HOT ELECTRON EFFECTS IN A 2D ELECTRON GAS AT THE GaAs/AlGaAs INTERFACE

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HOT ELECTRON EFFECTS IN A 2D ELECTRON GAS AT THE GaAs/AlGaAs INTERFACE

M. Inoue, S. Hiyamizu, H. Hida, H. Hashimoto, Y. Inuishi

To cite this version:

M. Inoue, S. Hiyamizu, H. Hida, H. Hashimoto, Y. Inuishi. HOT ELECTRON EFFECTS IN A 2D

ELECTRON GAS AT THE GaAs/AlGaAs INTERFACE. Journal de Physique Colloques, 1981, 42

(C7), pp.C7-19-C7-24. �10.1051/jphyscol:1981702�. �jpa-00221638�

JOURNAL DE PHYSIQUE

Colloque C7, supplément au n°10, Tome 42, octobre 1981 page C7-19

HOT ELECTRON EFFECTS IN A 2D ELECTRON GAS AT THE GaAs/AlGaAs INTERFACE

M. Inoue, S. Hiyamizu, H. Hida, H. Hashimoto and Y. I n u i s h i

Osaka University, Faculty of Engineering, Suita, Osaka, Japan Fujitsu Laboratories Ltd., Nakahara-ku, Kawasaki, Kanagawa, Japan

Résumé. - On décrit ici les.effets de porteurs chauds dans un gaz d'électrons bi-dimensionnel à très haute "mobilité. Les caractéristiques V-E et Te déduites expérimentalement nous ont donné des informations importantes. Les effets d'écran dus aux interactions électron-électron sont aussi discutés.

Abstract. - Hot electron effects of two dimentional electron gas with ultrahigh mobility are described. V-E characteristics and experimentally derived Te gave us important information.

The effects of (e,e) scattering and screening are also discussed.

1. Introduction.- In the field of high speed electron transport

devices recent interest has focused on the quasi-two-dimentional (2D) electron gas system which is built at the interface of modulation- doped (MD) GaAs/AlGaAs interface. It was found that Hall mobility in MD samples is superior to that of equivalently doped epitaxial bulk material. ' The mobility enhancement results from spatial 2 3 separation of electrons from their parent impurities. This strong improvement of transport properties has been also achieved at rela- tively high electric fields under operating conditions of devices. 4 This is particularly interesting from the point of view of physical understanding of hot 2D electrons as well as from the device aspect.

In this electron gas system, the effect of electron-electron, (e,e), scattering must be analyzed without the interference of additional scatterings by ionized impurities or holes. The objective of the present paper is to investigate hot electron effects of the electron gas at the MD GaAs/AlGaAs interface which yields essential information about the physics of high-speed performance of the device.

2. Ultrahigh Electron Mobility and Velocity-Field Characteristic.- Modulation-doped GaAs/AlGaAs heterostructures, as shown in Fig.l, were grown on semi-insulating GaAs substrate by molecular beam

o

epitaxy (MBE). An undoped AlGaAs layer (60 A) was introduced

between a high purity GaAs layer and the Si-doped Al Ga, As (x=0.27).

X X—X

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981702

C7-20 JOURNAL DE PHYSIQUE

The undoped AlGaAs l a y e r s h i e l d s d i f f u s i o n o f S i i m p u r i t i e s from n-AlGaAs i n t o t h e h i g h p u r i t y GaAs l a y e r . Consequently t h i s r e d u c e s Coulomb i n t e r a c t i o n between t h e e l e c t r o n g a s and p a r e n t d o n o r s i n n-AlGaAs. Cap l a y e r s of GaAs and AlGaAs w i t h graded composition were grown t o g e t good Ohmic c o n t a c t s . T h e r e f o r e , e x c e p t c o n t a c t a r e a s ,

t h e t o p l a y e r was removed by chemical e t c h i n g .

F i g u r e 2 shows t y p i c a l d a t a o f H a l l m o b i l i t y and s h e e t e l e c t r o n c o n c e n t r a t i o n i n t h e h e t e r o s t r u c t u r e a s a f u n c t i o n of t e m p e r a t u r e . A t low t e m p e r a t u r e s below 150 K , t h e e l e c t r o n c o n c e n t r a t i o n became c o n s t a n t . With d e c r e a s i n g t e m p e r a t u r e down t o 5 K , t h e e l e c t r o n

m o b i l i t y i n c r e a s e d monotonously and had _Thickness

1 prn)

no peak a s observed a t t e m p e r a t u r e s

SI-doped f

1

around 80 K i n most GaAs c r y s t a l s . R e g ~ o n N- A I ~ G O , . ~ A S

The maximum m o b i l i t y a t 5 K , 244000 N - A l o 2 7 G ~ 0 7 3 A s 0 03

/- . - - . . - -. - - - cm 2 / V - s , i s h i g h e r t h a n any p r e v i o u s l y ~ ~ ~ ~ ~ , " 0 7 3 A s

KydL

AlGaAs h e t e r o s t r u c t u r e s . One should n o t i c e t h i s c r u c i a l c h a r a c t e r i s t i c o b s e r v e d a t low t e m p e r a t u r e s . The 2D e l e c t r o n c o n c e n t r a t i o n i s

l o 2

Sernl- Insulating

/

I

t i m e s a s h i g h a s t h a t o f t h e r e s i d u a l F&: Schematic diagram of modulation-doped GaAs/AlGaAs i m p u r i t y c o n c e n t r a t i o n i n t h e p u r e GaAs

heterostructure.

l a y e r s . Such a n e l e c t r o n i c system h a s n e v e r been a t t a i n e d i n any o t h e r semi-

c o n c e n t r a t i o n i n c r e a s e d from t h e d a r k TEMPERATURE ( K ) 1ot4

-

v5 -

0 Z

r z w

U Z 0 U 2 1012 E

r L

kl u

I- W

&

&

conductors and under any e x p e r i m e n t a l , , , , , ,

,

v a l u e s a s shown i n F i g . 2 . T h i s i s

Fig.2 : Electron mobility and a t t r i b u t e d t o t h e p e r s i s t e n t e x c i t a t i o n - sheet electron concentration in GaAslAlGaAs as a function of e l e c t r o n s from deep t r a p s i n t h e of temperature.

m o b i l i t y a s w e l l a s s h e e t e l e c t r o n 3 10 loo 400

c o n d i t i o n s . Even under t h e i l l u m i n a t i o n

-

2

I GoAs/N

-

- ₁

w i t h l a s e r l i g h t , h o l e s a s w e l l a s

e l e c t r o n s were e x c i t e d . 5 r 6 We suppose

-

t h a t t h e i n t e r e s t i n g t e m p e r a t u r e depend- ; I - e n c e o f t h e e l e c t r o n m o b i l i t y below 50K

5

^!

r e s u l t s from t h e dominant s c r e e n i n g of -

z 104r -

t h e Coulomb i n t e r a c t i o n o f r e s i d u a l ₀ i o n i z e d i m p u r i t i e s i n t h e GaAs l a y e r [r I- u

W -

and a t t h e i n t e r f a c e . A f t e r t h e ^{_I W -} z

-

- --I

L

i l l u m i n a t i o n w i t h d a y - l i g h t , t h e ,03

,...

. .

AlGaAs l a y e r . We f e e l i n t h e p r e s e n t sample t h e undoped AlGaAs l a y e r e f f e c - t i v e l y c o n t r i b u t e s t o a n enhancement o f t h e m o b i l i t y . T y p i c a l enhanced m o b i l i t i e s and s h e e t e l e c t r o n c o n c e n t r a t i o n s were 330000 cm2/v.s and 1.03 x 1012 cm-2 a t 4.2 K , r e s p e c t i v e l y . v

F i g u r e 3 shows t h e v a r i a t i o n o f t h e v e l o c i t y and m o b i l i t y a t 4.2 K w i t h

a p p l i e d e l e c t r i c f i e l d . The V-E c u r v e _E

.

was deduced from p u l s e d c u r r e n t - f i e l d

c h a r a c t e r i s t i c s and p u l s e d e l e c t r i c F i g . 3 : Electron velocity and mobility as a function of the f i e l d dependent-Shubnikov-de Haas (SdH) electric field.

measurements. For d i f f e r e n t p u l s e d e l e c t r i c f i e l d s , t h e s h e e t e l e c t r o n

c o n c e n t r a t i o n was measured from t h e o s c i l l a t o r y p e r i o d o f t h e magneto- conductance. The d a t a were t a k e n by Boxcar I n t e g r a t o r u s i n g 0.5 p s e c a p e r t u r e g a t e p u l s e s . Measurements i n t h e f i e l d - s t r e n g t h r e g i o n s t u d i e d d i d n o t show any s i g n i f i c a n t v a r i a t i o n o f s h e e t e l e c t r o n c o n c e n t r a t i o n . A t low f i e l d s ( 0 . 2

-

3 . E l e c t r o n Temperature and E l e c t r o n - E l e c t r o n S c a t t e r i n g - The 2D c h a r a c t e r o f t h e e l e c t r o n system c a n b e e l e g a n t l y d e m o n s t r a t e d by SdH measurements. The SdH o s c i l l a t i o n s a p p e a r when t h e magnetic f i e l d

, H , i s a p p l i e d p e r p e n d i c u l a r t o t h e i n t e r f a c e , w h i l e no o s c i l l a t i o n s w e r e observed a f t e r r o t a t i n g t h e f i e l d p a r a l l e l t o t h e i n t e r f a c e . W e a n a l y z e t h e a m p l i t u d e dependence o f t h e quantum o s c i l l a t i o n s . I n t h e d e g e n e r a t e s e m i c o n d u c t o r s 7 , e l e c t r o n t e m p e r a t u r e s c a n be deduced from e l e c t r i c f i e l d - d e p e n d e n c e of t h e a m p l i t u d e s o f t h e SdH o s c i l l a - t i o n s . The d i s t r i b u t i o n f u n c t i o n of 2D e l e c t r o n g a s s u b j e c t t o an e l e c t r i c f i e l d i s a Fermi d i s t r i b u t i o n a t an e l e c t r o n t e m p e r a t u r e Te h i g h e r t h a n t h e l a t t i c e t e m p e r a t u r e TL. Applying t h i s e l e c t r o n t e m p e r a t u r e model t o t h e 2D e l e c t r o n g a s system, Te c a n be deduced

C7-22 JOURNAL DE PHYSIQUE

from a comparison between t h e t e m p e r a t u r e and e l e c t r i c f i e l d dependences o f t h e o s c i l l a t i o n a m p l i t u d e . F i g u r e 4 shows t h e t e m p e r a t u r e dependence o f t h e m a g n e t o - c o n d u c t i v i t y measured by t h e a p p l i c a t i o n o f a s h o r t p u l s e v o l t a g e . The e l e c t r i c f i e l d s t r e n g t h and t h e d u l a t i o n were 1 V/cm and 4 p s e c , r e s - p e c t i v e l y . I n F i g . 5 , t h e magneto- c o n d u c t i v i t y i s shown f o r d i f f e r e n t e l e c t r i c f i e l d s a t a f i x e d l a t t i c e t e m p e r a t u r e o f 4 . 2 K. From a comparison between two f u n c t i o n s of t h e o s c i l l a t o r y component,

A 4

and A 8 (TL) / d o , w e d e t e r m i n e d t h e e l e c t r o n t e m p e r a t u r e Te which c o r r e s p o n d s t o a c e r t a i n e l e c t r i c f i e l d . The a m p l i t u d e s of t h e o s c i - l l a t o r y component a t 4 5 KG a r e shown i n F i g . 6 and 7 .

The e l e c t r o n t e m p e r a t u r e s a r e shown i n F i g . 8 a s a f u n c t i o n of t h e e l e c t r i c f i e l d . The e l e c t r o n t e m p e r a t u r e a r e q u i t e low i n comparison w i t h t h a t of d e g e n e r a t e s e m i c o n d u c t o r s , which s u g g e s t s t h a t t h e u n u s u a l s c a t t e r i n g p r o c e s s e s a r e i m p o r t a n t i n t h e p r e s e n t 2D e l e c t r o n g a s . I n t h e low e l e c t r i c

Fig.6 :Amplitude of the conductivity oscillation. (TT) at 1 Vlcm and

Fig.4 : Magnetic field

dependence of the conductivity for different lattice tempera- tures. The applied electric field is 1 V/cm.

Fig. 5 :Magnetic field dependence of the conductivity at 4.2 K for different electric field.

-

H-45 KG as a function of the lattice Fig.7:Amplitude of the conductivity temperature. is normalized by the oscillation at 4.2 K and H=45 KG as a conductivity without magnetic field. function of the electric field.

f i e l d r e g i o n a t 4.2 K t ( e r e )

s c a t t e r i n g and s c r e e n i n g of i o n i z e d

7

i m p u r i t y s c a t t e r i n g must b e more i m p o r t a n t t h a n l a t t i c e s c a t t e r i n g . A t h r e e d i m e n s i o n a l model makes i t p o s s i b l e t o e s t i m a t e t h e s e e f f e c t s because t h e s c a t t e r i n g p r o c e s s due t o t h e s c r e e n e d Coulomb p o t e n t i a l i s e s s e n t i a l l y t h e same a s t h e 2D e l e c t r o n g a s .

F u : Electron temperature of I n s p i t e o f momentum and e n e r g y 2Delectron gas as a function of

the electric field.

c o n s e r v a t i o n d u r i n g ( e , e ) s c a t t - e r i n g s , t h e a v e r a g e v e l o c i t y i s

changed by ( e , e ) s c a t t e r i n g b e c a u s e i t c a u s e s a n e f f e c t on t h e d i s - t r i b u t i o n f u n c t i o n , c o n s e q u e n t l y on t h e p r o b a b i l i t y o f phonon

s c a t t e r i n g s . I n o r d e r t o g e t a q u a n t i t a t i v e e s t i m a t e o f t h e e f f e c t , we c a l c u l a t e f o r V and Te on e l e c t r o n c o n c e n t r a t i o n o f

lo1*

l o 6

l o 6

l o 6

.

e l e c t r o n t e m p e r a t u r e , e s p e c i a l l y Te, a l c n g w i t h f i e l d d i r e c t i o n , d e c r e a s e s due t o ( e , e ) s c a t t e r i n g . We b e l i e v e t h a t t h i s model r e a s o n a b l y i n t e r p r e t s t h e e x p e r i m e n t a l d a t a shown i n F i g . 8 .

Table 1 : Effects of (e,e) scattering SCREENING AND (e.e SCATTERING on the velocity and electron temperature.

Electron conc. : 1 x 1018 c m 3 Ionized impurity conc. : 1 x 10 15 cm-3 Lattice temperature 4.2 K.

w i t h ( e , e ) scatt. ( e v e ) scat*.

2.5 x 10

E 2

C7-24 JOURNAL DE PHYSIQUE

4 . Summary- We d i s c u s s e d h o t e l e c t r o n e f f e c t a t low e l e c t r i c f i e l d s i n a 2D e l e c t r o n g a s a t t h e MD ~aAs/AlGaAs i n t e r f a c e . A t f i e l d s h i g h e r t h a n t h a t employed i n t h e p r e s e n t e x p e r i m e n t , t h e 2D e l e c t r o n s s h o u l d be h e a t e d more r a p i d l y and c a u s e a dominant i n t e r a c t i o n w i t h p o l a r o p t i c a l phonons. I n t h i s c a s e i n t e r s u b b a n d s c a t t e r i n g and r e a l s p a c e t r a n s f e r o f h o t e l e c t r o n s must be i m p o r t a n t a 8 The two dimension- a l e f f e c t s w i l l d i s a p p e a r w i t h i n c r e a s i n g e l e c t r i c f i e l d . The

p r e s e n t s t u d y i s now b e i n g extended t o t h e h i g h f i e l d r e g i o n .

Acknowledgements

-

D r . T. Misugi and D r . 0. Ryuzan f o r t h e i r c o n t i n u o u s i n t e r e s t i n t h i s work.

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