MICROWAVE EXPERIMENTS INCLUDING AVALANCHE

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AVALANCHE

V. Dienys, A. Dargys

To cite this version:

V. Dienys, A. Dargys. MICROWAVE EXPERIMENTS INCLUDING AVALANCHE. Journal de Physique Colloques, 1981, 42 (C7), pp.C7-33-C7-49. �10.1051/jphyscol:1981704�. �jpa-00221640�

JOURNAL DE PHYSIQUE

Colloque C7, supplément au n°10, Tome 42, octobre 1981 page C7-33

MICROWAVE EXPERIMENTS INCLUDING AVALANCHE

V. Dienys and A. Dargys

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

Résumé. - Dans cet exposé sommaire, on décrit les principes des techniques le plus souvent utilisées des micro-ondes des- tinées à l'étude des^électrons cnauas dans les semiconducteurs;

on présente aussi l'état actuel des recherches dans le domaine des électrons chauds effectuées dans le champ électrique des micro-ondes. On souligne surtout les expériences ou l'on uti- lise la spécifité d'échauffement par le champ des micro-ondes aussi bien que celles qui ont permis de compléter l'informa- tion concernant le champ électrique continu.

Abstract. - The principles of the most popular microwave tech- niques for hot electron investigations in semiconductors are briefly described and the current status of hot electron inves- tigations with microwaves is reviewed. The emphasis is put on the experiments which make use of the specific features of mic- rowave heating or give an extra information in addition to that obtained from d.c. measurements.

1. Introduction. - The first microwave (mw) experiment on hot elect- rons was reported by Arthur et al. in 1956 /l/. It triggered a se- ries of works devoted to the application of mw's for hot electron investigations. During a subsequent decade a lot of different mw techniques were proposed. At first they were intended for measuring the hot electron mobility /2-7/, but soon it was realized that mw ex- periments can give a valuable information on the hot carrier energy relaxation /8-11/.

The main subject of the report will be concerned with the hot electron studies during the last decade. During this period no es- sentially new ideas have appeared in the field of mw techniques. The known methods were further developed or have undergone some modifi- cations and were applied to more refined physical problems. Therefo- re, at the begining of the paper the principles of the most popular mw techniques will be briefly described. The rest of the paper will be devoted to the recent hot carrier experimental results obtained with mw's. Only the bulk properties of semiconductors will be con- cerned.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981704

2. P r i n c i p l e s of mw techniques f o r hot e l e c t r o n i n v e s t i g a t i o n .

( i ) . D i f f e r e n t i a l mobility technique. This technique was proposed by Arthur e t a l . / 1 / and f u r t h e r developed by Gibson e t al. / 9 / . A sam- p l e i s mounted i n a waveguide, Fig. l a , which propagates a weak mw s i g n a l . Reflection

r

0 1 2 3 4 5

E, k v c m

a > b

F i 1: a ) . The p r i n c i p l e of t h e d i f f e r e n t i a l mobility technique.

'*. Experimental values of s t a t i c p,= vd/E , d i f f e r e n t i a l p d = d q / d E and high frequency (r(w) m o b i l i t i e s a s a function of dc e l e c t r i c f i e l d f o r n-type germanium, P =4.68 Qcm, T =300 K, w / 2 ~ = 34975 GHz /9/.

The a p p l i c a t i o n of strong pulsed dc e l e c t r i c f i e l d across t h e sample h e a t s t h e c a r r i e r s and a s a consequence modulates f and T which can be used t o f i n d t h e s m a l l s i g n a l conductivity Gtw) and t h e die- l e c t r i c constant &(w) a s a f u n c t i o n of t h e dc e l e c t r i c f i e l d . Typi- c a l experimental r e s u l t s f o r t h e high frequency mobilit y(t,,(w>.q(w)/en a r e shown i n Fig. l b i n t h e case of p a r a l l e l dc and mw f i e l d s . It i s c l e a r t h a t i n t h e zero frequency l i m i t

f i

E i s t h e e l e c t r i c f i e l d i n t e n s i t y . Inspection of Fig. l b shows t h a t

p(a)

pd .

( i i ) . I n t e g r a l mobility technique. With t h e sample mounted s i m i l a r l y , t h e c a r r i e r s a r e heated by t h e strong mw e l e c t r i c f i e l d E,cosot while sensing is made by t h e weak dc f i e l d E,

,

where T = ~ T / ~

.

SAMPLE E, ilNES

8 10

E,, k V c m

Fig. 2: a ) . The p r i n c i p l e of t h e i n t e g r a l mobility technique. 4 , G

and a r e t h e i n c i d e n t , r e f l e c t e d and t r a n s m i t t e d power, respec- t i v e l y .

b). Ratio of average c u r r e n t s with, <j>

,

,

i n t h e low frequency l i m i t when t b e r e l a x a t i o n e f f e c t s a r e negligib- l e , f o r example, by numerical techniques o r , as a common p r a c t i c e is, by r e s o r t i n g t o S c h l ~ m i l c h y s i n t e g r a l equation.

The main d i f f i c u l t y of t h i s $echnique i s t o determine E, i n s i d e t h e sample. Depending on the sample Upedance Z, two d i f f e r e n t ap- proaches a r e u s u a l l y used. If Z3 i s of t h e order of a waveguide im- pedance Zg t h e value of E, i s deduced from t h e amount of t h e absor- bed mw power by t h e sample / 4 / . On t h e o t h e r hand, i f Zs,b Z3 t h e mw

f i e l d i n t h e sample i s assumed t o be uniform and equal t o t h a t i n t h e empty guide /6/.

( i i i ) . Harmonic mixing technique. A s f a r back a s 1949 it was shown t h a t r a c t i f i c a t i o n can occur i n a symmetric nonlinear element i f ap- p l i e d s i g n a l c o n s i s t s of s e v e r a l sinusoids with frequencies i n a cen- t a i n r a t i o / 1 2 / . Experimentally t h i s was v e r i f i e d with magnetic c i r - c u i t s containing ferromagnetic m a t e r i a l . A s i m i l a r e f f e c t was obser- ved i n hot e l e c t r o n mw experiment by C a r l i n and Pozhela / 1 3 / i n 1965,

and a year l a t e r Schweitzer and Seeger proposed t o use it f o r t h e measurement of energy r e l a x a t i o n %ime /14/. I n t h e simplest case of homogeneous sample, having t h e s t a t i c c u r r e n t d e n s i t y - f i e l d cha- r a c t e r i s t i c

j =

E = E, cos (at+ cp) + E, cos 2wt ^{( 3 )}

produces a dc open-circuit f i e l d

3 ^{2-7/2 2}

E,=+p(l+4ok) E, E2ms2cy+p. ( 4 )

Here % i s t h e zero-field conductivity and

p

The schematic diagram of an experimental setup i s given i n Fig.

3a. TO f i n d Te it i s most convenient t o measure t h e phase s h i f t 7fr

hzi@

WAVEGUIDE

: a ) . Sample holder f o r harmonic mixing experiments.

.

-

-

-

with r e s p e c t t o t h e reference sample i n which t h e condition wl,<<l i s s a t i s f i e d o r C1-, i s known beforehand, and t h e n t o use ( 5 ) . Fig. 3b i l l u s t r a t e s t h e dependence of Te on l a t t i c e temperature obtained i n t h i s w a y .

( i v ) . Harmonic generation technique. F i r s t experiments on t h e har- monic generation by h o t e l e c t r o n s were concerned with t h e problem of constructing an e f f i c i e n t frequency m u l t i p l i e r /16,17/. However, t h e conversion e f f i c i e n c y of such m u l t i p l i e r s has been found t o be r a t - h e r low, e s p e c i a l l y , f o r high frequencies where t h e i n e r t i a of car- r i e r heating becomes t h e main l i m i t i n g f a c t o r / 1 8 / . A s a r e s u l t t h e frequency m u l t i p l i c a t i o n has not found a widespread a p p l i c a t i o n i n mw engineering. On t h e o t h e r hand, i n semiconductor physics it was s u c c e s s f u l l y applied f o r hot e l e c t r o n energy r e l a x a t i o n investiga- t i o n /18-20/. Fig. 4a i l l u s t r a t e s t h e i d e a of t h e experiment. A rod- shaped semiconductor s a p l e i s mounted in t h e middle of t h e window of a rectangular waveguide. If mw and dc f i e l d s a r e impressed i n t h e sample simultaneously i t i r r a d i a t e s t h e higher harmonics which could

: a ) . The p r i n c i p l e of %he harmonic generation technique.

.

be separated out, f o r example, by t h e guide tapered t o t h e smaller dimensions o r by a harmonic f i l t e r . !The amplitude and phase of t h e harmonic of i n t e r e s t depend on t h e c a r r i e r heating i n e r t i a , and t h i s property may be used t o obtain t h e energy r e l a x a t i o n time. For exam- p l e , t h e harmonic generation technique was used f o r t h e investiga- t i o n of t h e dependence of 3 on e l e c t r i c f i e l d i n n-Ge and n-Si /20/.

Some r e s u l t s of t h a t paper a r e p l o t t e d i n Fig. 4b.

( v ) . Cyclotron resonance technique. The cyclotron resonance experi- ments on semiconductors a r e u s u a l l y employed t o study t h e i r band

s t r u c t u r e . In a d d i t i o n t h e width of t h e resonance l i n e contains in- formation on t h e c o l l i s i o n frequency of c a r r i e r s with l a t t i c e imper- f e c t i o n s . This property can be used t o study t h e c a r r i e r heating i n t h e cyclotron resonance experiments by measuring t h e dependence of t h e l i n e shape on t h e absorbed mv power, Fig. 5.

PC?% 1

" for v k i o u s power l e v e l s

/21/. The absorbed mw power i n c r e a s e s with t h e number

'0

\- .

I

The described m techniques, i n some sense, may be considered a s fundamental ones. A few words should be mentioned of o t h e r r e l a - t e d techniques. In /22/ t h e method employing a c a v i t y with t h e s a p - l e p a r t i a l l y replacing t h e c a v i t y w a l l s was used t o measure t h e h o t c a r r i e r small s i g n a l complex conductivity. I n /23/ it was shown t h a t t h e observation of t h e complex conductivity a t t h e fundamental f r e - quency of high ^mup s i g n a l may be used t o f i n d t h e v e l o c i t y - f i e l d cha- r a c t e r i s t i c . I n /24/ a hybrid of mw and conventional time-of-flight techniques was proposed t o measure d r i f t v e l o c i t y i n t h i n low r e s i s - t i v i t y samples, and e t c .

3. Relaxation e f f e c t s .

-

!&us t h e mw frequency i s high enough f o r strong r e l a x a t i o n e f f e c t s t o appear, and d i r e c t observation of t h e i n e r t i a of physical proces- s e s under hot e l e c t r o n conditions i s possible. This i s of considera- b l e i n t e r e s t f o r semiconductor physics. The progress i n t h e relaxa- t i o n e f f e c t study during t h e l a s t decade was achieved mainly i n t h r e e aspects. F i r s t , apart from t h e t r a d i t i o n a l m a t e r i a l s Ge and S i a l s o o t h e r m a t e r i a l s , e s p e c i a l l y t h e group A B semiconductors, have

3 5

been extensively s t u d i e d , see e.g. /25-28/. Second, t h e experiments have become more s o p h i s t i c a t e d and comprehensive. A s a r e s u l t t h e

Pia. 6 : a ) . Energy r e l a x a t i o n time vs c a r r i e r concentration f o r n-ty- pe nermanium a t 77 K /29/.

b ) .'-The dependence of conductivity r e l a x a t i o n time 'i-, measured by t h e harmonic mixing technique on t h e p i a x i a l compressive s t r e s s

F i n n ype ermanium. T =80 K, E IIFll<177), ~ 4 2 % - ~9.41 GHz, -n =

= 2 . 4 x l d cm-5, ⁰ - n =5x1@2 cm-3 / 32,.

dependencies of t h e energy d i s s i p a t i o n r a t e on t h e e l e c t r i c f i e l d

i n t e n s i t y /20,25,27/

,

Fig. 7: Energy r e l a x a t i o n time v s u n i a x i a l s t r e s s i n p- type germanium a t d i f f e - r e n t temperatures. S t r e s s applied i n t h e <700> d i r e c - t i o n , ^T denotes t h e en- ergy reloaxation time a t zero s t r e s s /33/.

t t e r i n g mechanisms may be deduced from t h e s e and s i m i l a r data. For example, from t h e r e s u l t s displayed on Fig. 6 it can be concluded t h a t i n n-Ge t h e s t r e p g t h s of t h e i n t e r v a l l e y electron-electron

(e-e) s c a t t e r i n g and t h e i n t r a v a l l e y e-e s c a t t e r i n g a r e of t h e same order.

F i n a l l y , t h e i n v e s t i g a t i o n s of r e l a x a t i o n e f f e c t s i n t h e wide frequency range was r e c e n t l y undertaken /34-36/. I n c o n t r a s t t o t h e s i n g l e frequency r e l a x a t i o n e f f e c t measurements such i n v e s t i g a t i o n s can y i e l d more information, e s p e c i a l l y on t h e importance of various r e l a x a t i o n channels. We s h a l l dwell on t h e s e experiments i n more de- t a i l . T i l l now they have been performed i n t h e warm e l e c t r o n region where with t h e help of Eq. ( 1 ) one can show t h a t

Here (3* denotes t h e frequency dependent e f f e c t i v e w a r m e l e c t r o n co- e f f i c i e n t . I n p r i n c i p l e t h e a n a l y s i s of

/SX

where P i s t h e mw power absorbed i n a u n i t volume of t h e sample.

Eq.(7) may be considered as a new d e f i n i t i o n of t h e e f f e c t i v e warm e l e c t r o n c o e f f i c i e n t 4*

.

To i l l u s t r a t e t h e p o s s i b i l i t i e s of t h e method t h e dependence of

2 on t h e frequency f o r n-Si and p-Ge i s shown i n Fig. 8. In case of n-Si, Fig. 8a, t h e experimental r e s u l t s f i t w e l l t h e phenomenolo- g i c a l r e l a t i o n

where T, i s t h e momentum r e l a x a t i o n time. For p-Ge t h e dependence

8: The frequency pend n c g of t h e c o e f f i c i e n t ^d*

.

-%j. n-Si, n =2x10@ cm-?, E l<171), ^{0 -} 1 =80 K , ^{0 -} 7.290 ^I(. S o l i d curves represent t h e b e s t f i t of ^Eq.(8) with t h e experimental

d a t a /34,35/. ^-

b )

.

TII(IOD),

i s more complicated, Fig. 8b. The a n a l y s i s of experimental d a t a of P-Ge have shown t h a t i n t h i s case t h e conductivity r e l a x a t i o n i s de- termined not only by t h e energy d i s s i p a t i o n process but a l s o by t h e h o l e interband r e d i s t r i b u t i o n a s well a s by t h e accumulation of holes

i n the f i e l d d i r e c t i o n / 36/.

4. Impact i o n i z a t i o n .

-

a i r t h e e l e c t r i c f i e l d i n t e n s i t y i n a sample u s u a l l y does not exceed -3.10 4 V/cm. Such f i e l d s a r e too small t o i n i t i a t e t h e band-band impact i o n i z a t i o n i n many t r a d i t i o n a l semiconductors. Therefore, t h e mw induced c a r r i e r m u l t i p l i c a t i o n was observed mainly a s a r e s u l t O f

impurity breakdown a t l o w temperatures / 3 8 / , o r i n narrow-gap semi- conductors, s e e e.g. /39-441. In first experiments t h e onset of bre-

akdown was deduced from t h e transmitted m power l e v e l through a t h i n semiconductor p l a t e c o m p l e t e l y f i l l i n g the waveguide cross-sec- t i o n . Typical experimental r e s u l t s a r e shown i n Fig. 9. The break of

Fig. 9: & transmission

through InSb p l a t e a t 80 K /391

t h e curve i s i d e n t i f i e d with t h e onset of t h e c a r r i e r multiplica- t i o n . However, such measurements a r e used seldom s i n c e only a very crude estimation of t h e e l e c t r i c f i e l d i n t e n s i t y i n t h e p l a t e i s possible.

The i n t e g r a l mobility technique has been found a s a more s u i t a - b l e method f o r t h e i n v e s t i g a t i o n of avalanche p r o p e r t i e s i n semicon- ductors due t o t h e following reasons. F i r s t , t h e e l e c t r i c f i e l d i n t h e rod-shaped sample can be made uniform and found from t h e absor- bed ( Z s - Z 9 ) o r t h e transmitted (ZS>>Z3) power. Also, t h e i d e n t i f i - c a t i o n of t h e breakdown i s e a s i e r . Fig. 1 0 shows t h e dependence of t h e threshold f i e l d of impact i o n i z a t i o n ET on t h e l a t t i c e tempera- t u r e f o r p-InSb a t 10 GHz and 37 GEz a s found by t h i s method. 'Phe d i f f e r e n c e i n ET v s frequency i s a manifestation of t h e delay of t h e impact i o n i z a t i o n Drocess.

5.0 Fig. 10: !J%reshold f i e l d of irn- pact i o n i z a t i o n v s l a t t i c e temperature i n p-InSb a t

0

0 d i f f e r e n t mw frequencies.

0 -10 GHz, -37 GHz / 4 2 / .

0.3 _{Oo 0}

Recently it was demonstrated t h a t mw technique can be success- f u l l y employed f o r t h e study of t h e impact i o n i z a t i o n and magneto- t r a n s p o r t i n crossed e l e c t r i c and magnetic f i e l d s /41,43,44 /. At mw frequencies t h e e l e c t r i c f i e l d i s applied c o n t a c t l e s s l y , t h e r e f o r e , a premature breakdown a s observed i n dc e l e c t r i c and magnetic f i e l d s due t o s h o r t i n g of t h e H a l l f i e l d by c u r r e n t c o n t a c t s can be avoided.

Also,because of a f i n i t e charge r e d i s t r i b u t i o n time it i s p o s s i b l e t o c o n t r o l t h e magnitude of t h e mw H a l l f i e l d i n t h e samples with t h e H a l l geometry. For example, by choosing small enough c a r r i e r concentration o r by placing t h e sample in a high magnetic f i e l d B

((26>>11 one can reduce t h e now H a l l f i e l d nearly t o zero. I n Fig. 11

E,vs B is shown f o r n - W b a t 80 K. A t t h e frequency of measure- ment, 9.4 GHz, t h e mw H a l l f i e l d was n e g l i g i b l e and samples beha- ved a s i f being of t h e Corbino geometry. A s expected i n t h e high magnetic f i e l d region ET i n c r e a s e s n e a r l y l i n e a r l y with 6

.

E 3 -

Y

s

Lu;2

0 1 2 B,T

/ @

-

1 -

/ P

i I

Fig. 11: Threshold f i e l d of lmpact i o n i z a t i o n vs mag- n e t i c f i e l d f o r n-InSb samples with r e s i s t i v i t i e s a t 77 K,O.l7Qcmto) ,22Scm

( x)

,

!Phe nonlinear mw magnetoplasma resonance i n s m a l l samples was demonstrated t o be u s e f u l t o study t h e impact i o n i z a t i o n /44/. With samples i n t h e form of s m a l l d i s c s placed in a r e c t ~ u l a r guide, a dependence s i m i l a r t o t h a t presented i n Fig. 11 was obtained.

The avalanche breakdown i s associated with t h e p a i r production s c a t t e r i n g which may be described by introducing t h e i o n i z i n g c o l l i - s i o n time

T;:, .

Fig. 12: The dependence of d r i f t v e l o c i t y and nonequi, l i b r i u m c a r r i e r concentra- t i o n on e l e c t r i c f i e l d i n n-InSb obtained with doub- l e p u l s e mw technique /47/.

The d o t s are experimental r e s u l t s obtained by t h e ti- me-of-flight method /48/.

s t e e p l y increases a t f i e l d s higher than 250 V/cm. Tbe d r i f t v e l o c i t y reaches t h e maximum value a t 500 V/cm and then drops down. NO t r a n s i - t i o n from t h e negative t o t h e p o s i t i v e d i f f e r e n t i a l mobility i s ob- served a s predicted by t h e Monte Carlo c a l c u l a t i o n s / 4 6 / i f ioniza- t i o n frequency is assumed t o be l a r g e r than phonon s c a t t e r i n g f r e - quenc y

.

5. Ilegative d i f f e r e n t i a l mobility (ndm)

. -

i n t e g r a l mobility technique has been widely applied i n t h e i n v e s t i - g a t i o n s of GaAs and r e l a t e d compounds t o supplement t h e r e s u l t s ob- t a i n e d with o t h e r techniques. A t present p r a c t i c a l l y i t i s t h e only method t o obtaine a v-E curve possesing ndm i n high e l e c t r o n d e n s i t y

semiconductors because t h e most d i r e c t method, t h e time-of-flight method, unfortunately needs l o w c a r r i e r d e n s i t y material. A review of t y p i c a l experimental r e s u l t s and problems connected with mw mea- surements i n t h e ndm region may be found, e .g. in/49/

.

Most of t h e i n v e s t i g a t o r s dealing with t h e ndm have been i n t e - r e s t e d i n finding v-E c h a r a c t e r i s t i c . On t h e o t h e r hand, t h e depen- dence of t h e small s i g n a l complex conductivity on dc heating f i e l d

Fig. 13: Small s i g n a l conductivity ( a ) and d i e l e c t r i c constant ( b ) v s heating f i e l d f o r t h e cases of p a r a l l e l ( I1 ) and perpendicu- l a r (1 ) 50 GHz sensing f i e l d i n n-GaAs. The curves a r e normali- zed t o t h e zero heating f i e l d values. T 1300 K , =218cm 1501.

i n t h e ndm region i s of a considerable i n t e r e s t . It has been demons- t r a t e d t h a t t h e raw technique i s s u i t a b l e i n such s i t u a t i o n s / 5 0 / . To suppress t h e high f i e l d domain formation t h e b i a s high e l e c t r i c f i e l d has been c r e a t e d by applying 1 0 GHz mw's. A 50 GHz weak sen- s i n g f i e l d was applied simultaneously t o f i n d t h e complex small s i g -

~ a l conductivity a s a function of t h e b i a s f i e l d . Fig. 1 3 shows t h e r e a l and imaginary p a r t s of t h e small s i g n a l conductivity of n-GaAs a t 300 I( f o r p a r a l l e l and perpendicular d i r e c t i o n s of t h e heating f i e l d vector with respect t o the sensing one. The obtained r e s u l t s a r e valuable i n understanding hot e l e c t r o n dynamics.

I n 1511 t h e i n v e s t i g a t i o n of ndm i n t h e graded gap mixed crys- t a l s A 1 _X Gal

-

portant. The problem of t h e l a t e r a l t r a n s p o r t w i l l be t r e a t e d i n de- t a i l i n t h e paper by Hess a t t h i s conference.

6. Nonuniform s t r u c t u r e s .

-

,

L a t e r it was proposed t o use high r e s i s t i v i t y samples with gra- ded a+-n ( o r pt-p) junction /54/

.

,

A schematic arrangement f o r t h e l o n g i t u d i n a l thermopower measu- rement i s represented i n Fig. L4a, while Fig. 1 4 b shows t h e longi- t u d i n a l d i f f u s i o n c o e f f i c i e n t i n n-Si a t 300 K obtained with lit- hium d i f f u s e d n'-n junction. Later t h e same technique was extended t o Schottky b a r r i e r s f a b r i c a t e d on high r e s i s t i v i t y semiconductors /55/.

7. I n t e r a c t i o n between d i f f e r e n t R r O U P S of c a r r i e r s .

-

ron resonance experiments i n p-Ge through t h e dependence of l i n e - -width on t h e rn power /57,58/. A more d i r e c t observation of t h e in- t e r a c t i o n between groups would be possible i f s e l e c t i v e heating and

SAMPLE 4-i WAVEGUIDE

E, LINES.

I , 1

14: a ) . The p r i n c i p l e of t h e mw technique f o r t h e l o n g i t u d i n a l

1 fusion c o e f f i c i e n t measurement. Typical junction l e n g t h s a r e

%T from 0.1 t o 2 mm and concentration r a t i o nt/n i s from 2 t o 4.

b ) . Hot e l e c t r o n l o n g i t u d i n a l d i f f u s i o n c o e f f i c i e n t vs E i n a high r e s i s t i v i t y n-Si a t 300 K. The s o l i d l i n e represents t h e values of Dl/ obtained by mw's 1551 and c r o s s e s a r e measured by t h e time-of-flight technique /56/. The d a t a a r e normalized t o t h e zero f i e l d value of d i f f u s i o n c o e f f i c i e n t Do

.

sensing of t h e various groups of c a r r i e r s were performed a t d i f f e - r e n t frequencies. Such cross-modulation type experiments were demons- t r a t e d i n / 591. The modulation a t t h e sensing frequency was caused by t h e change of c a r r i e r d e n s i t y due t o t h e dependence of recombina- t i o n r a t e on t h e c a r r i e r energy. However it would be very i n t e r e s - t i n g t o c a r r y out s i m i l a r experiments a t constant c a r r i e r concentra- t i o n , with t h e modulation being caused by t h e energy exchange bet- ween d i f f e r e n t groups.

8. Conclusions.

-

I n conclusion it should be noted t h a t t h i s review i s t o o b r i e f t o do j u s t i c e t o a g r e a t d e a l of e x c e l l e n t work on m hot e l e c t r o n s t u d i e s . The authors apologize f o r an9 omission and must confess t o t h e normal s u b j e c t i v e view of t h e subject.

Acknowledments. The a u t h o r s a r e g r a t e f u l t o A.Matu1ioni.s f o r h i s c r i t i c a l reading of t h e manuscript.

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