Characteristics of the GaAs monolayer-doped structure and its applications for power field-effect transistor fabrication

Materials Science and Engineering, B 7 ( 1991 ) 275- 281

275

Characteristics of the GaAs Monolayer-doped Structure and Its Applications for Power Field-effect Transistor Fabrication WEN-CHAU LIU, CHUNG-YIH SUN and WEN-SHIUNG LOUR

Department of Electrical Engineering, National Cheng Kung University, Tainan (Taiwan) (Received June 14, 1990)

Abstract

A n ultimate artificial doping technique, to give a monolayer-doped (delta-doped) structure has been studied in this paper. First, two different methods, i.e., the Airy function and a modified analysis model, were used to simulate the theoretical properties of the monolayer-doped structure. By considering the free-carrier effect in each subband, the theoretical values of the modified-analysis method are consistent with the experimental results reported by other researchers. On the basis of theoretical analysis, a field effect transistor (FET) with a monolayer-doped channel has been fabricated successfully. Because of the high gate breakdown voltage and high output drain current capability, the monolayer-doped FET studied is suitable for power applications. 1. Introduction

For semiconductor devices, the scaling down of structures and the doping profile (spatial width) is an important concept in improving the device performance. The ultimate physical limit of the doping profile is that all doping impurities are localized within an atomic monolayer of the host semiconductor. A new artificial technology, monolayer doping or delta doping, to achieve this novel concept has been developed successfully over the past few years [1-6]. The monolayerdoping technique introduces some advantages, e.g. higher two-dimensional (2D) doping density and higher gate breakdown voltage, rather than the famous modulation-doped structure. Thus it has been used to fabricate GaAs field effect transitors (FETs) widely [7-9]. In this paper, the quantized subband properties of the monolayerdoped structure were analyzed and compared using an Airy function method [10] and a modified-analysis method [7]. Then a high breakdown

voltage power FET was fabricated successfully based on the monolayer-doped technique. 2. Theoretical analysis

The term monolayer doping means, strictly speaking, the confinement of dopant atoms within a 2D plane one atomic layer thick. A Dirac delta function can be used to describe the doping profile of a GaAs monolayer-doped structure by using silicon donors or beryllium acceptors. The basic concept of silicon-monolayer-doped GaAs is illustrated in Fig. 1. The silicon dopant atoms are located in an atomic monolayer of the (100)oriented GaAs host crystal, and the ionized siftcon donors of density ND2D provide a continuous positive sheet of charges [8]. Owing to the electrostatic attraction, the electrons remain close to their parent ionized donors and form a quasitwo-dimensional electron gas (2DEG) in the V-shaped potential well produced by the positive (a) GROJP ,,, ATOMS &

~ v A T ~ i

x

~

x

x

x

x

x

•

×

x

×

x

x

x

x

x

•

x

x

x

×

•

x

x

x

x

x

x

x

~>a~crl~ •

x

• Si

(b)

. . . . . . . . . . . . . . . . . . . . . . .

F~-

Fig. 1. (a) Schematic illustration of a GaAs lattice with silicon impurities localized in one monolayer. (b) The corresponding energy band diagram of monolayer-doped GaAs with the three lowest subband populated. Elsevier Sequoia/Printed in The Netherlands

276

sheet of charges [8]. In the narrow potential wells, the electron energies for perpendicular transport to the (100) growth surface are quantized into 2D subbands. In the following, we shall discuss the 2D electronic subband properties using an Airy function method [10] and a modified-analysis model.

E1

I I!

f

2.1. Airy function method By transforming the Schr6dinger equation into the Airy differential equation [10-12], the precise computation of eigenstate energies in a V-shaped potential well can be obtained. Using appropriate boundary conditions and an asymptotic expansion for the zeros of the Airy function and its derivative, the quantized subband energies can be obtained as follows:

E,,=(~)3213(n+~)213q2hn2DE°12/ l 3e(m,)l2 (1)

.z

Fig. 2. Schematic polygonal shape of the conduction band of a monolayer-doped semiconductor.

is matched to the width of the potential well according to (n+I)4~2UB -

2e

1

2--E, q nZDEO

n=0,1,2,...

and the subband energies are

[ e(m*)'/2J

En=(4~)2 - 2/3(n + 1)2/3 Jq2hnzDE~{ 2'~ where q is the elementary charge, h in Plank's constant, rtZDEGis 2D carrier concentration, m* is the electron effective mass and e is the semiconductor permittivity. Considering the residual acceptors influence, one obtains

by n+l

2.2. Modified-analysis method A modified-analysis method was proposed to calculate the subband structure of a V-shaped potential well [7]. The shape of the bottom of the conduction band in the potential well is obtained from Poisson's equation as illustrated in Fig. 2:

dE_ q dz

--

2

2e

rt2DEG

for z > 0

(3)

The electron de Broglie wavelength h

2d~ -(2m.E)l12

2

h

IZ

lz ''/2

(7)

(2)

where NDm is the 2D monolayer-doped density and NA 2D is the effective 2D background impurity density and gives qNA2D=(2eNAEg) 1/2 with N A and E g being the residual acceptor concentration and band gap energy respectively. To obtain the exact (non-asymptotic) subband energies the term n+½ in eqn. (1) has to be replaced by 0.437, 1.517, 2.484 and 3.508 for n = 0, 1, 2 and 3 respectively [10].

----

(6)

Thus the real-space extent of subbands is given

z.rt2DEG = ND 2D -- 2NA 2D

(5)

The wavefunctions are taken to have a sinusoidal shape as shown in Fig. 2. For more precise calculation, however, the band bending of the conduction band due to free carriers should be taken into account. Thus the energies of the bottom of the excited subbands decreases compared with eqn. (6). The band bending is assumed to occur at the discrete point z,,/2, where the wavefunction intersects the bottom of the conduction band. Therefore the GaAs conduction band is a polygonal curve, and the subband energies compared with eqn. (6) can be expressed as

E=E.-I+~ ND 21)for z,, i<~z<~z,,

where q is the elementary charge, h is Planck's

(8)

where nj is the free-carrier density in the jth subband and can be expressed as

nj=D f

(4)

E ill. (Z--Zn 1) 1=[)

1 +exp[

(Ej2eF) kT

dE

(9)

J:i

where D and E v are the 2D density of state and

277 ~600 >~

Ours

vE_500 IM

Airy EF

.....

NA = lxlO ~Scm-3

300"K

......... .......

E~o-~

,

,2 "-~-

,'

N "-c

/'

/"

~

i300-

E~ Eio

u'I

~¢~

I00-

0

. """

,"" l"" .'"

"

.- "

E4

,, .

300-

~

250-

~

. ~

.......

LOW Temp. - 300~K ..... Airy Z,

Z3 Z4

200-

,E1

- - - 7- " " "

1,(~2

3x10 n

NA=1X1015cm-3 350-- .......

tl//

400-

400-

~

1,(~3

zo ' 11 . . . . . . 3x10

2D DOPING CONCENTRATION N~°(crn-2)

12 10

. . . . . . .

2D DOPING CONCENTRATION N~O(cm-2)

Fig. 3. Subband energies E, vs. 2D doping concentration with a background acceptor concentration N A of 1 x lO Ls c m - 3 at 300 K.

Fig. 5. The real-space width zi of electron wavefunctions in the V-shaped potential well as a function of 2D doping concentration.

600 ~E 500L~-

Ours Airy

.........

EF

.

.

NA=lXlC~5cnf 3 .

.

.

.

Low Temp.

/'

,

.

400rr" 300" hi 200-

?

, :

k

tt) 100-

o

ld~

3xd'

1:

2D DOPING CONCENTRATION N~D(crn-2)

Fig. 4. Subband energies E i vs. 2D doping concentration with a background acceptor concentration NA of 1 X 10 ~5 cm 3 at a low temperature.

the Fermi energy level respectively. By combining eqns. (7) and (8), we can obtain the modified subband energies equation E3/2+[~-~---

ND2D- ~ nj

-Ei_ 1

E 1/2

/ =0

2e

N°2O- ~

n/ = 0

(10)

j =1)

Consequently, the monolayer-doped subband properties can be obtained by calculating and analysing the eqns. (7), (9) and (10) successively.

2.3. Computed results and analysis The relations between the 2D subband energies E~ and the 2D doping concentration ND2Dare shown in Figs. 3 and 4 at 300 K and at a low temperature respectively. The background acceptor concentration N A is 1 x 10' 5 cm- 3. Obviously,

the E i curves of the Airy function increase more rapidly than our data (the modified method) with increasing 2D doping concentration ND2D. From eqns. (1) and (2), the Airy function curves vary as (No2°) 2/3 while our data are reduced significantly owing to the consideration of free carriers in each 2D subband. In our curves the beginning of population of a specific subband is indicated by E,0. From Figs. 3 and 4, it is found that six subbands are already populated when ND2D is 1 x 1013 cm-2. Figure 4 shows the same characteristics at a low temperature. The Airy function curves provide the same data as Figs. 3 and 4 because of the temperature-independent characteristics as seen in eqn. (5). Yet in our model, the E i curves at low temperature are slightly lower than those at 300 K. At low temperatures eqn. (9) will be simplified to

ny=D(EF-E,.)

(11)

Because of the reduction in thermal energy, the probability that free carriers occupy the higher excited subbands is expected to be lower. Thus their occupied subband energy is lower than that at 300 K. From eqn. (7), the real-space width xi of 2D subbands will decrease with increasing 2D subband energy E~, i.e. with increasing 2D doping concentration in eqn. (6). Figure 5 illustrates the dependence of 2D doping concentration on the real-space widths x i of 2D subbands at a background acceptor concentration N A of 1 x 10 t5 c m -3. However, the decreasing trend is sharp initially, especially for Airy function curves, and then varies slowly or saturates for higher No 2D. In our calculated curves, the real-space width of a

278

specific 2D subband at 300 K is larger than that at a low temperature. This arises because electrons will occupy a higher energy subband when the environmental thermal energy is increased. T h e population n~ of 2D subbands as a func, tion of AID"~D is depicted in Fig. 6. T h e relations between ni and N~ :D are described in eqns. (9) and (11). T h e inset illustrates the electron concentration no and n~ in the lowest and the first excited subband respectively. As expected, the lowest subband is populated most strongly. At a N D 2D of 4.1 x l 0 1 2 c m - 2 for example, about 63.5% and 53.9% of all carriers are in the lowest subband at 300 K and at a low temperature. From Fig. 6, because of the thermal energy, it is clear that the population in each excited subband at 300 K appears earlier than that at a low temperature. In Table 1 we compare our calculated concentrations n, in the individual subbands with the experimental results obtained by Z r e n n e r et al. [13]. Their data were determined by Shubnikov-de Haas measurements. T h e y found that the lowest subband and the first three excited subband concentrations were no = 2.61 x 10~2 cm 2 n = 9 . 7 x 1 0 ~ cm --~, n~=4.1 x lO 11 cm 2

'~E 6 -o

"~- 5-

i

.m LOW Temp.

- -

300"K

......

3

I

,N,~= 1 xl015cm -3

%

/i

/ ,'1 [

,'"~

,"//

n~

:

2D DOPING CONCENTRATION N2D(cm-2) Fig. 6. T h e c a r r i e r p o p u l a t i o n in the s u b b a n d s as a f u n c t i o n of 2 D d o p i n g c o n c e n t r a t i o n . T h e i n s e t s h o w s the c a r r i e r c o n c e n t r a t i o n in the r e s p e c t i v e s u b b a n d w h e r e n : ~ c , = Z~n,.

TABLE 1

and n 3 = 1.1 x 101L c m - : respectively at a given ND" = 4.1 x 1012 cm -. Higher subband populations were not resolved in the measurements because of the long period of Shubnikov-de Haas oscillations from weakly occupied subbands. Our calculated subband concentrations for N A = 1 x 1015 cm 3 and ND2D=4.1 x 1() I-~ c m - : are n 0 = 2 . 5 8 × 1 0 j2 cm 2 n =8.2×10~1 cm -~n ~ = 3 . 9 x 10 ~ cm -2 and n3= 1.7x 1() ~ cm --~ at 300 K. T h e relative deviation values A n /il~~I'l) 2t> are also presented in Table 1 for comparison. Owing to the extremely small deviation, from 3.6% to 0.48%, it is clear that our calculated data provide good agreement with the experimental results. T h e influence of background acceptor concentration N A on the 2D subband energy E, at 300 K and at a low temperature are shown in Figs. 7 and 8 respectively. It is known that the Airy function curves slightly decrease with increasing N u 2D as seen in eqns. (5) and (6). However, in our calculated model the E, curves move to a slightly higher level when N~ is increased. At a higher background acceptor concentration, the subband potential well becomes narrower and gives a larger subband separation [7]. Consequently, the E, curves, in our model, are elevated by the increase in NA. T h e influence of residual acceptot concentration N A on the population n, of 2D subbands is illustrated in Fig. 9. Obviously, n~ decreases with increasing NA, especially for higher excited subbands. This is due to the reduction in net 2D carrier concentration n:DEO when N A is increased. Furthermore, only a small fraction of n2DEO are populated in higher excited subbands. Thus the decreasing trend is more apparent for higher excited subbands, e.g. n 5 and n~, can be neglected for the specific N A above 4x1()~ 5 c m 3 a n d 2 x 1 0 ' ~ cm 3 respectively at 300 K. At a low temperature, e v e n N A is greater t h a n 8 x l ( ) ~4cm ~ o r 2 x l 0 l~cm 3, a n d n 5 o r n 6 respectively can be neglected.

Comparison of calculated electron concentrations n~in the four lowest subbands

n,[131 (ND 2D = 4 . 1 x 10 j2 c m

(cm -2)

O u r results ( N A = 1 x 10 I5 c m

~)

2) n, at 3(X) K (cm 2)

A n i / ND 2D (%)

n i at a low temperature

(cm ~') n, nI n: n~

2.61 x 1() Jz 9.7 x 10 II 4.1 x l 0 II l . l x l O II

2.58 x 1() I~ 8.2 x 1() II 3 . 9 x IO LI 1 . 7 x 1 ( ) LI

0.73 3.6 [).48 1.4

2.15 1.07 5.25 2.31

x x x x

l(P 2 I'(P I 10 Ij 1() ~]

279 4001

E3 E~ E; E~ J__~ . . . .

...................

D

: EEE L6 5 4 :

G

\\\\\\ L/I-

I:..',.;'i)?.":3:1\ \ \ N . X N X .

.......................

200+_- ............. OJ

,2DEG _/____

-r--2

•

. . . . . . . .

t /

-4

E0 E1 E2

I

J

tn

100"I-- . . . . . . . . . . . . . . . . . . . . . . . ~Ours - "1 Airy . . . . . . . .

£

'o/EF

,--7,

S

_

~

\\\\\\~

L

k .........

-300"K

N~= 5xlOl2cm -2

,

id z'

\\\\\\\

Delta-Doped

I - -

.....

/

....... Monolayer

Undoped

p'- GaAs

.......

1015 BACKGROUND CONCENTRATION

Id 6 NA (cm-3)

Fig. 7. The influence of background acceptor concentration on the subband energies E i at 300 K.

Semi-lnsulating GoAs Substrate

Fig. 10. Schematicillustrationof the monolayer-dopedFET structure studied.

400

,,r 300250- . . . . . . . . . . i

200 =

Z~

150"~~E\E>E,

EO..~

1oo£

~_

Ours - 50- Airy ,Jl~=5xlu2cm -2 .ao Low Temp . EF . . . . . . . . . . . . . 0 . . . . . . . . i ' ' ' , .

10~

.

.

.

1015

~6

BACKGROUND CONCENTRATION NA(cm'3)

Fig. 8. The influence of background acceptor concentration on the subband energies E~at a low temperature.

'E u 3-

..................

v

0n.

Low Ternp

300"K

.........

N~DD=5XlJ2cm_2

......

k.)

described elsewhere [14, 15]. The substrate temperature was kept at 550 °C to obtain the monolayer-doped profile. Figure 10 shows the cross-sectional structure of the studied device. First, a 0,5/~m undoped GaAs buffer layer was grown directly. Then the gallium shutter was closed while the silicon shutter was opened for 5 min with a constant silicon flux intensity ( TSi = 1000 ° C ) . This introduced a silicon-atomicplanar-doped GaAs layer with a sheet doping concentration of 5 x 1012 cm -2. Finally, a 300 A undoped GaAs layer was grown which gave a narrow distance (300 A) between the 2 D E G channel and the gate metal. A u - G e was employed as the ohmic contact metal for the source and the drain regions and then sintered for 30 s at 450 °C. Aluminium was applied as the Schottky barrier gate on the surface. Because of the limitation of the laboratory facilities, a gate dimension of 5 /~m x 100 /~m was used in this study.

< en t13

N a

4. Results and discussion 0

lo"

'

. . . . . . .

,~'

BACKGROUND CONCENTRATION

,0~

NA(C m-3 )

Fig. 9. The dependence of subband population ni on the background acceptor concentration.

3. Experimental details The monolayer-doped F E T studied was grown by molecular beam epitaxy on a (100)oriented chromium-doped GaAs substrate. The details of the substrate preparation have been

The measured current-voltage characteristics at 300 K between gate and drain is shown in Fig. 11. The forward cut-in voltage is about 0.7 V whereas the reverse breakdown voltage exceeds 15 V. Obviously, the gate breakdown voltage of the monolayer-doped F E T studied is much higher than a conventional metal-semiconductor F E T with the same doping level in active channel. Therefore it provides a good potential for power applications. The output drain current-voltage characteristics of the device studied are depicted in Fig. 12 for depletion-type operation. The

280 50 M426C 300 "K

>

>-

~20

~_~ 40 x-~'~-~'~Z

E

± T

~0~

5x100 um 2

z LIJ

100t

z LLI~

z~30 oE ~E

--5Vdiv-{

I ] I F2Vdiv--

er E

80~E

Zt~

Fig. 11. The gate-to-drain l-V characteristics measured at room temperature.

6 0 zoE~

°l

4o g 2O z

16 1/-

M 426C 300'K VGs=- .

E

12 Z

Z~

I

I

I

-i.0 -1.s -2.0 APPLIED GATE

I

I

Q

-2.s -3.0 -3'.5 VOLTAGE VG (v)

5. Conclusions

2 0

_ ols

Fig. 13. The influence of the applied gate voltage Vo on the normalized transconductance gm and drain saturation current density los.

10

,," 8 mr" u 6 z z, er

]

0;

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 z.O /.5 5.0 DRAIN-SOURCE

VOLTAGE

VDs(V)

Fig. 12. Output characteristics of a depletion-mode monolayer-doped FET with a gate dimension of 5 #m × 100 Mm.

saturation curves are flat without hysteresis, which shows the good quality of the epitaxial layers. The maximum normalized transconductance gm and drain saturation current density Ids are 44 ms mm -1 and 128 mA mm- ~respectively with a gate dimension of 5 Mm × 100 Mm. If the laboratory facilities can be improved to a 1 #m gate length level, a higher transconductance and drain current density of over 200 mS m m - ' and 600 mA mm-1 respectively are expected. This higher output current density and transconductance are believed to be attributed to the much higher monolayer-doped sheet (5 x 1012 cm -2) in the active layer. The influence of the applied gate voltage Vo on the normalized transconductance gm and drain saturation current density IDS is illustrated in Fig. 13. It is known that the IDS is decreased monotonically with the applied gate voltage while gm is maintained at constant level over a significant VG range (from 0 V to about - 2 . 0 V). This wide-range operation of VG provides a flexible application of the monolayerdoped FET. Combined with a high gate breakdown voltage and high output drain current, the monolayer-doped structure studied is favourable for power FET operation.

A GaAs monolayer-doped profile VET structure was analysed and grown by molecular beam epitaxy. In a theoretical analysis, the 2D subband energies, real-space widths and population of subbands were studied by an Airy function method and our modified method. The results calculated by our method are consistent with the experimental data proposed by Zrenner et al. For the monolayer-doped FET studied, the gate-todrain forward cut-in voltage is about 0.7 V whereas the reverse breakdown voltage exceeds 15 V. The maximum normalized transconductance gm and drain saturation current density IDS of the depletion-mode monolayer-doped FET are 44 mS mm -1 and 128 mA m m - ' respectively. By combining these with the characteristics of a high transconductance, high gate breakdown voltage and high output drain current, the studied monolayer-doped structure is favourable for power FET operation.

Acknowledgments The authors wish to thank Miss H. R. Sze for her kindly assistance during this study. Part of this work was sponsored by National Science Council of Taiwan under Contract NSC79-0404-E006-10. References 1 c . E . C . Wood, G. M. Metzi, J. D. Berry and L. F. Eastman, J. Appl. Phys., 51 (1980) 383.

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10 11 12 13

14 15

T. H. Chiu, E Ren and C. G. Fonstad, J. Appl. Phys., 64 (1988) 3324. E. E Schubert, B. Ullrich, T. D. Harris and J. E. Cunningham, Phys. Rev. B, 38 (1988) 8305. E.J. Austin and M. Jaros, Phys. Rev. B, 31 (1985) 5569. H.X. Jiang and J. Y. Lin, J. Appl. Phys., 61 (1987) 624. A. Zrenner, H. Reisinger, K. Koch and K. Ploog, in J. D. Chadi and W. A. Harrison (eds.), Proc. 17th Int. Conf. on the Physics of Semiconductors, Springer, New York, 1985, p. 325. W. C. Liu, Y. H. Wang, C. Y. Chang and S. A. Liao, Proc. Inst. Electr. Eng., Part L 133 (1986) 47. W. C. Liu, W. C. Hsu, W. S. Lour, R. L. Wang and C. Y. Chang, Jpn. J. Appl. Phys., 28 (1989) L904.