IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 41, NO. 11. NOVEMBER 1994 20x7

A Noise Model for High Electron Mobility Transistors

A. F. M. Anwar and Kuo-Wei Liu

Abstruct- A model to explain the noise properties for AlCuAslCuAs HEMT’s, AlGuAsllnCuAslGuAs pseudomorphic HEMT’s (P-HEMT’s) and GuAslAlCaAs inverted HEMT’s (I-HEMT’s) is presented. The model is based on a self-consistent solution of Schrodinger and Poisson’s equations. The influence of the drain-source current, frequency and device parameters on the minimum noise figure I?,,,,,, and minimum noise temperature T,,,,,, for different HEMT structures are presented. The study shows that P-HEMT’s have a better noise performance than the normal and inverted HEMT’s. The present model predicts that a long gate I-HEMT device will exhibit a better noise performance than a conventional HEMT. There is a range of doped epilayer thickness where minimum noise figure is a minimum for pseudomorphic HEMT’s which is not observed in conventional and inverted HEMT’s. The calculated noise properties are compared with experimental data and the results show excellent agreement for all devices.

I . INTRODUCTION

HE high electron mobility transistors (HEMT), with its T high speed, is an ideal candidate for low-noise am- plification at microwave and millimeter wave frequencies [ I]-[9]. For a conventional quarter-micrometer gate-length AlGaAslGaAs HEMT, a noise figure of as low as 0.4 dB at 8 GHz and 1.8 dB at 60 GHz was reported by Duh et al. [I], [2] in 1986. Since then, progress has been rapid in the development of InGaAs based pseudomorphic HEMT’s, primarily as a result of their greater carrier confinement and the superior transport characteristics [4]-[9]. Tan et al. [4] reported the successful fabrication of W-band 0.1-pm pseu- domorphic HEMT (P-HEMT) achieving a noise figure of 2.1 dB at 93.5 GHz. Plana et al. [5] reported the noise properties of a 0.35 x 200p1n2 P-HEMT in the microwave range (4-18 GHz) as low as 0.4 dB at 4 GHz and 1.2 dB at 18 GHz, which are comparable to the noise of classical AlGaAslGaAs HEMT’s. Electron mobility enhancement has been shown in metal-GaAs-AlGaAs structures (inverted HEMT’s) which indicates that such devices may have higher transconductances than conventional normal HEMT’s [lo], [ I l l . This may lead the inverted HEMT’s (I-HEMT’s) (Type I and I1 structures [ IO] , [ l l ] ) to be an alternative for low-noise application. However, the noise properties of I-HEMT’s has not yet been demonstrated experimentally.

Manuscript received September 20, 1993; revised June 28, 1994. The review of this paper was arranged by Editor-in-Chief R. P. Jindal. This work was supported by a University of Connecticut Provost’s Grant Number 430727.

The authors are with the Department of Electrical and Systems Engineering, The University of Connecticut, Storrs, CT 06269-3157 USA.

IEEE Los Number 9405578.

Several theoretical models have been developed to study the noise properties of conventional HEMT’s [ 121-[ 141. Brookes [ 121 reported a noise model for conventional HEMT’s based on the treatment of Van der Ziel et al. [15], Puce1 et al. [16] and Statz et al. [ 171. His model failed to explain the U-shape in the noise properties versus drain-source current characteristics. This may be due to a nonself-consistent model. Moreover, the diffusion noise component was ignored in his noise model. Ando et al. [ 131 proposed a self-consistent model to study noise in normal and pseudomorphic HEMT’s. However, the model was unable to explain the low and high frequency minimum noise figures [14]. Recently, Anwar et al. [I41 have reported a noise model for AlGaAslGaAs HEMT’s which is based on the self-consistent solution of Schrodinger and Poisson’s equations. Moreover, a more realistic carrier velocity-electric field (wd - E ) is used. Based on this model, the calculated noise figures show an excellent agreement with the experimental data over a frequency range 8-60 GHz [14].

Based on the self-consistent model developed by Anwar et al. [14], [18], we present a general model to evaluate the noise properties for all kinds of 111-V materials based HEMT’s. These include AlGaAslGaAs HEMT’s, GaAslAlGaAs in- verted HEMT’s (I-HEMT’s) and AZGaAslInGaAslGaAs pseudomorphic HEMTs (P-HEMT’s). The paper is organized as follows: In Section 11, a general noise model for HEMT’s is discussed. In Section 111, the theoretical results are presented and compared to experimental data which is followed by a conclusion.

11. MODEL

The modeling of noise proceeds by first quantifying the quantum well (QW) and identifying a realistic velocity-electric field (wd - E ) characteristic for the carriers in the conducting channel. Instead of using a two-line [12], [I31 or an expo- nential [I91 approximation, the following improved ?Id - E characteristic, ‘ud = w, . & / J ( v s / p o ) 2 + &2, is used in this model [14], [18]. Here vs is the carrier saturation velocity, p o is the low field mobility and & is the applied electric field along the channel. This wd -& characteristic makes the current- voltage, dc small signal parameters [18] and noise properties [ 141 analytically tractable. The QW behavior is introduced in the calculation of noise by recognizing the functional dependence of the average distance of the electron cloud z,,, and the position of the Fermi level EF on the two dimensional electron gas (2DEG) concentration n, [ 141, [lS], [20]. z,, and EF may be expressed in the following functional forms [ 141,

00 18-9383/94$04.O0 0 1994 IEEE

2088 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 41, NO. 1 1 , NOVEMBER 1994

4) b

E F ( 0 ) (eV) I

HEMT P-HEMT I-HEMT I-HEMT Type I Type I1

1684.52 284.58 -589.8 -242.6 - 57.45 -7.968 23.35 10.85 - 1.085 - 1.25 -0.17 -0.193

0.06 0.098 . 0.01 0.01 1

[ 181, [20]-[22]:

x,,(x) = a + b . ln(ns(x)) (A) (1) E F ( ~ ) + 7 . In(.,(.)) (eV) (2)

where a , b, EF(O) and y for different HEMT structures are defined in Table I. In the present noise model, the effective channel width (Ad = x,, . ~ A ~ G ~ A , / ~ G ~ A , ) is calculated and modified along the channel depending on the 2DEG concentration n,. The channel is narrower at the source region and widens as one move towards the drain region. The I- HEMT's (Type I and Type I1 structures) show a unique behavior of the average distance of the 2DEG which increases with n,, a property unique to inverted structures [lo], [ l l ] , 1211.

The analysis of noise is based on the identification of the different noise sources that are present in the conducting channel [14], [17], [23], namely 1) Johnson noise (thermal noise) in the ohmic region (region I), 2) noise associated with spontaneous generation of dipole layers in the saturation region (region 11), 3) gate noise due to elementary voltage fluctuations in the channel, and 4) induced gate noise in the saturation region.

Based on the treatment of Puce1 et al. [16], Statz et al. [17], and Brookes et al. [12], one obtains an expression for the mean square noise voltage v:l (in region I) and the drain voltage fluctuation due to diffusion noise 8:2 in the saturation region (region 11). Considering the fluctuation of the gate current due to the capacitive coupling between the channel and the gate, we obtain the mean square Johnson noise induced gate current T 2 in the saturation region. However, by using an accurate estimation of the effective channel width Ad(= .tau . t A a i ~ a ~ s / t ~ a ~ s ) [141, [20] and an improved z'd - E relationship, the expressions of vd, , V d 2 , T i 1 , and ii2 are modified [23]. t are the dielectric constant of epilayer materials.

To facilitate the evaluation of noise performance of devices, dimensionless noise coefficients are used [ 141, [ 161:

92

-2 -2

(3)

where k is the Boltzmann constant, T is the operating tem- perature and A f is the frequency range. gm, r d , and C,, are the small-signal parameters of device, transconductance, drain resistance and gate capacitance, respectively [ 181. 7;

is the equivalent noise voltage at the drain region and T i is the equivalent noise induced gate current. PI , P2 and R I , R2 are of the same form as P and R, but with subscripts 1 and 2 on different noise sources in the region I (ohmic region) and region I1 (saturation region), respectively. The correlation coefficient, C , between different noise sources can be written as

where = vi /r; ,C1 = C11 ' JP1. R 1 / P ' R and C2 = C22 . 1/p2 . R2/P . R. Cll is the gate-drain noise current _ _ correlaiion coefficient in the ohmic region, C22 is the gate- drain noise current correlation coefficient in the saturation region and is suggested to be 1 [13], [16], [171.

Once all the noise sources and their correlations are deter- mined, the minimum noise figure, Fmin the noise conductance, gn and the minimum noise temperature, Tmin are defined as [141, 1161:

/ I

with

where rn and Zsopt are the noise resistance and optimized source impedance defined in [14], 2, = R,+jX, = R,+Rd+ R, - ( j / w .C,,). [(P . R . (1 - C2))/( P + R - 2 .C. m)], is the correlation impedance, R, and Rd are the source and drain resistance, R; = L,/(v, . Cgs) is the gate charging resistance. L, represents the length of the gate. fT is the unity current gain cut-off frequency (= g m / 2 . 7 r . e,,) [ 181. In several cases, the device is not matched for the minimum noise conditions and the mismatch effect on the noise figure and noise temperature can be expressed as [24]

and

where 2, = R, + j X , is the input termination or source impedance and Zs,opt is defined as the optimum .external source impedance. The above equations show that the mis- match effect is less sensitive for low values of the noise conductance gn and high value of the unity current gain cut-off frequency fT.

ANWAR AND LIU: A NOISE MODEL FOR HIGH ELECTRON MOBILITY TRANSISTORS 2089

0.25 p m - G a t e A l G a A s / G a A s HEMT

0 5 I , I

D r a i n - S o u r c e C u r r e n t (mA)

Fig. 1. Drain and gate noise coefficients, I? R and noise correlation coeffi- cient C are plotted as a function of drain-source current for a 0.25 x 300p1n~ AiCaAslGaAs HEMT.

111. RESULTS AND DISCUSSIONS

In Fig. 1, the drain and gate noise coefficients P, R and noise correlation coefficient C are plotted as a function of the drain-source current I d s for a 0.25 X 300 prn2 AlGaAslGaAs HEMT [I]. The behavior of P2, R2, and C2 are similar to that reported by Ando et al. [ 131. Due to the use of a different effective channel width Ad, their magnitudes differ. However, the behavior of P I , R I , and C1 are different than that was reported by Ando et al. [ 131. The gate noise coefficient R is larger because of smaller gate capacitance. The nature of C1 and C, are symmetric. CI is approximately equal to 2 at small drain-source current and approaches zero at high current, and C2 behaves just the opposite. The correlation coefficient G initially decreases and then again gradually increases with higher current. There is a dip at some intermediate value of drain current where the diffusion noise becomes more dominant than thermal noise in the channel. This dip in C always occurs at a drain-source current which is higher than that is needed to obtain the minimum noise figure Fmin.

In Fig. 2, the minimum noise figure, Fmin is plotted as a function of the drain-source current, I d s , for a AlGaAslGaAs HEMT (with gate length L, = 0.25pm, gate width z = 200 pm, donor layer concentration Nd = 1 x c111r3, donor epilayer thickness d d = 200 8, and spacer layer thickness d, = 20 ( M A } [24] at 12 GHz, P-HEMT at 94 GHz ( L , = O.l/LIll,z = 40pm.Nd 1 X 1018Cm-3.dd = 300 A and d, = 30 A) [4] and 12 GHz (L , = 0.25prn.z = 20 pni. Nd = 3 x crrP3, d d = 200 At and d, = 20 A) [25] and compared with experimental results [4], [24], [25]. It is observed that P-HEMT’s exhibit better noise performance than AlGaAslGaAs HEMT’s in the high drain-source current

12 GHz P-HEM1 ’ \ 12 GHz HEMT

I 7-7-

10 15 20 25 Drain-Source Current (mA)

OL Fig. 2. Minimum noise figure F,,;,, is plotted as a function of drain-source current for AICaAslGaAs HEMT, pseudomorphic HEMT and inverted HEMT. On the same plot, the experimental data for a AlGaAsiCaAs HEMT [24] at 12 GHz, P-HEMT at 94 GHz [4], and 12 GHz [25] are also shown. The solid line represents the theoretical calculation of F,,,,,, for a AIGaAslCaAs HEMT operated at 12 GHz and the dashed lines represent P-HEMT’s operated at 12 GHz and 94 GHz, respectively.

regime. This may be due to the fact that there is a better carrier confinement, higher low-field mobility and carrier saturation velocity for P-HEMT devices. With identical device parameters of a normal HEMT, the theoretical noise behavior of an I-HEMT (Type-I, z = 200pm,Nd = 1.1 x 1018cm-3, the GaAs layer thickness d = 200 A) is also shown in Fig. 2. At 12 GHz, the minimum noise figure of the of I-HEMT is slightly larger than that of normal and pseudomorphic HEMT’s. The noise performance of Type-I1 I-HEMT is similar to that of Type-I I-HEMT’s.

In Fig. 3, the calculated minimum noise temperatures are compared with room temperature experimental data and the theoretical results developed by Brookes [12] for a 0.35 x 300pm2A1GaAs/GnAs HEMT at 8 GHz (Nd = 1 x 1018c~n-3,dd = 280 A and d, = 20 A) [26] and 0.15 x 100 pm2 P-HEMT (Nd = 1 x lo1’ cmP3, d d = 300 A and di = 30 A) [27] at 30 GHz. ‘U, and p0 are assumed to be 1.0 x lO’(1.25 x 10’) and 4200 (7000) cm2 and the source resistance R, = 5.0Cl(4.5Cl) and the gate resistance R, = 5.OR(4.0R) are used for AlGaAslGaAs HEMT’s (P- HEMT’s) at room temperature. AS observed the agreement is excellent. We believe that the use of a self-consistent calculation to determine the effective channel width as a function of the 2DEG concentration and velocity-electric field characteristic that approximates the experimental results more closely enabled such an agreement. As observed from the figure, P-HEMT’s have lower noise temperatures. Due to better confinement of 2DEG in double barrier P-HEMT’s, the effective channel width Ad of P-HEMT device is smaller than that of normal HEMT (zav is smaller in P-HEMT device (see Table I)). This results in a greater gate capacitance C,, in P- HEMT device than that of the normal HEMT’s. Due to carrier mobility and saturation velocity enhancement, a higher gm is observed in P-HEMT’s as compared to that of AlGaAslGaAs

2090

200 4

300

30 G H z P - H E M T (dataO) 0

0 5 10 15 20

Drain-Source Current (mA)

Fig. 3. Minimum noise temperature Trnin is plotted as a function of drain-source current for a AlGaAslGaAs HEMT and P-HEMT. Also the experimental data for a AlGaAslGaAs HEMT [26] and P-HEMT 1271 are shown in the same plot. (Reprinted from: A . F. M . Anwar and K.-W. Liu, “Noise temperature modeling of AlGaAslGaAs and AIGaAsllnGaAslGaAs HEMTs,” Solid-state Eleciron., vol. 37, no. 9, pp. 1585-1588, 1994.)

300

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 41, NO. 1 I , NOVEMBER 1994

1.4 6.0

0.25 75

120.0 f 15 5.2 f 0.7 6.0 f 0.6 75 f 12

TABLE I1 COMPARISON OF THEORETICALLY CALCULATED AND

EXPERIMENTALLY OBTAINED NOISE PROPERTIES FOR A NORMAL AlGaAslGaAs HEMT AT ROOM TEMPERATURE

1.4 6.05 0.25 75

120.73 6.7

8.291 68.7

HEMT’s. The behavior of gm and C,, results in a higher cut- off frequency f~ for P-HEMT’s that results in a lower noise conductance gn (8) with a corresponding lower noise figure (6) and noise temperature (7). On the same plot theoretical results reported by Brookes et al. [12] for AlGaAslGaAs HEMT are shown. In the linear plot Brookes [ 121 assumed a constant transconductance g m , whereas, the other plot depends on the measured values of g m . However, both of the schemes failed to explain the experimental data [12]. In Table 11, the calculated equivalent noise properties, such as minimum noise temperature, Tmin, optimum external source impedance, Z,,o,t = R,,opt + j . Xs,opt, and equivalent noise conductance gn are shown and compared to the experimental data reported by Weinreb et al. [29] for a 0.25 x 75 pin2 AlGaAslGaAs HEMT at room temperature operated at 8.5 GHz.

In Fig. 4, the minimum noise figure Fmin and temper- ature Tmin, are plotted as a function of frequency for a 0.25 x 300 pm2 AlGaAslGaAs HEMT (device A, Nd = 1 x l0ls ~ m - ~ , d d = 450 A‘and d; = 40 A), 0.25 x 200 pm2 I-HEMT (device B, Nd = 1.1 x 1018cm-3, the GaAs layer thickness d = 200 A), 0.35 x 200pm2 P-HEMT (device C,

2.5

Q V - 2.0

LE

a 2 1.5

G U 5 ; 1.0

000 - Y U

; 800 b

d

m 1

600 E 400

0 z

E 200 ;

E 5

0

I IO 100

Frequency {CHz)

Fig. 4. Minimum noise figure Fnlin (dB) and minimum noise tempera- ture Tmin are plotted as a function of frequency for a 0.25 x 300pm2 AlGaAslGuAs HEMT (device A), 0.25 x 2 0 0 p m 2 I-HEMT (device B), 0.35 x 200pm’ P-HEMT (device C) and 0.1 x 50pm2 P-HEMT (device D). The solid ( Fmin) and dashed (Tmin) lines represent the theoretical results from this model. The experimental data for device A (diamond) [l], device C (square) 151, and device D (dot) [8] are also shown in the graph.

Nd = 1 x 10l8 cmP3, d d = 420 A and d; = 20 A) and 0.1 x 50 pm2 P-HEMT (device D, Nd = 1 x 10l8 cmP3, d d = 280 8, and d , = 20 A). Both Fmin and Tmin increase with increasing frequency for all devices. The solid (Fmin) and dashed (T&) lines represent the theoretical results from this model. The experimental data for device A (diamond) [l], device C (square) [5] and device D (dot) [8] are also shown in the graph. The theoretical calculation shows that the noise performance of P-HEMT’s are superior than that of conventional and inverted HEMT’s. As observed, the calculated noise properties show an excellent agreement with experimental data over a frequency range 8-60 GHz.

Fig. 5 shows the minimum noise temperature Tmin (K) as a function of gate length for conventional AlGaAslGaAs HEMT, GaAslAlGaAs I-HEMT and P-HEMT’s with dif- ferent QW width at 30 GHz operation. The gate width is assumed to be 200 pm. As observed, the noise temperature increases with increasing gate length. In the short gate length region, the inverted HEMT’s exhibit a comparable Tmin to that of normal and P-HEMT’s. Also, the noise performance of I-HEMT devices is less sensitive to the variation of the gate length than that of a normal HEMT, which may be due to the enhancement of device transconductance [ 101, [ 113, [28]. For a given gate length, the conventional HEMT exhibits a higher noise temperature than that of I-HEMT and P-HEMT’s. This can be explained in terms of the behavior of gm and f~ with .varying gate length [ 181. Both gm and f~ decrease with increasing gate length [ 181. However, AlGaAslGaAs HEMT is much sensitive to the gate length variation for both gm and f ~ . This results in a higher Tmin for AlGaAsIGaAs HEMT’s than that of PHEMT’s with varying gate length. Also PHEMT with wider QW width are less sensitive to gate length variation than the devices having smaller QW width [30]. This is mainly due to the decrease of gm [ 181 and increase in f~ with increasing &W width in PHEMT’s. The effective channel

ANWAR AND LIU: A NOISE MODEL FOR HIGH ELECTRON MOBILITY TRANS1

4000.

1 -HEMT

L

I T I

0.0 0.2 0.4 0.6 0.8 1 .o Gate Length ( p m )

Fig. 5. length.

Minimum noise temperature Tmin is plotted as a function of gate

width Ad increases for a wider QW resulting in a lower C,, and, therefore, to a higher f~ [30]. It should be mentioned that the unity current gain cut-off frequency f~ of P-HEMT is much less sensitive to the increasing gate length than that of a normal HEMT [ 181.

Fig. 6 shows the general behavior of the minimum noise figure Fmin (dB) as function of operating frequency and doped epilayer thickness for a 0.25 x 200pm2 P-HEMT. The minimum noise figure exhibits a minimum value around a doped epilayer thickness of 300 A. Fmin is large for a device with thin epilayer thickness. This may be due to the presence of the two barriers which reduces the effect of the conduction band discontinuity (difference of the conduction band discontinuity at the first heterointerface, AE,1 and at the second heterointerface, AECz) on the threshold voltage of the device. This shows that noise properties of P-HEMT’s are more sensitive to the variation of epilayer thickness that of normal and I-HEMT’s. Moreover, the present model finds that the minimum noise figure Fmin and minimum noise temperature Tmin are a weak function of donor concentration NO for all devices, which has been observed by Anwar et al. [14].

IV. CONCLUSION A model describing the noise properties for different

HEMT structures is presented. A self-consistent solution of Schrodinger and Poisson’s equations is used to determine the device noise properties. All the noise sources and their correlation coefficient in the channel are taken into account. The results show that P-HEMT’s exhibit a better noise performance than that of conventional and inverted HEMT’s. The present model also predicts that the noise performance of I-HEMT devices is comparable to or even better than that of conventional HEMT’s. The calculated noise properties are compared to experimental data for different devices and the match between theoretical results and experimental data are remarkable.

STORS 209 1

0 25x200 pm2 P-HEMT. 293K v*< = 2.0v A

Fig. 6. and doped epilayer thickness.

Minimum noise figure Fmi,, is plotted as a function of frequency

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A. F. M. Anwar was born in Jessore, Bangladesh. He received the B.S. degree in 1982 and the M.S. degree in 1984, both in electrical and electronic engineering from the Bangladesh University of En- gineering and Technology, Dhaka, Bangladesh. He received the Ph.D. degree in electrical engineering from Clarkson University, Potsdam, NY, in 1988.

He is now an Associate Professor in the Depart- ment of Electrical and Systems Engineering at the University of Connecticut, Storrs, CT. His research interests include transport in lower dimensional de-

vices and study of noise in HEMT’s, HBT’s, QW lasers, and other quantum size effect devices. He is also active in the growth and fabrication of Type I1 GaInSbflnAs-based quantum well far infrared detectors.

Kuo-Wei Liu received the B.S.E.E. from the Ocean University, Keelung, Taiwan, in 1986, the M.S.E.E. from Syracuse University, Syracuse, NY, in 1990, and the Ph.D. in electrical engineering from the University of Connecticut, Storrs, CT, in 1994. His Ph.D. dissertation was on the study of noise in HEMT’s.

He 15 presently a research engineer in the Op- toelectronics and Systems Laboratories, Industnal Technology Research Institute (ITN), Chutung, Hsinchu, Taiwan, ROC. His research interests

include device simulation, fabrication and noise performance of MESFET’s, HEMT’s, HBT’s, and Lasers.