Wurtzite silicon as a potential absorber in photovoltaics: Tailoring the optical absorption by applying strain

We present ab initio calculations of the electronic structure and the optical properties of wurtzite Si (Si-IV). We find an indirect band gap of 0.95 eV $\left({\mathrm{\Gamma }}_5\to M_1\right)$ and an optically forbidden direct gap of 1.63 eV $\left({\mathrm{\Gamma }}_5\to {\mathrm{\Gamma }}_{10}\right)$, which is due to a backfolding of the $L_1$ state of Si in the diamond structure (Si-I). Optical absorption spectra including excitonic and local-field effects are calculated. Further, the effects of hydrostatic pressure, uniaxial strain, and biaxial strain on the absorption properties are investigated. Biaxial tensile strains enhance the optical absorption of Si-IV in the spectral range which is relevant for photovoltaic applications. High biaxial tensile strains $\left(>4\%\right)$ even transform Si-IV into a direct semiconductor.

Figure 1

Quasiparticle band structure and density of states (DOS) per atom for Si-IV. Relevant high-symmetry states in the vicinity of the band gap are labeled. The nomenclature follows Refs. [22, 37]. The valence-band maximum is set to zero.

Figure 2

Imaginary part of the dielectric function $\varepsilon \left(\omega \right)$ of Si-IV calculated in the IQPA and including excitonic and local-field effects (BSE). Spectra are plotted for ordinary $\left(\mathbf{E}\perp \mathbf{c}\right)$ and extraordinary polarization $\left(\mathbf{E}\left|\right|\mathbf{c}\right)$. The imaginary part of the dielectric function of Si-I including excitonic and local-field effects is shown for comparison.

Figure 3

Illustration of the optical transitions that govern the absorption onset of Si-IV in the equilibrium structure (a) and for $+5\%$ of biaxial strain (b). First panel: QP band structures. Second panel: joint band structures for the optical transition energies. Third and fourth panel: oscillator strengths of the optical transitions for both polarizations. Transitions from the three highest valence bands (red, green, orange in the top panel) into the three lowest conduction bands (empty circles, squares, and triangles in the top panel) are represented by combining the respective colors and symbols in the lower panels.

Figure 4

Evolution of selected high-symmetry QP states of Si-IV with hydrostatic pressure, uniaxial, and biaxial strain. The nomenclature follows Refs. [22, 37]. For convenience, the corresponding states are marked in the band structure in Fig. 1. The variation of all states is plotted with respect to the ${\mathrm{\Gamma }}_5$ state whose energy is set to zero for all strains.

Figure 5

Absorption coefficient $\alpha \left(\omega \right)$ of strained Si-IV in the IQPA for ordinary $\left(\mathbf{E}\perp \mathbf{c}\right)$ and extraordinary $\left(\mathbf{E}\left|\right|\mathbf{c}\right)$ polarization. Strains are given in percents for the relative changes of $\mathrm{d}V/V$ (hydrostatic pressure), $\mathrm{d}c/c$ (uniaxial strain), and $\mathrm{d}a/a$ (biaxial strain). For comparison, the absorption coefficient of Si-I is shown as shaded area.

Figure 6

Imaginary part of the dielectric function $\varepsilon \left(\omega \right)$ of Si-IV including excitonic and local-field effects (BSE). The absorption of Si-IV is shown for the equilibrium structure (eq) and for $5\%$ of tensile biaxial strain (bs). Spectra are plotted for ordinary $\left(\mathbf{E}\perp \mathbf{c}\right)$ and extraordinary polarization $\left(\mathbf{E}\left|\right|\mathbf{c}\right)$. The imaginary part of the dielectric function of Si-I including excitonic and local-field effects and the solar spectral irradiance [40] are shown for comparison.