PHYSICAL REVIEW 8 VOLUME 18, NUMBER 10 15 NOVEMBER, 1978

Frequency dependence of conductivity of bulk amorphous seleniumand tellurium-doped selenium

R. M. Mehra, P. C. Mathur, A. K. Kathuria, and Radhey ShyamDepartment of Physics and Astrophysics, University of Delhi, Delhi-110007, India

(Received 9 August 1977)

The dc conductivity and ac conductivity of bulk amorphous selenium and selenium tellurides have been

measured in the temperature range 150 to 310 'K. The ac conductivity is found to follow the relation cr„aco". The value of n is found to increase with the decrease in temperature and with the increase of doping oftellurium in selenium. The value of the density of states at Fermi level, g(EF) is also found to increase with

the increase of tellurium doping. The results have been discussed with the existing theories for ac and dcconduction.

I. INTRODUCTION II. EXPERIMENTAL DETAILS

The frequency variation of the electrica) con-ductivity of noncrystalline solids (NCS} has beena subject of extensive studies since the first mea-surements on frequency-dependent conductivitywere reported by Pollak and Geballe' on com-pensated silicon. However, the measurements onNCS have been made on an extremely wide rangeof systems' ' and the physical insight into the.mechanism of the ac conduction process is stillinadequate. Even a correlation between the dcand ac components of the conductivity is not yetestablished. A distinction between dipolar con-duction and conduction due to a hopping processcannot be made with the help of conductivity vsfrequency variation alone because a sufficientlybroad distribution of relaxation times in a dipolarsystem or interfacial polarization effects' canproduce a frequency variation similar to that pro-posed by Pollak and Geballe for hopping conduc-tion. To distinguish between these two processesand even to identify the nature of the hopping mech-anism, measurements have to be made over awide temperature range in the appropriate fre-quency region in materials having closely similarstructure. Heterogeneity' of the materials andcontacts' may also affect the frequency dependenceof the conductivity.

The present paper reports. ac and dc conductivitymeasurements on bulk amorphous selenium andtellurium-doped selenium samples over a widetemperature range. The ac conductivity has beenfound to be proportional to ~". The exponent nhas been found to be dependent on temperature andpercentage of tellurium in selenium. The resultshave been discussed in the light of existing theoriesfor ac conduction.

Various samples of high-purity (99.999%) Se and

Se„Te, „ofdifferent composition were prepared.The exact proportions of Se and Te were weighedby using a microbalance. The samples were sealedin evacuated (-10'- Torr) quartz ampoule of about6 mm diameter. The ampoule containing Se wasfirst heated at about 200'C for 1-2 h and thenheated to 525 'C in an electric oven. The tempera-ture was kept constant for a period of 10-15 h.The ampoule containing Se„Te, „was heated to900'C and held at that temperature for 20-24 h

and was constantly agitated during heating to en-sure complete mixing. The molten samples werethen rapidly quenched in cold water. The quenchedsamples were taken out from the ampoule by dis-solving the ampoule in solution of HF+H, Q, forabout 16-20 h. Samples of different thicknesswere cut with a wire cutting machine and finallythey were lapped and mirror polished. X-raydiffractometer traces of the samples were taken.Absence of sharp peaks in these traces revealsthe amorphous nature of the samples.

Four samples used for the present work werehaving the following compositions:

Sample Thickness

(1) pure Se 0.091 cm,

(3) Se~9Tea, 0.073 cm,

(3}Se„,Te~ 0.093 cm,

(4) SeL,Te„, 0.055 cm.

Aluminum was evaporated on entire area of theopposite faces of the samples. The samples wereplaced in a metallic cell (which provides propershielding) in sandwiched configuration and the

18 5620

FREQUENCY DEPENDENCE OF CONDUCTIVITY OF BULK. . . 562l

current through it was measured by noting thevoltage across a standard resistance with a Keith-ley nanovoltmeter. Observations were also takenusing silver electrode material, but no differencein the experimental results was found.

ac conductance of the samples was measured byusing a capacitance bridge (Model No. GR V16-C)provided with external generator along with a nulldetection system. The measurements were madein the frequency range 10'-10' Hz. The lowerlimit of the frequency was limited by the sensitivityof the bridge.

III. RESULTS AND DISCUSSION

The variation of dc conductivity (o,) and totalconductivity o with temperature has been shown inFigs. 1—4 (for the four samples 1, 3, 3, and 4).The variation of the ac component of the conduc-tivity (o„=o- &xo) has also been shown with brokencurves in these figures. It shall be seen that thedc conductivity is thermally activated with activa-tion energies varying from 0.84 eV (for pure Sesample) to 0.68 eV (for 30/0 Te doped Se). Thevalues of the pre-exponential factor (o, ) obtainedfrom the intercepts of these plots ranges fromabout 4 to 20 0 ' cm ' as the atomic concentrationof Te is increased from 0/o to 30%%uo. The values ofo, are about three orders of magnitude lower than

10

Se 'Te0 10

10 Hz

10 Hz

'E 10OI

8~o 12

105.4 6-030 3g 4

)

FIG. 2. Semilog plots of the conductivity vs recipro-cal temperature for Se90Te&0, at different frequencies.

the preexponential factor C for conduction in theextended states, suggesting thereby that the con-duction is in the localized states above the valenceband via thermally activated hopping. The de-crease in the values of the activation energy with

10 910

Se80 2'0

0 Hz

E

12~10

Ci

OO

-1310

.84

E JOo1P

0-I

I

Cl

C)

310 qz

J43.0

1 I l I 1 I I

3.8 4.6 5,4 6.010 T ("K ')

FIG. 1. Semilog plots of the conductivity vs reciprocaltemperature for Se, at different frequencies.

1210

383.0 4.6 5g 6.0103

T('K ')FIG. 3. Seinilog plots of the conductivity vs recipro-

cal temperature for Se80Te20 at different frequencies.

RIA AND SHgAMMEHRA~ MATHUR ~ 18

-activatipn energy etower than dct h' her temperat

uctj pn actures,th re is Rn indxca

and may tetion that aer

may increaseac activation energyvalues. As the fre-' ation energy va ue ~ards dc Rctiva

- t. energy decreas esow

th Rctiva ypnquency jncreasesctivation natur~.the»ng e-R

. tRQd deviates from

th results is thant feature of e'th

A other impprtannonductjvj, yes

~ t S jnCrease W~twhile both dc an R

t dc cpnductivitlesdoping the ra '

that the dc con-tip pf ac toe

es which meansf tel-

(o /o, ) deere» ~

tb tbe increase oac o . Ses faSter W&ductivity increa

to ac conductivity.lurium doping as c Pduction process in

s comparedin «r

ected to be highs»f /~ obtained

is expecThe values p ~«cpn, u

t room emd ctipn prpce

pe»ture andb us fpr Se-Te yhpwn iQ Table

yuHz have beeRt frequency &

ptt have R t d pollg 's Rnal-Austin and Mo'de glasses. Thesx to the cRse of chalcogeni ehonon-Rss»te tun-sidered due o P

elhopping is con .t Rt Fermi leveling between the Rir of sy esne in

t is g venbyand the condu«i~"y,(y)))2yZ p~ 5[in(& ph/Id j

yo» sec )~

=(k&)~

bonon freIiuen y (where Pph is the p of the localized-stacr,bes the decay

& ) is tiie densitya with& P e( ~~), and g&z 'wave function e~ -™M

oi states at Fethe values ot ger)

rmi level.-& tpbe8A, ev

lesAssumgng

have been calculate dat2o p K fpr all the samP eown xn Table I . These values of

much larger thand have been shown in

the values ob-g y(E ) are very muc1-induced parama gnetic statest ined by optica -xnRin

ace-charge mmeasurements.an yth f t th tcould be due to e nP y

at temperature as low Rs 20both the processe,a be due to o

rmito conductivity m y

lazed states near Fei.e., con uc 'd tion in the localize s

tir band edge.

1The frequency variriation o

5622

70 30Se Ta

I/Hg-910

-1010

EI

11&10XO

-1210 I

645.43.8 4.63

T('K ')

lots of the conductivity vs recep-t d'ff tft perature for Se70Te30 atemperrocal

in can either be dueof tellurium dppangtll ito the decrea e g

due to e ith ncrease in thd..t. b.th th.o a e saba

ctor indicates anof tel-state with the increase of

fo h ih b bductivity as

nt-do d 1in the tellurium-dopele-activation en-' it shows a sing e-of the conductive y

in the high-tempera ure activation energy

uencies and &n

areregion, but thee values of the ac idc activation energy. rnp

iared to the c ac

s nearenergy values for dc

Ation should e eqaa

nd ac conducc conductivity

a an f

values for ac

s a and the ratio o

ctivation energy

ent n, e s at Fermi level, anntia a, ent n, density of states antial factor, exponent n, edS Td ofS,ac conducts yt to dc con uc

Material

Ac tivad, onenergy

4& (eV)

Preexponentialfactor

~g(~ 'cm ')Exponent n

at 200'K at 300 K

Density of statesat Fermi leve 1

-3gP~) (eV cm )fora=8 A

Ratio of acconductivity todc conductivity

at 300'K0~ (104 Hz)/00

SeSeI)Te g0

Se80Te20Se70Te30

0.840.770.720.68

4.885.287.52

15.9

0.720.820.850.89

0.630.690.760.83

4 24X10~89.3 xlp~81.8 x10&9

2.3 x 10

1.9 x 1p4.03 x10] .4 x 102

5.4 x 1p

18 FREQUENCY DEPENDENCE OF CONDUCTIVITY OF BULK. . . $62$

1P-9

T=300'K

Te&+

910

EI

L". J1

I—

O

J21p

I

J0& 10I

DCl'xOC3

~11

10lg

I I

10 10~ 4Snf)

I

10

1p1p2

I

1p3 1p44) (amp)

t

1p5FIG. 6. Frequency dependence of the conductivity at

300 K of Se, Se&OTe&0, Se80Te20, and SeYOTe3(}.

FIG. 5. Frequency dependence of the conductivity at200 K of Se, SeeoTe&&, SeaoTe&(), and SeTOTe3O.

for all the samples have been shown in Figs. 5 and6 for 200 and 300 'K. It shall be seen from thesefigures that 0„follows the well-established rela-tion o„~~". The values of n (shown in Table I)are found to decrease with the increase in tem-perature. Such a large variation of n cannot beexplained merely by considering the variation ofv» with temperature. A change in vph as large asfrom 10" to IO" shall correspond to change in nonly from 0.'?7 to 0.82 which is much smaller thanthe change of n observed by us. It may, however,be pointed out tha, t a much larger change in mph

is possible if there is a polaron formation, "whichis yet to be established in amorphous selenium.The decrease of n at high temperature has beenexplained by Pollak'4 by considering multiple hop-ping when paths containing different number ofsingle-site distances contribute to ac conductivity.If multiple hopping is the only cause for change inn, then o„(300'K)/a„(200 'K) should be same forall the samples. However, the observed results

are in contradiction to this. There are variousother mechanisms which predict decrease of nat high temperature. Scher and Lax" and Moore"have analyzed the problem of ac conduction byadopting a continuous-time random-walk model.Pike" has explained the decrease of n at high tem-perature by considering the classical hops overstatistically distributed barrier. Similar behavioris also observed in the phonon-assisted hoppingwith statistically distributed relaxation times withcorrelation effect.

Ne also see that as doping increases, the valueof 'n increases at any temperature. This showsthat n has some correlation with disorder, as Tecontent increases the material is expected to bemore disordered. It may be pointed out that it isvery difficult to establish a unique mechanismwhich is responsible for change in g.

ACKNOWLEDGMENT

One of us (AKK) is thankful to the Council ofScientific and Industrial Research (India) forfinancial assistance.

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F. Argall and A. K. Jonscher, Thin Solid Films 2, 185(1968).

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H. K. Rockstad, J. Non Cryst. Solids 8-10, 621 (1972).M. Sayer, A. Mansingh, J. M. Reyes, and G. Rosen-blatte, J.Appl. Phys. 42, 2857 (1971).

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A. K. Jonscher, J. Phys. C 6, 1235 {1973).N. F.. Mott and E. A. Davis, Electronic Processesin Non-Crystalline Materials (Clarendon, Oxford,1971).

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MEHRA, MATHUR, KATHURiA, AND SH YAM 18

~~S. G. Bishop, U. Strom, and P. C. Taylor, Phys. Hev.B 15, 2278 (1977).H. P. D. Lanyon, Phys. Hev. 130, 134 (1963).

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