J. Phys. Chem. B 2009, 113, 5803–5808
5803
X-ray Photoelectron Spectrum and Electronic Properties of a Noncentrosymmetric Chalcopyrite Compound HgGa2S4: LDA, GGA, and EV-GGA Ali Hussain Reshak,*,† R. Khenata,‡ I. V. Kityk,§ K. J. Plucinski,| and S. Auluck⊥ Institute of Physical Biology, South Bohemia UniVersity, Institute of System Biology and Ecology, Academy of Sciences, NoVe Hrady 37333, Czech Republic, Laboratoire de Physique Quantique et de Mode´lisation Mathe´matique de la Matie`re, UniVersite´ de Mascara, 29000 Mascara, Algeria, Electrical Engineering Department, Technological UniVersity of Czestochowa, Al Armii Krajowej 17/19, Czestochowa, Poland, Physics Department, Indian Institute of Technology Kanpur, Kanpur (UP) 208016, India, and Institute of Electronics, Military UniVeristy of Technology, ul. Kaliskiego 2, Warsaw, Poland ReceiVed: February 7, 2009
An all electron full potential linearized augmented plane wave method has been applied for a theoretical study of the band structure, density of states, and electron charge density of a noncentrosymmetric chalcopyrite compound HgGa2S4 using three different approximations for the exchange correlation potential. Our calculations show that the valence band maximum (VBM) and conduction band minimum (CBM) are located at Γ resulting in a direct energy gap of about 2.0, 2.2, and 2.8 eV for local density approximation (LDA), generalized gradient approximation (GGA), and Engel-Vosko (EVGGA) compared to the experimental value of 2.84 eV. We notice that EVGGA shows excellent agreement with the experimental data. This agreement is attributed to the fact that the Engel-Vosko GGA formalism optimizes the corresponding potential for band structure calculations. We make a detailed comparison of the density of states deduced from the X-ray photoelectron spectra with our calculations. We find that there is a strong covalent bond between the Hg and S atoms and Ga and S atoms. The Hg-Hg, Ga-Ga, and S-S bonds are found to be weaker than the Hg-S and Ga-S bonds showing that a covalent bond exists between Hg and S atoms and Ga and S atoms. 1. Introduction Mercury thiogallate, HgGa2S4 (HGS), possesses a combination of attractive properties for many applications. HGS crystals are chemically stable in air. It is a “defect” chalcopyrite derived from the I-III-VI2 chalcopyrite structure by the order substitution of group II atoms and vacancies on the group I sites.1 It was first synthesized in powder form by Hahn et al.2 HGS crystals are characterized with high nonlinear susceptibility coefficients, wide transparency range (from 0.5 to 13 µm), and considerable birefringence.3 The large birefringence ensures phase matching in a wide frequency range.4,5 HGS is considered to be very promising for operating in the mid-IR spectral range6,7 because of their superior nonlinearity and damage threshold. It can be used for mid-IR parametric oscillator with Nd:YAG laser pumping. HGS has promising values of effective nonlinear susceptibility, a wide transparent region, a low value of absorption coefficient, a variance of refractive indices, and a resistance to laser radiation8 thus making it useful for optical applications. Their conversion efficiency is more than two times larger than that of silver thiogallate.8 HGS shows a very large effective second order susceptibility coefficients (in particularly, tensor component d36 which is approximately 1.8 times that of AgGaS2,5 i.e. about 34 pm/V9). This material can be used for up conversion of the frequency of the CO2 laser radiation (λ ) 10.6 µm) with an efficiency of * Corresponding author. Phone: +420 777729583. Fax: +420-386 361231. E-mail address:
[email protected]. † South Bohemia University. ‡ Universite´ de Mascara. § Technological University of Czestochowa. | Military Univeristy of Technology. ⊥ Indian Institute of Technology Kanpur.
up to 60%, for detecting radiation in the atmospheric transmission window (10-12 µm), and for visualizing the spectra of fast processes in the range from 8 to 12 µm.1 Recently Rotermund and Petrov10 used HGS crystals as optical parametric generators (OPG) pumped by femtosecond pulses near 1.25 µm from a Cr:forsterite regenerative amplifier. This wavelength is very close to the signal wavelength from a Ti:sapphire laser pumped OPG that can be used for difference frequency generation (DFG) in the 3-12 µm spectral range. HGS is a negative uniaxial crystal (n0 > ne) with an energy gap corresponding to roughly 440 nm. There seems to be a lack of comprehensive experimental data and first principles calculations on the structural and electronic properties of HGS in the literature, except one report by Shu-Ping et al.11 using the CASTEP (Cambridge Serial Total Energy Package) program which is nonfull potential method. The calculated energy gap obtained by ShuPing et al. was 1.55 eV.11 It would be interesting to compare this gap with that obtained from a full potential calculation. In our earlier work, we had reported calculations of the optical properties of HGS.12 In this work, we concentrate on the electronic properties such as band structure, density of states and charge densities. We have used the full potential linear augmented plane wave (FP-LAPW) method which has proven to be one of the most accurate methods13,14 for the computation of the electronic structure of solids within a framework density functional theory (DFT). Our calculations will demonstrate the effect of using a full-potential on the electronic properties. Also it will highlight the effect of LDA, GGA, and EV-GGA on these properties.
10.1021/jp901142q CCC: $40.75 2009 American Chemical Society Published on Web 04/03/2009
5804 J. Phys. Chem. B, Vol. 113, No. 17, 2009 2. Experimental Procedure The synthesis of HgGa2S4 is complicated due to the necessity of using high vapor pressures associated with mercury and sulfur, which requires a hyperfine approach to the fabrication of the crystals. We have applied a method described in the ref.24 This method consists in a use of double-walled ampule for pregrowth a several quantities of starting material. Afterward the horizontal-gradient freeze technique was carried out to monitor and control the crystallization process. We have found that small 1.2 × 2.2 × 2.5 mm single crystals could be extracted from the oriented solidified polyphase ingots. The sample’s surface was bombarded with X-rays and the measurement of the concomitant photoemitted electrons which exhibit discrete kinetic energies. Those energies characterize the emitting atoms and their bonding states. We used high vacuum equal to 10-10 Torr. The high energy resolution analyzer allowed gave an opportunity to perform the photoemitted electrons analysis up to 0.12 eV. By minimizing the wave spread of the entering photoelectrons, the precision of energy determination was enhanced. Additionally, the spot size was decreased down to 22 µm. This enabled us to analyze different parts of the surfaces. X-ray beams imparted precise energy to the photoelectrons and allowed us to extract chemical and bonding information. Using monochromatic X-rays precisely helped to remove satellites from the Al K X-ray line. This ensured the precise impartation of energy to photoelectrons. 3. Theoretical Calculations In the past decade, first-principle calculations have been successfully used to obtain different properties of materials. The structural parameters and dynamical properties of crystals determine a wide range of microscopic and macroscopic behavior: diffraction, sound velocity, elastic constants, Raman and infrared absorption, inelastic neutron scattering, specific heat, etc. Mercury thiogallate, HgGa2S4, is a defect chalcopyrite semiconductor possessing space group S24(I4j).2,15 The equivalent positions are 2Hg (0 0 0); 2Ga1 (0 0 0.5); 2Ga2 (0 0.5 0.25); 8S (x y z) (x ) 0.2718; y ) 0.2675; z ) 0.1374).2 Calculations are performed at the experimental lattice constants a ) b ) 5.5106 Å and c ) 10.2392 Å.15 We have performed calculations using the all-electron full potential linearized augmented plane wave (FP-LAPW) method to solve the Kohn-Sham equations as implemented in the WIEN2K code.16 This is an implementation of the density functional theory (DFT)17 with different possible approximation for the exchange correlation (XC) potentials. The exchange correlation potential was calculated using the local density approximation (LDA),23 the generalized gradient approximation (GGA)18 and the modified GGA by Engel-Vosko.19 The Engel-Vosko GGA formalism19 optimizes the exchange correlation potential for band structure and optical properties calculations. It is well-known in the self-consistent band structure calculation within DFT, both LDA and GGA usually underestimate the energy gap.20 This is mainly due to the fact that they are based on simple model assumptions which are not sufficiently flexible to accurately reproduce the exchange correlation energy and its charge derivative. Engel and Vosko considered this shortcoming and constructed a new functional form of GGA19 which is able to better reproduce the exchange potential at the expense of less agreement in the exchange energy. This approach (EV-GGA) yields better band splitting compared to GGA. In order to achieve energy eigenvalues convergence, the wave functions in the interstitial regions were expanded in plane waves with a cutoff Kmax ) 9/RMT, where RMT denotes the smallest
Reshak et al. atomic sphere radius and Kmax gives the magnitude of the largest K vector in the plane wave expansion. The muffin-tin radii were assumed to be 2.0 atomic units (a.u.) for Hg, Ga, and S. The valence wave functions inside the spheres are expanded up to lmax ) 10 while the charge density was Fourier expanded up to Gmax ) 14 (a.u)-1. Self-consistency is achieved using 300 k-points in the irreducible Brillouin zone (IBZ). The band structure and density of states are calculated using 500 k-points of the IBZ. The self-consistent calculations are considered to be converged when the total energy of the system is stable within 10-5 Ry. 4. Results and Discussion Band Structure and Density of States. The calculated band structure and the total density of states (DOS) obtained using LDA, GGA, and EV-GGA are shown in Figure 1. Following Figure 1, our calculations show that the valence band maximum (VBM) and conduction band minimum (CBM) are located at Γ resulting in a direct energy gap of about 2.0, 2.2, and 2.8 eV for LDA, GGA, and EV-GGA, respectively. The LDA value of 2.0 eV is in better agreement with the experiment compared to an earlier calculation.11 This is due to our use of a full potential method. The calculated energy gap using EVGGA (2.8 eV) is very close to the experimental one (2.84 eV).21,22 This agreement is attributed to the use of full potential method within Engel-Vosko GGA formalism, which optimizes the corresponding potential for band structure calculations. Since EV-GGA yields better band splitting compared to LDA and GGA, the calculated total density of states along with the Hg-s/p/d/f, Ga-s/p/d, and S-s/p partial DOS are shown only for EV-GGA in Figure 2. The electronic structure of the upper valence band is dominated by the S-p and Ga-p states. The electronic structure of the lower conduction band is dominated by the S-p, Hg-s, and Ga-s states. The existence of S-p states in the upper valence band and lower conduction band has significant effect on the energy band gap. The band structure and the DOS can be divided into three distinct spectral groups/ structures separated by gaps. From the band structure and DOS, we note that the lowest bands in the energy range between -11.5 and -13.5 eV originate mainly from Ga-d and S-s states and there is small admixture of Hg-s and Ga-s/p states. The bands from -7.0 up to Fermi energy (second group) are mainly Hg-s/p/d and S-p and Ga-s/p S-p states. The last group has contributions from S-p, Ga-s/p, and Hg-s/p states and very small contribution of S-s and Hg-f states. The bandwidth to which Hg-d and S-p states make a large contribution is about 7.5 eV. Therefore, we can conclude that Hg-d and S-p electrons should be treated not as localized electron but as itinerant electrons. From the band structure and PDOS, one can see that there exists a strong hybridization between Hg-s and Ga-p states at around -12.0, -6.0, and -4.0 eV. Ga-s is strongly hybridized with Hg-s states at around -5.0 and +3.0 eV and from 5.0 eV and above. Also from 5.0 eV and above, Hg-f states are strongly hybridized with both Hg-s and Ga-s states. In the energy range between 4.0 and 10.0 eV, Ga-p states are strongly hybridized with Hg-p states. In the energy range from -4.0 up to Fermi energy, Hg-p states strongly hybridized with both Ga-s and Hg-s states. In Figure 2f, the experimental VB-XPS of HGS crystal is compared with the results of our full potential linear augmented plane wave method using the Engel-Vosko GGA
Noncentrosymmetric Chalcopyrite Compound
J. Phys. Chem. B, Vol. 113, No. 17, 2009 5805
Figure 1. Calculated; (a) Brillouin zone. (b) Band structure. (c) Total density of states (states/eV unit cell), for HGS using LDA, GGA, and EVGGA.
exchange correlation functional. The calculated TDOS spectra reproduces the general structure of the measured XPS valence band correctly probably due to the better representation of the wave functions in the FP-LAPW method. The valence
band density of states data was analyzed in the energy range in which the experiment was performed (-15.0 to 0.0 eV). We note a reasonable agreement in the matter of the general behavior and position of the peaks. However, the magnitude
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Reshak et al.
Figure 2. Calculated total density of states (states/eV unit cell) along with the partial density of states (states/eV unit cell): (a) Ga-d and Hg-d. (b) S-s and S-p. (c) Hg-p. (d) Hg-f. (e) Hg-s and Ga-s/p, using EVGGA. (f) Calculated total density of states using FP-LAPW method in comparsion with the measured total density of states using XPS technique for the valence band.
of theoretical DOS is significantly different from the experimental value. We would like to mention that the difference between the magnitudes of the experimental and the theoretical curves can be made smaller if we choose a larger broadening in our theoretical calculations. In the present calculation the broadening is around 0.003 eV. Also problems may arise due to nonstoichiometry near the surface of the titled crystals. As a consequence relative intensities of the XPS spectra may be different.
Consider now the bonding properties. To visualize the nature of the bond character and to explain the charge transfer and bonding properties of HGS crystal, we calculated the total valence charge density. We present in Figure 3 the total valence charge densities in the (1 1 0) plane. There is a strong covalent bond existing between the Hg and S atoms and Ga and S atoms (Table 1). The Hg-Hg, Ga-Ga, and S-S bonds are found to be weaker than the Hg-S and Ga-S bonds demonstrating that a covalent bond exists between Hg and S
Noncentrosymmetric Chalcopyrite Compound
J. Phys. Chem. B, Vol. 113, No. 17, 2009 5807 TABLE 2: Calculated Bond Angles bond type
calculated bond angle (deg)
Hg-S-Ga1 Hg-S-Ga2 Ga1-S-Ga2 S-Ga1-S S-Ga2-S S-Hg-S
102.67711 108.10873 110.97144 104.76968 103.83072 108.02768
thebondanglesbetweenHg-S-Ga1,Hg-S-Ga2,Ga1-S-Ga2, S-Ga1-S, S-Ga2-S, and S-Hg-S (Table 2). We found that Ga1-S-Ga2 angles are the same for all S atoms. 5. Conclusions We have performed a first principles calculation of the electronic properties for HgGa2S4, within the framework of FPLAPW method. Our calculations have shown that the valence band maximum (VBM) and conduction band minimum (CBM) are located at Γ resulting in a direct energy gap. Our LDA gap is closer to the experimental gap compare to a recent calculation using CASTEP.11 The value of our calculated energy gap using EV-GGA (2.8 eV) is very close to the experimental one (2.84 eV).21,22 This agreement is attributed to the use of the full potential method within Engel-Vosko GGA formalism, which optimizes the corresponding potential for band structure calculations. Our calculations are in good agreement with our XPS measurements. We would like to conclude by stating that the agreement between our calculated and measured DOS shows the reliability of the full potential calculations. We find a strong covalent bond existing between the Hg and S atoms and Ga and S atoms. The Hg-Hg, Ga-Ga, and S-S bonds are found to be weaker than the Hg-S and Ga-S bonds. Our calculated bond length shows better agreement with the experimental data than the pervious calculations. Acknowledgment. This work was supported from the institutional research concept of the Institute of Physical Biology, UFB (No.MSM6007665808), and the Institute of System Biology and Ecology, ASCR (No. AVOZ60870520). References and Notes
Figure 3. (a) Crystal structure of HGS. (b) Total valence charge densities in the (1 1 0) plane (2D). (c) Total valence charge densities in the (1 1 0) plane (3D).
TABLE 1: Calculated Bond Lengths in Comparison with Pervious Calculation and Experimental Data bond type
calculated bond length (Å)
experimental bond length (Å)
Hg-S Ga1-S Ga2-S
2.52894*, 2.60685a 2.28081*, 2.31190a 2.28344*, 2.31777a
2.52894b 2.28082b 2.28344b
* This work. a Reference 11. b Reference 15.
atoms and Ga and S atoms. Our calculated bond lengths show excellent agreement with the experimental data15 than the pervious calculations.11 This agreement is attributed to our use of the full potential calculations. Also we have calculated
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5808 J. Phys. Chem. B, Vol. 113, No. 17, 2009 (16) Blaha, P.; Schwarz, K.; Madsen, G. K. H.; Kvasnicka, D.; Luitz, J. WIEN2K, “an Augmented Plane WaVe + Local orbitals program for calculating crystal properties”; Techn. Universitat: Wien, Austria, 2001; ISBN 3-9501031-1-2. (17) Hohenberg, P.; Kohn, W. Phys. ReV. B 1964, 136, 864. (18) Perdew, J. P.; Burke, S.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (19) Engel, E.; Vosko, S. H. Phys. ReV. B 1993, 47, 13164.
Reshak et al. (20) Dufek, P.; Blaha, P.; Schwarz, K. Phys. ReV. B 1994, 50, 7279. (21) Beun, J. A.; Nitsche, R.; Lichtensteiger, M. Physica 1961, 27, 448. (22) Ursaki, V. V.; Ricci, P. C.; Tiginyanu, I. M.; Anedda, A.; Syrbu, N. N.; Tezlevan, V. E. J. Phys. Chem. Solids 2002, 63, 1823. (23) Perdew, J. P.; Zunger, A. Phys. ReV. B 1981, 23, 5048. (24) Schunemann, P. G.; Pollak, T. M. J. Cryst. Growth 1997, 174, 278.
JP901142Q
