Solid State Communications 149 (2009) 638–640

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Solid State Communications

journal homepage: www.elsevier.com/locate/ssc

Optical properties of amorphous III–V compound semiconductors from firstprinciples study

Liang Wang a, Xiaoshuang Chen a,∗, Wei Lu a,∗∗, Yan Huang a, Jijun Zhao b

a National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, Chinab State Key Laboratory of Materials Modification by Laser, Electron, and Ion Beams, School of Physics and Optoelectronic Technology and College of Advanced Science andTechnology, Dalian University of Technology, Dalian, 116024, China

a r t i c l e i n f o

Article history:Received 11 November 2008Received in revised form15 January 2009Accepted 15 January 2009by J.R. ChelikowskyAvailable online 25 January 2009

PACS:61.43.Bn61.43.Dq71.23.Cq78.40.Pg

Keywords:A. Amorphous semiconductorB. Optical propertyC. Dielectric function

a b s t r a c t

The optical properties of amorphous group III–V compound semiconductors were investigated throughthe first principles calculations. The imaginary parts (ε2) of dielectric function for amorphous GaAs, InAs,and InSb are given, respectively. There is a single broad peak found in the ε2 spectrum. By comparingwith the available experimental data of a-GaAs, it is found that the maximum of the ε2 spectrum issensitive to the topological local structures of amorphous materials. By comparison of the ε2 spectrumfor amorphous sample to that of the crystal, the dependence of the E1 and E2 peaks of the crystal on thelocal structures of amorphous sample becomes evident. The calculated results are in agreement with theavailable experimental data. The corresponding results should be generalized to cover the amorphousgroup III–V semiconductors.

© 2009 Elsevier Ltd. All rights reserved.

1. Introduction

There has been a considerable interest in amorphous (a-)semiconductors because of a number of physical properties as wellas numerous potential applications. Amorphous semiconductorsseem to be the most promising material for terrestrial solar cells.Remarkable economy can result from the simple technology ofthe amorphous when compared with the generation of singlecrystals. The amorphous group III–V semiconductors attract muchattention. For example, a-GaAs is a semiconductor materialof considerable interest due to the high efficiency at roomtemperature in the homojunction solar cells [1]. Much workhas been done to investigate the physical properties of suchamorphous semiconductors [1–8]. However, the possible use ofsuchmaterials for the photovoltaic devices requires the knowledgeof the optical response. The problems are still open. Therefore, the

∗ Corresponding author. Tel.: +86 21 65420850x24309; fax: +86 21 65830734.∗∗ Corresponding author. Tel.: +86 21 65420850x24315; fax: +86 21 65830734.E-mail addresses: xschen@mail.sitp.ac.cn (X. Chen), luwei@mail.sitp.ac.cn

(W. Lu).

0038-1098/$ – see front matter© 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.ssc.2009.01.022

optical properties of amorphous group III–V semiconductors arethe main focus of the present work.

2. Computational details

We have modeled the structures for a-GaAs, a-InAs, and a-InSb, following the idea of representing the structure of amorphoussemiconductors by ‘‘continuous random networks’’ (CRN) [9].Structures for amorphous samples to model containing 256 atomsare obtained by the first principles relaxation calculations withVasp code [10,11]. The Generalized Gradient Approximation(GGA) [12] for the exchange–correlation functional is used,as parameterized by Perdew and Wang [13]. The calculationshave been performed using ultra-soft pseudopotentials [14].Optical properties are calculated to perform the commercialCASTEP software [15,16]. All of the atoms in the cell arerepresented by Vanderbilt ultra-soft pseudopotentials [14]. TheSchrödinger equation is solved within the framework of thedensity function theory combined with the generalized gradientcorrection GGA–PBE of the exchange–correlation potential [17].The dielectric functions are obtained, and then other optical

L. Wang et al. / Solid State Communications 149 (2009) 638–640 639

Table 1Structural parameters for the amorphous compound semiconductor samples. The table shows the average number of coordination number (ACN), the fraction of ncoordination number (CNn), the average first-neighbor distance (d1) (Å) and the average second-neighbor distance (d2) (Å) of pair correlation functions g(r).

ACN CN3 (%) CN4 (%) CN5 (%) d1 d2 Ref.

a-GaAs 3.98 3.52 94.53 1.95 2.50 4.04 This work3.83 21.90 78.10 0 2.44 [18]4.09 14.00 66.00 18.00 2.44 [19]3.94 24.20 59.80 12.90 [20]3.95 4.60 95.40 0 [21]3.95 5.10 94.40 0.50 [21]3.93 2.48 [22]

2.51 4.07 [23]2.46 4.03 [24]

a-InAs 3.99 1.56 97.66 0.78 2.69 4.40 This work2.69 4.40 [6]

a-InSb 3.97 2.73 97.27 0 2.89 4.60 This work4.23 2.85 4.32 [25]3.9 2.86 4.70 [22]

properties can be calculated by Kramers–Kronig relation. Todiscuss the calculated results, we use 0.01 eV as smearing value.

3. Results and discussion

The structural parameters for our amorphous samples, togetherwith the data reported in other work, are summarized in Table 1.There are some fraction of dangling bonds (three-coordinatedatoms) or floating bonds (five-coordinated atoms) in amorphousstructures. And we can clearly see that the structural parametersof our samples are in good agreement with the available data bothexperimentally and theoretically [18–25]. These indicate that it isappropriate for our model to study their physical properties.In Fig. 1(a) the calculated results are presented for imaginary

part (ε2) of the dielectric function for a-GaAs and crystalline (c-)GaAs. The E1, E2 critical points (CP), labeled in ε2 spectrum ofcrystalline sample, occur as a result of singularities associatedwith symmetry points in the Brillouim zone. The band structurecalculations and some experimental work have shown that the E1transition takes place along the 〈111〉 directions (3) or at L pointsin the Brillouin zone [26]. However, the nature of the E2 transitionis more complicated since it does not correspond to a single, well-defined CP. This structure has been attributed to transitions at Xand along the 6 direction, to an extended region in the Brillouinzone where transitions in the 6 direction and along L–U line areimportant, and to a region in the 0–X–U–L plane [27,28]. In Fig. 1,it is seen that there is a single broad peak of amorphous casewhichlies close to the crystalline E1 peak. Moreover, the crystalline E2peak is absent entirely from the amorphous spectrum. The resultsare in agreement with the experimental data [29] and similar tothose of a-Ge and a-Si [30–32]. It is appropriate to identify therelation between the crystalline and amorphous spectra. In Fig. 1it is clearly shown that the selective effect of disorder on thecrystalline ε2. E2 is sensitive to the disorders. On the other side,it seems that E1 is not completely destroyed by the disorders. Thisresult arises from the different origins of the E1 and E2 peaks. Inamorphous materials, the absence of long-range order renders theBloch theorem inapplicable and leaves the crystalline momentumh̄k undefined. Therefore, the element that influences the matrixelement, which contributes to the strength of E2 peak, is absentin the amorphous phase [32]. In particular, it is confirmed that theE2 peak is selectively lowered with respective to the E1 peak as thenumber of the disorder increasing [33].The single broad peak found in the ε2 spectrum is a typical

behavior of amorphous semiconductors. Although a few resultsobtained by calculations or from experiment of ε2 spectrum for a-GaAs are similar in shape [1–3,29], there also occurs discrepancy.That is the site of the maximum in the single broad peak ofa-GaAs. The available experimental data of ε2 spectrum can be

Fig. 1. Imaginary part (ε2) of dielectric function. The solid line and dash line arethe calculated date for amorphous sample and crystalline sample, respectively.(a) GaAs, (b) InAs.

obtained in the amorphous structure because of ion-implantedtechnique or a flash-evaporated method. In Ref. [1] a-GaAs hasbeen obtained by ion implantation with 400 keV Te ions in c-GaAs at room temperature. And Ref. [3] reported that a-GaAs wasproduced by deep ion implantation of 270 keV As+ ions in c-GaAs. In Ref. [29], a-GaAs has been evaporated onto substratesat −50 ◦C. By comparison, it can be found that the maximumof ε2 spectrum reported in Ref. [3] is close to that of samplereported in Ref. [29], which occurs in the vicinity of 3.5 eV.Moreover, they are shifted towards lower energies with respectto that of sample reported in Ref. [1]. Such discrepancy betweentwo a-GaAs samples obtained by ion-implantation should mainlyarise from the topological disorders induced by choice of differentimplantation ions. In compound semiconductors deviations fromtopological disorder may induce drastic changes in the physicalproperties in addition to those associated to defects and impurities.In addition, the a-GaAs sample obtained by ion implantation with400 keV Te ions in c-GaAs might introduce the impurities into thesample, which induce stoichiometric compositions different fromthat of sample produced by As+ ion implantation. However, it islikely for topological disorders to be dominant.There is also a single broad peak for the ε2 spectrum of a-InSb,

which likes that of a-GaAs and a-InAs. From Fig. 2, it can be seenthat the refractive index (n) and the extinction coefficient (k) arebasically in agreement with the experimental data in shape withphoton energy range from 1.5 to 5.3 eV. Moreover, the featuresof the corresponding spectrums are provided qualitatively withphoton energy range from 0 to 1.5 eV.

4. Conclusions

The structural parameters for the modeled samples are allin good agreement with the available data experimentally or

640 L. Wang et al. / Solid State Communications 149 (2009) 638–640

Fig. 2. Refractive index (n) and extinction coefficient (k) spectrum for a-InSb. Thesolid line is the calculated data in the present work. The open circles and opentriangles are the experimental data obtained from Ref. [5], respectively.

theoretically. It is found that there is a single broad peak in theε2 spectrum for all the amorphous samples, in agreement withthe available experimental data. It can be generalized that a singlebroad peak found in the ε2 spectrum is a typical behavior ofamorphous group III–V semiconductors. By comparing with theavailable experimental data for a-GaAs, it can be concluded that themaximum of the ε2 spectrum is sensitive to the topological localstructures induced by the choice of different implantation ions inthe process of producing the sample.

Acknowledgments

This work was supported in part by grants from the StateKey Program for Basic Research of China, National NaturalScience Foundation of China (10725418, 10734090 and 60576068),Key Fund of Shanghai Science and Technology Foundation(08JC1421100), the Knowledge Innovation Program of the ChineseAcademy of Sciences (C2-23). The authors thank the ShanghaiSuper-computer Center for its computational support.

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