Optical properties of ZrS2

Physica 105B (1981) 156-158 North-Holland Publishing Company

OPTICAL P R O P E R T I E S OF ZrS2 H. ISOM,~KI and J. von B O E H M Electron Physics Laboratory, and Department o[ General Sciences, Helsinki University of Technology, SF-02150 Espoo IS, Finland

The optical spectra of ZrS2 are calculated with the self-consistent symmetrized orthogonalized-plane-wave (OPW) method (X,,, a = 1, 240 OPW at each of 131 symmetry independent k-points). The main peak of e2 at 2.q eV is principally determined by the transitions from the two uppermost chalcogen p-type valence bands to the lowest metal d-type conduction band (only partially of the dz2-character).The positions of the peaks of the optical spectra agree well with the experimental results below ~5.5 eV.

The absorbing transitions of the electrons from the valence states to the conduction states determine the optical properties of the semiconductors in the eV region. The central optical quantities, such as the reflectivity R and the absorption coefficient K, are related via simple relations to the imaginary part of the complex, frequency-dependent permittivity, e2, which in turn is determined by the joint density of states (JDOS) weighted with the appropriate k-dependent oscillator strengths. Often there have been attempts to relate the experimental results back to the underlying band structure, but this is usually hampered by the lack of knowledge of JDOS and the oscillator strengths and of the way they are connected with the band structure. In this paper we study theoretically the optical properties of the 1T layer crystal ZrS2 by starting from a good quality ab-initio band structure and the associated Bloch eigenstates. We present an analysis of how the features of the original band structure [1] appear in the experimental spectra. This analysis may be extended to apply qualitatively to other IVA transition metal dichalcogenides as well. The calculation of e2 proceeds as follows. The valence and the conduction eigenstates are calculated in the final self-consistent (SC) symmetrized orthogonalized-plane-wave (SOPW) X~ potential [1] (general, non-muffin-tin, a = 1, 240 SOPW used at each of the high symmetry points

F, A, K, H, M and L in the SC iteration) with 240OPWs at 131 symmetry independent regularly spaced k-points. The optical matrix elements (f[pli) are calculated rigorously between the eigenstates at these k-points. The eigenenergies and the matrix elements are then evaluated in a finer grid corresponding to 9216 kspace integration cells in the first Brillouin zone by using the quadratic Lagrangian interpolation. The final spectra are calculated with the GilatRaubenheimer method [2] and the KramersKronig relation. The k-space integration is similar to the calculation of the density of states described in detail in [3] and [4]. The transitions from the six uppermost valence bands (the socalled chalcogen p-bands) to the three lowest conduction bands (the lower group of the socalled metal d-bands [1]) are included in the present calculation. This ensures an accurate JDOS and e2 up to ~ 5 . 5 e V , where the transitions to the two uppermost d-like bands would start. The lacking of these transitions is reflected via the Kramers-Kronig relation into the whole spectra of el (the real part of the permittivity), K and R. This holds especially for energies larger than ~5.5 eV. The SCSOPW JDOS, e2 and el (for the incident light normal to the layers) together with the semi-empirical tight binding (SETB) J D O S of Murray et al. [5] and e2 and el from the electron energy loss experiments of Bell and

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157

H. Isomiiki and J. yon BoehmlOptical properties of ZrS2

Liang [6], are shown in fig. 1. First of all it is interesting to notice what a dramatic effect the oscillator strengths have. The highest peak of the S C S O P W J n O S at 5 . 8 e V has almost disappeared in the S C S O P W e2, whereas the weak shoulder-like peak at 2 . 9 e V has grown to the main peak of the S C S O P W e2. T h e SETB J D O S is quite different from the t~

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S C S O P W J D O S (fig. la). T h e SETB J D O S has a minimum at ~ 4 e V where the experimental window appears. Although such a clear minimum is missing from the S C S O P W J D O S , it turns out that the S C S O P W K nevertheless has a clear minimum just above 4 eV. The positions of the main peaks of the S C S O P W and the experimental e2 and et [6] (fig. lb and lc) below 6 e V agree quite accurately. However, the peak sizes should not be directly c o m p a r e d because the physical situation of the energy loss experiment differs from that of the optical absorption. The sharp peak of the S C S O P W e2 (fig. lb) at 2.9 eV is mainly formed by the transitions from the two uppermost chalcogen p-type valence bands to the lowest conduction band which is only partially of d,2-type. The small peak at 5.7 eV is formed mainly by the transitions from the two uppermost valence bands to the second and third d-type conduction band. However, this peak will probably grow to some extent and shift to a higher energy when the transitions to the fourth and fifth d-like conduction band (starting at = 5 . 5 eV) are taken into account. T h e S C S O P W K together with the experimental result of Beal et al. [8] are shown in fig. 2. The sharp peak at 3.0 eV of the S C S O P W K is mainly derived from the main peak of the S C S O P W e2 (fig. lb). The second p e a k at

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--~3.3eV follows from the contribution of the negative values of el (fig. lc). Beal et al. [8] speculate that the sharp experimental peak at 3.0 eV (fig. 2) could be of an excitonic nature. However, our calculation shows that it is also possible to get a sharp peak at the same energy from a bulk band structure calculation. Both the SCSOPW and the experimental K have a higher absorbing region between 2.5 and 4 eV. The SCSOPW R and the experimental Rspectrum of Greenaway and Nitsche [9] both show a region of higher reflectivity between 2 and 4 e V (fig. 3) in the same way. The peak structures of the SCSOPW and the experimental K and R spectra are somewhat different but a closer analysis is not possible until more complete spectra including also the missing transitions above 5.5 eV are obtained [10].

In conclusion, the whole bulk of the energy bands is essential for describing the optical quantities. The large oscillator strengths between the two uppermost p-type valence bands and the lowest d-type conduction band (only partially of dz2-type) are responsible for the main peak of the SCSOPW e2 at 2.9eV. This peak agrees well with the experimental electron energy loss result [6] and it is seen to play a central role in determining the other optical quantities.

Acknowledgements We wish to express our gratitude to Professors T. Stubb and M.A. Ranta for their continuous support. We also want to thank the staff of the Computer Center of the Helsinki University of Technology for their amicable co-operation. Our sincere thanks go also to Mrs. T. Aalto for her patient and expert typing of this work.

Relerenees [1] H. Isom/iki and J. yon Boehm, J. Phys. C: Solid State Phys., submitted. [2] G. Gilat and L.J. Raubenheimer, Phys. Rev. 144 (1966) 390. [3] H. Isom/iki and J. von Boehm, Physica 99B (1980) 255. [4]-J. yon Boehm and H. Isom~ki, J. Phys. C: Solid State Phys. 13 (1980) 3181. [5] R.B. Murray, R.A. Bromley and A.D. Yoffe, J. Phys. C: Solid State Phys. 5 (1972) 746. [6] M.G. Bell and W.Y. Liang, Advan. Phys. 25 (1976) 53. [7] G. Lucovsky, R.M. White, J.A. Benda and J.F. Revelli, Phys. Rev. B7 (1973) 3859. [8] A.R. Beal, J.C. Knights and W.Y. Liang, J. Phys. C: Solid State Phys. 5 (1972) 3531. [9] D.L. Greenaway and R. Nitsche, J. Phys. Chem. Solids 26 (1965) 1445. [10] H. Isomiiki and J. yon Boehm, to be published.