NOISE AND DIFFUSIVITY OF HOT ELECTRONS IN n-TYPE InSb

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NOISE AND DIFFUSIVITY OF HOT ELECTRONS IN n-TYPE InSb

V. Bareikis, A. Galdikas, R. Miliu¡yté, J. Pozhela, Viktoravičius

To cite this version:

V. Bareikis, A. Galdikas, R. Miliu¡yté, J. Pozhela, Viktoravičius. NOISE AND DIFFUSIVITY OF

HOT ELECTRONS IN n-TYPE InSb. Journal de Physique Colloques, 1981, 42 (C7), pp.C7-215-C7-

220. �10.1051/jphyscol:1981725�. �jpa-00221662�

NOISE AND DIFFUSIVITY OF HOT ELECTRONS IN n-TYPE I n S b

V. B a r e i k i s , A. Galdikas, R. Miliu^yte, J. Pozhela and V. Viktoravicius

Semiconductor Physics Institute, Lithuanian SSR, Academy of Sciences, Vilnius, USSR

Abstract. - The experimental results and Monte-Carlo calcula- tions of hot electron noise are presented for n-InSb at 77 K and 10 K. The influence of inelastic optical as well as ioni- zed impurity scattering on the noise characteristics is exa- mined.

1. Introduction. - Thermal fluctuations of hot electrons in semicon- ductors have been studied by many workers /1,2/.

So far, the experimental and Monte-Carlo calculation results of hot carrier noise and closely related phenomenon diffusion have been mainly reported for Ge and Si. Only several publications are availa- ble for n-InSb /3-5/. In this semiconductor the inelastic scattering by polar optical phonons at low temperatures is rather effective and therefore the pecularities of noise in microwave range due to this scattering is expected. In this note we present experimental results and Monte-Carlo calculations of hot electron noise in InSb at 77 K and 10 K.

2. Experimental and calculation techniques. - The noise along oc di- rection is characterized by the spectral density of current fluctua- tions SjtfJot and the noise temperature T

, which are related as

where k is the Boltzmann constant, &(f)^ is the small signal a.c. conductivity at the frequency f in the presence of a steady high electric field E. The T

was measured in microwave range

(10 GHz) using a pulse (5 AS duration, 22 Hz repetition) technique described elsewhere /6/. In the parallel (II) direction G(p

JOURNAL DE PHYSIQUE

Colloque C7, supplément au n°10, Tome 42, octobre 1981 page C7-215

Résumé. - On a mesure et à l'aide, de la méthode de Monte-Car- lo, on. a calculé le bruit des électrons chauds dans n-InSb à la température 77 K et 10 K. On a examiné l'influence de la dispersion des porteurs de charge par les phonons optiques ainsi que par les impuretés ionisées sur les caractéristi- ques de bruxt de 1'antimoniure d'indium.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981725

C 7 - 2 1 6 JOURNAL DE PHYSIQUE

i s assumed t o be equal t o t h e d i f f e r e n t i a l conductivity, while f o r t h e transverse

1

d i r e c t i o n i t was taken t o be t h e same a s t h e s t a t i c conductivity. I n t h e samples under t h e i n v e s t i g a t i o n t h e e l e - c t r o n concentrations were n

~ m ' ~ ; 3 . 1 0 ~ ~ and mobili- t i e s f.l

6 . 1 0 ~ cm2/v*s,

cm2/v.s respectively. Simple rectan- g u l a r s t r i p s a s well a s dumbbell shape samples were used. Typical sample dimensions a r e 2.5x0.3x0.3 mrn 3 . ^An e l e c t r i c f i e l d was applied p a r a l l e l t o (110) d i r e c t i o n . The s p e c t r a l d e n s i t y of e l e c t r o n velo- c i t y f l u c t u a t i o n s Sv(f)* and d r i f t v e l o c i t y was c a l c u l a t e d by Mon- te-Carlo procedure described i n / 7 / . Svff)* i s simply r e l a t e d with

aj ^(fJa

^$(f&

^e

ⁿ SV(f)& , where e i s t h e e l e c t r o n charge.

The model used f o r c a l c u l a t i o n s included only one i s o t r o p i c and non- parabolic minimum of conduction band. Polar o p t i c a l , acoustic and

ionized impurity s c a t t e r i n g was accounted. The deformation p o t e n t i a l f o r acoustic phonon s c a t t e r i n g was taken t o be 30 eV. The o t h e r pa- rameters were t h e same a s i n /

3. Results and discussion. - Experimental and c a l c u l a t e d noise *em- p e r a t u r e as w e l l a s s p e c t r a l d e n s i t y of c u r r e n t f l u c t u a t i o n s v s el- e c t r i c f i e l d a r e p l o t t e d in Figs.

and 3.

A l l t h e curves except

i n Fig.

( t h e noise temperature a t 1 0 K) a r e obtained f o r dumbbell shape samples. A t 77 K t h e r e s u l t s f o r both types of samples a r e i d e n t i c a l .

A t both temperatures f o r n

cm-3 experimental and theore- t i c a l G,, f o r comparatively high E a r e found t o be higher than

T , , however Sj(f),,

Sj(f), . These r e s u l t s agree with t h e main

Figs. 1 and 2: Experimental and c a l c u l a t e d T,,

74 -3

1

10K n-1.2.10

a ) b

Pig. 3: Experimental and c a l c u l a t e d 8 j ( f ) o L / S o vs

a t 77 K,

-spe- c t r a l d e n s i t y of c u r r e n t f l u c t u a t i o n s a t E

0 ( a ) ; vs E a t

l o K ( b ) ; f

1 0

conclusions of t h e f l u c t u a t i o n theory f o r q u a s i e l a s t i c s c a t t e r i n g mechanisms / 1 / a s well as with t h e d a t a obtained by Monte-Carlo met- hod f o r noise temperature i n InSb a t 77 K

A s f a r a s agreement of our c a l c u l a t e d and experimental d a t a i s con- cerned a t 77 K t h e b e s t f i t i s obtained when t h e acoustic phonon de- formation p o t e n t i a l i s assumed t o be 30 eV. A t 1 0

t h i s agreement f o r dumbbel shape samples i s worse as compared t o t h a t a t 77 K. The main reasons a r e supposed t o be t h e experimental e r r o r s

1 5 % f o r T, and 25 % f o r S j ( f )

heating of the l a t t i c e , neglect of electron- e l e c t r o n and piezoacoustic s c a t t e r i n g i n t h e adopted model.

For t h e rod-like shape samples a t 1 0 K a considerably higher value of T,,, was observed. This i s a t t r i b u t e d t o t h e e l e c t r o n t r a n s i t through the p o t e n t i a l b a r r i e r a t t h e contact.

A t

10 K and l o w e l e c t r i c f i e l d s , however experimentally and theore- t i c a l l y i s obtained t h a t Sj(f),, > S j (flL (Fig. 3b). Consequently, t h e s i g n of anisotropy of

i s opposite t o t h a t observed a t high e l e c t r i c f i e l d s a s well as a t 77 K.

The existence of such anisotropy f o r i n e l a s t i c s c a t t e r i n g by o p t i c a l phonons was predicted t h e o r e t i c a l l y i n / 91. The Monte-Carlo calcula- t i o n s i n t h e case when t h e ionized impurity s c a t t e r i n g i s neglected show t h a t t h i s e f f e c t i n InSb a t

K i s s i g n i f i c a n t (Fig. 4 ) .

S,(f)ll has a maximum a t t h e frequency equal t o t h e r e c i p r o c a l time

necessary t o a c c e l e r a t e t h e e l e c t r o n from energy

t o t h e en-

ergy of o p t i c a l phonon (Fig. 4a). The resonant c h a r a c t e r of s,($),,

C7-2 18 JOURNAL DE PHYSIQUE

a

> ^{b 1}

Fig. 4: Yonte-Carlo c a l c u l a t i o n s a t 1 0 K of S,(f), ( a ) and autocorre- l a t i o n function ?(T& (b). n i

corresponds t o t h e o s c i l l a t i o n s of autocorrelation function of velo- c i t y

v s time

(Fig. 4b). A t higher temperatures and elec- t r i c f i e l d s t h e maximum i s reduced due t o t h e increase of e l e c t r o n gas randomization (Fig. 4a

5).

Ionized impurity s c a t t e r i n g a l s o causes the randomization. Theref ore t h e IUaXiJiUID i s reduced when t h i s type of s c a t t e r i n g i s accounted (Fig. 6 ) .

Fig. 5: Uonte-Carlo c a l c u l a t i o n s Fig. 6 : Monte-Carlo c a l c u l a t i a a s

of

a t 77 K;

S f 81 :i-Bi

ni

1.2-10

Ionized impurity s c a t t e r i n g e f f e c t s considerably t h e value of t h e n o i s e temperature

i t s anisotropy too. The experiment and calcu- l a t i o n s show t h a t i n n-InSb with ni

3 1015 ~ m ' ~ a t 77 K GI, (Fig. 7 ) i s decreased a s compared t o t h a t f o r

l , 2 * l o f 4 Besides, t h e c a l c u l a t i o n s show t h a t t h e degree of doping has an influence on t h e s i g n of 7;, anisotropy i n low f i e l d region (compare Figs. 1 t o

Fig. 7: Experimental and c a l c u l a t e d

.

F i n a l l y , it should be mentioned t h a t f o r low e l e c t r o n d e n s i t i e s

n = 1014 S,(f,16 i s simply r e l a t e d with t h e d i f f u s i o n coef- f i c i e n t L&: Sj[f),=4e2nDd / 1 / .

4. C onelusions .

1. The high frequency (10 GHz) hot e l e c t r o n n o i s e i n n-InSb i s measured.

2. The influence of t h e s t r e a i n g motion of e l e c t r o n s on t h e h o t e l e c t r o n noise i s Observed.

3. Ionized impurity s c a t t e r i n g s i g n i f i c a n t l y e f f e c t s on t h e value of e l e c t r o n n o i s e temperature and i t s anisotropy.

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Barker and

Jacoboni. New York: Plenum Press, 1980, pp. 415 -

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