Extrinsic Extraction Pocedure For a Small-Signal GaN-HEMT Model

Mohamed Laredj, louay Degachi, Ahmed Birafane, Ammar kouki,

Electrical Engineering Department École de technologie supérieure, Montréal, QC,

Canada H3C 1K3 ahmed.birafane@lacime.etsmtl.ca

Fadhel M. Ghannouchi, Electrical and Computer Engineering Department

Schulich School of Engineering, University of Calgary, NW Calgary, AB, Canada T2N 1N4

Abstract—This paper presents an extrinsic extraction procedure for a small-signal GaN-HEMT model with a distributed gate model using Z-parameters equations. Experimental validation is performed on multifinger 4x20 and 2x100 µm HEMTs.

Keywords- GaN HEMT modeling; small-signal model; parameter extraction; parasitic effects;

I. INTRODUCTION Today, GaN technology, through GaN HEMT transistors,

is poised to become the next disruptive technology for HPAs bringing unparalleled performance in efficiency and linearity thanks to its intrinsic characteristics. GaN-HEMT based design requires reliable large-signal model capable of capturing the device’s electrical behavior in the operation mode of interest.

Accurate small-signal extraction is a key step in bottom-up large-signal HEMT modeling. Of particular importance is extrinsic extraction, where parasitic effects must be accurately determined and efficiently eliminated to avoid any error propagation towards the intrinsic circuit parameters.

In this paper, a distributed model is considered. Layout parasitic effects are eliminated by calibrating RF measurements up to the transistor edges. The electrode effects are determined using Z-parameters equations. Intrinsic extraction is then performed using an already published technique [1].

Section II presents the adopted model topology. In section III, the extrinsic extraction is described. In section IV, experimental validation is presented.

II. SMALL-SIGNAL MODEL The adopted HEMT small-signal equivalent-circuit model

is shown in fig. 1. Layout parasitics are eliminated from the outset by calibrating the RF measurement setup up to transistor edges, using OPEN and SHORT calibration standards. Cgsi, Cdsi and Cgdi represent inter-electrode capacitances, while Lg, Ld and Ls represent the electrode

inductances. The remaining elements have their usual significances.

III. EXTRINSIC EXTRACTION PROCEDURE In order to extract the extrinsic inductances and

resistances, the transistor is biased in cold weak pinch-off condition. The inter-electrode capacitances are assumed to be absorbed by the internal capacitances. The equivalent circuit becomes less complicated. The internal resistances are still taken into account, because in the weak pinch-off condition, the chanal is not completely depleted.

A distributed gate model is adopted in our circuit to put in evidence the internal resistance effect in this bias condition.

We observe that the real part of Z-parameters decrease in the low frequency range and remain constant over the high frequency range; this behavior can be explained by analyzing the real part of Z parameters equations, we observe that the term jω Cds Rch is most dominant in the low frequency range, and can be neglected in the high frequency range.

The resulting model is shown in fig.2. A distributed RC network is used to represent the HEMT channel under the gate at Vds = 0 V. The circuit Z-parameters are given as follows [2]:

Figure 1. Adopted HEMT small-signal model

978-1-4577-2209-7/11/$26.00 ©2011 Crown

Figure 2. Weakly pinched-off cold HEMT model

The real and imaginary parts are illustrated in figs. 3 and 4,

respectively. The intrinsic capacitances are evaluated from imaginary parts. As mentioned in ref [3], extrinsic resistances are evaluated from the real parts of Z-parameters in high frequency range and the extrinsic inductances are obtained from the slope of the imaginary part of Z-parameters versus .

Figure 3. Real part of Z-parameters.

Figure 4. Imaginary part of Z-parameters

IV. EXPERIMENTAL VALIDATION In order to validate and assess the accuracy of the

extraction procedure, two multifinger HEMTs are investigated. Measurements are performed over the frequency range 1-26 GHz. The extraction procedure is implemented as a Matlab program. The first transistor is a 4x20 µm. The extrinsic elements are given in table I.

TABLE I. EXTRINSIC PARAMETERS FOR THE 4X20 µM HEMT

Rg (Ω)

Rd (Ω)

Rs (Ω)

Lg (pH)

Ld (pH)

Ls (pH)

5.38 3 25.0 2.33 1.75 1.61

Figs. 5 shows comparisons between measured and simulated S-parameters at the bias point Vgs = - 3 V and Vds = 5 V. Table II shows the extracted values of the different circuit elements.

The second transistor is a 2x100 μm. The extrinsic elements are given in table III. Figs. 5 shows comparisons between measured and simulated S-parameters at the bias point Vgs = -1 V and Vds = 5 V.

S11

S21

S12x2S22x2

Figure 5. Measured (o) and simulated (-) S-parameters for a 4 x 20 μm HEMT (Vgs = - 3 V and Vds = 5 V).

TABLE II. INTRINSIC PARAMETERS FOR THE 4X20 µM HEMT

Element Vgs = - 3 V, Vds = 5 V

Ri [Ω] 2.6167 x 10-5 Rgd [Ω] 2.8416 x 10-5 Rds [Ω] 2.312 x 103

Cgs [fF] 257.84 Cgd [fF] 15.107 Cds [fF] 9.746 Gmo [S] 0.0231 τ [ps] 2.154

TABLE III. EXTRINSIC PARAMETERS FOR THE 2X100 µM HEMT

Rg (Ω)

Rd (Ω)

Rs (Ω)

Lg (pH)

Ld (pH)

Ls (pH)

4.35 0.3148 4.823 0.525 0.365 0.67

S11x2

S22

S12x2

S21

Figure 6. Measured (o) and simulated (-) S-parameters for a 2 x 100 μm

HEMT (Vgs = - 1 V and Vds = 5 V).

TABLE IV. EXTRINSIC PARAMETERS FOR THE 2X100 µM HEMT

Element Vgs = - 1 V, Vds = 5 V

Ri [Ω] 1. 515 x 10-5 Rgd [Ω] 4 x 10-6 Rds [Ω] 575.887

Cgs [fF] 458.49 Cgd [fF] 55.2 Cds [fF] 34.63 Gmo [S] 0.05 τ [ps] 3.803

V. CONCLUSION In this paper, an extrinsic parameter extraction method is

presented for GaN HEMT small-signal model

Excellent agreement is obtained between modeled and measured S-parameters, for two multifinger transistors. The results indicate the accuracy and consistency of this method.

ACKNOWLEDGMENT The authors wish to acknowledge the assistance and

support of Mr. TongXi Wu and Daniel Gratton to accomplish this work.

REFERENCES

[1] G. Dambrine, A. Cappy, F. Heliodore, E. Playez, “A new method for determining the FET small-signal equivalent circuit,” IEEE Trans. Microwave Theory and Techn., vol. 36, no. 7, pp. 1151–1159, July 1988

[2] R. G. Brady, C. H. Oxley, T. J. Brazil, “An Improved Small-Signal Parameter-Extraction Algorithm for GaN HEMT Devices” IEEE Trans. Microwave Theory and Techn., vol. 56, no. 7, pp. 1535–1544, Jul 2008.

[3] M.-Y. Jeon, B. –G. Kim, Y. –J. Jeon, Y. –H. Jeon, “A technique for extracting small signal equivalent-circuit Elements of HEMTs ” , IEICE Trans. Electron., vol. E82-C, no.11, pp. 1968–1976, Nov. 1999.