New Nonlinear Device Model for Microwave Power GaN HEMTs Pedro Miguel Cabral, José Carlos Pedro and Nuno Borges Carvalho

Instituto de Telecomunicações - Universidade de Aveiro, Aveiro, Portugal

Abstract — This paper presents a new nonlinear device

model, for microwave power GaN HEMTs, amenable for integration into a commercial harmonic balance simulator. All the steps taken to extract it are explained, starting with the extrinsic elements’ determination and ending with the intrinsic ones. This model was validated by comparing measured and simulated output power and intermodulation distortion data of a GaN HEMT. Very good agreement was obtained from small- to large-signal excitation regimes.

Index Terms — Power Transistors, Modeling, Intermodulation Distortion.

I. INTRODUCTION

Standard nonlinear characterization methods still rely on quasi small-signal two-tone tests and figures like third order intercept point, IP3. However, it is widely recognized that large-signal distortion has its origins in physical device characteristics that are distinct from the ones determining these 3dB per dB slope IMD curves.

On the other hand, it is also a fact that good figures of power added efficiency, PAE, can only be achieved when the device is biased at very low quiescent currents, and excited with a signal level in which output power, Pout, capabilities are fully explored. Unfortunately, this implies power saturation and thus large amounts of distortion, which can only be obviated by complex linearization circuits or convenient output power back-off. At the end, a good compromise between PAE, Pout, and IMD, is generally reached close to the 1dB compression point, a zone where a convenient IMD description results from the interaction of the small- and large-signal distortion characteristics [1].

It is known from Volterra series analysis that, if one wants to describe adjacent channel distortion, or close side-band IMD, he will need to accurately reproduce the I/V and Q/V characteristics, at least up to the 3rd order, while an alternate channel distortion level would need, at least, 5th order detail. In mathematical terms, this implies that 3rd or 5th order derivatives of I/V and Q/V functions must be carefully extracted and reproduced.

Unfortunately, such a local model is not capable of reproducing the full range of large-signal device characteristics.

For that, an accurate description of the devices strong nonlinearities as saturation - to triode-zone transition,

current cut-off, gate-channel diode conduction and gate-channel breakdown, are required. This leads to the necessity of a nonlinear global model.

Although various nonlinear global models obeying these requirements have been proposed for many different microwave device types [1], GaN power HEMT technology is still in its infancy as, to the best of the authors’ knowledge, no nonlinear model conceived to reproduce its distortion properties was ever published.

Green et al. [2] and Lee et al. [3], introduced a Curtice Cubic nonlinear model which has no IMD prediction capabilities. More recently, Raay et al. [4], used the Angelov-Zirath Model but also no IMD data is presented.

However, for taking full advantage of the low distortion and high efficiency expectations of GaN based power amplifiers, in the highly competitive wireless market, foundries must rapidly supply nonlinear global models for their devices.

This paper deals with the extraction of such a nonlinear global model for a microwave GaN power HEMT device, paying particular attention to the prediction of small- and large-signal output power and intermodulation distortion.

II. GAN HEMTS

The device used was a GaN HEMT on Si substrate, with 2mm gate periphery, encapsulated in a standard high power microwave package.

Figure Fig.1 shows measured Ids vs Vds characteristics under static conditions, for six different biases. It can be seen that this device is a depletion mode transistor with a pinch off voltage of -4.3 V drawing a maximum current of 1 A when the gate voltage is set to zero.

Fig. 1. Measured I-V characteristics under static conditions.

0 1 2 3 4 5 6 7 8 9 100

100

200

300

400

500

600

700

800

900

1000

1100

V gs = - 5 V

V gs = -3 V

Vgs = -2 V

V gs = -1 V

V gs = 0 V

Vgs = -4 V

Vds (V)

Ids

(mA

)

Figure Fig. 2 depicts the transfer characteristic of the same GaN HEMT with a fixed drain voltage of 6 V. The peak transconductance is 330 mS.

Fig. 2. iDS(vGS) transfer characteristic (–) and Gm (--) for a

constant drain voltage of 6 V.

III. MODEL TOPOLOGY

In this section, an empirical large-signal model is described. The equivalent circuit model topology used, presented in Fig. 3, includes both extrinsic and intrinsic elements that were separately extracted.

Fig. 3. Equivalent circuit model topology used.

A. Extrinsic Elements’ Extraction

As it can be seen in Fig. 3, besides the usual extrinsic FET elements, there are three R-C networks: one at the gate, one at the drain, and another connecting both ports. These networks were first introduced by Chumbes et al., in [5] and then by Manohar et al., in [6]. Their introduction tries to reproduce the impact of the p-Si/GaN/metal structure on the S-parameters, especially a pronounced resistive component observed under channel current cut-off (cold FET operation).

The determination of all the parasitic resistances and inductances was performed using low frequency S-parameter measurements, taken under forward gate bias conditions as described by Dambrine et al. [7]. This was possible since, as reported in [6], the RC networks have minimum effect on the Z-parameters.

After that, an optimization for the cold FET (VDS=0V, VGS=-8V) S-parameter measurements was performed, using a commercial CAD tool. The extrinsic elements obtained are summarized in TABLE I.

B. Intrinsic Elements’ Extraction

In order to determine the intrinsic elements, we used the standard method of [7]. Considering the intrinsic element values this way extracted, we considered Cds and Ri as invariant with vGS. Furthermore, since such devices are primarily intended for highly efficient and low distortion power amplifier applications, and are thus usually kept in the saturation region, Cgd was also assumed invariant. Their values are shown in TABLE II.

Considering the microwave power amplifier application

in view, a quasi-static global model is needed for each of the remaining nonlinear elements: iDS(vGS,vDS) and Cgs(vGS).

B.1. Chalmers Model Extraction

As this device uses a HEMT structure, the first choice for the nonlinear functional description of iDS(vGS,vDS) was the standard Chalmers, or Angelov-Zirath, Model [8], commonly accepted for GaAs HEMT devices. Its major advantage resides on its capability in reproducing the typical bell-shaped transconductance of HFET devices, usually explained by the so-called “parasitic MESFET” behavior, observed at high channel currents. The best fit provided by the Chalmers Model to the measured Gm(vGS) is depicted in Fig. 4a.

Fig. 4. Gm (a), Gm2 and Gm3 (b), measured (.) and modeled (–) with the Chalmers Model, for a constant VDS in the saturation zone.

TABLE I EXTRINSIC ELEMENT VALUES

Lg Lg_B Rg Ld Ld_B Rd Ls Rs 0.9nH 0.7nH 1.67Ω 1.7nH 1.0nH 0.9Ω 0.1nH 0.1Ω

R11 C11 R21 C21 R31 C31 20Ω 2.3pF 70Ω 1.2pF 5Ω 0.1pF

TABLE II INVARIANT INTRINSIC ELEMENT VALUES

Ri Cgd Cds 5Ω 0.3pF 3.2pF

+

-

Rg

Rs

RdLg_B

Ls

Ld_BLg Ld

R11

R31

R21

C11 C21

C31

Ri

Cgs

Cgd

CdsIds(Vgs',Vds')

G

S

D

Vgs'Vds'

+

-

Intrinsic

Extrinsic

V g s (V )

Ids

(A)

& G

m (

A/V

)

-8 -7 -6 -5 -4 -3 -2 -1 0

0 .1

0 .2

0 .3

0 .4

0 .5

0 .6

0 .7

0 .8

0 .9

1

0

0-8 -7 -6 -5 -4 -3 -2 -1 0 -8 -7 -6 -5 -4 -3 -2 -1 0

-0.10

-0.05

0

0.05

0.10

0.15

0.20

0.05

0.1

0.15

0.2

0.25

0.3

0.35

a b

Vgs (V) Vgs (V)

Gm

2 (

A/V

2)

& G

m3

(A

/V3 )

Gm

(A

/V)

Although these results may not be considered

dramatically bad, in a mean square error sense, they were considered unacceptable as they completely failed the higher order derivatives, in particular ∂ 3iDS/∂ vGS

3, as seen in Fig. 4b. Hence, this compromises the accuracy of any future in-band intermodulation distortion prediction [1].

A detailed study of these disappointing results led us to the puzzling conclusion that this difficulty of the Chalmers Model, in reproducing this HEMT I/V characteristic, probably comes also from its referred main advantage: it tends to produce pronounced bell-shaped Gm(vGS) forms. In fact, as it basically describes the iDS(vGS) dependence as an hyperbolic function, it tends to produce Gm(vGS) of a distinct sech(vGS)2 form. As it is widely known, this is a symmetric function across the transconductance’s peak, notoriously distinct from the one extracted from S-parameter measurements, and shown in Fig. 4a.

B.2. Alternative In-House Model Extraction

After this first unsuccessful modeling trial, we directed our attention to other possible mathematical model formulations, having adopted a new in-house model proposed by Fager et al. [9]. Although capable of also reproducing the desired bell-shaped transconductance of a HEMT, it is capable of a much more flexible iDS(vGS) fit. Indeed, and contrary to the 1+tanh[α(vGS)] form of the Chalmers Model, this new f1(x).[1+f2(x)]-1 current saturating function, in which x is another saturating function of vGS, allows a much more independent control of turn-on abruptness, and subsequent Gm(vGS) saturation smoothness and peak broadness.

The extraction of the model’s parameter set was started by fitting the small-signal Gm(vGS), and then complemented by a manual optimization for measured iDS(vGS,vDS) characteristics and low-frequency small-signal harmonic measurements [1]. In TABLE III the obtained model parameter set is presented, while Fig. 5a and Fig. 5b show the resulting prediction of the small-signal Gm(vGS), and its derivatives: Gm2(vGS) and Gm3(vGS).

Fig. 5. Gm (a), Gm2 and Gm3 (b), measured (.) and modeled (–) with the In-House Model, for a constant VDS in the saturation zone.

For the nonlinear gate-source capacitance, Cgs(vGS), we used the model proposed in [9]. Measured and simulated Cgs(vGS) results are compared in Fig. 6.

Fig. 6. Comparison between measured (.) and predicted (–) Cgs(vGS) values.

IV. MODEL VERIFICATION

In order to prove the ability of this model in describing large-signal behavior of our GaN HEMT device, several output power and intermodulation measurements and simulations were conducted for a reasonably fine grid of VGS values (thus of quiescent IDS bias currents), while VDS was kept constant at 6V. This allowed a thorough study of the device model behavior for various power amplifier operation classes: C, AB and A, at 900 MHz.

Figures Fig. 7, Fig. 8 and Fig. 9 illustrate the measured and simulated output power and IM3 vs input power for the three classes above mentioned.

Fig. 7. Measured (x) and simulated (–) output power and IM3 vs input power for Class C.

TABLE III IN-HOUSE MODEL PARAMETERS

β VTO VST VK ∆ VL λ α psat plin γ 0.40 -4.425 0.15 4 5 1.35 0.0256 0.40 -0.62 1 0

- 4 0 - 3 5 - 3 0 - 2 5 - 2 0 - 1 5 - 1 0

- 7 0

- 5 0

- 3 0

- 1 0

1 0

- 9 0

2 5

Pout

(d

Bm

)

P i n ( d B m )

C l a s s C

0-8 -7 -6 -5 -4 -3 -2 -1 0 -8 -7 -6 -5 -4 -3 -2 -1 0

0.05

0.1

0.15

0.2

0.25

0.3

-0.10

-0.05

0

0.05

0.10

0.15

0.200.35

a b

Vgs (V) Vgs (V)

Gm

(A

/V)

Gm

2 (

A/V

2)

& G

m3

(A

/V3)

-8 -7 -6 -5 -4 -3 -2 -1 01.0

2.0

2.5

3.0

3.5

4.0

Vgs (V)

Cgs

(pF)

1.5

Fig. 8. Measured (x) and simulated (–) output power and IM3 vs input power for Class AB.

Fig. 9. Measured (x) and simulated (–) output power and IM3 vs input power for Class A.

As seen in these figures, measured and simulated results compared remarkably well in all operation classes. Indeed, not only the general output power and IMD behavior are represented, as the details of the IMD versus input power pattern are accurately described.

For class C, in addition to a very good small-signal IMD description, our model can also predict, with very good accuracy, the so-called large-signal IMD sweet-spot.

A handy property of these GaN HEMT devices is the presence of a notorious distortion valley in the IMD pattern, observed when the device is biased for class AB (Fig. 8). This has practical significance since it is known that, in this operation class, the device tends to present its optimized values of Pout and PAE. Therefore, this valley can be used as an important tool to design highly efficient wireless power amplifiers of also very good linearity. Previous studies conducted for other FET device types [9], [10], led to the conclusion that those valleys, or, sometimes, even double minima, can be explained as the interaction of small- and large-signal IMD. Their prediction is thus determined by the model’s ability in precisely describing the iDS(vGS,vDS) higher order derivatives [1], as discussed in Section III B.1 and B.2.

In class A, no large-signal IMD sweet spot is predicted by the model or observed in the measurements.

V. CONCLUSION

An equivalent circuit nonlinear global model was proposed and its parameter set extracted for a 2mm GaN power HEMT. Modeling studies proved that the functional form now adopted for the iDS(vGS,vDS) characteristic was found more flexible than the standard HEMT model developed for GaAs devices. That allowed a precise fitting of the measured small-signal Gm(vGS), and thus of its higher order derivatives. As expected, this played a paramount role in the accurate prediction of the device’s large-signal output power and intermodulation distortion.

ACKNOWLEDGEMENT

The authors would like to acknowledge Nitronex Corporation for providing the GaN HEMT devices and Portuguese Science Bureau, F.C.T., for the Ph.D. grant Ref. 11323/2002, given to the first author.

REFERENCES

[1] J. C. Pedro and N. B. Carvalho, Intermodulation Distortion in Microwave and Wireless Circuits, Artech House, 2003.

[2] B. M. Green et al., “Validation of an Analytical Large-signal Model for AlGaN/GaN HEMTs”, IEEE MTT-S Int. Microwave Symp. Dig., pp. 761-764, Jun. 2000.

[3] J. W Lee et al., “Scalable Large-Signal Device Model for High Power-Density AlGaN/GaN HEMTs on SiC”, IEEE MTT-S Int. Microwave Symp. Dig., pp.679-682, May 2001.

[4] F. v. Raay et al., “Large-signal Modeling of AlGaN/GaN HEMTs with Psat>4 W/mm at 30 GHz suitable for Broadband Power Applications”, IEEE MTT-S Int. Microwave Symp. Dig., vol. 1, pp.451-454, Jun. 2003.

[5] E. Chumbes et al.,“AlGaN/GaN High Electron Mobility Transistors on Si(111) Substrates”, IEEE Trans. Electron Devices, Vol. 48, No. 3, pp. 420-426, Mar. 2001.

[6] S. Manohar et al., “Characteristics of Microwave Power GaN HEMTs on 4-Inch Si Wafers”, IEEE MTT-S Int. Microwave Symp. Dig., vol. 1, pp. 449-452, Jun. 2002.

[7] G. Dambrine et al., “A new method for determining the FET small-signal equivalent circuit”, IEEE Trans. Microwave Theory & Tech, vol. 36, pp.1151-1160, Jul. 1988.

[8] I. Angelov, et al., “A New Empirical Nonlinear Model for HEMT and MESFET Devices”, IEEE Trans. Microwave Theory & Tech, vol. 40, No. 12, pp. 2258-2266, Dec. 1992.

[9] C. Fager et al., “Prediction of IMD in LDMOS Transistor Amplifiers Using a New Large-Signal Model”, IEEE Trans. Microwave Theory & Tech, vol. 50, pp.2834-2842, Dec. 2002.

[10] N. B. Carvalho and J. C. Pedro, “Large and Small Signal IMD Behavior of Microwave Power Amplifiers”, IEEE Trans. on Microwave Theory and Techniques, vol. MTT-47, No 12, pp.2364-2374, Dec. 1999.

- 4 0 - 3 5 - 3 0 - 2 5 - 2 0 - 1 5 - 1 0

- 7 0

- 5 0

- 3 0

- 1 0

1 0

- 9 0

2 5

P i n ( d B m )

Pout

(d

Bm

)

C l a s s A B

- 4 0 - 3 5 - 3 0 - 2 5 - 2 0 - 1 5 - 1 0

- 7 0

- 5 0

- 3 0

- 1 0

1 0

- 9 0

2 5

P i n ( d B m )

Pout

(dB

m)

C l a s s A