Electronic and Optical Properties of HgI 2
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ELECTRONIC AND OPTICAL PROPERTIES OF HgI 2 YIA-CHUNG CHANG', HOCK-KEE SIM*,t, and R. B. JAMES** *Department of Physics and Materials Research Laboratory, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801 SDepartment of Physics, National University of Singapore, Singapore 0511 "**Advanced Material Research Division, Sandia National Laboratories, Livermore, CA 94550 ABSTRACT We present theoretical studies of electronic structures, optical responses, and phonon modes of undoped Hg12 in its red tetragonal form. The electronic band structure is studied via an empirical nonlocal pseudopotential model, including the spin-orbit interaction. The electron and hole effective masses, optical matrix elements for interband transitions, and complex dielectric function are computed. Excitonic effects on the absorption coefficient near the fundamental band gap are included within the effectivemass approximation. The resulting absorption spectra and their polarization dependence are compared with experiment with favorable agreement. The phonon modes of HgI 2 are studied with a microscopic model and a good fit to the neutron scattering data is obtained. Electronic structures We first present an empirical nonlocal pseudopotential calculation of the electronic and optical properties of HgI 2 , including the effects of the spin-orbit interaction. Details of the calculations have been presented elsewhere.[1] In this paper, we only summarize the important results. The unit cell of HgI2 consists of two Hg atoms and four I atoms (see Figure 1). The solid has inversion symmetry about the mid point between the two Hg atoms in a unit cell. With the inversion symmetry, the Hamiltonian matrix elements between any two plane waves are real, and the eigenvalue problem can be solved efficiently. The parameters for describing the local and nonlocal pseudopotentials are adjusted to fit the experimental band gap, the heavy-hole light-hole splitting, and the over-all band structures calculated by a first-principle method.[2] Figure 2 shows the calculated band structure of HgI91 including the spin-orbit interaction. All bands are rigidly shifted by a constant so that the valence band maximum is at zero. Throughout the paper, we have chosen the z direction to be parallel to the c axis of the crystal. In Figure 2, we see four pairs of doubly degenerate levels at the zone center with energies between -2 and 0eV. They correspond to the I 5p. and 5p, non-bonding states (see Ref. 2). The two non-degenerate levels near -1.5eV and -2.5eV correspond to the I 5p, non-bonding states. The two remaining I 5p. orbitals interact with the two Hg 6a orbitals to form two bonding states with energies between -4.5eV and -3eV and two antibonding states with energies between 2.3eV and 3.5eV. The I 5s levels are near -1leV (not shown). The Hg 6p and I 5d levels are distributed from 3.5eV to 10eV, among which the doubly degenerate ones can be identified as the Hg p, and p. states. Note that the Hg 5d levels, which are between the I 5a an
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