HOT ELECTRON TRANSPORT IN THE Ga1-xAlxAs SYSTEM

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HOT ELECTRON TRANSPORT IN THE Ga1-xAlxAs SYSTEM

G. Hill, P. Robson

To cite this version:

G. Hill, P. Robson. HOT ELECTRON TRANSPORT IN THE Ga1-xAlxAs SYSTEM. Journal de

Physique Colloques, 1981, 42 (C7), pp.C7-335-C7-341. �10.1051/jphyscol:1981741�. �jpa-00221678�

JOURNAL DE PHYSIQUE

Colloque C?, supplément au n°10, Tome 42, octobre 1981 page C7-335

HOT ELECTRON TRANSPORT IN THE G

_

Al

As SYSTEM

G. Hill and P.N. Robson

Department of Electronic and Electrical Engineering, The University of Shef- field, Mappin Street, Sheffield SI ZJD, United Kingdom

Résumé. - La vitesse des électrons dans un champ intense à été étudiée par plusieurs techniques, pour une gamme étendue de compositions Gai_

Al

As. Les caractéristiques courant-tension d'échantillons en forme de H ont été mesurées et normalisées, grâce à des mesures de Hall détaillées, et ces résultats comparés aux simulations par la méthode de Monte Carlo. Des informations supplémentaires ont été obtenues sur les diodes à hétérojonction GaAs/Gai-

Al

As, ooérant dans des conditions limitées de charge d'espace.

Abstract. - The high field drift velocity of electrons in Gai-xAl

As has been investigated for a wide range of compositions using several techniques. I-V characteristics of H-shaped samples have been measured and normalised using detailed Hall measurements. These results have been compared with .'tonte Carlo simulations. Further information has been obtained from GaAs/Gai-

Al As heteroiunction diodes operated under space-charge limited conditions.

1. Introduction - Ga, Al As is used extensively in devices where large electric fields are present. Microwave devices such as the DOVETT

' and DOVATT* ' structures incorporate GaAs-Ga, 11 As hetero- junctions, GaAs FET's are increasingly being fabricated with Ga, Al As layers , and a range of novel quantum well structures have been reported, which involve GaAs-Ga, Al As heterojunctions. The high field electron drift velocity in Ga, Al As is therefore of considerable interest, particularly in the DOVETT type device, whose efficient operation depends upon there beincr a low value of saturated drift velocity obtainable in material of intermediate aluminium content 0.4 < x < 0.45.

Several techniques have been used to investigate the electron drift velocity in Ga, Al A s , namely measurements of i-V characteristics of H-shaped samples, Monte Carlo calculations and measurements of space- charge limited resistance of n p n GaAs-Ga, Al As heterojunction diodes. These techniques are considered below.

2. I-V Characteristics of H-shaped Samples. - These measurements were performed on undoped n-type Ga, Al As layers grown on semi-insulating

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981741

C7-336 JOURNAL DE PHYSIQUE

GaAs s u b s t r a t e s by LPE. These l a y e r s were 4-13pm t h i c k and had room t e m p e r a t u r e c a r r i e r c o n c e n t r a t i o n s o f 2-10

1 0 l ~ c m - ~ . P l a n a r H- shaped d e v i c e s were d e l i n e a t e d by p h o t o l i t h o g r a p h y and Ag-Sn c o n t a c t s were e v a p o r a t e d o n t o t h e end r e g i o n s and a l l o y e d i n . 50ns v o l t a q e p u l s e s were a p p l i e d t o t h e samples and t h e e l e c t r i c f i e l d d - i s t r i b u t i o n was d e t e r m i n e d u s i n g a lOpm d i a m e t e r n i c k e l p r o b e ( 5 ) . Uniform e l e c t r i c f i e l d s were observed a l o n g t h e l e n g t h o f t h e a c t i v e r e a i o n , t h e s e f i e l d s b e i n g a b o u t f o u r t i m e s l a r q e r t h a n t h o s e i n t h e broad r e q i o n n e a r t h e ohmic c o n t a c t s . Sample c u r r e n t was observed u s i n g a c u r r e n t m o n i t o r i n g r e s i s t o r .

From t h e s e measurements, a s e r i e s o f

c h a r a c t e r i s t i c s were o b t a i n e d f o r a r a n g e of a l l o y c o m p o s i t i o n s . I n o r d e r t o n o r m a l i s e t h e s e c u r v e s t o o b t a i n t h e v ( E ) c h a r a c t e r i s t i c s it i s n e c e s s a r y t o deduce t h e low f i e l d d r i f t m o b i l i t y f o r e a c h sample. H a l l m o b i l i t i e s were determined from van d e r Paul? measurements on e a c h s l i c e . Because o f t h e c l o s e n e s s i n e n e r g y of t h e r , L and

v a l l e y s , f o r i n t e r m e d i a t e a l l o y

c o m p o s i t i o n s , i t i s n o t p o s s i b l e t o a s s m e t h a t pH/pD = 1.

I f it i s assumed t h a t f o r e a c h c o n d u c t i o n band minina

1, t h e n f o r t h r e e - v a l l e y t r a n s p o r t t h e r a t i o pH/pD i s g i v e n by

For t h e composition r a n q e 0.2

0.6 pH/pg i s a s t r o n q l y v a r v i n q f u n c t i o n o f X and i s v e r y s e n s i t i v e t o t h e v a l u e s chosen f o r n

i-,L,X and r , L , x -

I n o r d e r t o e v a l u a t e t h i s e x p r e s s i o n , d e t a i l e d H a l l measurements ( 6

were performed on samples from each s l i c e used i n t h e ~ r o b i n g measure- ments, nH and pH b e i n g measured a s a f u n c t i o n o f t e n y e r a t u r e and h y d r o s t a t i c p r e s s u r e . These c u r v e s were t h e n f i t t e d w i t h a model which i n c l u d e d t h e F , L and X c o n d u c t i o n bands, t h r e e donor l e v e l s and one a c c e p t o r l e v e l . Data o b t a i n e d from t h i s a n a l y s i s was used i n E q u a t i o n (1) t o o b t a i n pH/pD a s a f u n c t i o n o f c o ~ " . p o s i t i o n , which i s p l o t t e d a s t h e s o l i d l i n e i n Fig.1.

Using t h i s c u r v e and t h e measured H a l l m o b i l i t i e s , t h e I - V c h a r a c t e r -

i s t i c s were n o r m a l i s e d t o t h e l o w - f i e l d d r i f t m o b i l i t y and a r e shown

a s t h e s o l i d l i n e s i n Fig.2. The o n l y p r e v i o u s lreasurements were p e r -

formed by Immorlica and earso on'^) which s u g g e s t t h a t f o r

0.38 t h e

d r i f t v e l o c i t y s a t u r a t e s a t a v a l u e o f 3.3

106cm

f o r f i e l d s

above 2.4kV cm-', t h i s r e s u l t b e i n g shown by t h e d o t t e d l i n e .

F i g . 1

uH/uD a s a f u n c t i o n o f Gal-xAlxAs cornnosition

Fig.2

V e l o c i t y - f i e l d c h a r a c t e r i s t i c o f e l e c t r o n s i n Gal-xAlxAs

3 .

Monte C a r l o S i m u l a t i o n s . - 3 o n t e C a r l o c a l c u l a t i o n s were performed u s i n g t h e model o f Fawcett e t a 1

w i t h t h e a d d i t i o n o f a l l o y s c a t t e r i n g and space-charge s c a t t e r i n g . I n i t i a l c a l c u l a t i o n s were p e r - formed t o f i t t h e H a l l m o b i l i t y d a t a o f Saxena") a s a f u n c t i o n o f

composition and h y d r o s t a t i c p r e s s u r e , u s i n g t h e band s t r u c t u r e de-

t e r m i n e d by Saxena ( 7 , 8 ) . F i g u r e 3 shows t h e e x p e r i m e n t a l

JOURNAL

DE

104L---T--T--T--

. . . .

KANEKOetal

STRINGFELLOW

-

o NEUMANN

MONTE CARLO

103

\

' - - -

1 0 ' ~ I

.2 ..l .6 .B ^{10; , 5} l ? - - - " - " ' 15 20 KYOHOSTATIC PRESSLJRE kbar

I

AI Fraction x/2xAt%

Fig.3

Variation of pHwith Fig.4

Variation ofuHwith hydro-

composition static pressure

data of several authoys (8r14r 15) and the Monte Carlo results without the inclusion of alloy or space-charge scattering. One Monte Carlo point is also shown for Ga.81 A1.19 As which gives good agreement of Hall mobility using an Ns.Q product for space charge scattering of 0.7~10~cn-'. This is lower than the value of 1.25~10~cm-' gredicted by Kaneko et a1 (l2) for X

0.19, using the equation:

NsQ

5x10~ + 6 . 3 ~ 1 0 ' ~ (cm-'

(2) For X

and X

0.3 good agreement was obtained without the

inclusion of space-charge scattering, but in the ranqe

X

0.3, space-charge scattering was required to obtain good agreement. Due to the significant scatter in experimental results it was not possible to provide a very detailed fit. Monte Carlo results were also calculated as a function of hydrostatic pressure for several compositions. Fia.4 shows a comparison of the Monte Carlo result and Saxena's result for X

0.38.

The Nonte Carlo calculations were then extended to high fields and these results are shown in Fig.2 as the dashed lines. For X

0.3 the Monte Carlo results yield a rather smaller comuositional dependence of

saturation velocity, and a rather higher minimum saturation velocity than the probe results.

This difference is partly due to the difference in pH/+, ratio pre-

d i c t e d by t h e Monte C a r l o r e s u l t s , r e l a t i v e t o t h a t c a l c u l a t e d by

~ a x e n a " ) . The Monte C a r l o r e s u l t i s shown a s t h e dashed l i n e i n F i g . 1.

a f u r t h e r comparison, t h e r a t i o nT/nH i s p l o t t e d from t h e r e s u l t s of Kaneko e t a 1 ( l 2 ) where nT i s t h e f r e e c a r r i e r c o n c e n t r a t i o n measured by C-V, and nH i s t h e H a l l c a r r i e r c o n c e n t r a t i o n .

I t can be s e e n t h a t i n t h e Monte C a r l o c u r v e uH/pD f a l l s more r a p i d l y i n t h e r a n g e 0.4

X

0 . 6 t h a n t h e r e s u l t s o f Saxena. T h i s i s

b e c a u s e t h e Monte C a r l o c a l c u l a t i o n s p r e d i c t t h a t pH f a l l s v e r y r a p i d - l y a s t h e r - v a l l e y s t a r t s t o c r o s s o v e r t h e

and X - v a l l e y s , f a l l i n g a s low a s 400cm2

a t X

0 . 4 5 , w i t h j u s t 8 % o f t h e e l e c t r o n s p o p u l a t i n g t h e r - v a l l e y . I n t h e a n a l y s i s o f ~ a x e n a " ) , it i s d i f f i - c u l t t o e s t i m a t e pr i n t h i s r e a i o n , s i n c e most o f t h e e l e c t r o n s p o p u l a t e t h e X-valleys.

Hence i t can be s e e n t h a t t h e r e i s s t i l l c o n s i d e r a b l e u n c e r t a i n t y i n t h e s a t u r a t e d d r i f t v e l o c i t y o f e l e c t r o n s i n Gal-xAlxAs f o r i n t e r - m e d i a t e aluminium c o m p o s i t i o n s . To r e s o l v e t h i s u n c e r t a i n t y a

t e c h n i q u e was needed which r e q u i r e s n e i t h e r t h e knowledge of t h e r a t i o pH/pDl n o r d e t a i l e d knowledge o f t h e s c a t t e r i n g p a r a m e t e r s f o r Gal-*

A l x A s .

4. Space-Charge R e s i s t a n c e Xeasurements. - T h i s t e c h n i q u e i n v o l v e s t h e measurement o f t h e

c h a r a c t e r i s t i c o f an n-p-n s t r u c t u r e made up of an n + - ~ a ~ s s u b s t r a t e , a 2um t h i c k l a y e r of p-type Ga

+ ^l-X

doped t o "5

1 0 ' ~ c r n - ~ w i t h Ge, and an n -GaAs t o p c o n t a c t l a y e r 0 . 2 ~ t h i c k doped t o 5

10"cm-~ w i t h Sn. The s u b s t r a t e s were t h i n n e d down t o 100pm, and In-Ge-Au c o n t a c t s were e v a p o r a t e d on b o t h s i d e s and a l l o y e d a t 4 0 0 ~ ~ . The samples were t h e n c l e a v e d i n t o 300pm s q u a r e d i c e V o l t a g e p u l s e s o f 0 . 5 p s d u r a t i o n were a p p l i e d t o t h e s a m ~ l e s and t h e v o l t a g e i n c r e a s e d beyond t h a t r e q u i r e d f o r punchthrough. Under t h e s e c o n d i t i o n s t h e sample c u r r e n t i s l i m i t e d by t h e i n j e c t e d space-charqe.

Under t h e s e c o n d i t i o n s t h e d i f f e r e n t i a l r e s i s t a n c e o f t h e I - V c h a r a c t -

where L i s t h e sample l e n g t h ,

t h e sample a r e a and vs t h e s a t u r a t e d d r i f t v e l o c i t y .

Samples were grown by LPE, w i t h

c o n p o s i t i o n s of 45%, s i n c e t h i s i s t h e main r e g i o n o f i n t e r e s t , w i t h low s a t u r a t e d d r i f t v e l o c i t i e s .

c h a r a c t e r i s t i c s were found t o be l i n e a r f o r l a r g e a p p l i e d b i a s e s . The i n c r e m e n t a l r e s i s t a n c e was measured and s u b s t i t u t e d i n e q u a t i o n ( 3 ) t o g i v e v , t h e s a t u r a t e d d r i f t v e l o c i t y .

S

C7-340 JOURNAL DE PHYSIQUE

For X

0.45, saturated drift velocities of 4.8 k0.5

106cm

for applied fields in excess of 30kV cm-'. Reference to Fig.2 shows that this is more in agreement with the Monte Carlo results than the probe results.

Similar measurements (l3) were per£ ormed on DOVETT (l) structures, which

+ - - ₊

are n -GaAs, p -GaAlAs, n -GaAs, n GaAs devices, gave a saturated drift velocity of 4.7x106cm

in good agreement with that obtained from the n-p-n devices.

5. Conclusions. - Extensive probing measurements have been performed on H-shaped samples of Gal-xAlxAs. Normalisation of these to give v(E) characteristics is prone to error due to uncertainties in the ratio vH/vD which is a strong function of conposition. Monte Carlo simulations have been performed to fit

as a function of composition and hydrostatic pressure and the results have then been extended to high fields.

Space charge resistance measurements on Ga.ssAl.ssAs heterojunction diodes and DOVETT structures yield a saturated drift velocity of 4.8+

0.5

106cm S-', which is in reasonable agreement with the Monte Carlo results.

6. Acknowledgements. - The significant contributions of T. Sugeta, A.K. Saxena, A.W. Nelson, J.H. Marsh and A. .?4ajerfeld are gratefully acknowledged.

3ef - erences

1. J.E. Sitch, A. Majerfeld, P.N. Robson, F. Hasegawa, Electron.

Lett., S, 457 (1975).

2. M.G. Adlerstein, H. Statz, IEEE Trans. Electron. D e v i c e s , ~ , 817 (1979).

3. W.I. Wang, S. Judaprawina, C.E.C. Wood, L.F. Eastnan, Appl. Phys.

Lett. 2 , 708, (1981).

4. T.H. Glisson, J.R. Hauser, M.A. Littlejohn, X. Hess, B.G.

Streetman, H. Shichijo, J. Appl. Phys. 51, 5445 (1980).

5. A. Najerfeld, K.E. Potter, P.N. Robson, J. Appl. Phys. 45, ^3681,

(1974).

6. A.K. Saxena, Appl. Phys. Lett. 36, 79 (1980).

7. A.K. Saxena, Phys. Stat. Sol. (b) 96, K77 (1979).

8. A.K. Saxena, Ph-D. Thesis, Sheffield University, (1978).

9. A.A. Imorlica, G.L. Pearson, Apwl. Phys. Lett. 2, 570 (1974).

10.

F a w c e t t ,

Boardman, S . Swain, J. Phys. Chem. S o l i d s , 2_1, 1 9 6 3 ( 1 9 7 0 ) .

11.

Ruch, W. F a w c e t t ,

Appl. P h y s . , 41, 3843 ( 1 9 7 0 ) .

1 2 .

Kaneko, X. Ayabe,

Watanabe, I n t . Phys. Conf. S e r . G, ²¹⁶

( 1 9 7 7 ) .

13.

N e l s o n , Ph.D. T h e s i s , S h e f f i e l d U n i v e r s i t y , ( 1 9 5 1 ) . 1 4 . G.B. S t r i n g f e l l o w ,

Appl. Phys. 50, 4178 ( 1 9 7 9 ) .

1 5 . H. Neumann,

F l o h r e r , Phys. S t a t . S o l . ( a ) 2 5 , K145, ( 1 9 7 4 ) .