ARTICLE IN PRESS

Vacuum 74 (2004) 113–116

*Correspondin

0042-207X/$ - see

doi:10.1016/j.vac

Observation of Meyer–Neldel rule in vacuum evaporatedthin films of a-Se75In21Pb4 in presence of light

D. Kumar*, S. Kumar

Department of Physics, Christ Church College, Kanpur–208 001, India

Glassy Se–In alloys have drawn great attentionbecause of their potential application in solar cells[1,2]. The effect of a incorporation of a thirdelement in binary chalcogenide glassy alloys hasalways been an interesting problem in obtainingrelatively stable glassy alloys, as well as to changethe conduction type from p to n as most of theseglasses show p-type conduction only. In Ge–Seand Se–In systems, some metallic additives havebeen found [3–8] to change conduction from p-type to n-type and hence these binary systems areof great importance.In general, in case of semiconductors, conduc-

tivity (s) varies exponentially with temperature(T), i.e.,

s ¼ s0 exp ½�DE=kT �; ð1Þ

where DE is called the activation energy and s0 iscalled the pre-exponential factor.In most of the semiconducting materials, s0

does not depend on DE: However, in manyorganic and amorphous semiconductors, s0 isfound to increase exponentially with DE [9–13].This is called the Meyer–Neldel (MN) rule [11]. Incase of glassy semiconductors, MN rule is ob-served [9,10] by the variation of DE on changingthe composition of the glassy alloys in a specificglassy system. Dark conductivity is measured as afunction of temperature for this purpose. In caseof a-Si:H also such a rule is reported [14–16] where

g author.

front matter r 2003 Elsevier Ltd. All rights reserv

uum.2003.10.009

DE is varied by doping, by surface absorption orby light soaking.When one changes the DE by changing the

composition in a particular glassy system, thereare changes in the density of defect states and itsdistribution with energy due to compositionaldisorder. Since the distribution of density of defectstates determine the statistical shift which isresponsible for the observation of MN rule, it isdesirable to observe MN rule in a sample which isnot affected by these complications. The activationenergy of a particular glass composition can bechanged in the presence of light by varying theintensity of light. This has the advantage thatthe distribution of the density of defect statesin the material remains unchanged with a changein the activation energy.Considering the above point of view, we have

measured the temperature dependence of conduc-tivity at different intensities in amorphous thinfilms of Se75In21Pb4. The present glass composi-tion is chosen at a Pb concentration, where n-typeconduction starts in Se75In25�xPbx glassy system.Glassy alloy of Se75In21Pb4 is prepared by the

quenching technique. High-purity (99.999%) ma-terials are weighed according to their atomicpercentages and are sealed in quartz ampoules(lengthB5 cm and internal diameterB8mm) witha vacuum B10�5mbar. The ampoule containingSe75In21Pb4 is heated to 1000�C and held at thattemperature for 10–12 h. The temperature of thefurnace is raised slowly at a rate of 3–4�C/min�1.During heating, the ampoule is constantly rocked,

ed.

ARTICLE IN PRESS

D. Kumar, S. Kumar / Vacuum 74 (2004) 113–116114

by rotating a ceramic rod to which the ampoule istucked away in the furnace. This is done to obtaina homogenous glassy alloy.After rocking for about 10 h, the obtained melt

is cooled rapidly by removing the ampoule fromthe furnace and dropping to ice-cooled water. Thequenched sample of Se75In21Pb4 is taken out bybreaking the quartz ampoule.Thin films of these glasses are prepared by

vacuum evaporation technique keeping glass sub-strates at room temperature. Vacuum evaporatedindium electrodes at the bottom are used for theelectrical contact. The thickness of the films isB500 nm. The co-planar structure (lengthB1.2 cmand electrode separation B0.5mm) are used forthe present measurements. Before measuring theconductivity, the films are first annealed at 340Kfor 1 h in vacuum B10�2mbar.Thin films samples are mounted in a specially

designed sample holder, which has a transparentwindow to shine light. A vacuum B10�2mbar ismaintained throughout the measurements. Thetemperature of the films is controlled by mountinga heater inside the sample holder, and measured bya calibrated copper–constantan thermocouplemounted very close to the films.

a-Se75

-11.5

-11

-10.5

-10

-9.5

-9

-8.5

2.95 3 3.05 3.1

1000/

ln σ

( o

hm

-1cm

-1)

Fig. 1. Plot of the conductivity as a function of recip

The source of light is a 200W tungsten lamp.Interference filters are used to obtain a desiredwavelength. The present measurements have beenmade at a wavelength of 620 nm. The intensity oflight is varied by changing the voltage across thelamp and measured by a lux-meter.

I2V characteristics are found to be linear andsymmetric upto 30V. The present measurementsare, however, made by applying only 2V acrossthe films. The resulting current is measured bya digital Pico-Ammeter. The heating rate iskept quite small (0.5Kmin�1) for these measure-ments.The conductivity measured on co-planar sam-

ples in the form of thin films has been comparedwith the conductivity measured on bulk samples ina sandwich structure. The results are found to bewithin an experimental error of 2%.The temperature dependence of conductivity is

studied in the dark as well as in the presence oflight at different intensities. Fig. 1 shows suchresults for amorphous thin films of Se75In21Pb4between 306 and 336K. The conductivity (s)varies exponentially with temperature as ln s vs.1000T�1 curves are straight lines (see Fig. 1). Sucha behaviour is consistent with Eq. (1).

In21Pb4

3.15 3.2 3.25

T (K-1)

Dark11 LUX29 Lux60 Lux124 Lux200 Lux288 Lux390 Lux

rocal temperature at different light intensities.

ARTICLE IN PRESS

Table 1

Semi-conduction parameters for a-Se75In21Pb4

DE (eV) s0(O cm)�1 s0 ¼ s00 exp ½DE=kT0� ðkT0Þ�1 (eV)�1 s00(O cm)�1

0.54 2.67� 104 2.33� 104 35 1.44� 10�4

0.53 2.13� 104 1.64� 104 35 1.44� 10�4

0.51 1.13� 104 8.16� 103 35 1.44� 10�4

0.50 5.75� 103 5.75� 103 35 1.44� 10�4

0.47 2.49� 103 2.01� 103 35 1.44� 10�4

0.45 1.20� 103 9.99� 102 35 1.44� 10�4

0.43 5.55� 102 4.96� 102 35 1.44� 10�4

0.41 3.15� 102 2.46� 102 35 1.44� 10�4

a-Se 75In21Pb4

5

6

7

8

9

10

11

0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56

∆E (eV)

ln σ

0 0 (o

hm-1

cm-1

)

Fig. 2. Plot of pre-exponential factor s0 vs. activation energy DE:

D. Kumar, S. Kumar / Vacuum 74 (2004) 113–116 115

From the slope and the intercepts of Fig. 1, thevalues of DE and s0 have been calculated. Fig. 2shows a plot of ln s0 vs. DE; which is a straight lineindicating that s0 varies exponentially with DE

following the relation:

s ¼ s00 exp ½�DE=kT0�: ð2Þ

The slope of ln s0 vs. DE curve yields thevalues of ðkT0Þ

�1 B35 (eV)�1 and s00B1:44�10�4 O�1 cm�1 for a-Se75In21Pb4 thin films. Usingthese values of ðkT0Þ

�1and s00; the expected s0values have been calculated for the above glassyalloy and compared with the reported values (seeTable 1). An overall good agreement confirms thevalidity of the Meyer–Neldel rule.

From the present results it is evident that theconductivity in the present glassy system isthermally activated and exhibits a temperaturedependence similar to Eq. (1). The activationenergy in this case, however, depends on the lightintensity. The pre-exponential factor in the pre-sence of light also satisfies the same Meyer–Neldelrule as observed in the case of dark conductivity.In the case of dark conductivity, Roberts [17]

has given a model which considers the exponentialtailing of localized states with energy and distancenear valence and conduction bands which is, ingeneral, accepted in case of glassy semiconductors.Based on the above model the MN rule can beunderstood as follows:

ARTICLE IN PRESS

D. Kumar, S. Kumar / Vacuum 74 (2004) 113–116116

In case of semiconductors, the Fermi level (Ef ) istemperature dependent and the position of Ef isdetermined by the charge neutrality. Normally,only states within a couple of kT above Ef haveany significant occupancy and control the tem-perature dependence of Ef : If the ratio ofconduction band tail states to the midgap densityof states is large, then states ckT from Ef havesignificant occupancy and can influence the mo-tion of Ef and in turn gives rise to the MN rule.This happens because the DOS increases at least asfast as the Fermi function falls off the energy dueto the exponential distribution of density of stateswith energy. The wings of the Fermi functioncontribute to occupancy. In the presence of light,the Fermi level splits into quasiFermi levels, theposition of which depends on intensity [18]. Theconditions which prevail in the dark might alsoprevail in the presence of light which may causeMN rule in the present case.

Acknowledgements

We are grateful to Dr. V.K. Srivastava, Head,Department of Physics, Christ Church College,Kanpur for his valuable suggestions during thecourse of this work. Financial assistance from theU.G.C., New Delhi in the form of Major ResearchProject is also acknowledged.

References

[1] Nang TT, Matsushita T, Okuda M, Suzuki A. Jpn J Appl

Phys 1977;16:253.

[2] Matsushita T, Suzuki A, Okuda M, Sakai T. Jpn J Appl

Phys 1980;S19:123.

[3] Tohge N, Minami T, Tanaka M. J Non-Cryst Solids

1980;37:23.

[4] Nagel P, Ticha H, Tichy L, Triska A. J Non-Cryst Solids

1983;59–60:1015.

[5] Tohge N, Hideaki M, Minami T. J Non-Cryst Solids

1987;95–96:809.

[6] Bhatia KL, Parthasarathy G, Gopal ESR, Sharma AK.

Solid State Commun 1984;51:739.

[7] Bhatia KL, Parthasarathy G, Gosan DP, Gopal ESR.

Philos Mag B 1985;51:L63.

[8] Kohli S, et al. Phys Stat Sol A 1991;125:273.

[9] Arora R, Kumar A. Phys Stat Sol A 1991;125:273.

[10] Dwivedi SK, Dixit M, Kumar A. J Mater Sci lett 1998;

17:233.

[11] Meyer W, Neldel H. Z Tech Phys 1937;18:588.

[12] Many A, Harnik E, Gerlick D. J Chem Phys 1955;23:

1733.

[13] Eley DD. J Polym Sci 1967;C17:73.

[14] Carlson DE, Wronski CR. In: Brodsky MH, editor.

Amorphous semiconductors, Berlin, Heidelberg, New York:

Springer; 1979.

[15] Overhof H, Beyer. Philos Mag 1981;B43:4376.

[16] Overhof H, Thomas P. Electronic Transport in Amorphous

Semiconductors. Tracts in Modern Physics, vol. 114.

Berlin: Springer; 1989. p. 122.

[17] Roberts GG. J Phys 1971;C4:3167.

[18] Rose A. Concepts in photoconductivity and allied

problems. New York: Wiley-Inter-science Publishers;

1963.