Current-voltage characteristics of submicrom GaAs MESFETs with nonuniform channel doping profiles

Solid-State Efecrronics Vol. 35, No. 11, pp. 163~1644, 1992 Printed in Great Britain. All rights reserved

0038-I101/92 $5.00+ 0.00 Copyright 0 1992Pergamon Press Ltd

CURRENT-VOLTAGE CHARACTERISTICS OF SUBMICROM GaAs MESFETs WITH NONUNIFORM CHANNEL DOPING PROFILES Ko-MING

!&III-I? and D. P. KLEMER

NSF/Center for Advanced Electron Devices and Systems, Department of Electrical Engineering, University of Arlington, Arlington, TX 76019, U.S.A. and

Electrical Engineering Department,

J. J. LIOU University of Central Florida, Orlando, FL 32618, U.S.A.

(Received 25 January

1992; in revised form

I I April 1992)

Abstract-We present a physics-based model for GaAs metal semiconductor field-effect transistors (MESFETs). The present model improves an existing model by allowing the possibility that the electric field near the source region can exceed a critical field, which is likely in an advanced submicrom MESFET operated in the quasi-saturation or saturation region. Furthermore, a realistic and nonuniform channel doping profile was considered in our calculations. Experimental data measured from a low-noise, ion-implanted MESFET are included in support of the model. The effects of different doping profiles and velocity profiles in the channel on the MESFET current-voltage characteristics were also investigated.

have been presented only for the simplified case where

1. INTRODUCIION

The GaAs metal-semiconductor field effect transistor (MESFET) has been used in microwave applications for decades because of its relatively simple processing and its high-speed and low-noise performance. To achieve fast and optimum circuit design, an accurate computer-aided design tool is indispensable. Several numerical MESFET models which solve the two-dimensional Poisson equation have been reported[l-31. It is obvious that a reliable analytical model is more desirable since it does not require extensive computation time and can provide physical insight into the MESFET behavior. Unfortunately, most analytical models were developed based on a number of oversimplified assumptions. For instance, the two-piece velocity-field equation[4] and the assumption that voltage drop along the channel is negligible are often employed to develop analytical models. Recently, Chang and Day[S] have overcome these shortcomings by using a more accurate velocityfield equation[6] and by solving the two-dimensional Poisson equation analytically. They, however, assumed that the field at the source side of the MESFET channel is below a critical field. Furthermore, although their model takes into account the nonuniform channel doping concentration, calculations tPresent address: Electrical and Computer Engineering Department, Mercer University, Macon, GA 31207, U.S.A.

the doping is uniform throughout the channel. This paper improves the model by Chang and Day[S] by allowing the possibility that the electric field in the channel near the source can exceed a critical field, which is likely in a submicrom MESFET. In addition, we calculate the I-V characteristics of GaAs MESFETs having different channel doping profiles and different velocity profiles. Measurements obtained from a submicrom, ion-implanted MESFET are also included to support the model. 2. MODEL DEVELOPMENT

The model developed here follows the approach used by Chang and Day[S]. The electron drift velocity V, as a function of the electric field in GaAs can be expressed as[6] ud =

@/{

1 +

U@

-

‘%)[@

-

EC,)/Ec12}o~5

tl)

where pL is the low-field mobility, E is the electric field, U is the step function, EC = us/p, (v, is the saturation drift velocity for GaAs), and E,, is the critical field E, = OS& + (E: - 4Ef)‘.‘]

(2)

where ET is the threshold field at which the electron velocity attains the maximum value. ET can be calculated by taking the first derivative of (1) with respect to E and setting this derivation equal to zero at E=E,.

1639

Ko-MING SHIHet al.

1640

buffer layer and semi-insulating substrate Fig. 1. Schematic diagram of a GaAs MESFET indicating the channel length L, channel width Z, and channel thickness a.

Figure 1 shows the structure of a GaAs MESFET. The channel under the gate can in general be divided into L,, Lb, and L2 (Fig. 1), depending upon the magnitude of the electric field, and L, is the region between the gate and drain. L, and Lb are the lowfield regions; the electric field is below E, for 0 < x < L, and the electric field is between E, and ET for L, < x < L, + L,. L2 and L, are the high-field regions in which the electric field exceeds ET. Depending on the applied drain and gate voltages, Z-V characteristics of the MESFET can be divided into three regions: the linear region, knee region (or quasi-saturation region), and saturation region. The corresponding electric-field regions under the gate are shown in Fig. 2. 2.1. Linear region When the applied drain voltage Vn is sufficiently low such that EBs (the electric field under the gate at the source end) and EBd (the electric field under the gate at the drain end) are both smaller than E,, the channel is described by L, (Fig. 2), and the behavior of the MESFET is similar to that of a resistor. Including the drain and source resistances, R, and R,, the drain current In is given by[5] Zn = Zc + ]I’, - Z&K, +

WIIRP

(3)

where Zc is the channel current and RP is the parallel resistance associated with the buffer layer. Zc can be calculated from hL Nnth)h L = (q2Z/ZcQ s ho 1

1

where h is the channel height (Fig. 1), h, = h(x = 0), h, = h(x = L), Z is the gate width, L is gate

length, Nn is the channel doping concentration, L, is the dielectric permittivity, and p(y) = Q/E is the position-dependent electron mobility. 2.2. Knee region As the drain voltage increases, the field under the channel is not entirely below E,,. Based on the magnitude of EBs (the electric field under the channel at the source end), we can divide this situation into two cases as shown in Fig. 2: Case K-l, with EGa< E,,, has two regions L, and L,; and Case K-2, with EBs> E,, has only Lb region. Note that Chang and Day considered only Case K-l. 2.2.1. Case K-l. For this case, the channel consists of two regions: the region 0 < x < La with E below E,, and the region L, < x < L with E between E, and ET. L, can be obtained from (4) by replacing hL with h, = h(x = L,) (Fig. 1) h. N,(h)h L, = (q2Z/Zcc,) s ho X [S

1

aM_di4_ddy h

a.

The length Lb can be obtained from integrating Poisson equation from x = L, to x = L

(3

the

.k Lb = [q/+%(1

+

c2)1 N,(h) s h.

xh{l+[(l+~~)~~-c~]~~~}dh

(6)

where c = EC/E0 and B=qZE,

’ W_Y)~Y) sh

dylk

(7)

The channel current Zc can be calculated from the equation L = L, + L,.

1641

MESFETs with nonuniform doping profiles

Linear

region Source

iFy,,,q

Drain

Egd Egs < E8d ’ E. Knee region (K-1)

case

(K-2) case

Source :*A

Drain

Ecl

Source E,_,_4

Drain

lzs

Egd

Egd

Egs < E, < E,, < E, Saturation

region (S-1)

Source

case

(S-2)

Gate \\\\\\\\\\\’

E gs < E,
case

Drain

E, < E,, < E, < Egd

gd

Fig. 2. Definition of the lengths in the channel applicable to each operation region.

2.2.2. Case K-2. For this case Eps> E,, and the entire channel region is denoted as Lb (L = Lb). The L-V relation under this condition can be described using (6) by replacing h, with h, hL Lb = [qlc,J%(l + c2)1 N,(h) I ho x h { 1 + [(l + cz)/7’ - c*]“~‘}dh. (8) 2.3. Saturation region If the drain voltage is increased further, the electric field EBdin the channel at the drain side can become larger than ET. The operation can be divided into two cases: Case S-l, with Em< E,, and L,, Lb, and L2

regions; and Case S-2, with Ep > E,, and only Lb and L2 regions. Again, only Case S-l was considered in [6]. 2.3.1. Case S-l. Equation (5) still applies to the regionOcx~L,.FortheRegionL,
s h

4 =

[qlQo(l

+

c*)l

N,(h)

ha

x h(1 + [(l + c*)B’ - c*l”.‘}dh

(9)

where hT = h(x = L, + Lb). For the high-field region, x > L, + Lb, the lengths L2 and L, can be obtained

Ko-MING

1642

SHIHet al.

by using the boundary condition of E(L,) = &[5]. Once L, is found, then the current can be calculated from L=L,+L,+L,.

10’8 ‘m

k

(10) E ._ !! E 8

2.3.2. Case S-2. For the case Em > E,,, only two regions Lb and L2 exist, and L = Lb + Lz. The lower integration limit of (9) needs to be replaced by h,

z L .E k

hr Lb

=

~ql&d

+

C*)l

N,(h)

s ho xh{l The

other

equations

+[(l

+~*)/3*-c2]~~~}dh.

in Case S-l

given

\ 7 ‘,.\ ’ .\ ‘1 ‘\A--‘\

‘O”

Original C-V data

Gaussian

fit lo profile

‘\ .\,

‘1,

Original data point shifted by 141 angstroms

n

0”

(11)

are still

10’6

applicable here.

1

I

0

0.05

I

I

I

0.10

0.15

Profile depth (microns) 3. ILLUSTRATION

We first compare the model against experimental data measured from a typical Texas Instruments low-noise GaAs MESFET. The device has a gate length 0.5 pm, gate width 300pm, channel height 0.35 pm, and channel implant dose of 1.138 x lo’* cm-*. The velocity profile used has a low-field mobility of 4000 cm2/s, a threshold field of 4200 V/ cm, and a saturation drift velocity of 8 x 106cm/s. The resistances associated with the MESFET were estimated as R, = 4.8 R, RD = 4.77 R, and R, = 4000 iI from dc measurements. The doping profile in the ion-implanted channel is determined by the C-l/ measurement, as shown with the dashed lines in Fig. 3. We curve-fit the data and obtained the Gaussian distribution donor doping profile as (shown with a solid-line in Fig. 3) N,,b)

= 10” exp{ -0.5[0,

+ 1.4 x 1016)/ 3.7 x 10-612). (12)

The black squares show the original C-l/data shifted by 141 angstroms, which was necessary to achieve a good fit between measured and computed results.

Fig. 3. Channel doping profile obtained from C-V measurement (dashed lines), from the Gaussian fit to the measurement (solid line), and from measurement data shifted by 141A.

Comparison of the experimental data and model predictions for the MESFET is given in Fig. 4(a) and (b). The drain current and the transconductance g, calculated as a function of gate voltage and drain voltage are plotted in Figs 5 and 6, respectively. Next, the effects of different channel doping profiles and different velocity profiles on the Z-V characteristics of a MESFET having a 0.42 pm gate length and 1 mm gate width are investigated. For the total charge constrained to be constant in the channel, the 1-V characteristics calculated for four different channel doping profiles (three constant and one Gaussian profiles) are shown in Fig. 7(a) and (b). Since the total charge is conserved, the active channel thickness will decrease as the peak doping concentration decreases [Fig. 7(a)], as would be expected during an implant activation. As shown in Fig. 7(b), the drain saturation current decreases as the channel thickness decreases corresponding to a reduced knee

(4 lb)

0.04

0.05 Vdz3

* Measurement data

r

* 3

0.04

1

o.03

pP-*-’

vg-

o.25

I

/ /* .E

E n

0.01

*

Measurement

data

0

1

2

3

4

5

Drain voltage (V) Fig. 4. Comparison of the model (solid line) and measurement (asterisks) of (a) drain current versus gate voltage at a fixed drain voltage; and (b) drain current vs drain voltage for three different gate voltages.

MESFETs with nonuniform doping profiles

1643

0.025

Id

Fig. 5. Drain current as a function of gate voltage and drain voltage.

voltage for the device. To illustrate the dependence of Z-V characteristics on the velocity profile, we consider four different velocity profiles described by the low-field mobility and the threshold field. Note that velocity profiles a, b, and c [Fig. 8(a)] have the same low-field mobility but different threshold fields. This is because the threshold field is a function of the low-field mobility as well as the saturation

velocity, and different saturation velocities have been used for the profiles. The corresponding drain current-voltage relations are given in Fig. 8(b). The results are consistent with the physics that if the low-field mobility pL remains constant, increasing the threshold field Er will increase the drift velocity, thus resulting in a higher drain saturation current.

0.06

c.m

Fig. 6. Transconductance as a function of gate voltage and drain voltage.

Ko-MING SHIH et al.

1644

Low field mobility

(a) 8 z E _o

17.5

Threshold

field

4

r\ 17.0

._s E E %

16.5

z

1

16.0

-

15.5

-

F ‘5

0”

15.00

I

I

0.2

0.4

1 0.6

Depth, Y,WU 0 Doping concentrarion (cm-9

Channel

2.1~10’6

1.642

23

1.05.10’6

0.366

2.1.1017

43

I

I

I

I

10

15

20

25

(b)

a

0.350

b

0.164

I

I 30

Electric field (kV)

thickness (urn)

13

I

5

:

z E k a .G

!!

1

2 0.4

0

3 4

2

1

3

Drain voltage

0.3

4

5

(V)

Fig. 8. (a) Four different velocity-field profiles used in calculations. (b) I-V characteristics corresponding to the

0.2

velocity profiles in (a) with gate voltage equals to 0 V and a uniform channel doping concentration of 6.5 x lOI6cn?.

0

0.1

I 0

1

2

3

Drain voltage

4

5

(V)

Fig. 7. (a) Four different channel doping profiles with total charge constrained to 3.87 x 10’2cm-2. (b) I-V characteristics corresponding to the profiles in (a) with gate voltage equals to OV.

that, for the total charge in the channel constrained to a constant, a lower peak doping concentration in the channel will yield a larger drain saturation current. We also show that a velocity-field profile having a larger threshold field and larger lowfield mobility can also improve the MESFET performance. REFERENCES

4. CONCLUSION

An analytical d.c. model useful for the computeraided analysis and design of GaAs MESFETs has been developed. The present model allows for arbitrary channel doping profiles and employs a realistic velocity-field relationship. Furthermore, it includes essential physical and process-related parameters and does not rely on fitting parameters. The model compares favorably with data measured from a TI submicrom GaAs MESFET. Our results suggest

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3. B. Himsworth, Solid-St. Electron. 15,1353 (1972). 4. R. A. Pucel, H. A. Haus and H. Staz, Adu Electron. Electron Phys. 38, 195 (1975). 5. C.-S. Chang and D.-Y. Day, IEEE Trans. Electron Devices 36, 269 (1989).

6. C.-S. Chang and H. R. Fetterman, Solid-St. Electron. 29, 1295 (1986).