The structural, electronic and optical properties of the chalcopyrite semiconductor ZnSiAs2

ARTICLE IN PRESS Physica B 404 (2009) 1326–1331

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The structural, electronic and optical properties of the chalcopyrite semiconductor ZnSiAs2 Bin Xu a,, Hongpei Han b, Jinfeng Sun c, Lin Yi d a

Department of Mathematics and Information Sciences, North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450008,China College of Electro-Information Engineering, Xuchang University, Xuchang 461000, China College of Physics and Information Engineering, Henan Normal University, Xinxiang 453007, China d Department of Physics, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China b c

a r t i c l e in f o

a b s t r a c t

Article history: Received 21 November 2008 Received in revised form 11 December 2008 Accepted 12 December 2008

Full-potential linearized augmented plane wave plus local orbital method (FPLAPW+lo) calculations were performed for the chalcopyrite semiconductor ZnSiAs2 in order to investigate the structural, electronic and optical properties. It is found that the calculated band gap of 1.152 eV is direct. Furthermore, other experiments and theory also show that this material has a direct band gap. It is noted that there is quite strong hybridization between with 3p states of Si atom and 4p states of As atom, which belongs to the (SiAs2)2 below the Fermi level. Our calculated reflectivity spectra, the imaginary parts of the dielectric function and the energy loss spectra are in good agreement with the experimental results. On the other hand, the contributions of various transitions peaks are analyzed from the imaginary part of the dielectric function. Furthermore, the different optical properties have been investigated. Crown Copyright & 2009 Published by Elsevier B.V. All rights reserved.

PACS: 71.20.b 78.20.Ci 71.20.Nr Keywords: Electronic band structure Optical properties Semiconductor

1. Introduction Ternary ABC2, semiconductors which crystallize in the chalcopyrite structure [1] form a wide family of materials, which II IV V includes AI BII C VI 2 and A B C 2 (roman numerals I, II, III, IV, V,y are the group of periodic table of elements) type compounds. They have technological interest related to their nonlinear optical properties; for some of the AII BIV C V2 pnictide compounds (A ¼ Mg, Zn, Cd; B ¼ Si, Ge, Sn; and C ¼ P, As, Sb), their narrow gaps make them suitable as infrared detectors. The larger degree of freedom with respect to that of their binary analogs provides a valid reason for interest in their possible device applications due to the wide variety of optical gaps offered by this class of materials. The AII BIV C V2 semiconductors normally crystallize in the chalcopyrite structure and have physical properties similar to those of the familiar AIII BV zinc-blende semiconductors. Although the two crystal structures are quite similar, the anisotropy of chalcopyrite crystals gives rise to many interesting properties not possible in zinc-blende crystals. The triple degeneracy of the G15, valence band maximum in zinc-blende is removed in chalcopyrite

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E-mail address: [email protected] (B. Xu).

by the combined effects of the noncubic crystalline field and spin–orbit interaction. The doubling of the unit cell in the Z direction in chalcopyrite relative to zinc-blende causes the appearance of pseudodirect energy-band gaps. Early work was based on comparison to the zinc-blende (ZB) parent BIIICV compound GaP and suggested either a so-called pseudodirect band gap or an indirect band gap. The conduction-band minimum of GaP at one of the X points of the ZB Brillouin zone is folded onto the G point of the chalcopyrite superstructure, while the other ones fall at G. These pseudodirect band gaps have the potential technological importance of especially for high luminescence efficiency (e.g., ZnGeP2, may be a pseudodirect gap). The physical and chemical properties of ABC2, semiconductors have been extensively studied [2–4]. Among the ternary compounds having the chalcopyrite structure, ZnGeP2 is currently being studied intensively for its promising nonlinear optics application [5]. The favorable properties of this group of semiconductors for second-harmonic generation were predicted by Levine [6]. Also, it was recently proposed that AII BIV C V2 compounds could be useful as buffer layers in heterovalent epitaxial growth. Alerhand et al. [7] suggested that the interface charge neutrality would be more easily satisfied by these materials grown on Si(0 0 1) than by GaAs. Their argument is simply based on the electron count per bond.

0921-4526/$ - see front matter Crown Copyright & 2009 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2008.12.016

ARTICLE IN PRESS B. Xu et al. / Physica B 404 (2009) 1326–1331

2. Computational details The calculations of the electronic structure and optical properties for ZnSiAs2 are carried out using the FPLAPW method implemented in the WIEN2K package [12]. The generalized gradient approximation (GGA) in the scheme of Perdew et al. [13] (PBE) is used for the exchange-correlation functional, and the relativistic effects are taken into account in the scalar approximation. The lattice parameters we used are a ¼ 5.6 and b ¼ 10.88 A˚ [14]. We take RmtKmax equal to 8.5 and make the expansion up to l ¼ 10 in the muffin tins spheres (MT). The use of the full-potential ensures that the calculation is completely independent of the choice of the sphere radii. Nonoverlapping MT sphere radii of 2.44, 2.21 and 2.17 a.u. were used for Zn, Si and As atoms, respectively. We have used 10  10  10 meshes for this material, which represent 1000 k-points in the first Brillouin zone. Self-consistency is considered to be achieved when the total energy difference between succeeding iterations is less than 10–5 Ry per formula unit. The imaginary part of the dielectric tensor is directly related to the electronic structure near by to the surface, so it can be computed from the knowledge of the single-particle orbitals and energies approximated by the solutions of the Kohn–Sham equations. Assuming the one-electron rigid-band approximation and neglecting the electron polarization effects (Koopmans’ approximation), in the limit of linear optics and of the visible– ultraviolet range [15,16], the imaginary part of dielectric function 2 ðoÞ is given by Z 4p2 e2 X 2dk 2 ðoÞ ¼ 2 2 jhjfk je:pjjik ij2 dðEf ðkÞ m o i;f BZ ð2pÞ3  Ei ðkÞ  _oÞ

(1)

For a vertical transition from a filled initial state jjik i of energy Ei ðkÞ to an empty final [17] state jf k of energy Ef ðkÞ, with wave

vector k, and jfk (jik) the crystal wave function corresponds to energy eigenvalue Ef ðkÞ (Ei ðkÞ). o is the frequency, e the electron charge, m the free electron mass, and p the momentum operator. By using the familiar Kramers–Kronig transformation, the real parts of the dielectric function can be related to its imaginary parts e2(o). In the tetragonal phase, e(o) is anisotropic and have two different components, exx(o) and ezz(o) (We present an average [17] over the two components as [2exx(o)+eyy(o)]/3) for the tetragonal phase. Using the e(o) (where e(o) ¼ e1(o)+ie2(o)), as output, we calculated various optical constants [17] such as spectral reflectivity R(o), absorption coefficient I(o), [17] electron energy loss function L(o), real part n(o), and imaginary part k(o) of the refractive index with a simple independent program.

3. Results and discussion ¯ The crystal structure of the tetragonal cell has I42d space group. There are four zinc, four silicon, eight arsenic in primitive cell of ZnSiAs2. As in the closely related sphalerite and diamond structures, all atoms are in position of tetrahedral coordination. In the chalcopyrite structure, each Zn and Si atom is surrounded by four equidistant As atoms and each As atom has two equidistant Zn atoms and two equidistant Si atoms as nearest neighbors. Fig. 1 shows the band structure and total DOS of the ZnSiAs2. Where the zero of energy is chosen to coincide with the top of the valence band in analogy with Wang et al. [18–20] who studied the energy band of insulating cubic perovskite. The band structure of the ZnSiAs2 plotted along the high symmetry axes of the Brillouin zone in Fig. 1. The bottom of the conduction bands (CB) is at G point; its energy is 1.152 eV. The top of the valence bands (VB) is also at G point. Hence, based on our calculation, the ZnSiAs2 compound has a direct band gap: 1.152 eV. Therefore, the ZnSiAs2 structure is semiconductor as expected. Previous studies suggested that the direct band gap of ZnSiAs2 was 2.10 [21], 2.1670.03 [22] and 2.1270.02 eV [23]. Other workers reported the room-temperature energy gap to be 1.64 [24] and 1.76 eV [25]. It is noted that our calculations in the local density function approximation have the combined disagreement of band gap between the theoretical predictions and experimental measurements resulting in narrower theoretical band gap is a well-known artifact of the local density approximation and usually dose not have significant effect on the rest of the band structure [26]. The valence band maximum appears to be triple degenerate levels at the G points for ZnSiAs2.

8 6 4 2 Energy (eV)

ZnSiAs2 is examples of the AII BIV C V2 type compounds predicted by Goodman [8]. Stroudt et al. [9] showed that the mixed compounds between ZnSiP2 and ZnSiAs2, grown as single crystals by an iodine vapor transport method, are n-type. ZnSiP2 grown by iodine transport is n-type and resembles the mixed compounds rather than n-type ZnSiP2 grown from tin solution. ZnSiAs2 grown by direct fusion is p-type. Excess phosphorus and iodine impurities are proposed as the donors in the phosphoruscontaining compounds, and the acceptors in ZnSiAs2 are associated with an arsenic deficiency. The ternary compounds have single activation energies, and the mixed compounds show evidence for double donor activation energies. Shay et al. [10] reported electroreflectance spectra for the chalcopyrite crystal ZnSiAs2. The structure observed in ZnSiAs2 is attributed to ‘‘pseudodirect’’ band gaps which result from the doubling of the unit cell in the Z direction in chalcopyrite relative to zinc-blende. They studied the electroreflectance spectra of a crystal which should have a pseudodirect transition as its lowest band gap. They also observed the dichroism of ZnSiAs2 at a wavelength slightly below the lowest direct band gap. The aim of this paper is to present the results of a theoretical investigation of the structural, electronic, and optical properties for ZnSiAs2, based on the full potential linearized augmented plane wave (FPLAPW) method. The rest of this paper is organized as follows. A brief description of the theoretical approach is given in Section 2. Section 3 contains the results for the band structure, density of states and optical properties of ZnSiAs2. The optical spectra are discussed through the study of a comparison with the experiment [11] made. The conclusions of this work are given in Section 4.

1327

0

EF

-2 -4 -6 -8 -10 -12 -14

Γ

Δ

Η

N Σ Γ Λ P 0

10

20

DOS Fig. 1. Band structure along the high symmetry directions in the Brillouin zone and the total density of states.

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Fig. 2 shows the partial DOS of ZnSiAs2. There are a few single bands around 11 eV in Fig. 1. This can be assessed that these bands consist of Si 3p and As 4s orbitals. The very small dispersion of these bands implies its localized character. The next higher bands, ranging from about 7.0 to 5.0 eV are valence bands that are composed mainly of 3d states of Zn atom, 3 s states of Si atom

Zn

0.6

s p d

0.4 0.2

DOS

0.0 0.6

Si

0.4 0.2 0.0 0.6

As

0.4 0.2 0.0 -10

-5

0 Energy (eV)

Fig. 2. Partial density of state ZnSiAs2.

5

and 4s, 4p states of As atom. The bands, ranging from about 5.0 eV up to the Fermi level, are valence bands that are composed mainly of 3p states of Si atom and 4p states of As atom. We see that there is quite strong interaction between with 3p orbitals of Si atom and 4p orbitals of As atom, which belongs to the (SiAs2)2 below the Fermi level. The conduction bands are composed mainly of Si atom and 4p orbitals of As atom, which also forms to the (SiAs2)2. The strong interaction implies that the interaction between Si and As is highly covalent. Fig. 3 shows the valence charge density of ZnSiAs2 in the (0 11) and (11 0) planes. Looking at the contour picture, one can find an important structure. A significant overlapping can be observed between Si–As bonding, showing a covalent character. Then, the overlapping of Si–Sn is smaller than that of Si–As, showing a ionic character Si–Sn. The results coincide with the density of states showing stronger orbitals hybridization between Si and As. It has been found earlier that the calculated optical properties for CeBO3 and CeB3O6 [27] SrX (X ¼ Se, Se, and Te) [28] and YTiO3 (Y ¼ Ba, and Sr) [29] are in excellent agreement with the experimental findings, and we have therefore used the same theory to predict the optical properties of ZnSiAs2. The imaginary parts of the dielectric function for ZnSiAs2 are shown in Fig. 4. As we know, the imaginary part of dielectric function e2(o) is the pandect of the optical properties for any materials. Apart from the fact that the LDA underestimates the energy band gaps, the imaginary part of the calculated dielectric function is in a good agreement with the experimental one [11]. When we compare our

Fig. 3. Valence charge density plot in the /0 11S and /11 0S planes of ZnSiAs2.

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20

1329

20

ZnSiAs2

2.0 A B

ε2

Dielectric constant 2

C

15

10

(x10)

5

15

1.5

10

1.0

5

0.5

0 0

8

16

24

32

0.0 0

8

16

24

32

Energy (eV)

Photon energy h [eV]

0.5

0.5

0.4

0.4

Reflectivity

Reflectivity R

Fig. 4. Experimental (a) and calculated (b) imaginary parts of the dielectric function for ZnSiAs2.

0.3

0.2

0.3

0.2

0.1

0.1

0.0 0

8 16 24 Photon energy h [eV]

32

0

8 16 24 Phonon energy (eV)

32

Fig. 5. Experimental (a) and calculated (b) reflectivity spectra for ZnSiAs2.

results with experimental ones, we should keep in mind that our calculations are essentially for a perfect static crystal (zero temperature and neglecting zero point vibrations), while the experimental measurement may be affected by the presence of phonons at finite temperature and the contamination with defects or impurities. We should also be aware of the fact that only pseudo-eigenvalues are available in the DFT approximation. Fig. 4(a) and (b) show the experiment and calculations for e2(o). Fig. 4(b) shows the calculations for e2(o) give two major peaks A and B, each of which commonly corresponds to the transition from Si 3p VB to As 4p CB (the peaks II of DOS of As 4p), are compared with the first important peak of the experimental e2(o). The peak C of the calculated e2(o) corresponds to the second important peak of the experimental e2(o), which corresponds to the transition from Si 3p VB to Zn 3p CB (the peaks I of DOS of Zn 3p). The optical properties of critical peaks are ascribed to the transitions of inner electron excitation from near VB semicore states to CB. It is noted that a peak in e2(o) does not correspond to a single interband transition since many direct transitions may be found in the band structure with an energy corresponding to the same peak. At the same time, it is noted that our calculated results are higher than the experiment at low energy.

As the reflectivity is one of the parameters which decide the optic figure of merit, it is of relevance to study the reflectivity as a function of energy. The variation of reflectance as a function of photon frequency is displayed for the ZnSiAs2 in Fig. 5. The dynamic reflectance corresponds to the ratio of the intensities of the incident and reflected electric fields. Our calculated e1 at zero frequency equals around 0.25 shown in Fig. 5b, well comparable to the experimental value around 0.27 [11]. For the ZnSiAs2, our calculation is able to reproduce the overall trend of the experimental reflectivity spectra [11] in the whole energy region. Fig. 6a and b shows the energy loss spectra L(o) of the ZnSiAs2. The loss function L(o) describes the energy loss of a fast electron traversing through the material. The sharp peaks are associated with the plasma oscillation. The function L(o) shown in Fig. 6b describes the energy loss of fast electron traveling the material [27]. These peaks of the L(o) spectra were observed at around 16.925 and 17.795 eV, respectively. Our results are in a good agreement with the experimental one [11]. However, the peak positions incombined the energy scale are shifted towards higher energies relative to those in the experimental spectrum. For example, the highest peak around 17.795 eV corresponds to the highest peak of the experimental result, whereas for the low peak around 16.925, the experimental results do

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2

1.5

Lossfunction -Imε-1

Lossfunction -Im -1

2.0

1.0

0.5

1

0 0

8 16 24 Photon energy h (eV)

32

0

8 16 24 Phonon energy (eV)

32

I (ω)

ε1 (ω)

Fig. 6. Experimental (a) and calculated (b) imaginary parts of the energy loss function for ZnSiAs2.

of the ZnSiAs2 by using the FPLAPW method. Our calculated band gap of 1.152 eV is indirect. Furthermore, other experiments and theory also shows that this material has a direct band gap. It is noted that there is quite strong hybridization between with 3p states of Si atom and 4p states of As atom, which belongs to the (SiAs2)2 below the Fermi level. Our calculated reflectivity spectra, the imaginary parts of the dielectric function and the energy loss spectra are in good agreement with the experimental results. On the other hand, the contributions of various transitions peaks are analyzed from the imaginary part of the dielectric function. Furthermore, the different optical properties have been investigated.

20 10 0 100

K (ω)

0 2

n (ω)

0 3 0 0.1

1 Energy (eV)

10

Fig. 7. Calculated optical parameters of ZnSiAs2 as a function of the photon energy eV. The imaginary parts of the dielectric function e1(o), the absorption coefficient, the extinction coefficient k(o) and the refractive index n(o).

not exist. It should be pointed out that the discrepancy of L(o) in the above cases was derived from plasma excitation. Also, the sharp structure may correspond to rapid decrease of reflectance at the same energy points. The good agreement between the theoretical and experimental optical spectra implies that the present calculations reasonable and reliable. Fig. 7. shows the calculated real parts of the dielectric function e1(o), the absorption coefficient I(o), the extinction coefficient k(o) and the refractive index n(o) as a function of the photon energy for ZnSiAs2. From the e1(o) pattern, the static dielectric constant e1(0) is equal to 12.114. The dielectric constant is directly related to the polarizability of the crystal. The polarizability, which represents the deformability of the electronic distribution, is to be connected with the shape of the valence charge density. It is interesting that the profiles of both I(o) and k(o) are rather similar with different magnitude. The extinction coefficient n(o) is attenuation index.

4. Conclusion In summary, we have given more detailed first-principles calculation on the electronic structure and linear optical properties

Acknowledgments The work is supported by Program for Science & Technology Innovation Talents in Universities of Henan Province in China under Grant no. 2008HASTIT008 and the National Natural Science Foundation under Grant no. 10574039. References [1] J.L. Shay, J.H. Wernick, Ternary Chalcopyrite Semiconductors: Growth, Electronic Properties, and Applications, Pergamon Press, New York, 1975. [2] D.G. Holah (Ed.), Ternary compounds, IOP Conference Proceedings no. 35, Institute of Physics, Bristol, 1977. [3] T. Ogino, M. Aoki, Japan J. Appl. Phys. 19 (1980) 2395. [4] P. Manca, Nuovo Cimento D 2 (1983) 1609. [5] G.C. Xing, K.J. Bachmann, J.B. Posthill, M.L. Timmons, in: J.T. Glass, R. Messier, N. Fujimori (Eds.), Diamond, Siliwn Nitride, and Related Wide Bandgap Semiconductors, MRS. Symposia Proceedings no. 162, Materials Research Society, Pittsburgh, 1989, p. 615 (and references therein). [6] B.F. Levine, Phys. Rev. B 7 (1973) 2600. [7] O. Alerhand, R.D. Meade, T. Arias, J.D. Joannopoulos, Bull. Amer. Phys. Soc. 37 (1992) 665. [8] W.C. Clark, R.F. Stroud, J. Phys. C Solid State Phys. 6 (1973) 2184. [9] R.F. Stroudt, W.C. Clark, J. Phys. D Appl. Phys. 9 (1976) 273. [10] J.L. Shay, E. Buehler, J.H. Wernick, Phys. Rev. B 3 (1971) 2004. [11] H. Boudriot, K. Deus, R. Grundler, H.A. Schneider, T. Stockert, Phys. Status Solidi B 143 (1987) K125. [12] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, Computer code WIEN2K (Vienna University of Technology, 2002), improved and updated Unix version of the original [P. Blaha, K. Schwarz, P. Sorantin, S.B. Trickey, Comput. Phys. Comm. 59 (1990) 399]. [13] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [14] M.D. Lind, R.W. Grand, J. Chem. Phys. 59 (1973) 5415. [15] D. Lynch, E.D. Palik, (Ed.), Handbook of Optical Constants of Solids, Academic Press, New York, 1985.

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