Phonon-Assisted Optical Absorption in Silicon from First Principles

Abstract

The phonon-assisted interband optical absorption spectrum of silicon is calculated at the quasiparticle level entirely from first principles. We make use of the Wannier interpolation formalism to determine the quasiparticle energies, as well as the optical transition and electron-phonon coupling matrix elements, on fine grids in the Brillouin zone. The calculated spectrum near the onset of indirect absorption is in very good agreement with experimental measurements for a range of temperatures. Moreover, our method can accurately determine the optical absorption spectrum of silicon in the visible range, an important process for optoelectronic and photovoltaic applications that cannot be addressed with simple models. The computational formalism is quite general and can be used to understand the phonon-assisted absorption processes in general.The phonon-assisted absorption of light in materials is an important optical process both from a fundamental and from a technological point of view. Intraband light absorption by free carriers in metals and doped semiconductors requires the additional momentum provided by the lattice vibrations or defects, while phonon-assisted processes determine the onset of absorption in indirectband-gap semiconductors (Fig. 1). Moreover, the value of the direct band gap in silicon (3.4 eV [1]) is large and precludes optical absorption in the visible. However, silicon is a commercially successful photovoltaic material because of the indirect optical transitions that enable photon capture in the spectral region between the indirect (1.1 eV [2]) and direct band gaps.Despite their importance, at present, only a very limited number of first-principles studies of phonon-assisted optical absorption spectra exist. Ab initio calculations of direct optical absorption spectra including excitonic effects have already been performed for Si and other bulk semiconductors [3] and the underlying methodology is presently well established [4,5]. Phonon-assisted absorption studies are more involved, however, and the associated computational cost is much higher than the direct case. The calculation of the indirect absorption coefficient involves a double sum over k-points in the first Brillouin zone (BZ) to account for all initial and final electron states. In addition, these sums must be performed with a very fine sampling of the zone to get an adequate spectral resolution. The computational cost associated with these BZ sums is in fact prohibitive with the usual methods. Phonon-assisted absorption calculations have been done for the special case of free-carrier absorption in semiconductors [6], where the carriers are initially limited to a region near the Γ point of the first BZ, but a full calculation using brute-force methods for the general case remains beyond the reach of modern computers.The difficulty of zone-integral convergence can be addressed with the maximally-localized Wannier function interpolation method [7]. Using this technique, the quasiparticle energies [8] and optical transition matrix ele...

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