GaN HEMTs: Experiment and simulation of DC characteristics

Solid-State Electronics 50 (2006) 1051–1056 www.elsevier.com/locate/sse

AlGaN/GaN HEMTs: Experiment and simulation of DC characteristics Elias W. Faraclas *, A.F.M. Anwar Department of Electrical and Computer Engineering, University of Connecticut, 371 Fairfield Road, Unit 1157, Storrs, CT 06269-2157, USA Received 13 April 2006; accepted 20 April 2006

The review of this paper was arranged by A.A. Iliadis and P.E. Thompson

Abstract This paper presents simulated DC characteristics, using the commercially available software DESSIS, of an AlGaN/GaN HEMT, along with corroborating experimental measurements for validation, providing a framework for future optimization. The 2D simulations are reported using theoretically predicted values of polarization charges along with surface traps in the source–gate and gate–drain access regions. The necessity of including hydrodynamic (energy balance) transport, quantization models for accurate simulations is demonstrated along with insight into the inclusion of a lumped thermal resistance which is extended to non-isothermal simulations.  2006 Elsevier Ltd. All rights reserved. Keywords: GaN HEMT; Numerical simulation; Modeling; Experimental I–V; Transconductance

1. Introduction Considerable efforts in the realization of high power and high temperature devices and circuits have resulted in devices operating up to 750 C with power density as high as 32.2 W/mm at 4 GHz from an AlGaN/AlN/GaN HEMT on SiC substrate with a field plate [1,2]. However, such improved performance is still subject to the influence of surface and buffer traps that are attributed responsibility for dc current collapse and RF current slump [3–5]. Experimental correlation between deteriorated RF performance and surface traps has been demonstrated however, the exact mechanism, as well as the trap dynamics, of which are still clearly not understood. Mishra et al. have proposed a model that is based upon electron injection from the metal to the surface states between gate and drain [3] to explain observed current collapse. Eastman et al. have proposed electron leakage from the 2D channel to the surface states as a possible mechanism to explain the role of *

Corresponding author. Tel.: +1 860 486 0054; fax: +1 860 486 2447. E-mail address: [email protected] (E.W. Faraclas).

0038-1101/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.sse.2006.04.014

surface states [5]. However, an experiment that will clearly resolve the role and dynamics of traps is not available yet. The role and dynamics of traps and their effect on observed device performance requires as a prerequisite the calculation of the DC transfer and output characteristics that are in agreement with experimental data. Meneghesso et al. reported simulated DC ID–VD curves which were in agreement with experimental data as well as simulated pulsed VG and VD characteristics while exploring surface induced drain lag effects [6]. However, these simulations were performed in the absence of both a hydrodynamic and quantization model and the concentration of surface traps was assumed to be equal in magnitude to the polarization charge. The effect of the surface charge was demonstrated by varying the trap energy level and simulating the transients arising from a pulsed gate and drain without reporting the effect on DC characteristics. Braga et al. have reported simulated ID–VD and transfer characteristics, of AlGaN/InGaN/GaN HEMTs, which were in agreement with experimental data [7,8]. However, it is not in evidence that the parameters used to fit the experimental data from a double heterojunction, InGaN channel device are directly

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applicable to the typical AlGaN/GaN structures. Moreover, the simulations were performed in the absence of any surface states. It is to be noted that these researchers have used the commercially available device simulation software DESSIS to carry out their 2D numerical calculations. Saito et al. also used DESSIS to explore the relationship between breakdown voltage and gate leakage current and the effect of field plates [9,10]. Other commercial device simulators have also been successfully used to investigate GaN-based device performance as demonstrated by the use of ATLAS to explore the effect of a field plate on breakdown voltage [11]. In this paper we use DESSIS to report the simulated DC output and transfer characteristics supported by experimentally data for AlGaN/GaN HEMTs by incorporating the density gradient method to simulate the effects of the quantum well in GaN at the AlGaN/GaN heterojunction. Moreover, the simulations are carried out using polarization charges with magnitudes within 0.5% of the theoretically predicted value as opposed to deviations as high as 18% made by previous researchers [6–8]. It should be pointed out that this is the first report where both the simulated ID–VD and ID–VG characteristics of AlGaN/GaN HFET are compared to experimental data to show good agreement. 2. Experimental and numerical device structures The physical devices studied in this paper are unpassivated Al0.22Ga0.88N–GaN grown on semi-insulating SiC substrates. The structure consists of a 1-lm AlN nucleation layer followed by 3 lm of unintentionally doped (UID) GaN, followed by the AlGaN layers. The AlGaN layers ˚ UID spacer layer, 110 A ˚ of n-type consist of a 30 A 18 3 AlGaN, doped 1 · 10 cm , and a UID AlGaN Barrier ˚ (see Fig. 1). The gate length is 0.25 lm layer of 110 A and the gate width is 200 lm (2 · 100 lm). The source–gate and source–drain spacings are 2.0 lm and 4.0 lm, respectively.

Source

Gate

Undoped AlGaN Barrier

Drain N-s1

Na3

N+ AlGaN Supply Layer

Na3

Undoped AlGaN Spacer

Na3

Undoped GaN Buffer

2DEG

Na1,Na2

+ Nint , Naint

N+s1,N-s2

AlN Nucleation Layer SiC Substrate Fig. 1. Schematic cross section of the studied AlGaN–GaN HEMT including additional charge and trap distributions. Figure not to scale.

Room temperature DC measurements are carried out using an Agilient 4156C Semiconductor Parameter Analyzer. The numerical analysis was performed using the 2D-device simulator DESSIS. The nominal dimensions and doping for all layers detailed in the fabricated device were used with the exception of the SiC substrate. The SiC substrate was omitted to speed up simulation times as is was determined not to affect the DC characteristics of the simulated devices. Additionally, fixed interface charges, interface traps, and bulk traps were added to the model as shown in Fig. 1. The bulk trap levels Na1, Na2, and Na3 all have concentrations of 1 · 1017 cm3 with energy levels of 1.8, 2.9, and 2.2 eV below the conduction band, respectively [12,13]. The remaining sheet charges have been fitted to account for the role of surface states and polarization charges [13]. On the ungated surface, N s1 are fixed negative charges with areal concentration of 6 · 1012 cm2. At the heterointerface, Nþ Int are fixed positive charges with areal concentration of 8.25 · 1012 cm2 while Na,Int are acceptor traps located in the middle of the bandgap with an areal concentration of 6 · 1012 cm2. Finally, at the GaN/AlN interface, Nþ s1 are acceptor traps located in the middle of the bandgap with an areal concentration of 6 · 1012 cm2 and N s2 are fixed negative charges with concentration 13 3 · 10 cm2. Electron and hole capture cross sections of 1 · 1015 cm2 is used for all trap levels which is consistent with other reported 2D numerical simulations [9]. 3. Analysis and discussion In order for 2D-device simulations to be useful in predicting the performance of future optimized devices, it is imperative that the simulated characteristics of existing devices are in agreement with the experimental data. Ultimately, it is the RF performance of these devices, as high power amplifiers, that is of utmost interest. However, it is important that appropriate DC characterization is performed as a prerequisite to the RF analysis. For proper DC characterization, through a 2D numerical model, it is important that the model be calibrated for appropriate transport, charge control, and contact resistances. 3.1. Transport parameters It has been well established that the traditional drift-diffusion transport model is often inaccurate, especially for deep submicron gate lengths. Two obvious inadequacies of the drift-diffusion model are its inability to reproduce velocity overshoot effects and often overestimating impact ionization rates [14,15]. In simulations of submicron GaN permeable base transistors and GaN MESFETs it was shown that the drift-diffusion model yields significant discrepancies between experimental and simulated results and thus is inadequate for predicting device characteristics whereas the hydrodynamic model (energy balance) allows

E.W. Faraclas, A.F.M. Anwar / Solid-State Electronics 50 (2006) 1051–1056

results consistent with Monte Carlo simulations [15,16]. In the simulations reported in this paper, an optimization between speed and accuracy was achieved by using the hydrodynamic model for electron transport and the driftdiffusion model for holes. The differences between the hydrodynamic model and the drift-diffusion model are seen in Fig. 2. It is evident that at higher fields yield significant discrepancies between experimental and simulated results are observed when using the drift-diffusion model. At low bias, the results are nearly identical. However, significant deviation can be seen for increasing fields under the gate at higher bias resulting in an underestimation of the drain current by the drift-diffusion model. The simulated results are based upon the hydrodynamic Caneli mobility model given by [14]: l l ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffilow ffi 1þ

a2 ðx

b

c

 x0 Þ þ aðxc  x0 Þ

b=2

2=b ;

where llow is the low field mobility, b is a constant whose value was 0.75, xc = 3kBTc/2 is the average carrier thermal energy, x0 = 3kBTL/2 is the equilibrium thermal energy, Tc and TL are the average and lattice temperatures in  carrier b=2 llow 1 degrees K, a ¼ 2 qse;c v2 , vsat is the saturation velocity sat

and se,c is the carrier relaxation time. This model has the advantage of including the effects of hot electrons and device self-heating. A low field mobility of llow = 1100 cm2/ V s and saturation velocity [16] of vsat = 1.94 · 107 cm/s were used. The validation of the transport model is shown in Fig. 2, which shows experimental DC current–voltage (I–V) characteristics along with simulated results. On the same plot simulated I–Vs using the drift-diffusion model is presented. The magnitude of the drain current, the knee voltages, and self-heating, of the simulation using the

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hydrodynamic model, are all in excellent agreement with experimental results. However, the effects of hot electrons and device self-heating were not adequately reproduced using this model. This will be addressed in subsequent sections. 3.2. Charge control For devices that have features on the quantum mechanical scale, the wave-like nature of electrons and holes cannot be neglected. This is obviously true for HEMTs that rely on a quantum well for the formation and confinement of the two-dimensional electron gas (2DEG). Among others, the effects of quantization can be attributed to a shift in threshold voltage as well as a change in gate capacitance [14,17]. Thus it is extremely important to include them in both DC and RF simulations. Fig. 3 shows the simulated electron distribution as a function of position with and without invoking the density gradient quantization model. It is important to note that the quantization model more accurately reproduces the electron distribution yielding a ˚ away from the heterointerpeak electron concentration 7 A face. On the other hand, a straight forward simulation, without using density gradient, erroneously results in the peak located at the heterointerface. As corroborated in Fig. 4, the threshold voltage is indeed shifted inappropriately by neglecting the density gradient model. It is expected that this will play an even greater role in properly simulating device RF characteristics. In addition to the formation of the 2DEG, an adequate numerical model of device charge control implies proper modulation of the 2DEG with applied gate bias. Fig. 4 shows the experimental transfer characteristics as a function of applied gate bias. The plots are obtained for an applied drain bias of 5 V. The simulated ID–VG is also Density Gradient

1400

1

1200

Energy (eV)

Id (mA/mm)

0.5

4.0E+19

0

3.5E+19

-0.5 800 600 400

3.0E+19

-1

2.5E+19

-1.5 2.0E+19

-2

1.5E+19

-2.5

200 0 0

2

4

6

8

10

Vd (V) Fig. 2. Experimental and simulated I–V. Experimental results are shown in triangles, hydrodynamic results shown in solid lines, and drift-diffusion results shown in dotted lines; VG = 0 V, 1 V, and 2 V are shown.

4.5E+19

-3

1.0E+19

-3.5

5.0E+18

-4 0.015

0.02

0.025 y (microns)

0.03

Electron Concentration (cm-3)

1000

Without Density Gradient

0.0E+00 0.035

Fig. 3. Band diagrams and electron density with and without the quantization model.

Id (mA/mm)

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Table 1 Average lattice temperature (K) for various values of Rth

1200

Rth Tave

1000

VG = 0 V and VD = 10.0 V.

0.0001 321

0.001 405

0.002 493

0.004 649

0.006 803

0.008 1016

800

closely approximates the shape of the I–V characteristic as well as (b) lies within an appropriate range for the lattice temperature [18].

600 400

4.2. AlGaN barrier layer thickness

200 0 -3

-2.5

-2

-1.5

-1

-0.5

0

Vg (V) Fig. 4. Experimental and simulated transfer characteristics. Simulated results are shown with solid lines. The dashed line is the deviation without including the Quantum correction Model; VD = 5.0 V.

plotted to show good agreement with the experimental data.

Inclusion of the lumped thermal resistance resulted in a shift in the threshold voltage as seen in the transfer characteristics of Fig. 6. The undoped AlGaN barrier layer was ˚ to obtain an optimal fit with experimenextended to 140 A tal data. It should be noted that any modification in the polarization charges will also change the threshold voltage significantly. Thus, the variation in barrier thickness was performed iteratively with that of polarization charges, as outlined in the following section. 4.3. Polarization charges

4. Calibration for thermal effects 4.1. External thermal resistance As seen in Fig. 2, the present model does not accurately reproduce the reduction in drain current due to heating effects. It is difficult to accurately model realistic devices in a two-dimensional framework due to erroneous thermal boundary conditions. To estimate the full thermal characteristics, it is important to calibrate the lumped external thermal resistance, Rth in K W1 cm2. The variation in the I–Vs with Rth can be seen in Fig. 5. Also, Table 1 shows the simulated average lattice temperature (K) for various values of Rth. A value of Rth = 0.002 is chosen as it (a) most

As outlined in Section 2, both polarization charges as well as the doping in the barrier-AlGaN layer have been included in the present simulation. Although AlGaN/ GaN HEMTs undisputedly rely on polarization charges for operation, there is a distinct disparity between theoretically predicted polarization charges [19,20], those used in the simulations in Section 3 [6,7] and those needed to perform the non-isothermal simulations. Meneghesso et al. used a concentration of 1.2 · 1012 cm2 to represent the difference in polarization charges between AlGaN and GaN of an Al0.35Ga0.65N/GaN interface, which is theoretically predicted to be 1.466 · 1012 cm2. Braga et al. used a concentration of 1.15 · 1013 cm2 to represent the difference in

1400

Id (mA/mm)

1200 1000 800 600

Experimental 400

Rth = 0.002 Rth = 0.004

200

Rth = 0.006 Rth = 0.008

0 0

2

4

6

8

Vd (V) Fig. 5. I–Vs for various values of Rth; VG = 0 V.

10

Fig. 6. Variation in transfer characteristics with modified thickness d of the undoped AlGaN barrier layer; VD = 3.0 V.

E.W. Faraclas, A.F.M. Anwar / Solid-State Electronics 50 (2006) 1051–1056

1400

700 1200

600

Experimental T=300 T=300 T=400 T=500 T=600 T=700

500 800

gm (mS/mm)

Id (mA/mm)

1000

1055

600 Experimental 400

9.50E12

9.00E12

100

0 0

2

4

6

8

10

0 -3.0

Vd (V) Fig. 7. Variation in I–V-characteristics with

Nþ Int

300 200

9.25E12

200

400

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

as a parameter; VG = 0.

Vg (V)

polarization charges at the Al0.3Ga0.7N/In0.015Ga0.985N interface, which is theoretically predicted to be 1.297 · 1013 cm2. Fig. 7 shows the variation in I–V-characteristics based with different values of polarization charges, N þ Int . 12 2 The optimal value of N þ was obtained Int ¼ 9:0  10 cm from fitting the threshold voltage and drain current simultaneously. It should be noted that this is in excellent agreement with the theoretically predicted concentration of 9.042 · 1012 cm2 for an Al0.22Ga0.88N/GaN interface. 4.4. Non-isothermal simulations As GaN-based devices are expected to operate in the high temperature range, it is critical that non-isothermal characteristics of devices can also be predicted. Fig. 8 shows the variation of the I–V characteristics with temperature. Fig. 8 shows a net reduction in the drain current with Experimental

T=300

T=500

T=700

1400 1200

Id (mA/mm)

1000 800

Fig. 9. Transconductance (gm) with temperature as a parameter; VD = 3.0 V.

increasing temperature. However, for VG = 0, it also shows a negative slope in the saturation region for temperatures of 300 K and 400 K, a flat curve for T = 500 K, and a positive slope for 600 K and 700 K. Also, Fig. 8 shows the limitations of the non-isothermal model as it overestimates the drain current significantly for gate biases lower than zero. The correction for this is the topic of ongoing research. Fig. 9 shows the variation of transconductance with increased temperature. The peak transconductance of 670 mS/mm, at 300 K is in excellent agreement with the experimentally determined transconductance of 615 mS/ mm. However, the peak of the simulated transconductance is close to VG = 1.5, as opposed to the experimental value near VG = 1.0 V. This shift in the transconductance peak is attributed to the same phenomena seen in Fig. 8 which overestimates the drain current for gate biases lower than zero. However, while the peak location in the transconductance curve is shifted, its shape is in excellent agreement with experiment. As such, Fig. 9 shows excellent performance with a peak transconductance over 260 mS/mm at T = 700 K. 5. Surface traps

600 400 200 0 0

2

4

6 Vd (V)

8

10

Fig. 8. Temperature dependence of I–V-characteristics for T = 300, 500, and 700 K and gate biases of VG = 0, 1, 2 V.

Although evidence of surface traps has been demonstrated in AlGaN/GaN HEMTs, their exact type, mechanism, and effects are still not understood. While surface trap states have specifically been correlated with RF current slump through fitting the transients for gate and drain lag measurements, their effects can also be seen in DC simulations as well. Fig. 10 shows the change in drain current for various magnitudes of surface charge concentrations. Specifically, the decrease in transconductance with increased negative surface charge is due to an increased

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E.W. Faraclas, A.F.M. Anwar / Solid-State Electronics 50 (2006) 1051–1056

Experimental -2.0E+12 -4.0E+12

1400

References

-1.0E+12 -3.0E+12 gm

800 700

1200

600 1000

800

400

600

300

gm (mS/mm)

Id (mA/mm)

500

200 400 100 200

0

0

-3.5

-100

-3.0

-2.5

-2.0 -1.5 Vg (V)

-1.0

-0.5

0.0

Fig. 10. Transfer characteristics and transconductance (gm) with surface 2 charges (N  s1 cm ) as a parameter. The experimental transconductance was extrapolated from a best fit polynomial to the experimental data.

resistance in the source–gate and gate–drain access regions. This is consistent with the literature which attributes current collapse to changes in resistance caused by surface traps [3]. 6. Conclusions This paper has presented a numerical framework for theoretical experimentation based on simulations calibrated with experimental data. The simulated I–Vs as well as transfer characteristics are shown to be in agreement with experimental data. Key features, such as the threshold voltage, transconductance and drain current in the saturation region are reproduced excellently. Also, this paper corroborates the necessity of including hydrodynamic (energy balance) transport as well as quantization models for accurate simulations. This paper demonstrates the effects of varying both the surface as well as the polarization charges. For the first time, 2D simulations are reported where the optimal value for the difference in the polarization charges at the barrier/channel heterointerface are in excellent agreement with theory. Additionally, this paper provides insight into the calibration of the lumped thermal resistance which is extended to non-isothermal simulations. It is important to note that a unified model that will accurately reproduce device characteristics across all operating parameters is still yet to be reported.

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