IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 43, NO. 4, AUGUST 1994 655

Short Paper

GaAsFET and HEMT Small-Signal Parameter Extraction from Measured S-Parameters

Larry T. Wurtz

Abstmct-An improved method for extracting small-signal model pa- rameters including package parasitics for GaAsFET and HEMT devices is described. Monte Carlo simulation techniques result in optimized model component values for minimum error between measured and modeled S- parameters. Simulation time is reduced by starting from initial component values derived from an improved direct extraction procedure.

I. INTRODUCTION Before any device model can be used, its parameters must be

determined by a process called parameter extraction. Despite the fact that parameter extraction is important to the modeling of transistor devices, it has been largely neglected for microwave transistors. Using the technique described in the following, the small-signal model components shown in Fig. 1 can be extracted from any set of measured S-parameters.

The small-signal model shown in Fig. 1 is a standard topology for accurately representing GaAsFET devices at microwave frequencies and, accordingly, was chosen for the parameter extraction procedure [ 11. The model is equally applicable to high-electron-mobility tran- sistor (HEMT) devices. The model consists of intrinsic components inside the dashed box to model the physical layout of the transistor device. Extrinsic components outside the dashed box model package parasitics.

The intrinsic elements form a hybrid-pi model where drain current is controlled by voltage across the gate-to-source capacitance Cgs [2], [3]. Because the transconductance G m cannot respond instan- taneously to change in gate voltage at microwave frequencies, a transconductance delay, r , is included to provide phase shift in the drain current. A gate-charging resistance Rgs is included to improve the match to measured S-parameter S11.

Parasitic inductances Lg, Ls, and Ld and parasitic resistances Rg, Rs, and Rd are needed to model bonding pads deposited on the device surface and bond wires. In most cases, bond wire parasitics are on the order of 100 to 300 pH and dominate pad parasitics.

Extrinsic inductances Lpg, Lps, and Lpd and extrinsic resistances Rpg, Rps, and Rpd represent the gate, source, and drain package lead parasitics, respectively. It is essential to properly model these parasitics to minimize the error between measured and modeled S-parameters [l], [4]-[6].

Extrinsic package capacitances between the gate lead and source substrate and drain lead and source substrate are modeled by elements Cpgs and Cpds, respectively. The capacitance between gate and drain leads, from point A to B in Fig. 1, was found to be insignificant.

S-parameter percent error is given as follows:

%ERROR = { 2 lSijK measured - SijK modeled!

Manuscript received April 6, 1993; revised January 24, 1994. The author is with the Department of Electrical Engineering, The University

IEEE Log Number 02049.

x 100 (1) 1 lSijK measuredl K=l

of Alabama, Tuscaloosa, AL 35487 USA.

Gute-

I I 1 ; I L.......... ................... 1

source

Fig. 1. Small-signal model for GaAsFET and HEMT devices.

where n is the number of measured S-parameter frequencies and Sij individually represents S-parameters S11, S12, S21, S22. The proposed procedure uses the robustness of Monte Carlo simula- tion techniques to optimize modeled components for minimum S- parameter percent error. To reduce the simulation time, intrinsic components and bond wire inductances Lg, Ls, and Ld will be given initial values from an improved direct extraction procedure.

11. DIRECT EXTRACTION OF INTRINSIC COMPONENTS The intrinsic hybrid-pi model shown in Fig. 2 is such that a

y-parameter analysis of the circuit results in the expressions:

Rgs x Cgs2 x w2 + j ( T + C g d ) (2) D y l l =

(4) Gm x e-iwr

l + j x Rgs x Cgs x w - j x w x Cgd y21=

y 2 2 = G d s + j x w x ( C d s + C g d ) ( 5 ) where

(6) D = 1 + w2 x Cgs2 x Rgs2.

Using these relationships, intrinsic small-signal parameter values can be determined directly from measured y-parameters. Measured y-parameters can be derived from the measured S-parameters. Re- lationships to convert between y-, z-, and s-parameters can be found in a number of circuit texts. It is important to point out that because package parasitics are unknown, conversion from measured S-parameters to measured y-parameters will not account for extrinsic package parasitics shown in Fig. 1. Accordingly, the directly extracted intrinsic component values will not be exact. Directly extracted component values, however, will serve as excellent initial values to reduce the simulation time using Monte Carlo techniques for the final component values.

Minasian [7] and other authors have discussed direct extraction procedures for GaAsFETs [4], [5] and HEMTs [6]. An improved direct extraction procedure described below has resulted in exact expressions for derivation of all intrinsic component values.

An expression for Cgd is found by equating the imaginary terms of (3). Cgd is expressed as

(7) a imag (y12) Cgd = -

20

0018-9456/94$04.00 0 1994 IEEE

656 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 43, NO. 4, AUGUST 1994

Similarly, Cds is found by equating the imaginary terms of (5) and substituting (7) for Cgd. Cds is given as

(8) a imag(y22) + a imag (y12) c a s =

W

Rds is found by equating the real parts of (5). Rds is given as

Exact expressions for Cgs and Rgs are taken from (2) and given as

(10) R ( y l 1 ) x (1 + w2 x K2) c g s = K x w2

and

respectively. In order to derive an expression for Gm, Gm x e-iwr in (4) is

replaced with Gmr + jGmi. Solving for Gmr and Gmi results in

Gmr = R(y21) - a imag (y21) x Rgs x Cgs x w - w2 x Cgd x Cgs x Rgs

and

Gmi =R(y21) x Rgs x Cgs x w

+ a imag (y21) + w x Cgd.

Gm and r are given as

Gm = (Gmr' + Gmi2)'/2 and

Table I shows intrinsic component values given by the direct extraction equations at each measured frequency for an Avantek ATFlOl36 low-noise GaAsFET. Intrinsic component deviations are due to noisy S -parameter measurements, modeling inaccuracies, and most importantly due to the fact that extrinsic package parasitics have not been taken into account. Other GaAsFETs and HEMTs examined resulted in similar values as reported in Table I.

A linear least-squares fit procedure was used to determine single representative component values. Because extrinsic package par- asitics have not been determined, directly extracted values have greater accuracy at low frequencies where package parasitics have the least effect. Because Rgs and r model high-frequency device performance, values for these two components are more accurately extracted at high frequencies. Consequently, the linear least-squares method was applied to components Cgd, Cgs, Cds, Rds, and Gm in a low-frequency range and Rgs and r in a high-frequency range. The lowest S-parameter percent error of 29.8% was found by

TABLE I INTRINSIC PARAMEIER VALUES FROM D m m

EXTRACTION FOR AN AVANTEK ATF10136 GaAsFET

Lau-frsqumcy range: lGaZ - 5 G B I3igh-frcquency range: SGHz - 9GHz

selecting a low-frequency range from 1 GHz to 5 GHz and a high range from 5 GHz to 9 GHz.

111. EXTRACTION OF BOND WIFE INDUCTANCES

Table I1 shows the improvement in S-parameter percent error which was achieved by de-embedding bond wire inductances. The bond wire inductances Lg, Ls, and Ld, shown in Fig. 2, can be found quickly from the directly extracted intrinsic component values. Bond wire inductances can be de-embedded from measured S- parameters by converting to measured z-parameters zzlmeas, and applying the following relationships:

zllint = ~ l l m e a s - j x w x (Lg+ Ls) (16) (17) (18)

(19)

where ztJint are the intrinsic z -parameters. Values for Lg, Ls, a n d L d are set to zero initially. Convert the intrinsic z-parameters to intrinsic y-parameters and determine intrinsic model parameters using direct extraction. Generate modeled intrinsic y-parameters using (2) through (6) for each measured frequency. Convert modeled intrinsic y-parameters to modeled intrinsic z- parameters +mod. Expressions for bond wire inductances are given as

212lnt =zlZmeas - j x w x LS Z2l in t = ~ ~ l m e a s - j x w x LS z22mt = z22meas - j x w x (Ld + Ls)

aimag(a1mea8) - aimag(z1lmod) x (Lg+ Ls) (20)

a imag (zlzmeas) - a imag (Z12mod) = w x Ls (21)

a imag (z21meas) - a imag (Z2lmod) = w x Ls (22)

a imag (mmeas) - a imag (Z22mod) = w x (Ld + Ls) . (23)

A single value for Ls at each measured frequency may be found by averaging the values determined from (21) and (22). With Ls determined, Lg and Ld can be calculated from (20) and (23), respectively. A linear least-squares fit can be used to determine single best-fit values for Lg, Ls, and Ld. Like all package parasitics shown in Fig. 1, bond wire inductances have the greatest effect at high frequencies. Accordingly, similar to determining Gm and r , a high- frequency range from 5 GHz to 9 GHz was selected for a best-fit calculation. Bond wire inductance values are optimized by inserting newly derived values for Lg, Ls, and Ld into (16) through (19) and iterating the procedure for minimum S -parameter percent error.

The following steps summarize the procedure: 1) Convert measured S-parameters to measured z-parameters. 2) With (16) through (19), de-embed bond wire inductances from

measured z-parameters to give the intrinsic z-parameters. 3) Convert intrinsic z-parameters to intrinsic y -parameters.

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 43, NO. 4, AUGUST 1994

0.21 - 020 - 018 - 0.17 -

a0 15 - U 0 1 4 - 2 0 1 3 - = 0 1 1 - m o l 0 - 0008 - 2 0.07 -

0 0 6 - 004 - 0 0 3 -

.-

651

TABLE II OFTIMJZED PARAMErER VALUES

Directly extract the intrinsic small-signal parameters with the expressions derived in the previous section and determine best- fit parameters. For each measured frequency, determine modeled y-parameters using (2) through (6). Convert the modeled y-parameters to modeled z -parameters to modeled S-parameters. Determine S-parameter percent error using (1). If percent error is a minimum, the procedure is completed. Otherwise, Determine bond wire inductances using (20) through (23) for each measured frequency and calculate best-fit values. Retum to Step 2 to repeat the process.

Iv. SIMULATION OF MODELED COMPONENTS simulation of the model shown in Fig. 1 using Monte Carlo

techniques where parameters were randomly perturbed by a delta value resulted in the lowest S-parameter percent error. Results for the Avantek ATF10136 GaAsFET and ATF35576 low-noise HEMT are reported in Table II. Similar results were found for other GaAsFETs and HEMTs studied.

Executing on a 386-based PC, the simulation with initial model component values zeroed required over 24 hours to reach minimum S-parameter percent error. Starting with the intrinsic small-signal and bond wire inductance values derived in the previous section and reported in Table 11, it required roughly 30 minutes of simulation time to reach the same approximate results.

The simulation procedure was most robust by considering modeled components in groups. Intrinsic small-signal components composed the first group. Extrinsic package lead reactances, package capac- itances, and package bond wire reactances composed the second, third, and fourth groups, respectively. Working with each group individually, while other group component values were held constant, model parameter values were randomly perturbed by a specified delta value. The S-parameter percent error was calculated and if percent error improved, the component values were updated with the perturbed values. Otherwise, component values were not changed. This random process was iterated 500 times for each group of components. After all groups were considered, the procedure retumed to the first group of modeled components.

Table 11, under the simulation column headings, reports final optimized model parameter values for a GaAsFET and HEW. Figs.

1 00 0 95 0 90 0 85

a 0 8 0 :075 % 0 70 C 0 65 FO 60

0 50 0 45

5 0 55

000000000000000000000000000000 ~ ~ ( O ? - m ~ o - N ~ f l n ( O ? - m m o - ~ ~ ~ l n m ~ m m o - ~ , ~ - - - - - - - - - - N N N N N N N N N ~ , m ~ ~ m

Anqle (deqrees)

Fig. 3. Measured versus modeled s11-Parameters.

5.25 5 00 4 75 4 50

~ 4 25 4.00

3 3 75 Y 3.50 C 3 2 5 g3.00 2 75 2 50 2.25 2 00 175

Fig. 4. Measured versus modeled 5'21-Parameters.

icLLv measured Onone diiect extroction 4 A M A slmulotlon lGHz

0 0 0 0 0 0 ~ 0 0 0 0 0 0 0 0 0

Anqle (deqrees)

0 0 1 4 I I I I I I I I , I I I , , I

b m m b " - N m * O m ? - m I I I I I I I

Fig. 5. Measured versus modeled ,912-Parameters.

0.49 - 045 -

a040 - 2 0.36 - .?0.31 - c 0.27 - g0.23 -

0 1 4 - 0.09 - 005 -

2 0 1 8 - tlu measured QOUW direct extroction m simulation

o o o d I I I I I I I I I I I I I , , ~ ~ ~ ~ ~ ~ 0 0 0 0 0 0 0 - " * o m

Anqle (deqrees) I I I I I I I

Fig. 6. Measured versus modeled S22-Parameters.

3-6 compare the S-parameters from measurement, direct extraction, and simulation for an Avantek ATF10136 GaAsFET.

V. CONCLUSIONS The ability to model microwave transistors allows SPICE-like

circuit simulators to extract device performance between and be- yond physically measured values. The proposed procedure accurately extracts intrinsic and extrinsic package parasitics from measured S-

658 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 43, NO. 4, AUGUST 1994

parameter data to form a linear model of GaAsFET and HEMT devices. The procedure offers the robustness of Monte Carlo sim- ulation techniques with reduced execution time due to initial values from an improved direct extraction procedure.

REFERENCES

[l] R. Vaitkus, “Uncertainty of the values of the GaAs MESFET equivalent circuit elements extracted from measured two-port scattering parame- ters,” in Proc. IEEEICornell Conf. High-speed Semiconductor Devices Circ., Aug. 15-17, 1983, pp. 301-308.

[2] P. R. Gray and R. G. Meyer, Analysis and Design of Analog Integrated Circuits. New York Wiley, 1984.

[3] A. Grenbene, Bipolar and MOS Analog Integrated Circuit Design. New York Wiley, 1984.

[4] G. Dambrine, A. Cappy, F. Heliodore, and E. Playez, “A new method for determining the FET small-signal equivalent circuit,” IEEE Trans. Microwave Theory Technol., vol. MTT-36, pp. 1151-1159, July 1988.

[5] E. Arnold, M. Golio, M. Miller, and B. Beckwith, “Direct extraction of GaAs MESFET intrinsic element and parasitic inductance values,” IEEE Microwave Theory Technol. Symp. Digest, pp. 359-362, May 1990.

[6] B. Hughes and P. J. Tasker, “Bias dependence of MODFET intrinsic model element values at microwave frequencies,” IEEE Trans. Electron Devices, vol. ED-36, pp. 2267-2273, Oct. 1989.

[7] R. A. Minasian, “Simplified GaAs MESFET model to 10 GHz,” Electron. Lett., vol. 13, no. 8, pp. 549-551, 1977.

Low-Frequency Noise Measurements on Semiconductor Devices Using a Probe Station

Lana R. Chaar and Arthur D. van Rheenen

Abstruct- We report a measurement technique that would allow the mapping of the low-frequency noise characteristics of devices across a wafer. We show that we can reliably measure the noise by using a probe station. We also show that the sensitivity of the setup is not limited by the probes.

I. INTRODUCTION Over the past several years it has been recognized more and

more that noise measurements are an important tool to study several important aspects of semiconductor transport phenomena. Noise measurements have been used to characterize deep-level defects and impurities [1]-[3], as well as surface states [4], hot-electron phenom- ena [5], etc. In addition, phenomena such as electron migration in interconnections [6], 171 and point contact effects [8], [9] have been characterized using noise measurements.

With the realization of the importance of low-frequency noise measurements it has become apparent that the major drawback of taking such measurements is the amount of time they take. Wafers need to be cut, and dies need to be bonded and packaged. In addition, the measurements themselves are time consuming. The latter cannot be sped up in a simple manner. To address the former we investigated the possibility of measuring the low-frequency noise using a probe station. High-frequency (GHz) noise figures are routinely measured

Manuscript received April 21, 1993; revised October 18, 1993. The authors are with the Department of Electrical Engineering, University

IEEE Log Number 9402047. of Minnesota, Minneapolis, MN 55455 USA.

Fig. 1. Circuit representation of measurement setup. Sketched here are the powersupply, the bias resistor ( RP,), which is much larger than the device impedance, the coupling capacitor (C), the low-noise amplifier (LNA), and the spectrum analyzer (SA).

this way, but the shielding is simpler in that case. The idea to use a probe station to measure low-frequency noise is not new. Chen [IO] published experimental results and concluded that the noise of the probe-pad contact can be modeled as that of a resistor. In that work the pressure from the probe on the pad was varied so that the contact resistance could be varied.

Here, we compare two techniques to measure the noise: 1) on bonded and packaged devices with the extemal circuitry soldered to the device package leads and 2) on the same devices using probes that contact the bonding pads of the devices. We covered a large range of resistance values (37 0-70 kn) . We show that the probe-pad contacts are not limiting the sensitivity of the noise measurement setup. This is backed by the sensitivity analysis we performed. Finally, we use the experimental results to extract the noisiness parameter a. This parameter is a measure for the magnitude of the l/f noise.

11. DESCRPTION OF EXPERIMENT When using a probe station to measure very small signals it is

important that the devices are properly shielded from extemal fields and isolated from vibrations. The latter is of importance because of the mechanical nature of the probe-pad contact. These goals are met by placing the probes and the vacuum chunk, which holds the wafer, inside a metal box and placing the box on an optical table. The essence of our experiment is a direct comparison between the noise we measured on a packaged device and the noise we measured on the same device using probes. To accomplish this we removed the package lid and placed the probes directly on the pads, right next to the bonding wires which connect the device to the package leads. The probes (we used only two probes) delivered the bias current and sensed the noise signal. Schematically, this is sketched in Fig. 1 .

We shall present measurement data taken on a variety of semi- conductor structures: silicon resistors and GaAs resistors. These structures have different metalizations, and their impedances range from 37 O to 70 kO. We used tungsten probe tips with a diameter of 25 pm. At the moment the setup is fit to hold 3“ wafers or parts of a wafer of that size. The noise measurement procedure is standard and has in essence been described elsewhere [ l l ] . Important components of the setup are the ultra-low-noise amplifier EG&G 5004 and the HP 3561 FFT spectrum analyzer.

111. ANALYSIS OF SENSITIVITY OF SETUP In our experimental setup we use an ultra-low-noise amplifier. Its

noise is characterized by an equivalent voltage noise source with intensity 0.8 nV f and an equivalent current noise source of 92 f A / f i , both at 1 kHz. The input impedance of the amplifier is R, = 5 MO. The amplifier voltage noise source sets a lower limit to

0018-9456/94$04.0001994 IEEE