A.C. conductivity of amorphous Ga-Se-Te system

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A.C. conductivity of amorphous Ga-Se-Te system

A.S. Maan, D.R. Goyal, A. Kumar

To cite this version:

A.S. Maan, D.R. Goyal, A. Kumar. A.C. conductivity of amorphous Ga-Se-Te system. Re- vue de Physique Appliquée, Société française de physique / EDP, 1989, 24 (12), pp.1071-1075.

�10.1051/rphysap:0198900240120107100�. �jpa-00246144�

1071

REVUE DE PHYSIQUE APPLIQUÉE

A.C.

conductivity

amorphous

system

A. S. Maan (1), ^{D. R.} Goyal (1) ^{and A. Kumar} (2)

(1) Physics Department, ^Maharshi Dayanand University ^{Rohtak - 124001, India}

(2) Department ^of Physics, Harcourt Butler Technological Institute, Kanpur 208002, ^India (Reçu ^{le 8} juin ^{1989, révisé le 7 août} 1989, accepté ^{le 7} septembre 1989)

Résumé. ²⁰¹⁴ Cet article donne la dépendance ^en température ^et fréquence de la conductivité a.c.

(03C3a.c.) ^{dans un} système a-Ga40SexTe60-x (x ^{= 40, 30,} 20). ^La dépendance ^en température ^de 03C3a.c. dans ^ce

système ^{a été} interprétée ^{en termes} de contributions des mécanismes de saut de bipolaron ^{et de} polaron unique. 03C3a.c. varie approximativement comme 03C9s dans le domaine de fréquence observé, ^{où s est} toujours plus petit que 0,8 ^et dépend peu de la température pour ^{x = 20 et} 40 lorsqu’elle ^est inférieure à 200°. Cependant,

pour l’échantillon ^{x =} 30, ^la variation de s avec la température ^est relativement importante. ^{A basse} température, la valeur de s augmente ^{avec le} pourcentage ^{de Te.}

Abstract. ²⁰¹⁴ Present communication reports ^the temperature ^and frequency dependence ^{of a.c.} conductivity (03C3a.c.) ⁱⁿ a-Ga40SexTe60-x system (x ^{= 40, 30,} 20). Temperature dependence ^of 03C3a.c. in this system ^{has been} interpreted ^{in terms of} contributions from bipolaron ^and single polaron hopping mechanisms. The 03C3a.c. varies as ~ 03C9s in the observed frequency ^range. Frequency exponent s ^is always smaller than 0.8 and shows

a weak temperature dependence ^{below 200 K for x =} 20 and 40. However for x ⁼ 30 sample ^the variation of s

with temperature ^is relatively pronounced. ^{At low} temperature ^{the value} of s increases with increasing ^Te percentage.

Classification

Physics ^Abstracts

72.80N - 77.20 ^- 77.40

Introduction.

Amorphous semiconductors due to technologically important electrical properties ^{have drawn enormous}

attention is recent years. Study of electronic struc- ture of the materials is important ^{so as to decide the} possible ^use of these materials in different fields.

Measurement of a.c. conductivity ^{is a} powerful ^tool

to probe the presence of localized ^states in the energy gap. Present paper reports ^{the a.c. conduc-} tivity measurements of a-Ga40SexTe60-x (x ⁼ 20, 30, 40) system.

The a.c. conductivity (~a.c.) in a-semiconductors is expressed by ^the usual relation

where w is angular frequency and A and s are constants. In order to explain ^{the mechanism of a.c.}

conduction in a-semiconductors a number of models

[1-3] ^{have been} proposed. Recently the variation of o’ac and s in majority ^of chalcogenide glasses ^have

been explained ^{on the} basis of correlated barrier

hopping (CBH) ^model [3] which is based on the concept ^{of the} charged ^{defect states in these} glasses.

Experimental.

a-Ga~Se/Te~o _ ~ samples ^were obtained in bulk form

by using ^{elements of 5 Nines} purity. The elemental constituents weighed ^{in desired} proportion ^were

sealed in the evacuated quartz ampules (10- 3 Torr)

and the ampules ^{were then} placed ^{in a furnance with} rocking arrangement. ^The ampules ^{were heated at a}

constant rate of 3-4 °C/min under continuous rocking

and were kept ^{at -} 1 000 °C for - 10 hours. There- after, ^{these were} quenched ^{into ice cooled water.}

Bulk material as obtained was used for preparation

of pallets ^for experimental ^use. Pallets of diameter 1.3 cm and thickness -0.14cm were prepared by compressing ^the finely grounded power in ^a die in a

hydraulic press ^{under a} pressure - (108 kg/M2).

Aquadec electrodes were used for making ^contacts

and the sample ^{was then} tightened ^{between two steel}

electrodes in a cell.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/rphysap:0198900240120107100

1072

Reported measurements were carried out in ^a

vacuum of 10- 3 Torr. A capacitance conductance

bridge, Genrad model AP-1620 A was used for conductance and capacitance mesurements. Liquid nitrogen ^{was used to} cool down the sample ^and

measurements were started from 100 K. The DSC measurements confirmed the glassy ^{nature of the} alloys and gave the glass Transition temperatures

(Tg).

Results and discussion.

Experimental values of frequency dependent ^con- ductivity u (ev) ^of Ga40Se40 Tezo ^{glass are} plotted against 1000/T ⁱⁿ figure ^{1. o~} (w ) ^{is almost} indepen-

Fig. ^{1. -} Temperature dependence ^{of total} conductivity u (CJ.) ) ^of Ga40Se40 Te20 ^{at various} frequencies.

dent of temperature ^{at low} temperatures ^{at all the} frequencies in the range 0.1 kHz-10 kHz. Variation of d.c. conductivity (aa,C, ) ^with 1000/T ^{is also}

shown in the figure. ^At higher temperatures ^{the a.c.}

conductivity values and its temperature dependence

becomes almost those of the d.c. conductivity. ^A large number of semiconductors [4, 5] ^{have been} reported ^{to show this} type of behaviour. Figure ² represents the variation of log ~ (m ) ^with 1000 / T

for different compositions ^at 10 kHz. Results in

figure 2 show that the samples ^become less conduct-

ing ^with increasing Se : Te ratio. The temperatuee dependence ^{of total} conductivity (cr (w » ^{is more} pronounced ^{at low} frequencies ^{in all} three compo- sitions.

Variation of 109 Od.c. ^with 1000 / T (Fig. 1) ^{is a} straight ^line implying that d.c. conductivity ^{is an}

activated process. The ^same is true for other compo- sitions as well. In chalcogenide glasses this activated nature of d.c. conductivity indicates that the conduc- tion is taking place through the carriers in extended states beyond ^the mobility edge [6] ^{instead of}

variable range hopping of electrons between states

Fig. ^{2. -} Temperature dependence ^{of total} conductivity

0" (w ) of various compositions (x ⁼ 20, 30, 40) ^{at 10 kHz.}

at the Fermi level [7]. ^{If the a.c.} and d.c. conduction arise from completely separate and different pro-

cesses or if the same basic process is responsible ^for

both types ^of conductivity, ^{but the states} giving ^rise

to a.c. conductivity ^{do not} constitute a percolation path throughout ^the sample and hence do not contribute to d.c. conduction [8], the total measured

conductivity ^{at a} given frequency (w ) is then separ- able into d.c. and ^a.c. components ^as

The above assumption is valid in case of chal-

cogenide glasses ^as U a.c. is due ^to relaxation processes and U d.c. is attributed ^to the band conduction.

a.c. conductivity mechanism in a-semiconductors may be broadly divided into three categories. ^{In a}

band conduction mechanism, U a.c. is independent ^of frequency up ^to the U.H.F. region and thereafter should decrease as (ù - 2 under the condition that

frequency exceeds the inverse of carrier relaxation time [6]. Thus, there should be no contribution of extended states to a.c. conductivity (O’a.c.) up to a frequency ^{107 Hz. If the a.c.} hopping ^conduction primarily ^takes place ^{in the} Anderson localised states at the conduction band edge, U a.c. will show ^an

exponential activation _energy [9]. ^{In the case of} hopping conduction, ^the temperature dependence ^of

0-a.c. has been predicted ^{to be similar to that of the}

d.c. conductivity [6]. ^Such type of mechanism has been reported ^{in the cases of} As2-Te3 ^and Te2-As ^Si [5] ^{where a.c.} conductivity ^has been attributed to the

hopping ^{in localized states. In a} pair approximation approach, Pollak and Geballe [1] proposed ^that thermally ^assisted tunneling ^is responsible ^{for con-}

duction between localized states lying deep ^{in the}

energy gap. In this model U a.c. is proportional ^to

temperature (T) ^and the value of frequency ^ex- ponent ^{has been} predicted ^{to be 0.8. In the} present system ^the behaviour of _0-a.,,:. can not be explained

even on the basis of pair approximation ^model.

Electrical properties ^of chalcogenide glasses ^have

been attributed to the presence of charged ^defect

states in the energy gap [10, 11]. Temperature dependence ^{of a.c.} conductivity calculated for

bipolaron hopping ^mechanism (two ^electrons hop- ping ^{between D+ and D-} states) agrees with

experimental ^{results at low} temperatures ^{in a number} of chalcogenide glasses [12, 13]. ^In bipolaron hop- ping (B.P.H.) mechanism electrons in charged ^defect

states hop ^{over the} coulombic barrier whose height

is given ^as

where WM is the maximum barrier height, ^{e’ the}

bulk dielectric constant, ^r the distance between the

hopping sites, e the electronic charge ^{and n the}

number of electrons to hop which is 2 for bipolaron hopping. Bulk dielectric constant e’ was calculated from the capacitance component ^{of the} sample. ^On

the basis of CBH model [3, 12, 14] ^a.c. conductivity

for bipolaron hopping ^is given ^as

where N represents the total density ^of charged

defect states, Np the number of pairs contributing ^to

a.c. conduction and Tg ^{the glass} transition tempera-

ture. Reù represents ^the optimum hopping ^distance

and is given by

The maximum barrier height (WM) ^is regarded ^as

the band gap [3] ^and ro is the characteristic relax- ation time which is of the order of ^an atomic vibrational period.

In chalcogenide glasses bipolaron hopping ^ac-

counts for a.c. conductivity only in the low tempera-

ture range ( ²⁵⁰ K) [12, 13]. ^{In order to account}

for strong temperature dependence ^{of a.c. conduc-} tivity single polaron hopping ^{mechanism has been} suggested by ^Shimakawa [15]. In this mechanism DO

states are produced by thermal excitation of D+

and/or D- states, and ^{one electron} hopping ^between DO and D+ (or D-) contributes to a.c. conductivity

at high temperature. ^The height ^{of the} potential

barrier between the defects depends upon their

separation. Conductivity by single polaron hopping (S.P.H.) ^{mechanism is} expressed by the relation [15]

where n is the density ^{of localized states where}

carriers exist, np ^{is the} density of the localised states to which they hop ^and r CI) is the optimum hopping

distance and can be expressed ^as

wm is the maximum barrier height ^{over which the}

carriers must hop ^and corresponds ^to the thermal energy turning ^{DO state into D+ or D- state and is} equal ^to half of the band gap ^or smaller.

The numerical calculations are performed ^{with the} assumption ^{that the} U a.c. of present samples ^consists

of the above two components ^i.e.

In figure 3 the results of numerical calculations are

shown in comparison ^{with the} experimental ^results

for x ⁼ 40. S and B are the contributions due to

single ^and bipolaron hopping ^{and S + B} represents their sum. The values of products _nnp, NN P ^and

wM ^are adjusted, ^{so as to fit the} experimental ^results.

Values of parameters ^used for calculations are given

in table I. Also listed in the table ^are the values of

WM ^{for different} samples. Fitting ^{is made at the}

Fig. ^{3. -} Temperature dependence ^{of a.c.} conductivity

~~a.~. ) in x ^{= 40 at various} frequencies. ^{Dashed lines are}

the contributions from single polaron hopping ^{and Dash}

dotted lines are the contributions from bipolaron hopping.

Solid lines represent ^{the sum of two} contributions and

points represent ^the experimental ^data.

1074

Table 1. ^- Various parameters used ⁱⁿ the calculation

o f B. P. & S. P. hopping contributions.

frequency ^{of 1 kHz at low} temperatures ^{and the}

same values ^are used for other frequencies. ^{As seen}

in the figure 3, calculated curves are in fair agree- ment with the experimental results for all the

frequencies ^for Ga40Se40Te2o (x ⁼ 40). Similarly figure ⁴ depicts the calculated and experimental

results for different x values at 10 kHz. It is clear from figure ^{4 that} _{u a.c2} ^{due to} bipolaron hopping

accounts for the experimental ^results below 200 K for all the samples. It has been observed that the

bipolaron ^and single polaron contributions account for the experimental ^{results in case of x = 40 whereas}

for x ⁼ 20, ^{30 the} single polaron contribution is much smaller. For x ⁼ 20 the bipolaron contribution is sufficient to explain the observed experimental

values.

It is observed that the condition » 1 ^does

not hold at high temperature for small values of

Fig. ^{4. -} Temperature dependence ^{of a.c.} conductivity (0" a.c.) of various compositions ^{at 10 kHz.} Symbols ^used

are as in figure ^3.

wM. In such ^{a case} the curve can not be extended to the high temperature region because there will be a

dielectric loss peak ^{at the} frequency (ÙM [3, ^14, 16]

where

wm corresponds ^{to the barrier} height ^for single polaron hopping. ^{The a.c.} conductivity ^{due to dielec-}

tric loss [15] (ua.,l ^{cc m ~)} may be smaller than due ^to

bipolarons ^as has been observed in the present ^case.

Contribution by ^the single polaron hopping ^{seems to}

be decreasing ^with decreasing x ^values owing ^to

smaller value of _wm.

Figure ⁵ represents ^the frequency dependence ^of

u a.c. for Ga40Se40 Te 20 sample ^{at various} tempera-

tures. Plots of log U a.c. ^vs. log m ^{are linear} indicating

Fig. ^{5. -} Frequency dependence ^{of a.c.} conductivity ^for

x ⁼ 40 at various temperatures.

that _{U a.c.} increases with frequency and follows power law, U a.c. "" cù’in the observed frequency range. The

slopes ^{of the curves} (d log ^U a.~, /d log w ) ⁱⁿ figure ⁵ represent ^the exponent ^{s. For} comparison ^{of fre-}

quency dependence ^{of various} compositions plotted

in figure ^{6 is} the variation of log U a.c. with log w ^for

different x values at 100 K. It is clear from figure ⁶

that power ^{law is} followed in case of other compo- sitions as well. Using ^similar plots, values of s have also been calculated for other compositions ^{at differ-}

ent temperatures.

Figure ⁷ represents ^the variation of s with _tempera-

ture for different samples. ^{The maximum value of} frequency exponent s is 0.74 for x ⁼ 20 at 100 K which reduces to 0.62 for x ⁼ 40. This is clear from

Fig. ^{6. -} Frequency dependence ^{of a.c.} conductivity ⁱⁿ

various glasses (x ^{= 20, 30,} 40) ^{at 100 K.}

figure 7 that s has a feeble temperature dependence

in the low temperature regime ^{for x =} 20, ^40.

However the variation of s as a function of T is

relatively sharp ^{for x = 30. There is a cross over in s}

vs. T curves at higher temperatures. ^{The more} conducting glasses ^have higher s ^values [17] ^and

when the temperature ^is increased, a cross over in s

vs. T curves can be expected ^if temperature depen-

dence of a.c. conductivity ^is different. Similar type of behaviour has been reported ^{in the case of As-Se-}

Te glass [17] ^also.

It is concluded that the combined mechanism of

bipolaron ^and single polaron hopping satisfactorily

accounts for the a.c. conductivity ^{of the} present

Fig. ^{7. -} Variation of s with temperature ^{for different} glasses.

system. The calculation of the single polaron ^contri-

bution however could not be extended in the high temperature range due ^to small values of _wM. Total

density ^of charged ^{defect states N} when evaluated from the value of NN P {N P ⁼ N /2 ) corresponds ^to 1017 -- 1018 cm-3 as observed from other _exper- iments in different chalcogenide glasses [6].

Acknowledgments.

The authors wish to thank Dr. A. K. Sharma, Physics Dept. I.I.T. Delhi for his help ^{in the D.S.C.}

measurements of the samples.

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