Chiang Mai J. Sci. 2013; 40(6) 1013

Chiang Mai J. Sci. 2013; 40(6) : 1013-1019http://epg.science.cmu.ac.th/ejournal/Contributed Paper

Calculation of Electronic Structure andThermoelectric Properties of Ge(1-x)Six AlloyM. Nambuddee [a], and P. Moontragoon* [a, b, c][a] Material Science and Nanotechnology, Faculty of Science, Khonkaen University, Khonkaen,

Thailand 40002.[b] Integrated Nanotechnology Research Center (INRC), Department of Physics, Khon Kaen University,

Khon Kaen, 40002, Thailand.[c] Nanotec-KKU Center of Excellence on Advanced Nanomaterials for Energy Production and Storage.*Author for correspondence; e-mail: mpairo@kku.ac.th

Received: 11 April 2012Accepted: 4 September 2012

ABSTRACTThe electronic structures and thermoelectric properties, including thermal conductivity,

electrical conductivity and Seebeck coefficient, of Ge(1-x)Six alloy in various composition of xwere calculated by means of the principle calculation on Generalized Gradient Approximation(GGA) , packaged in ABINIT code, and the semi-classical Boltzmann transport theory,packaged in the BoltzTraP respectively. The Ge(1-x)Six alloy was modeled as 1x1x2 super-cell indiamond structure which consists of 16 atoms. The germanium (Ge) and silicon (Si) affect theelectronic and thermoelectric properties that were studied by comparing the results of puresilicon, pure germanium and alloys. The results indicated that the energy band gap of alloy willdecrease when the Ge of alloy increase. For thermoelectric properties, the result showed thatthe figure of merit (ZT) of silicon-rich doped with germanium atom is higher than puresilicon, pure germanium, germanium-rich doped with silicon atom, and GeSi alloy in zinc-blend structure. This is because of the Ge-atom-defect which plays an important role as aheavy-ion phonon scatter in reducing thermal conductivity.

Keywords: Ge(1-x)Six semiconductors, thermal conductivity, electrical conductivity, thermoelectricmaterial

1. INTRODUCTIONThe direct energy conversion between

heat and electricity based on thermoelectriceffects without moving parts is attractiveform any applications in power generationand heat pumping. The efficiency of thethermoelectric energy conversion is anincreasing function of the materials nondimensional figure of merit,

where s is the electrical conductivity, S is theSeebeck coefficient, T is the temperature, ke

is the electronic thermal conductivity, and ke isthe electronic lattice thermal conductivity[1]. Therefore, a good thermoelectric material

(1)

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must be a large Seebeck coefficient, highelectrical conductivity and low thermalconductivity. The combination ofthese properties can be obtained fromsemiconducting materials, or by adjustmentdoping level of solid solution alloys[1] because of their band structure andelectronic properties at high temperatures.

Ge(1-x)Six alloys have attracted researchattention as promising materials foroptoelectronic applications [2-3], such asinterband lasers,detectors, and solar cells,because they are environmental friendlysemiconductors, of which energy band gapbetween 0.67-1.2 eV, and fully compatiblewith Si-based technology. Offering thepossibility of emission and absorption inthe visible, near- and mid-IR range, theyhave the prospect of applications for solarcell, photodetectors, electro-absorption.Moreover, another well-known application ofGeSi alloys is as a material for thermoelectricpower generators at high temperatures.For example, it has been successfully used asa power generator with radioisotope in deepspace. Therefore, Ge(1-x)Six alloys has attractedincreasing interest as a optoelectronic andthermoelectric materials as an environmentalcompatible materials.

The thermoelectric efficiency of theGe(1-x)Six alloys, however, is still low whencompared to Bi2Te3 and Bi2Se3. Therefore,many researchers try to improve thethermoelectric efficiency of this alloy, i.e.by taking advantage of a nanostructure.It has been proven that nanostructuresenhance the thermoelectric figure of merit(ZT) of semiconductors in comparison withbulk. For example, single Si nanowires (NWs)exhibit a 60 times higher ZT than Si bulk [4].The nanowires were fabricated by growingthe Si1-xGex layers on lowly doped p-Si

substrates using RP-CVD. A linearly gradedrelaxed Si1-xGex layer was deposited first toovercome the lattice mismatch between Siand SiGe, followed by a 3 μm thick constantcomposition layer. Then, the arrays ofnanowires were prepared using metalassisted electro less chemical etching [5].The Seebeck coefficient and thermalconductivity of the SiGe nanowires aremeasured via a comparative technique.These measurements show that the SiGecontaining nanowires has higher Seebeckcoefficient than the bulk material. Thelonger SiGe nanowire array gives a higherSeebeck coefficient, and the maximumtemperature difference that can be maintainedacross the sample increases with increasingGe concentration and with increasingnanowire length. This indicates that thethermal conductance is decreasing withincreasing Ge concentration and nanowirelength [7].

The main purpose of this paper is tocalculate the thermoelectric properties ofGe(1-x)Six by various levels of Ge in diamondstructure and compare the relationshipbetween thermoelectric properties, includingfigure of merit (ZT), electrical conductivity ,thermal conductivity, and power factor withtemperature. Moreover, we also calculate theelectronic properties, electron density anddensity of states, changing of density ofstates to find energy band gab.

2. MATERIALS AND COMPUTATIONALMETHODS2.1 Material Structures

This paper has been studying fordiamond structure of Ge(1-x)Six alloy whensilicon content (x) = 0.0, 0.0625, 0.5, 0.9375,and 1.0, respectively. The unit cell of this alloycontains 16 atoms, as shown in Figure 1.

Chiang Mai J. Sci. 2013; 40(6) 1015

Figure 1. The structures (blue represents Si atoms and violet represents Ge atoms) and isosurfaceof high electron density (labeled as yellow colour) of the Ge(1-x)Six alloys when (a) x=0.0, (b)x=0.0625, (c) x=0.5, (d) x=0.9375, and (e) x=1.0.

The lattice constant of Ge(1-x)Six alloy wascalculated by using the Vegard’s law withthe bowing correction, by using quadraticinterpolation of lattice constants of siliconand germanium as given by Eq. (2),

where aGe(1-x)Six, aGe, and aSi are the latticeconstants of Ge(1-x)Six alloy, germanium, andsilicon respectively. The bowing parameter forlattice constant of Ge1-xSix, θSiGe, is -0.026.

The electronic and thermoelectricproperties of Ge(1-x)Six alloys were calculatedby the first principle calculation onGeneralized Gradient Approximation(GGA), packaged in ABINIT code[8], andthe semi-classical Boltzmann transport theory,

(2)

packed in the BoltzTraP[9] respectively.The calculation was performed using self-consistent pseudo-potential plane wave. TheGe(1-x)Six alloys were modeled using a 1×1×2super-cell in diamond and zinc blendstructures, totally contains 16 atoms, withoutstructural optimization, as shown in Figure 1.A 21×21×11 Monkhorst-Pack k-pointmesh and 100 bands were used for theGe(1-x)Six alloys super-cell calculation.A plane wave with cutoff energy of 14Hartree was used to assure convergentresults. According to the ABINIT calculation,we will obtain the energy (εn,k) of the alloysin various wave vector (k) and band (n).Then, we use the Boltztrab program for findthermoelectric properties of the materials.The conductivity tensor is explained by the

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transport distribution as,

where ε is energy, N is the number of k-pointssampled. The σαβ(n, k) are the conductivitytensors which can be obtained as,

where vα(n, k) is group velocity and τn,k isrelaxation time. The group velocity can becalculated from the energy (εn,k) as,

where is Planck’s constant over 2τ. Then,the transport properties tensors can becalculated as,

Figure 2. The electron density in (110) plan of Ge(1-x)Six

alloys when (a) x=0.0, (b) x=0.0625, (c) x=0.5,(d) x=0.9375, and (e) x=1.0 (red color indicates high densityand blue color indicates low density).

where is the electronic part of thermal

conductivity, T is temperature, and μ is thechemical potential. The Seebeck coefficientand electronic thermal conductivity at zeroelectric current can be calculated from

respectively.

3. RESULTS AND DISCUSSIONS3.1 Electronic Properties

From electron density of the alloys, asshown in Figure 1 and 2, the high electrondensity is located between two atoms, i.e.Si-Si, Ge-Ge, and Si-Ge, and the two atomsshare each other the valence electrons as acovalence bond. The valence electrons inSi-Si bond of pure silicon are moredelocalized than those in Ge-Ge bond ofpure germanium. Therefore, the valenceelectrons in Si-Si can travel from siliconatom to another silicon atom more than thatin Ge-Ge. Whereas the Ge0.5Si0.5 alloy whichis modeled as zinc-blend structure, the valenceelectrons are the most localized. Accordingto the density of states of the alloys, shownin Figure 3, they indicate that the energy bandgap of the alloys will decrease when theGe concentration of the alloys increase.

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Figure 3. The density of states of Ge(1-x)Six alloys when(a) x=0.0 with Fermi energy = 0.044 Hartree, (b) x=0.0625with Fermi energy = 0.053 Hartree, (c) x=0.5 with Fermienergy = 0.069, (d) x=0.9375 with Fermi energy = 0.217Hartree, and (e) x=1.0 with Fermi energy = 0.310 Hartree.

Thermoelectric propertiesFrom the electronic conductivity over

relaxation time and electronic thermalconductivity over relaxation time, as shownin Figure 4(a) and 4(b) respectively, theelectronic conductivity and electronic thermalconductivity increase when the temperatureincrease. This can be described by theWiedemann-Franz’s law, i.e. the electronicthermal conductivity is proportional of theelectrical conductivity, and the electronicconductivity of semiconductor can beexpressed as,

σ = neμ

where μ is carrier mobility which decreaseswith increasing temperature, e is electroncharge, and n is carrier density which

increases faster with increasing temperature.As a result the electronic conductivity insemiconductor increases with increasingtemperature. According to the Power factor,Seebeck coefficient and the figure of merit(ZT), as shown in Fig. 4(c), 4(d) and 4(e)respectively, the results indicates that theSi0.9375Ge0.0625 has the figure of merit, Seebeckcoefficient, and power factor higher than thepure silicon and pure germanium. It is ingood agreement with the experiment [7], i.e.the thermal conductance is decreasing withincreasing Ge concentration, because thedoped germanium atom create point defectwhich is heavy-ion with large vibrationamplitudes contained within partially filledstructural sites to scatter phonons within theunit cell crystal. This indicates that the thermalconductance of Ge(1-x)Six alloys is decreasing

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with increasing defecting Ge atoms. Incontrast, Ge-rich doped with Si has higherthermal conductivity because the defect(Si atom) is not a heavy-ion compared togermanium.

However, we should note that thecalculated dimension less figure of merit ishigher than the experimental value [10-14]because of a couple of approximationswe have still made in the calculation.For example, the lattice thermal conductivity,which usually is higher than electronicconductivity in semiconductor, was not takeninto account, and the atomic positionrelaxation in the super-cell calculation (due todifferent radii of Si and Ge atoms) was nottaken into account. Moreover, althoughGGA give good results for ground stateproperties, usually it underestimates the energyband gap values. Therefore, the input (energy,εn,k, in the conduction band) in the Boltztrabprogram will be underestimated as well.

4. CONCLUSIONThe electronic structures and

thermoelectric properties of Ge(1-x)Six alloywere calculated by means of the principlecalculation on Generalized GradientApproximation (GGA) and the semi-classicalBoltzmann transport theory. The resultsindicated that the calculated energy bandgaps of alloys are underestimated and willdecrease when the Ge of alloy increase.For thermoelectric properties, the resultshowed that the figure of merit (ZT) ofsilicon-rich doped with germanium atom isthe highest because of the Ge-atom-defectwhich plays an important role as a heavy-ionphonon scatter in reducing thermalconductivity.

ACKNOWLEDGEMENTSThis work was financially supported by

the National Research University Project,Khon Kaen University through the

Figure 4. The thermoelectric properties (a) electronic conductivityover relaxation time, (b) electronic thermal conductivity overrelaxation time, (c) power factor, (d) Seebeck coefficient, and(e) the dimension less figure of merit.

Chiang Mai J. Sci. 2013; 40(6) 1019

research grant no. M54417, and IntegratedNanotechnology Research Center (INRC),Khon Kaen University, Thailand, theNanotechnology Center (NANOTEC),NSTDA, Ministry of Science and Technology,Thailand, through its program of Center ofExcellence Network.

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