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Physica B 403 (2008) 624–630

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Compositional dependence of the physical propertiesin a-Ge–Se–In glassy semiconductor

Ishu Sharmaa,�, S.K. Tripathib, P.B. Barmana

aDepartment of Physics, Jaypee University of Information Technology, Waknaghat, Solan, H.P. 173215, IndiabDepartment of Physics, Panjab University, Chandigarh, India

Received 20 August 2007; received in revised form 7 September 2007; accepted 7 September 2007

Abstract

Physical properties viz. mean bond energy (/ES), glass transition temperature (Tg), cohesive energy (CE), average heat of atomization

ðHsÞ, density (r), molar volume (Vm) and compactness (d) of Ge20Se80�xInx (x ¼ 0, 5, 10, 15, 20) bulk glassy alloys have been examined

theoretically. Mean bond energy (/ES) is proportional to glass transition temperature (Tg). The cohesive energy (CE) of the investigated

samples has been calculated using the chemical bond approach (CBA) method. The relation between photon energy (E04) is discussed in

terms of average heat of atomization Hs and average coordination number (/rS). The compactness (d) of the structure of the glass is

determined from measured density of the glasses in order to display the chemical threshold in the system using Phillips–Thorpe

topological models. Maximum of the compactness has been observed at floppy to rigid transition point occurring in networks. Molar

volume (Vm) has been calculated from the experimentally measured densities and on the basis of number of atoms per unit volume (N);

Vm follows the same trend as that of optical band gap.

r 2007 Elsevier B.V. All rights reserved.

Keywords: Mean bond energy; Glass transition temperature; Cohesive energy; Heat of atomization; Structure compactness

1. Introduction

An increased tendency of glass formation in chalcogen-ide compounds with predominantly covalent chemicalbonds and technically important applications in solid-statedevices, nanotechnology, future prospects [1–6] and inconnection with the modification of their properties ondoping with metal impurities [7,8], chalcogen semiconduc-tors truly emerged as multipurpose materials. Se-richchalcogenide glasses is of special interest because of itsdevice applications such as rectifiers, photocells, xerogra-phy, switching and memories device, etc. [1,9], but exhibithigh-resistivity values implying certain limitations (shortlifetime and low sensitivity) in their applications. So toproduce changes in the properties of new complex glass, it

front matter r 2007 Elsevier B.V. All rights reserved.

ysb.2007.09.065

ng author.

esses: ishuphy@gmail.com (I. Sharma), surya@pu.ac.in

parthabarman@yahoo.com (P.B. Barman).

is worth adding more than one component into theselenium matrix to get rid of limitations.Ge–Se system is a widely studied system and glass

formation in this system occurs predominantly in alloysenriched with Se and containing 0–25 at% of Ge [10].Chalcogenide glasses in Ge–Se system are used as switch-ing, memory elements and optoelectronic devices and areinteresting material for infrared optics too. It has beenestablished that physical properties in this system arehighly composition dependent [11–13].For Ge20Se80 glassy alloy, elastic recovery of deforma-

tion is maximum [14]. Ge20Se80 composition glass networklies at the threshold of the mode change i.e. floppy2in-termediate region having an average coordination number/rS ¼ 2.4. According to constraint model and develop-ment theories [15,16], by equating the number of operativeconstraints to the number of degrees of freedom, /rS ofthe most stable glass is shown to be =2.4. So the additionof third element in Ge–Se tetrahedral glassy networkmakes the glass an interesting material and new properties

ARTICLE IN PRESSI. Sharma et al. / Physica B 403 (2008) 624–630 625

are expected. The addition of indium (In) into Ge20Se80system in an effective way controls its electrical, optical andphysical properties as this will lead the system towards theintermediate region.

The Ge–Se–In system is of special interest in view of thefact that it forms glasses over a wide domain ofcompositions. The glass-forming region in the ternaryGe–Se–In system extends to about 20 at% In and about60–90 at% Se, with the rest being Ge [17]. Therefore, it is asuitable system for the investigation of the variation ofcertain physical properties. In the present paper, correla-tion between glass transition temperature and mean bondenergy has been studied using the Tichy–Ticha approach[18,19]. Other physical parameters viz. cohesive energy,average heat of atomization, density, compactness andmolar volume has also been investigated. The variationof these parameters has been shown in terms of composi-tion or equivalently with the average coordinationnumber, /rS.

2. Experimental details

Bulk samples of Ge20Se80�xInx (x=0, 5, 10, 15, 20) wereprepared by melt-quenching technique. High-purity (5N)elements Ge, Se and In, in the appropriate weightproportion, were vacuum sealed (10�6mbar) in quartzampoules and heated up to 1000 1C in a rocking furnace ata heating rate of 3–4 1C/min. The ampoules were frequentlyrocked at the highest temperature for 10 h to make the melthomogeneous. The quenching was done in ice-cold waterimmediately after taking out the ampoules from thefurnace. The amorphous nature of the bulk samples wasconfirmed by the X-ray diffraction technique, as no sharppeak was observed in spectra.

3. Result and discussion

3.1. Correlation between mean bond energy (/ES) and

glass transition temperature (Tg)

In the present paper, considerable attention has beendevoted to measuring and predicting the Tg of chalcogen-ide based glasses. Tg represents the temperature abovewhich an amorphous matrix can attain various structural

Table 1

Values of /rS, R, /ES, Tg for Ge20Se80–xInx composition and bond energies

Ge20Se80–xInx /rS R /ES (eV/

x ¼ 0 2.40 2.000 2.35

x ¼ 05 2.45 1.579 2.45

x ¼ 10 2.50 1.273 2.57

x ¼ 15 2.55 1.040 2.71

x ¼ 20 2.60 0.857 2.66

– – – –

configurations and below which the matrix is frozen into astructure which cannot easily change to another structure.Therefore, it is reasonable to assume that Tg must berelated to the magnitude of the cohesive forces within thenetwork, since these forces must be overcome to allowatom movement. It is thus, not surprising, that predictionsof Tg are generally based on simple models in which it isassumed that Tg is proportional to another materialparameter (such as mean bond energy /ES), whichstrongly depends on the cohesive forces or the rigidity ofthe network.Tichy et al. [20] were the first to point out that the value

of Tg should not be only related to connectedness of thenetwork (which is related to /rS), but should also berelated to the quality of connections, i.e. the mean bondenergy between the atoms of the network. From bondenergy values (given in Table 1) strong heteropolar bondsi.e. Ge–Se and In–Se are calculated using Pauling relation[21] and can be well differentiated from weak homopolarbonds i.e. Ge–Ge, In–In and Se–Se bonds [19]. Sincethe difference in the corresponding bond energies issubstantial, chemically ordered networks are expectedwhere the number of heteropolar bonds is maximized i.e.they are more favorably formed than homopolar bonds.Since bulk glasses are considered, a chemical bond order-ing model is assumed. Based on this assumption /ES isgiven by

hEi ¼ Ec þ Erm, (1)

where Ec is the overall contribution towards bond energyarising from strong heteropolar bonds, Erm is thecontribution arising from weaker bonds that remain afterthe strong bonds have been maximized i.e. the averagebond energy per atom of the ‘remaining matrix’.For GexSeyInz system (where x+y+z ¼ 1);Case I: In the selenium-rich region (R41), there are

heteropolar bonds and chalcogenide–chalcogenide bonds:

Ec ¼ 4xEGe2Se þ 3zEIn2Se (2)

and

Erm ¼½2y� 4x� 3z�

hriESe2Se, (3)

where ESe–Se is the homopolar bond energy of Se–Se bonds.

of their respective bonds

atom) Tg(K) Bonds Bond energies

(kcal/mol)

451 Ge–Se 49.10

484 Se–Se 44.00

520 Ge–Ge 37.60

562 In–Se 48.20

547 In–In 29.83

– Ge–In 33.72

ARTICLE IN PRESS

0.8 1.0 1.2 1.4 1.6 1.8 2.02.30

2.35

2.40

2.45

2.50

2.55

2.60

2.65

2.70

2.75

<E

>

R

Fig. 1. Variation of /ES with R for Ge20Se80�xInx (x ¼ 0, 5, 10, 15, 20).

I. Sharma et al. / Physica B 403 (2008) 624–630626

Case II: In the selenium poor region (Ro1), there areheteropolar and metal–metal bonds present:

Ec ¼2yð4xEGe2Se þ 3zESe2InÞ

4xþ 3z(4)

and

Erm ¼ð4xþ 3z� 2yÞ

hriEhi, (5)

where

Ehi ¼ 1=3½EGe2Ge þ EIn2In þ EGe2In� (6)

denotes the average bond energy of metal–metal bond forRo1.

3.1.1. Determination of R

It is the parameter which determines the deviation ofstoichiometry and is expressed by the ratio of covalentbonding possibilities of chalcogen atom to that of non-chalcogen atom. Values of R were found to be larger thanunity for such glasses which indicate chalcogen-richmaterials and less than unity for the glass which showschalcogen-poor material. For GexSeyInz system, thequantity ‘R’ is defined by [18,19]

R ¼yCNðSeÞ

xCNðGeÞ þ zCNðInÞ, (7)

where x, y and z are, respectively, the atomic fractions ofGe, Se and In.

However, the calculation of ‘R’ also requires theknowledge of coordination number (CN) of all theconstituents of glassy alloys. For the investigating system,CN(Ge) and CN(Se) respect the Mott ‘‘8–N’’ rule [22],where N is the number of outer shell electrons. Coordina-tion number of In in GexSeyInz system has been welldiscussed by Saiter et al. [23,24].

3.1.2. Determination of average coordination number /rSNearest-neighbor coordination in a ternary system is

particularly suitable for testing the validity of thesetopological concepts [25], because of its large glass-formingregion. /rS in our system is defined by

hri ¼aX þ bY þ cZ

aþ bþ c, (8)

where X, Y, Z are the percentage atwt. of Ge, Se and In,respectively, and a ¼ 4, b ¼ 2, c ¼ 3 are their respectivecoordination numbers. The obtained values of /rS for thefive compositions of Ge20Se80�xInx with x ¼ 0, 5, 10, 15and 20 are listed in Table 1.

The threshold at R ¼ 1 (the point of existence of onlyheteropolar bonds) is evident. For R41, the system ischalcogen rich and for Ro1, the system is chalcogen poor.For the present investigating system the values of R alongwith /ES are tabulated in Table 1.

Using a set of 186 glasses, Tichy and Ticha [18,19]illustrated an impressive correlation of Tg, ranging from

(�320–760K), with /ES in the form

Tg ¼ 311½hEi � 0:9�. (9)

In particular, they demonstrated that the compositionaldependence of Tg in numerous glassy system presentsmaximum value near to the chemical threshold i.e. R=1,because the chemical bond energies are maximized at thiscomposition.Applying this model to Ge20Se80�xInx system, we

evaluated /ES and using the above relation (Eq. (9)), Tg

has been calculated. It is evident from Table 1, that Tg isproportional to /ES. With the increase in In content inGe–Se glassy alloy, /ES along with glass transitiontemperature increases, reaches a maximum at R ¼ 1,corresponding to composition Ge20Se65In15 and thendecreases as shown in Figs. 1 and 2, respectively. Themajor limitation of the model is that, it does not accountfor the molecular interaction, which plays a vital role in therelaxation process in the glass-transition region.

3.2. Calculation of cohesive energy (CE) and

electronegativity (w)

Using the chemical bond approach (CBA) method [26],the CE (the stabilization energy of an infinitely large cluster

ARTICLE IN PRESSI. Sharma et al. / Physica B 403 (2008) 624–630 627

of material per atom) for investigated samples has beencalculated. According to CBA the bonds are formed in thesequence of decreasing bond energy until the availablevalence of atoms is satisfied and the bond energies areassumed to be additive. Thus the CEs were calculated bysumming the bond energies over all bonds expected in thematerial.

Calculated values of CE along with the chemical bondof distribution for all the compositions are tabulated inTable 2. The results indicate that the CE of these glassyalloys show an increase with increasing In content up to15 at% and it subsequently decreases at 20 at% . Change inCE with In content follows the same trend as that of /EScalculated above.

0 5 10 15 20440

460

480

500

520

540

560

580

Tg

(K

)

x at %

Fig. 2. Variation of Tg with In content (x at%).

Table 2

w , Eoptg , Distribution of chemical bonds and cohesive energy in Ge20 Se80–x I

Composition w Eoptg (eV) Distribution of chemica

Ge–Se In–S

Ge20Se80 2.43 1.69 0.5000 –

Ge20Se75In05 2.38 1.72 0.5333 0.10

Ge20Se70In10 2.34 1.75 0.5714 0.21

Ge20Se65In15 2.30 1.67 0.6153 0.34

Ge20Se60In20 2.26 1.51 0.6667 0.22

It can be concluded that increase in Eoptg with increasing

In content is due to increase in average stabilization energyand decrease in electronegativity of the system which iscalculated using Sanderson’s principle [27]. According tothis principle electronegativity of the alloy is the geometricmean of electronegativity of its constituent elements. It isevident from Table 2, electronegativity decreases as theoptical band gap increases.

3.3. Relation between E04, Hs and /rS

It is interesting to relate the E04, the photon energy, with

average single bond energy, ðHs=hriÞ. E04 is the arbitraryquantity defined as photon energy at which opticalabsorption coefficient has the value of 104 cm�1. Thephoton energy at a ¼ 104 cm�1 is about 0.2 eV larger than

the optical band gap ðEoptg Þ [28]. The obtained E04 values

along with calculated Eoptg value [29] are given in Table 3.

To correlate these values for Ge20Se80�xInx system, wecalculate the average heat of atomization.

3.3.1. The average heats of atomization

According to Pauling [21], the heat of atomization

HsðA� BÞ at standard temperature and pressure of a binarysemiconductor formed from atoms A and B is the sum ofheat of formation (DH) and the average heats of atomiza-

tion ðHAs Þ and ðH

Bs Þ, respectively, that corresponds to the

average non-polar bond energy of the two atoms:

HsðA� BÞ ¼ DH þ 1=2ðHAs þHB

s Þ. (10)

The term (DH) in above equation is proportional to thesquare of the difference between the electronegativities wA

nx system

l bonds Cohesive

energy(kcal/mol)

e Se–Se In–In

0.5000 – 46.55

00 0.3667 – 47.14

43 0.2143 – 47.81

61 0.0386 – 48.59

22 – 0.1111 46.76

Table 3

Values of Eoptg , E04 , Hs and Hs

�or4 for Ge20 Se80�x Inx system

Ge20Se80–xInx Eoptg

(eV)

E04

(eV)Hs (kcal/g

atom)

Hs=or4(kcal/g

atom)

x ¼ 0 1.69 1.89 57.52 23.96

x ¼ 05 1.72 1.92 57.95 23.65

x ¼ 10 1.75 1.95 58.38 23.35

x ¼ 15 1.67 1.87 58.81 23.06

x ¼ 20 1.51 1.71 59.24 22.78

ARTICLE IN PRESS

0 5 10 15 20

20

25

1.5

2.0

E04 (

eV

)H

s/<

r> (

kcal/gm

-ato

m)

x at. %

Fig. 3. Variation of E04 and Hs=hri with In content (x at%).

Table 4

Density (r), molar mass (m), molar volume (Vm) and compactness (d) forGe20Se80�xInx system

Composition r (g/cm3) M (g/mol) Vm (cm3/mol) d

Ge20Se80 4.268 77.696 18.20 �0.13002

Ge20Se75In05 4.226 79.489 18.81 �0.15985

Ge20Se70In10 4.200 81.282 19.35 �0.18515

Ge20Se65In15 4.380 83.075 18.97 �0.17036

Ge20Se60In20 4.640 84.867 18.29 �0.14153

I. Sharma et al. / Physica B 403 (2008) 624–630628

and wB of the two atoms:

DH a ðwA � wBÞ2. (11)

In order to extend this idea to ternary and higher ordersemiconductor compounds [30], the average heat of

atomization Hs (kcal/g atom) is defined for a compoundAaBbCg as a direct measure of the cohesive energy and thusof average bond strength, given by

Hs ¼aHA

s þ bHBs þ gHC

s

aþ bþ g, (12)

where a, b and g, and g are the ratios of A, B and C,respectively. In the present ternary glassy system, theaverage heat of atomization is calculated by Eq. (12) usingthe values of heat of atomization 90, 49.4 and 58 in kcal/gatom for Ge, Se and In, respectively. Average heat of

atomization Hs (kcal/g atom) and average single bond

energy ðHs=hriÞ are given in Table 3, where /rS is theaverage coordination number.

In semiconductors, the bonding band forms the valenceband and the antibonding forms the conduction band.However, in chalcogenide glasses containing a highconcentration of a group VI ‘‘Se in our case’’, valenceband (s–bonding) originates from lone pair (LP) electronstates, whereas the conduction band arises from antibond-ing (s*) states [31]. It is, therefore, interesting to relate theoptical band gap with the average single bond energy,and the parameters we use to specify the bonding are Hs

and /rS. The relation between the energy gap and theaverage heat of atomization was discussed by Aigrain et al.[32]. According to them there exists a linear correlationthat can be expressed for the semiconductors of thediamond and zinc-blende structure by

DE ¼ aðH � bÞ, (13)

where a and b are characteristic constants. It is suggestedfrom the above equation that the average heat ofatomization is a measure of the cohesive energy andrepresents the relative bond strength, which in turn iscorrelated with the energy gap of isostructural semicon-ductors. Fig. 3 represents the variation of optical gap E04

and average heat of atomization per single bond Hs=hri asa function of composition parameter x (at%) in Ge–Se–Inglassy system. Furthermore, comparing E04 with Hs (givenin Table 3), there is an increase in E04 up to 10 at% of Inand then it decreases with further In addition. However,the average heat of atomization ðHsÞ shows very smallincrement with In addition. But according to Ref. [31], E04

for overconstrained materials with higher connectivity i.e.3p/rSp4 depends more strongly on Hs than for glasseswith lower connectivity, 2p/rSp3. In our case, the valueof /rS varies from 2.4 to 2.6, which can be correlated withlow-connectivity glasses. This further suggests that theparameter Hs=hri is almost constant with compositionalparameter x at% (of In) and has a very negligible effect onE04, which is also evident from Fig. 3. Similar results havealso been reported by various workers [12,33].

3.4. Compactness and molar volume

The density of the glasses were measured by theArchimedes method using double-distilled water as areference liquid, which has a density of 1.0 g/cm3 at20 1C. The density was calculated from the formula

r ¼w1

w1 � w2

� �rwater, (14)

where w1 and w2 are the weight of the sample in air and theweight of the sample in the reference liquid, respectively.The calculated density values are reported in Table 4. Theerror in the density measurement and consequently in d,obtained by measuring the density of some pure elementswere estimated to be less than 71%. The compactness d

ARTICLE IN PRESSI. Sharma et al. / Physica B 403 (2008) 624–630 629

was calculated by the formula [34]

d ¼

Pi

ciAi

ri�P

i

ciAi

rPi

ciAi

r

, (15)

where ci is the atomic fraction, Ai is the atomic weight, ri isthe atomic density of the ith element of the glass and ris the measured density of the glass. Thus, d is a measure ofthe normalized change of the mean atomic volume due tochemical interactions of the elements forming the networkof a given solid [19]. Consequently, it is more sensitive tochanges in the structure of the glass network as comparedto the mean atomic volume.

The molar volume (Vm) was determined from the densitydata by the equation

Vm ¼1

r

Xi

xiMi, (16)

where Mi is the molecular weight of the ith component andxi is the atomic percentage of the same element in thesample.

Table 4 summarizes the density of the investigatedcompositions, their corresponding compactness and molarvolume. The compositional variation of compactness,characterized by /rS of the investigated glassy alloys isshown in Fig. 4. From the figure, it is evident that maxima

2.40 2.45 2.50 2.55 2.60-0.20

-0.19

-0.18

-0.17

-0.16

-0.15

-0.14

-0.13

-0.12

-0.110 5 10 15 20

18.0

18.2

18.4

18.6

18.8

19.0

19.2

19.4

19.6

Com

pactn

ess

<r>

Mola

r volu

me

x at.%

Fig. 4. Variation of molar volume (Vm) and compactness (d) with x at%

and average coordination number /rS.

of the compactness occurs at /rS ¼ 2.4, which can be wellunderstood in light of constraint theory and rigiditypercolation concept [35,36]. The stability of the networkwith /rS=2.4, where the mechanical threshold takes placecan be associated with atomic arrangements that becomemore tightly bound with shorter bond lengths resulting insmallest mean atomic volume of the network and hencecompactness rises to the maximum. Thus, this maximumobserved compactness at /rS=2.4 for Ge20Se80 glassyalloy, is attributed to the floppy-to-rigid transitionoccurring in these network glasses.The variation of molar volume (Vm) with composition

(x at%) is shown in Fig. 4. From the figure it is clear thatmolar volume first increases upto 10 at% In concentrationand then decreases with further In addition. The variationin optical band gap also follows the same trend with Inconcentration [28]. In chalcogenide glasses, the energy ofthe conduction band edge is decided by number of atomsper unit volume (N). A decrease in N leads to an increase inthe energy of conduction band edge, hence to an increase inoptical band gap. From Fig. 4, N decreases up to 10 at%In, which corresponds to increase in optical band gap andwith more In addition, N increases with subsequentdecrease in optical band gap.

4. Conclusion

The addition of In to Ge20Se80 glassy alloy leads tochange in physical properties. Mean bond energy /ES andhence glass transition temperature Tg increases in chalco-genide-rich region while it decreases in chalcogenide-poorregion. The cohesive energy of the composition has beencalculated using CBA and follows the same trend as that of/ES with In content. An increase in photon energy wasobserved upto 10 at% of In and it subsequently decreasedthereafter. Average single bond energy shows almostconstant trend with composition. No correlation betweenphoton energy and average single bond energy was foundfor low-connectivity glasses. The density and the compact-ness vary due to the variation of In content in the glassyalloy. Compactness has been observed to be maximum atpercolation threshold of the system under study. Molarvolume first increases to its maximum value up to 10 at%of In content and then decreases with further In addition toGe–Se alloy.

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