

6. Calculating the corresponding errors using (1) for the reproduced offspring vectors. 7. Reinsertion by replacing the vectors with most errors in the old population (parents) with vectors in the new reproduced population (offspring).

8. The generational counter is incremented, and the steps from 5 to 9 are repeated until generation Number N = Nmax or when the error of one of the vectors is less than or equal to a fixed threshold value e. Under this condition the process stops and the values included in the minimum error vector are chosen as optimal values for the fitting parameters. The Matlab program has been developed to implement the mentioned GA optimization steps. The proposed modeling approach has been applied to DC drain and gate currents of the packaged GaN HEMT device over a wide range of bias conditions (VDS: 0–48 V and VGS: 6 to 2 V). The optimization process is

Fig. 9. Measured (cross) and simulated (lines) S-parameters of a 4-W GaN HEMT at: (a) VGS = 4 V, VDS = 0 V and (b) VGS = 2 V, VDS = 0 V.

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started by generating an initial population of 1000 vectors. Each vector includes randomly assigned values for the model fitting parameters. Two stop conditions are used concurrently for the procedure: the maximum number of generation (Nmax = 100) and the minimum error (e = 0.001). Thus the optimization process stops if the error reaches e before attaining the Nmax’s iteration, otherwise the process will continue up to Nmax. Initially, the optimization procedure has been applied to the zone 1 measurements to find optimal values for ao, p1, Vc1, bo, Vto, D, VK, VST, psat, plin, and VL fitting parameters. The obtained optimal values for these fitting parameters are listed in Table 2. Fig. 6a shows variation of the minimum error versus the number of generation during

optimization. Fig. 6b shows an excellent fitting for the drain current in zone 1 using these optimized parameters. This process is re-applied on the measurements of zones 2 and 3. The optimization results are presented in Figs. 7 and 8 and the optimized values of the corresponding fitting parameters are listed in Table 2. The same optimization program has been implemented to find the fitting parameters of the gate current model. The complete optimized values of the fitting parameters are listed in Table 2. As can be seen in Fig. 8, the model can efficiently reproduce the nonlinear behavior of the drain and gate currents. The drain current model also simulates the kink effect in a very good manner. The model also accurately predicts the typical self-heating induced collapse of the DC drain current in the high power dissipation area. 5. Model implementation and verification

Fig. 12. Measured (symbols) and simulated (lines) output power, gain and efficiency for a class-AB (VGS = 1 V and VDS = 28 V) operated packaged 4-W GaN HEMT in a 50 X source and load environment at 2.35 GHz.

The whole modeling procedure including extrinsic and intrinsic parameters extraction has been applied to the considered GaN HEMT. The developed large-signal model was implemented in Advanced Design Software (ADS) from Keysight Technologies Inc. The parasitic elements Cgp, Cdp, Lg, Ld, Ls, Rd, Rg and Rs in addition to Crf, Rrf and Cth are represented by lumped elements. The intrinsic network, including the nonlinear elements Cgs, Ri, Cgd, Ids and Igs, is implemented by a symbolically defined device (SDD) component. The ADS-implemented model has been used to simulate DC IV and S-parameters measurements. The results of this validation are shown in Figs. 8 and 9 with a very good agreement between the simulations and measured data. Single-tone large-signal RF measurements under different bias conditions (classes of operation) are carried out for the same device and compared with the

Fig. 13. Realized (a) and simulated (b) inverse class-F switching mode power amplifier in 50 X source and load environment at 2.35 operating frequency.

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25

mode power amplifier, and a very good agreement is obtained with RF measurements of the fabricated amplifier. Acknowledgments The authors acknowledge the support from the University of Sharjah, Sharjah, United Arab Emiratis, and the University of Calgary, Calgary, Canada. References

Fig. 14. Measured (symbols) and simulated (lines) output power, gain, and efficiency at 2.35 GHz frequency for the inverse class-F switching-mode PA with VDS = 28 V and VGS = 2.5 V.

model simulations. The results of this comparison are presented in Figs. 10–12, which show output power, gain and power-addedefficiency versus input power. As can be observed, the model can efficiently predict the AM–AM/AM–PM characteristics of the device under different operating conditions up to its 4 W (36 dBm) rated power. 6. Inverse class-F power amplifier The developed model has been demonstrated by designing and simulating an inverse class-F switching-mode power amplifier based on the same considered 4-W packaged device [11]. The amplifier has been designed and fabricated at 2.35 GHz operating frequency (see Fig. 13a). Input 50-X matching circuit was used to enhance the output power and the gain. Output 50-X matching network was designed and optimized to provide the fundamental and harmonic impedances for inverse class-F and maximize the power-added-efficiency. As illustrated in Fig. 13b, the amplifier was implement in ADS using the developed model and simulated under 2.35-GHz single-tone stimulus with 50-X terminations (see Fig. 14). The simulated power-sweep was compared with real measurements for the fabricated inverse class-F amplifier. Fig. 14 shows simulated and measured output power, gain and PAE for the amplifier at 2.35 GHz and under 2.5 and 28 V gate and drain bias voltages, respectively. As can be seen, the model can accurately simulate the device and this accordingly validates its applicability for designing nonlinear circuits. 7. Conclusion In this paper an enhanced analytical current model that predicts self-heating and trapping-induced kink effects was developed along with its improved fitting parameters GA-based optimization procedure. Instead of using the whole IV measurement, different zones are used for fitting parameters optimization. The first zone of self-heating and kink-free measurements are used to optimize the fitting parameters of the general nonlinear behavior of the drain current. The second zone of kink-affected measurements are used to optimize the related fitting parameters of the model. The whole measurements, including the high-power dissipation area, are then used to optimize the remaining fitting parameters. The developed model shows very good results for simulating a packaged GaN HEMT even for out of range measurements. The model is embedded in the adopted large-signal equivalent circuit model and validated by DC and RF (small- and large-signal) measurements at 2.35 GHz for the same considered device. The model is also demonstrated by simulating an inverse class-F switching

[1] Carvalho NB, Pedro JC. Large-and small-signal IMD behavior of microwave power amplifier. IEEE Trans Microw Theory Tech 1999;47:2364–74. [2] Parker AE, Rathmell JG. Broad-band characterization of FET self-heating. IEEE Trans Microw Theory Tech 2005;53:2424–9. [3] Meneghesso G, Verzellesi G, Pierobon R, Rampazzo F, Chini A, Mishra UK, et al. Surface-related drain current dispersion effects in AlGaN–GaN HEMTs. IEEE Trans Microw Theory Tech 2004;51:1554–61. [4] Vetury R, Zhang NQ, Keller S, Mishra UK. The impact of surface states on the DC and RF characteristics of AlGaN/GaN HFETs. IEEE Trans Electron Dev 2001;48:560–6. [5] Yang S, Bay CW, Zhou C, Jiang O, Lu J, Huang B, et al. Investigation of buffer traps in AlGaN/GaN-on-Si devices by thermally stimulated current spectroscopy and back-gating measurement. Appl Phys Lett 2014;104. 013504–013504-4. [6] Liu L, Edgar JH. Substrates for gallium nitride epitaxy. Mater Sci Eng 2002; R37:61–127. [7] Binari SC, Ikossi K, Roussos JA, Kruppa W, Park D, Dietrich HB, et al. Trapping effect and microwave power performance in AlGaN/GaN HEMTs. IEEE Trans Electron Dev 2001;48:465–71. [8] Kompa G. Basic properties of III–V devices – understanding mysterious trapping phenomena. Kassel: Kassel University Press GmbH; 2014. [9] Lee J-W, Webb K. A temperature-dependent nonlinear analytic model for AlGaN–GaN HEMTs on SiC. IEEE Trans Microwave Theory Tech 2004;52:2–9. [10] Jarndal A, Kompa G. Large-signal model for AlGaN/GaN HEMT accurately predicts trapping and self-heating induced dispersion and intermodulation distortion. IEEE Trans Electron Dev 2007;54:2830–6. [11] Jarndal A, Aflaki P, Negra R, Kouki A, Ghannouchi FM. Large-signal modeling methodology for GaN HEMTs for RF switching-mode power amplifiers design. Int J RF Microwave Comput Aided Eng 2010;21:45–50. [12] Jarndal A, Markos AZ, Kompa G. Improved modeling of GaN HEMT on Si substrate for design of RF power amplifiers. IEEE Trans Microw Theory Tech 2011;59:644–51. [13] Root D, Xu J, Sischka F, Marcu M, Horn J, Biernacki R, et al. Compact and behavioral modeling of transistors from NVNA measurements: new flows and future trends. In: IEEE custom integrated circuits conference, San Jose, CA. p. 1–6. [14] Jardel O, De Groote F, Reveyrand T, Jacquet J-C, Charbonniaud C, Teyssier J-P, et al. An electrothermal model for AlGaN/GaN power HEMTs including trapping effects to improve large-signal simulation results on high VSWR. IEEE Trans Microw Theory Tech 2007;55:2660–9. [15] Angelov I, Desmaris V, Dynefors K, Nilsson PA, Rorsman N, Zirath H. On the large-signal modelling of AlGaN/GaN HEMTs and SiC MESFETs. In: Gallium arsenide and other semiconductor application symposium, Paris. p. 309–12. [16] Jarndal A. Genetic-algorithm based neural-network modeling approach applied to AlGaN/GaN devices. Int J RF Microwave Comput Aided Eng 2013;23:149–56. [17] Fager C, Pedro JC, Carvalho NB, Zirath H. Prediction of IMD in LDMOS transistor amplifiers using a new large-signal model. IEEE Trans Microwave Theory Technol 2002;50:2834–42. [18] Saidia I, Cordierb Y, Chmielowskab M, Mejric H, Maarefa H. Thermal effects in AlGaN/GaN/Si high electron mobility transistors. Solid-State Electron 2011;61:1–6. [19] Kaushik JK, Balakrishnan VR, Panwar BS, Muralidharan R. On the origin of kink effect in current–voltage characteristics of AlGaN/GaN high electron mobility transistors. IEEE Trans Electron Dev 2013;60:3351–7. [20] Haruyama J, Negishi H, Nishimura Y, Nashimoto Y. Substrate-related kink effects with a strong light-sensitivity in AlGaN/InGaAs PHEMT. IEEE Trans Electron Dev 1997;44:25–33. [21] DiSanto D, Sun H, Bolognesi C. Ozone passivation of slow transient current collapse in AlGaN/GaN field effect transistors: the role of threading dislocations and the passivation mechanism. Appl Phys Lett 2006;88:013504. [22] Ghosh S, Dinara S, Mukhopadhyay P, Jana S, Bag A, Chakraborty A, et al. Effects of threading dislocations on drain current dispersion and slow transients in unpassivated AlGaN/GaN/Si heterostructure field-effect transistors. Appl Phys Lett 2014;105:073502. [23] Darwish A, Bayba AJ, Hung HA. Channel temperature analysis of GaN HEMTs with nonlinear thermal conductivity. IEEE Trans Electron Dev 2015;62:840–6. [24] Wang M, Chen KJ. Kink effect in AlGaN/GaN HEMTs induced by drain and gate pumping. IEEE Electron Dev Lett 2011;32:482–4. [25] Hassan R, Cohanim B, deWeck O, Venter G. Comparison of particle swarm optimization and the genetic algorithm. In: 46th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Austin, TX.