CONTRIBUTION OF SINGLE POLARON HOPPING TO AC CONDUCTION IN AMORPHOUS CHALCOGENIDES

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CONTRIBUTION OF SINGLE POLARON HOPPING TO AC CONDUCTION IN AMORPHOUS

CHALCOGENIDES

K. Shimakawa

To cite this version:

K. Shimakawa. CONTRIBUTION OF SINGLE POLARON HOPPING TO AC CONDUCTION IN

AMORPHOUS CHALCOGENIDES. Journal de Physique Colloques, 1981, 42 (C4), pp.C4-167-C4-

170. �10.1051/jphyscol:1981434�. �jpa-00220890�

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JOURNAL DE PHYSIQUE

CoZZoque C4, supple'ment au n0lO, Tome 4 2 , octobre 1981 page C4-167

C O N T R I B U T I O N OF S I N G L E POLARON HOPPING TO AC CONDUCTION I N AMORPHOUS CHALCOGENIDES

K. Shimakawa

Department of Physics, University of Leicester, Leicester, Engknd.

Abstract

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Although it is now fairly well established that defects in amorphous chalcogenide semiconductors are normally charged (D+ and D-), it is proposed that neutral defects D o (generated by the reverse reaction of 2D0 + D+ + D-) can be important for a.c. conductivity. It is shown that the contribution to a(w,T) from correlated barrier hopping of single polarons ex- ceeds that of bipolarons at high temperatures (T) and/or low frequencies

(a). An expression for a(w,T), which includes terms due to electrons hopping between Do and D+ and holes between DO and D-, as well as two electrons hopping between D- and D+ (bipolarons), is able to account for all the features observed in many materials. The energy levels and densities of the defect states for Se, two Se-Te alloys, As2Te3 and As2Se3 are deduced from a comparison of the theory with experimental data.

Introduction

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Correlated barrier hopping (CBH) of bipolarons (i.e. two electrons hopping between charged defects D+ and D-) has been proposed by Elliott (I) to interpret the frequency dependence of a.c. conductivity in amorphous chalcogenides

(oat % A@). The theory has explained many features at relatively low temperatures.

However, it does not predict the strong temperature dependence of oat which has been observed at higher temperatures in some materials.

It is proposed that an increasing density of neutral defects D o at higher temperatures is important and that CBH of single polarons (holes hopping between Do and D- and electrons between D o and D+) is then the dominant contribution to a.c.

conduction in amorphous chalcogenides*.

Expression for the a.c. conductivity due to CBH of bipolarons and single polarons

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The expression for the real part of oac derived for CBH with a random distribution of centre is written as (I)

where N is the total density of levels participating, Np the number of carriers, K

the bulk dielectric constant, and u the angular frequency.

R,, the distance of pairs for which W T = 1, is given by

-

*

Interestingly Elliott assumed that single polarons were present in as-deposited evaporated films giving rise to dielectric-loss peaks; however he did not take the expected temperature-dependent concentration of D o defects explicitly into account when interpreting a.c. data.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981434

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JOURNAL DE PHYSIQUE

where e is the electronic charge, WM the maximum barrier height, -to the charac- teristic relaxation time (5 x 10-l2 s in the present study), and n = 2 for bipolarons and n = 1 for single polarons.

For bipolarons (process I), NNp in eq. (I) can be written as N.N/2 = ~ ~by 1 2 assuming N- = N+ (we denote by N- and N+ as spatial densities of D- and D+ centres, respectively), and WM is defined by B

-

^W1⁺W2 as shown in Fig.l(a). For single polarons, No, the density of DO, can be determined by the law of mass action (see Fig. 1 (b)) as

We thus obtain No as

C.B.

B ¹

--7

V . B . ( a )

Fig.]: Thermal energy levels (a) and configurational diagram (b) associated with D+, DO and D-.

We assume here that half of the DO^ created by the reaction (eq. (3)) contribute to relaxation between DO and D- (holes: process 11) and the other half to relaxation between DO and D+ (electrons: process 111). The situation is shown schematically in Fig.2. NNp in eq.(l) for single polarons is obtained as

-

^~2

NNp = N

.-

⁼^-exp(-Ueff /2kT) , (process 11) 2 4

- N 2

- N+.

-$

⁼

$

exp(-Ueff/skT)

.

(process 111)

WM is equal to W l for process I1 and to W2 for process I11 as shown in Fig.I(a).

The a.c. conductivity can then be represented as

-

Process I ----* Process I

(...- Process N

Fig. 2: Three hopping processes contribute to the a.c. conduction.

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= ab ⁺ash +

,

( 6 ) where ob is the bipolaron contribution (process I), and ash and ose are the single polaron contributions of processes I1 and 111, respectively. The last two terms in eq.(6) produce a large temperature dependence of the a.c. conductivity due to botha small value of WM than that for the bipolaron process and also an increasing num- ber of thermally activated pairs.

Application of the model to experimental data

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Fitting eq.(6) to experimental data produces the values for the band gap B, the energy of the bound state W1 and W2, the bulk dielectric constant K , and the total spatial density of charged defects N. All these are tabulated in Table I.

Fig.4: Temperature dependence of aac in glassy S e g ~ T e l ~ (data from Mehra et al. (3)). Fig.3: Temperature dependence of

aac in glassy Se (data from Lakatos and Abkowitz (2)).

---

s

(measurement

Fig.5: Temperature dependence of Uac in

3 5 7 9 11

1631 r AspTeg film (data from Rockstad (4) )

.

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C4- 178 JOURNAL DE PHYSIQUE

The total conductivity (aT = oac + adc) of both the experimental data and calculations (solid curves) are shown in Figs. 3 glassy Se (2), 4 glassy SegoTe10

( 3 ) , and 5 As2Te3 films (4). Quantitative agreement with experiment is fairly

good. The dashed and dash-dotted curves, S and B, are contributions from single polarons (the last two terms in eq.(6)) and for bipolarons, respectively. A depar- ture from "bipolaron-like'' behaviour at higher temperatures and/or low frequencies which so far has been regarded as quantum-mechanical tunnelling at the band edge (I),

(4)-(6), can equally well be accounted for by "single polaron" hopping.

The sac(= UT

-

udc) in As2Te3 films falls below adc at higher temperatures as shown in Fig.5 (dash-two dotted curve; S + B), indicating that oac due to single polarons is smaller than adc. Similar results have been observed in many materials

(5), (6). The strong temperature dependence has not been observed in glassy As2Se3 (7), suggesting that the contribution of single polarons may be entirely dominated by adc in this material.

A large temperature dependence of a,, can only be observed in materials which have a small negative-Ueff and/or a large energy difference between extended states and the Fermi level.

The physical parameters tabulated in Table 1 estimated from the present model are plausible, and can be supported by values from the Stokes shift of the photoluminescence, drift mobility and d.c. conductivity studies, although the total spatial densities are larger than that from other estimates (8). The values of W1 (0.28 eV) and Wp (0.33 eV) in Se estimated from drift mobility (9) are smaller than those of the present study. The large Stokes shift of the photoluminescence in Se

(lo), however, cannot be explained by a small W1 and Wp. The shallow traps estimated from drift mobility in Se thus cannot originate from randomly distributed charged defects.

TABLE 1

Conclusions

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It has been demonstrated that the combined mechanism of bipolaron and single polaron hopping satisfactorily accounts for all the features observed experi- mentally in amorphous chalcogenides. The energy levels and densities of charged defects were estimated frornthe present model for given materials.

Acknowledgements

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The author wishes to thank Professors Sir Nevi11 Mott and E.A. Davis and Dr. S.R. Elliott for valuable discussions. The support of the Japan for the Promotion of Science and the Royal Society for a visiting fellowship is gratefully acknowledged.

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,

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(1980) 5433.

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