Preparation and some physical properties of semiconducting GeSb2Te4 crystals

Mat. R e s . Bull. Vol. 7, pp. 1 0 7 5 - 1 0 8 6 , P r i n t e d in the United S t a t e s .

197Z,

Pergamon Press,

Inc.

PREPARATION AND SOME PHYSICAL PROPERTIES OF SEMICONDUCTING

GeSb2Te 4 CRYSTALS M. Frumar, L. Tich~, J. Horik and J. Klikorka Technical University of Chemistry and Technology Pardubice, Czechoslovakia

( R e c e i v e d A u g u s t 8, 1972; R e f e r e e d )

ABSTRACT High purity single crystals of GeSb~Te 3 were prepared. Values of the electrical conductiviZy, thermoelectric power, Hall constant, Nernst-Ettingshaus@n coef~cient and of the IR reflectivity in the plasma oscillation region were obtained. Analysis of the results yielded the dielectric constant ( ~ = 39), index of refraction n ~ o = 6.15, the character 6f scattering of the free carriers, the Fermi level (E~ = 0.31 eV) ~ e relaxation time of the free carriers ( < T ~ = 0.86xi0- ~s) and the value of N /m o To interpret the results, three-valley model of Pth~ energy band was proposed and values of the Hall structure factor (~ = 0.67), the Hall scattering factor (M~ = 0.7), the free-hole concentration ( N = 4.8 x l O m ± c m ~ ) and of the conductivity effective ma~s m~ = 0.55 and m I = mo = 1.34 mo, mo = 0.36 m~ were c~iculated. ~ ~ u Introduction The compound GeSb2Te 4 carl be prepared by means of a peritectic reaction

(I) from germanium and antimony tellurides. The

crystal belongs to hexagonal class with lattice parameters a = 4.21 ~, c = 40.6 ~, its space group being D~d - R 3m (2). Using polycrystalline GeSb2Te 4 samples kosov

(of 99.9% purity) Abri-

(I) obtained values of the Seebeck thermoelectric coeffi-

cient ~ = +18.6~V deg -I, the electrical conductivity = 3800 Jq-lcm-l, thermal conductivity ~ = 6.3xlO-3cal cm -I sec -i and of the melting point (615°C). The present study aimed at the synthesis of high-purity compound, the growth of its single crystals and at the investigation of fundamental physical properties of these crystals. 1075

1076

GeSbpTe 4 CRYSTALS

Vol. 7, No. 10

Crystals growth Synthesis

of the compound was carried out in evacuated

quartz ampoules

(630°C; 3-5 hours) from the elements of 99.999%

purity. Gradual cooling of the melt resulted in coarse-grained crystalline ingots of metallic appearance. Measurements on the electron micro-probe

analyzer with X-ray micro-analyzer

Jeolco, Japan) has confirmed the homogeneity

(JXA-5

of the samples.

The purity of the samples prepared was checked by emision spectral analysis that revealed only traces of Ca, Cu, Bi, Si ( c ~ 10-3%). The structure of the compound prepared was verified by Debye-Scherrer

powder analysis.

Obtained values of the interpla-

nar crystal distances are in good agreement with the data by Abrikosov

(i)° The X-ray micro-structure

the incongruent

analysis reconfirmed

character of the melting point of GeSb2Te 4. Samp-

les that were rapidly quenched from temperatures

above the melting

point were of the two-phase character and their X-ray powder patterns exhibited lines corresponding tals (Fig. la).

to the Sb2Te 3 and GeTe crys-

Single crystals of the GeSb2Te 4 compound were grown usir~g Bridgman and Czochralski techniques as well as the technique of transport

reaction~. The largest and best quality samples could

be obtained by means of the Bridgman technique. The single-crystals obtained

(i x o.5 cm) were of metallic

sheen and they were

perfectly cleavable along the (0001) plane. Their orientation was confirmed by means of the Laue back-reflection

technique.

Individual samples were prepared by cutting or cleaving larger single-crystalline

blocks. Electrical

properties

The crystals investigated were of the p-type conductivity, ~ = 4.3 x iO3fl-lcm-l(3oO°K)o(The symbols ~ and ]J refer to the direction of the crystal's C3-axis.) Electrical conductivity in the direction perpendicular to the cleavage planes of the material was determined using the four-point method according to Tredgold (3). The distances of points from the sample's edges were chosen so as the correction factors, mentioned

in (4),

Vol. 7, No. I0

GeSbzTe 4 CRYSTALS

r

1077

T

r

~

tl

Z/L

5

,I

I i

i

b 40

,L

o

d

I

o,1

o

I

4

o,4

o,2

6

10sl T ('K -~)

din (nm)

FIG. Values

I

FIG.

of interplanar

spacings

T e m p e r a t u r e dependence the Hall m o b i l i t y

a - rapidly quenched melt; b - mixture of G e T e + S b o T e ~ ( l : l ) ; c GeSb2Te 4 single crystals; d - A b r i K o s o v data (i) I/I ° is the relative intensity of the lines

would

be equal to unity°

obtained°

Electrical

the cleavage tion

planes)

A value

of ~I : 1 . 8 x l O 3 ~ - i c m - I

conductivity

is thus 2.4 times larger than

found to decrease

conductivity

of

was

along the crystal layers

perpendicu~lar to the cleavage The e l e c t r i c a l

2

(in

in the direc-

planes°

of the GeSb2Te 4 crystals was

with temperature

in the

interval

-160 - +160°Co

The Hall

coefficient

is in the same temperature

constant

and reaches

the value R H = 6 x I O - 3 c m 3 A - i s -I for E-i =

O.i V cm -I and vectors tivelyo

ell

of applied

= 7.5 'x IO-5Vosocm-2o 3± electric

field and magnetic

region almost

and ~ll

are the

induction, respec-

1078

GeSbzTe 4 C R Y S T A L S The temperature

u H = RH. ~

dependence

can be described

Such a dependence semiconductors

by s relation

(5) and corresponds for

u -

m

energy a n d ~ T ~ f o r

e -

C

T--3/2; where,

zed impurities

(Fig. 2).

of degenerate

to the s c a t t e r i n g

m

C

symbols,

~

on acoustic

(i)

stands for the

time of the current

carriers

effective mass.

lower than 300 K the slope

decreases.

of the u = f(I/T)

One can argue that the s c a t t e r i n g

starts

, ~II )

~ -1/2 " ( -) " ~-~0o kT

the r e l a x a t i o n

and m c is the c o n d u c t i v i t y

dependence

in a number

apart from usual

At t e m p e r a t u r e s

u NI/T

(~l

(5):

e<~>

~ooN

of the Hall m o b i l i t y

has been observed

lattice vibrations,

Vol. 7, No. 10

to assert

itself more strongly

on ioni-

at lower

temperatures. The value rature

of the S e e b e c k

coefficient

(Fig. 3) and its temperature

the relation for degenerate

dependence

semiconductors

= 2 g2/3k2md(r+l)

(~)

rises with tempecomplies well to

(6)

. T

(2)

35/3e ~2 N2/3 where m d is the density-ofstates

effective mass, N is

the number

of free carriers

per unit volume i

r

I

and r is the

scattering parameter.

,C 40

F r a m the observed value

~u,V. ,K "f

30

of the S e e b e c k calculated

20

coefficient

the Fermi

one

level

(EF) , since it holds - a s s u m i n g 10

the d e n s i t y - o f - s t a t e s I

I

I

mass m d change

only slightly

with temperature FIG.

3

Temperature dependence Seebeck t h e r m o e l e c t r i c coefficient

of the

effective

- that

Vol. 7, No. I0

G e S b z T e 4 CRYSTALS

I o6

-

Fr+ 2 (;n)

1079

- ~I

(3)

k e

Fr+ I (~) where Fn (~)

=

(

0 are the Fermi integrals,

~ fo 9

) xndx

(4)

X

fo = [I + exp(x-~

)]-i

_

E

kT (reduced energy of the current carriers) and = EF/kT is the reduced Fermi energy. For the scattering on acoustical phonons

(r = o) one calculates

~ = 12.0,

,

x

i.e. the Fermi energy

is 0.31 eV less than the top of the valence band. Hence, GeSb2Te 4 is a strongly degenerate semiconductor, which is also in agreement with other experimental

results.

The value of the Nernst-Ettingshausen constant QI , obtained from the relation E = -Q± . B . ~ T / ~ x, amounts to QI = 1.196 x lO-3cm2deg-ls-i Y Vector of the induced electric field E was Y -2 perpendicular to that of magnetic induction (311 = 7.5xlO-5V s cm ) and of the temperature

gradient

( ~ T i : I0 K).

Infrared reflectivity Spectral dependence of the reflectivity of GeSb2Te 4 single crystals is shown in Fig. 4. The reflectivity curve exhibits a pronounced minimum in the vicinity tions° The reflectivity dependence

of 6 p m due to plasma oscilla-

curve was used to calculate

the spectral

of the index of refraction n, according to the well-

-known relation

where k is the extinction coefficient. R(K)curve have ( 7 ,)

where ~ < ~ R m i n

n2 (X)

-

k2

(~)

For that part of the

it holds that n 2 > =• n 2 : Cg

-

4 ~

= 6 C

k 2. Then we

g

-

AX

2

(6)

where A = Ne2/4 ~ 2 c 2 G o m c , ~ o is the dielectric constant of vacuum and m is the conductivity effective mass° Extrapolation of the linearc dependence n 2 ( ~ ) = f( ~ 2 ) for ~ 0 one arrives

1080

GeSbzTe 4 C R Y S T A L S

a L a value

of ~g

Relatively

38 and of -She refractive high value

of the refractive ter of bonds

Vol. 7, No. I0

of the dielectric

equations

2nk

~p

-

-

:

l-l/I(

can be described

)2

1

time. a set of curves R ( ~ ).

and experimental

6 g = 39, plasma f r e q u e n c y GZ4 So The value time < ~ = 0.86 x

39 agrees well with that calculated iz evident

part of the r e f l e c t i v i t y ~ g a c c o r d i n g to

For the correct

thet k < n

curve,

from the relation

in the s h o r t - w a v e l e n g t h

as we have assumed

ximation,

Discussion

of results

evaluation

of the experimental

m i s s i n g for this compound.

one can assume

lence band is located

the m a x i m u m being single extremumo does not lead to consistent vallpy model

the s t r u c t u r e - c h e m i c a l

results data

In the first approof the va-

of the B r i l l o u i n This assumption,

results.

It appers

zone, however,

that more

can be arrived at using the many-

of the energy band,

and bismuth tellurides,

Requisite

that the energy m a x i m u m

in the centre

interpretation

in calcu-

(6).

one has to know the energy band structure. are, however,

values

for

and r e l a x a t i o n 3 makes

(7)

of the f r e e - c a r r i e r

(5-8) one computered

(Fig. 3) was attained

(6). Fig.

)2

(8)

is the mean relaxation

The best fit of the theoretical

correct

curve

~JP

f~ < T / ~

Solving Eqs.

lating

charac-

of the Drude theory for the free

is the angular f r e q u e n c y

plasma and < ~

~g

and

carriers

n

where

constant

The whole r e f l e c t i v i t y

in the region near the plasma f r e q u e n c y current

6.~.

index indicate a c o v a l e n t - m e t a l l i c

in this compound.

using classical

index

as it was used for a n t i m o n y

which are more or less similar, f r o m point of v i e w

(5,8,9). The transport

Vol. 7, No. I0

coefficients 1

:

GeSbzTe 4 C R Y S T A L S

1081

are then given by the following relations N

e

Ull

-

~:

U ll

e Nu±

e ~__a_~ (s 2 c2 mI + ~2 )

-

9)

Fr+l F3/2

uA- 2m Ie~r (c 2 + ~2 s 2 +

~i )

io)

li)

Fr+l F3/2

where F n are one-parameter Fermi integrals

(see Eq° 4),

s = sin ~ , c = cos ~ , ~ i = ml/m2' ~2 = ml/m3 are the parameters of the energy band extremum, m i being the components

of the effective mass tensor

( II a n d i r e f e r

again to

the trigonal crystal axis C3)o The Hall coefficient

is then given by the r@ation

RH =

(12) N

where

P

. e

/3 is the structure factor that

(for

B~t

, EL

equals to (5): 4 ,,¢"1(C 2 +

~2 s 2 )

(c2 * ?2 s2 + For dominant

scattering on acoustic

for the quantity MI( m

tl )2 phonons

(13) (r = O) we have

) - which characterizes

the scattering

(5) - a relation

MI(~

) :

F3/2

. FI/2 2

(14)

FI GeSb2Te 4 is a degenerate

semiconductor.

In a degenerate

semiconductor with arbitrary number of valleys

is the

density-of-states md :

L2/3

effective mass m d given by a relation (i0) h2 ~2N)2/3 (m I m2 m3)i/3 _ e ( QI +c0) (3 k RH. ~ ~ 2 . k¢

(15)

108Z

GeSbzTe 4 CRYSTALS

where

L

is the number of valleys

A s s u m i n g that ml/m 3 = surfaces are rotational

~2

Vol. 7, No. I0

(energy extrema).

A i, the constant-energy

or n e a r l y - r o t a t i o n a l

Assumption like this is often fulfilled as reasonable

ellipsoids.

(11,12) and appears

in our case, too.

Relations

(6-14) and the experimental

values have been

used to calculate N/m~ = 8.5 x 1020cm -3, the Fermi ( m = 12.0), the Hall structure factor ~ = 0.67, scattering factor M 7

0.7 and the free-carrier

energy

the Hall

concentration

Np = 4.8 x iO20cm-Jo ~ A c c o r d i n g to the Lyden's quadratic lation

re-

(13) m2 c

(3 ~g -])(I/~ 2) + 5 + 8 ~ 2) C m 4 Eg(6g-l)

(1+311 2 )

+ ( 3 6 g - 2 ) ( l + 2 Q 2) c

26g(6g_l)2(l+3112) (16)

where C : Ne2/mo @ o ~ o 2 , ~

= ~ o
@ o being the angular

frequency in the reflectivity minimum, m o the free electron mass and

~ o the permitivity

of vacuum,

one found the con-

ductivity effective mass m ~ = 0.55. The numerical values c of the obtained parameters were further used to calculate m I = m 3 = 1.34 m o and m 2 = 0.36 m o. These values and the relation

(15) yield a value of ~ = 3.03 ~ 3 as the number of

valence band extremao Therefore

it seems that the three-val-

ley model is a good approximation GeSb2Te 4 crystals. in our opinion,

for the valence band of

The acceptability

of this conclusion

is,

strongly supported by the fact that such

model has been already proposed for Sb2Te3, which is both structurally and chemically similar to t h e m a t e r i a l in question. In Table I. are compared the physical parameters GeSb2Te 4 obtained

of

in this work with those of pseudobinary

components of this compound, i.e. GeTe and Sb2Te 3. The crystals of all three compounds are isostructural and of p-type electrical conductivity.

Their physical properties

Vol. 7, No. I0

GeSbzTe 4 C R Y S T A L S

vary monotonously

1083

in the sequence GeTe-GeSb2Te4-Sb2Te 3. I

1

I

I

I

I

I

to

n,k

70

5

4

6O 3

5O

2

l"

4O

f

7

e.--.-" ,i

3

]

4

L

5

I

6

i

7

I

8 X (,fm)

]

9

J

0

FIG. 4 Spectral dependence

of the reflectivity R, index of re-

fraction n and of the index of extinction k Open circles (o) mark the experimental points. Solid clrcles (e) and lines represent theoretical curves calculated from Eqso (4,6,7). Electric field vector of incident radioation has been perpendicular to the trigonal axis of the crystal (C3) , i.e. E ± C 3

Conclusion In the present work one succeeded to grow pure single crystals of ternary compound GeSb2Te 4 and to determine their fundamental physical properties. Results of the measurements show that the compound GeSb2Te 4 is a degenerate semiconductor with high free-carrier concentration. Their character places the GeSb2Te 4 crystals in the groups of semiconducting compounds with layer structure and p-type electrical conductivity. The structure of the energy band

1084

GeSbzTe 4 CRYSTALS

Vol. 7, No. I0

TABLE 1 S u m m a r y of E x p e r i m e n t a l R e s u l t s .

Crystal

GeTe

GeSb2Te 4

Space group

D5 d

D5 d

Conductivity type

p

p

Conductivity ~ .10 -3 (~-Icm-i)

9,7

4,3

Hall mobility (cm2/V s)

5,5

Sb2Te 3 D5 d

3,78

uH 30

168

Free-carrier concentration N . 10-20 (cm-3) P

9,4

Energy gap Eg (eV)

0,I

Fermi level E F (eV)

0,4

0,31

0,08

Mean relax, time<~>.lol4(s)

0,38

0,86

1,9

Dielectric constant Refractive index Ref.

n

gg

37,5 6,1 14,16,17

4,8

1,5 0,23

39 6,2

50 7,1 15

extremum can be described using the three-valley model. Acknowlegements The authors feel indebted to Mrs. D. Va~kevd and Dr° A. Va~ko (Prague) for their kind measurements of the reflectivity spectra°

Vol. 7, No. 10

GeSbzTe 4 CRYSTALS

1085

References I. N. Ch. Abrikosov, G. T. Dan]lova-Dobrjakova, Izvo Akad. Nauk SSSR, Neorg. Mater. i, 264 (196~). 2. K. A. Agaev, A. G. Talybov, Kristallografija ii, 454 (1966). 3. R. Ho Tredgold, A. Clark, Phys. Stat. Sol. (1970).

(a) 2, K 189

4. L. B. Valdes, Proc. IRE 42, 420 (1954). 5. B. M. Askerov, Kineti~eskije effekty v poluprovodnikach, pp. 74-80, Nauka, Leningrad (1970). 6. Ju. Io Ravin, B. A o Efimova, I. A. Smirnov, Metody issledovanija poluprovodnikov v primemenii k chalkogenidam svinca, p. 160, Nauka, Moskva (1968). 7. W. G. Spitzer, H. Y. Fan, Phys. Rev. 106, 882 (1957). 8. J. R. Drabble, R. Wolfe, Proc. Phys. Soc. B 69, ii01 (1956). 9. J. R. Drabble, R. Wolfe,

ibid 71, 430 (1958).

i0. M. K. 9itinskaja, V. I. Kajdanov, Tverd. Tela 8, 295 (1966).

I. A. Cernik, Fiz.

II. S. Katsugi, Sumitomo Eectr. Rev. 83, 102 (1963). 12. H. Schwartz, G. Bjoerek, D. Beckmann, Solid State Commun. 5_, 905 (1967). 13. H. A. Lyden, Phys. Rev. 134, A 1106 (1964). 14. R. Tsu, W. E. Howard, L. Esaki, Solid State Commun. 5, 167 (1967). 15. J. Hordk

, L. Tich~, A. Va~ko, M. Frumar, %o be published.

16. J. E. Lewis, M. Rodot, P. Haen, Phys. Star. Sol. 29, 743 (1968). 17. J. E. Lewis, M. Rodot, Jo Physique 29, 352 (1968).