ELECTRON TRANSFER EFFECT IN INTRINSIC TELLURIUM SINGLE CRYSTALS

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ELECTRON TRANSFER EFFECT IN INTRINSIC TELLURIUM SINGLE CRYSTALS

R. Asauskas, V. Balynas, Z. Dobrovolskis, A. Krotkus, W. Hoerstel

To cite this version:

R. Asauskas, V. Balynas, Z. Dobrovolskis, A. Krotkus, W. Hoerstel. ELECTRON TRANSFER

EFFECT IN INTRINSIC TELLURIUM SINGLE CRYSTALS. Journal de Physique Colloques, 1981,

42 (C7), pp.C7-329-C7-334. �10.1051/jphyscol:1981740�. �jpa-00221677�

ELECTRON TRANSFER EFFECT IN INTRINSIC TELLURIUM SINGLE CRYSTALS

R. Asauskas, V. Balynas* z . D o b r o v o l s k i s t A. Krotkus* and W. Hoerstel**

Kaunas Polytechnic Institute, Kaunas, USSR

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

**Sektion Physik der Humboldt-UniversitSt Berlin, Berlin, DDR

Abstract.- Experimental and theoretical studies of charge transport and hot carrier effects have been made in intrinsic tellurium. Pulse measurements of current-voltage characteris- tics have shown a negative differential resistance at fields above 3.5 kV/cm. Moving high-field domains were observed by potential probe measurements. The velocity of the domain was 7*10° cm/s. Hydrostatic pressure measurements of threshold field and Hall coefficient were performed at elevated tempera- tures, which suggest the existence of a second, low mobility conduction band located 0.26 - 0.38 eV above the first one.

Reasonable agreement was obtained between the measured magni- tudes of threshold field and electron mobility and the results of Monte Carlo calculations.

1. Introduction.- Semiconducting tellurium always shows p-type con- duction in the extrinsic range. Therefore,the investigation of the conduction electron properties is possible in the intrinsic conduc- tion range only. Recent experimental investigations of high field transport in intrinsic tellurium shows that the current-voltage characteristics exhibits a voltage-controlled negative differential resistance (n.d.r.) at fields above 3.5 kV/cm /1/. The present work deals with a further examination of this effect. The measurements of

Colloque C7, supplément au n°10, Tome 42, octobre 1981 page C7-329

Résumé.- Des recherches expérimentales et théoriques concernant le transfert des porteurs et les effets des porteurs chauds en tellure intrinsèque ont été effectuées.

les caractéristiques courant - tension enregistrées au moyen de la technique des impulsions nanosecondes indiquent une ré- sistance différentielle, si l'intensité du champ dépasse une valeur de 3.5 xV/cm.

A l'aide de sondes électriques des domaines mouvants de champs intensifs ont été mis en évidence.

La vitesse de dérive monte â 7*10

&

cm/s.

Le champ seuil et le coefficient de Hall ont été mesurés aux températures élevées et a une pression hydrostatique.

Les résultats indiquent 1* existence d'une deuxième bande de conduction, qui se trouve 0.26 - 0.38 eV au-dessus de la première bande, et avec une mobilité des porteurs

relativement faible.

Les valeurs du champ seuil et de la mobilité électronique, obtenues selon la méthode Monte-Carlo, correspondent bien

aux valeurs expérimentales..

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981740

C7-330 JOURNAL DE PHYSIQUE

c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s and

H a l l

e f f e c t were made under

hy-

d r o s t a t i c p r e s s u r e t o o b t a i n information about t h e n a t u r e of n.d.r..

Monte Carlo c a l c u l a t i o n s have a l s o been c a r r i e d o u t u s i n g t h e most probable v a l u e s of parameters i n o r d e r t o e x p l a i n t h e experimental r e s u l t s .

2,

Sample p r e p a r a t i o n , - The samples i n v e s t i g a t e d were c u t from Te s i n g l e c r y s t a l s w i t h a h o l e c o n c e n t r a t i o n of 5.10'~ cm-3 and a mobil- i t y of 5000 cm2/vs a t 77

K

p a r a l l e l t o t h e c-axis. They were dumbbell shaped t o eleminate t h e i n f l u e n c e o f e l e c t r o n e x t r a c t i o n i n t h e near- cathode region. The f i e l d d i s t r i b u t i o n a l o n g t h e sample was measured u s i n g two g o l d w i r e p o t e n t i a l probes, The first one was a l l o y e d t o t h e middle t h i n p a r t of t h e sample. The v o l t a g e of t h i s probe was t h e b a s i c p o t e n t i a l . The second w i r e was p r e s s e d t o t h e sample a t v a r i o u s d i s t a n c e s from t h e a l l o y e d probe,

3. Measurements a t atmospheric pressure.- Pig.

1

shows c u r r e n t -

v o l t a g e c h a r a c t e r i s t i c s measured under atmospheric p r e s s u r e

a t

v a r i - ous temperatures and 5 n s a f t e r p u l s e beginning.

A

v o l t a g e c o n t r o l l e d

1 :

Current-voltage c a r a c t e r i s t i c s of i n -

%!+ t r i n s i c t e l l u r i u m sample.

The c u r r e n t d e n s i t y i s d i v i d e d by t h e i n t r i n s i c c a r r i e r c o n c e n t r a t i o n a t t h e corresponding

temperature.

0 I

2

3

U / l

, ^kV/cm

n.d.r. i s observed a t e l e c t r i c f i e l d s t r e n g t h s above 3.5 kV/cm.

It

must be noted t h a t no superohmic i n c r e a s e

of

t h e c u r r e n t was d e t e c t e d

a t f i e l d s below t h e t h r e s h o l d of n.d.r., which would be t y p i c a l f o r

impact i o n i z a t i o n . The c u r r e n t p u l s e s show a s i n g l e k i n k

^as

t h e f i e l d

i s j u s t a t t h e t h r e s h o l d . O s c i l l a t i o n s can be observed on t h e growing

o u r r e n t when t h e f i e l d i s i n c r e a s e d f u r t h e r . The n.d.r, e x i s t s i n t h e

i n t r i n s i c conduction range only. No n.d.r. was observed a t 183

K

where h o l e Conduction p r e v a i l s / I / . I n / I / i t i s shown t h a t a h i g h

f i e l d domain i s formed a t t h e t h r e s h o l d of n.d.r.. We made p o t e n t i a l

probe meaeurements t o e s t a b l i s h t h e v e l o c i t y of t h e domain. The po-

t h e p u l s e s shows t h a t t h e h i g h f i e l d domain propagates i n t h e sample i n t h e d i r e c t i o n toward t h e anode w i t h a v e l o c i t y of 7 . 1 0 ~ cm/a. The d i r e c t i o n of t h i s propagation a s w e l l a s t h e disappearance o f n.d,r.

a t low temperatures i n t h e h o l e conduction range g i v e s evidence t h a t t h e n.d.r. i s connected w i t h conduction e l e c t r o n s . The f i e l d and time range i n which t h e i n s t a b i l i t y i s observed suggest t h a t t h e most probable cause o f t h i s e f f e c t i s an e l e c t r o n t r a n s f e r t o a h i g h e r l y i n g conduction band.

A

c l a s s i c a l t e a t f o r t h e e l e c t r o n t r a n s f e r model i s t h e h y d r o s t a t i c p r e s s u s e experiment. Therefore, we made i n - v e s t i g a t i o n s under h y d r o s t a t i c p r e s s u r e

up

t o 1500 MPa.

2: P o t e n t i a l

%

pro e pulses. The av- e r a g e f i e l d i n t h e sample i s 4.2 kV/cm, t h e temperature o f t h e measurement 223

K.

The d i s t a n c e from t h e b a s i c probe towards t h e cathode i s noted i n micromet era.

4. H y d r o s t a t i c p r e s s u r e measurements.- Application o f h y d r o s t a t i c p r e s s u r e changes t h e energy spectrum of e l e c t r o n s i n t h e c r y s t a l and t h e occupation change of p a r t i c u l a r l e v e l s t h u s l e a d s t o an i n c r e a s e o r d e c r e a s e of t h e t h r e s h o l d f i e l d f o r i n t e r v a l l e y t r a n s f e r of h o t e l e c t r o n s , F o r t e l l u r i u m however n e i t h e r t h e p o s i t i o n of t h e second conduction band n o r t h e p r e s s u r e dependence of t h e i n t e r b a n d separa- t i o n a r e known, Therefore, i t was necessary t o determine a t l e a s t t h e s i g n of t h e p r e s s u r e c o e f f i c i e n t from an independent experiment. We have measured t h e p r e s s u r e dependence of t h e anomalous s i g n r e v e r s a l i n t h e H a l l c o e f f i c i e n t /3/.

I n t e l l u r i u m t h e H a l l c o e f f i c i e n t shows a twofold s i g n r e v e r s a l a s

t h e temperature i n c r e a s e s : i n t h e t r a n s i t i o n r e g i o n from e x t r i n s i c t o

i n t r i n s i c conduction and a t temperatures above 500 K. The second s i g n

r e v e r s a l i s explained i n terms of t h e thermal occupation of a h i g h e r

l y i n g low-mobility conduotion band a t e l e v a t e d t e m p e r a t u r e s /2/. We

have found i n /3/ t h a t t h e i n v e r s i o n temperature

Ti

d e c r e a s e s

with

C7-332 JOURNAL DE PHYSIQUE

i n c r e a s i n g h y d r o s t a t i c p r e a s u r e , Ti i s equal t o 475

K

and 440

K

a t 500 MPa and 800 MPa reap.. T h i s means t h a t t h e i n t e r b a n d s e p a r a t i o n which i s p r o p o r t i o n a l t o

Ti

/3/ d e c r e a s e s under h y d r o s t a t i c p r e s s u r e . One can a n t i c i p a t e t h e r e f o r e a d e c r e a s e of t h e t h r e s h o l d f i e l d f o r n.d.r.

i f

t h e l a t t e r i s caused by i n t e r b a n d t r a n s f e r of e l e c t r o n s .

The experimental d a t a p r e s e n t e d i n f i g . 3 support t h i s suggestion.

A s can

be seen from f i g . 3, t h e t h r e s h o l d f i e l d d e c r e a s e s under hy- d r o s t a t i c p r e s s u r e .

A t

p r e s s u r e s exceeding 1000 HPa t h e c u r r e n t i n - c r e a s e s a t f i e l d s below t h e n.d,r. t h r e s h o l d due t o impact i o n i a a - t i o n .

If

t h i s i o n i z a t i o n i s caused by e l e c t r o n s , one can e s t i m a t e t h e i n t e r b a n d s e p a r a t i o n a t p r e s s a r e s where t h e i o n i z a t i o n o n s e t o v e r t a k e s t h e n.d.r, t h r e s h o l d . The i n t e r b a n d s e p a r a t i o n E12 a t t h i s

w: P r e s s u r e de- pen ences of t h e t h r e s h o l d f i e l d s f o r n.d,r. and impact i o n i - z a t i o n .

The

temperature of t h e measurement was

- - 213 t o 233 K.

\

\

-.

I -

^{Ei i}

0 0

500 1000 1500

P,

MPa

p r e s s u r e must be e q u a l t o o r greatel. t h a n t h e i o n i z a t i o n energy f o r an e l e c t r o n Ei

=

E (2me + %)/(me + %). The energy gap

E

of

8 g

t e l l u r i u m a t 1000 MPa i s e q u a l t o 0.175 eV /4/, which g i v e a a value of 0.21 eV f o r Ei and a l s o f o r t h e minimum i n t e r b a n d s e p a r a t i o n a t t h i s preasure. The p r e s s u r e dependence of E i n t e l l u r i u m i s exponen- t i a l /4/ due t o t h e s t r o n g n o n l i n e a r i t y of c o m p r e s p i b i l i t y ; t h e r e -

Q

f o r e , one can a n t i c i p a t e t h a t t h e dependence of E12 h a s

t h b

same c h a r a c t e r . The e x t r a p o l a t i o n of E12 t o atmospheric p r e s s u r e

with

t h e s l o p e o b t a i n e d from t h e H a l l - e f f e c t a n a l y s i s /1/ g i v e s a minimum value of E12 a t atmospheric p r e s s u r e of 0.26 eV.

Furthermore, because no impact i o n i z a t i o n o c c u r s a t f i e l d s below t h e n.d.r. t h r e s h o l d , t h e i n t e r b a n d s e p a r a t i o n st atmospheric pres- s u r e must be h i g h e r than Ei f o r e l e c t r o n s . T h i s g i v e s E12

=

0.38 eV a s t h e maximum value f o r t h e i n t e r b a n d s e p a r a t i o n a t atmospheric p r e s s u r e .

%Monte Carlo cralcu1ations.-

We

made c a l c u l a t i o n s of 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 s and of t h e low-field e l e c t r o n m o b i l i t y a t v a r i o u s

t e r i n g parameters. The low-field m o b i l i t y was found from t h e calcu- l a t e d low-field d i f f u s i o n c o n s t a n t . A two-level s t r u c t u r e of t h e con- duction band was assumed. An e l e c t r o n mass of 0.06

mo

was used i n t h e loweat

H

v a l l e y s , c a l c u l a t i o n s were performed both w i t h a p a r a b o l i c model and a two-band nonparabolic Kane model f o r t h e H v a l l e y s . An a n a l y s i s o f galvanomagnetic e f f e c t s i n i n t r i n s i c t e l l u r i u m shows t h a t t h e e f f e c t i v e mass must be ectremely h i g h i n t h e second conduction band. We have used a value of 10 mo Por m;! i n o u r c a l c u l a t i o n s . E12

=

0.3 eV was chosen, The f o l l o w i n g s c a t t e r i n g meohanisms were taken i n t o account: p o l a r o p t i c a l aa w e l l a s o p t i c a l and a c o u s t i c a l deformation p o t e n t i a l i n t e r a c t i o n

w i t h

phonons, and s c a t t e r i n g by i o n i z e d c e n t e r s

with

a c o n c e n t r a t i o n of

1016

cmm3.

A

comparison was made w i t h t h e temperature dependence of e l e c t r o n m o b i l i t y measured i n

/5/ and w i t h t h e v a l u e s of t h e t h r e s h o l d f i e l d f o r n.d.r..

A

p r e l i m i - nary a n a l y s i s shows t h a t t h e agreement between measured and calcu-

4: C a l c u l a t e d f i e l d epen ences o f e l e c t r o n

9% d r i f t v e l o c i t y a t v a r i o u s l a t t i c e temper- a t u r e s ,

l a t e d d a t a i s t h e b e s t f o r t h e model i n c l u d i n g o n l y a weak nonpara- b o l i c i t y of t h e

H

bands ( n o n p a r a b o l i c i t y c o n s t a n t 2 e ~ " ) and domi- n a n t o p t i c a l deformation p o t e n t i a l s c a t t e r i n g w i t h a coupling con- s t a n t of 1 0 eV/cm. I n f i g . 9

4

some 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 s a r e shown c a l c u l a t e d on' t h e b a s i s of

this

model. The c a l c u l s t i o n s show t h a t t h e e l e c t r o n t r a n s f e r e f f e c t

i t 1

t e l l u r i u m i s c h a r a c t e r i z e d by a r a t h e r h i g h peak-to-valley r a t i o of t h e d r i f t v e l o c i t i e s Vpeak/vvalley

=

5 a t 215

K,

6. Conclusions.- N.d.r. and moving h i g h f i e l d domains i n i n t r i n s i c

t e l l u r i u m s i n g l e c r y s t a l s were observed. I n v e s t i g a t i o n s made under

C7-334 JOURNAL DE PHYSIQUE

h y d r o s t a t i c p r e s s u r e have shown t h a t t h e n.d.r.

i a

due t o e l e c t r o n t r a n s f e r i n t o a second conduction ban l y i n g a t a p p r o x i m a t e l y 0.26

-

0.38 eV above t h e f i r e t one. 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

a

h i g h peak-to-valley r a t i o s u g g e s t i n g t h a t n-type t e l l u r i u m woufd be a good m a t e r i a l f o r e f f e c t i v e Gunn o s c i l l a t o r s .

Acknowledgement.- We a r e g r a t e f u l t o Prof. J. P o z e l a f o r h e l p f u l discussions and support.

References

/1/

V.

Balynas, Z. Dobrovolskis, W. H o e r s t e l , A. Krotkus, phye. s t a t . s o l .

( a ) 62,

K 9 (1980)

/2/ F. G, d * A i l l o n , C,

H.

Champness, Phys. Rev, B ?2205 (1975) I,

/3/

V. Balynas, 2, Dobrovoskis, W. H o e r s t e l , A. Krotkus, phya.

stat.

s o l . (a)

&,

^K 115 (1981)

/4/ V. B.

Anein, Ed.

I.

Eremets,

Y.

V. Kosichkin, A. I. Nadeshdinskii A.

BB.

Sfiirikov,

phys. s t a t . s o l . ( a j

g,

385 (1977)

/5/ W.

H o e r s t e l , W i s s . Z. Humboldt-Universitiit, Math.-Nat. R.

X X V I I , 599 (1978)