Electronic energy band parameters of $\mathrm{CuInS}{\mathrm{e}}_2$: Landau levels in magnetotransmission spectra

Magnetotransmission (MT) at magnetic fields up to 29 T was used to study the electronic structure of $\mathrm{CuInS}{\mathrm{e}}_2$ in thin polycrystalline films. The zero field absorption spectra exhibited resolved A, B, and C free excitons. Quantum oscillations, due to diamagnetic excitons comprising electrons and holes from Landau levels quantized in the conduction and valence band, respectively, appeared in the MT spectra at fields over 5 T. Spectral energies of Landau levels and binding energies of the corresponding diamagnetic excitons, theoretically calculated assuming a quasicubic approximation of the $\mathrm{CuInS}{\mathrm{e}}_2$ tetragonal lattice structure, helped to identify the character of the experimentally observed diamagnetic excitons. Spectral energies of diamagnetic excitons in the MT spectra with different circular polarizations were used to determine the electron and light hole effective masses, whereas heavy hole masses as well as the γ and ${\gamma }_1$ Luttinger parameters, $E_p$ Kane energy, and F parameter of the influence of remote bands, as well as their polaron values, were calculated using the Luttinger theory.

Figure 1

SEM micrographs of the $\mathrm{CuInS}{\mathrm{e}}_2$ films: plan view (a) and cross section (b). XRD pattern (c).

Figure 2

The A and B excitons in an absorption spectrum of $\mathrm{CuInS}{\mathrm{e}}_2$ thin films plotted on a linear scale (a). The inset shows a wider plot with A, B, and C excitons in the zero-field absorption spectrum plotted on a logarithmic scale (b).

Figure 3

The evolution of normalized MT spectra with magnetic field B (showing Landau fans) measured using nonpolarized light (a), the higher the normalized intensity I(B)/I(0T) the lighter is the grey scale density. A normalized MT spectrum measured at 29 T (b).

Figure 4

Chalcopyrite lattice structure of $\mathrm{CuInS}{\mathrm{e}}_2$ (a), quasicubic approximation of the lattice structure of $\mathrm{CuInS}{\mathrm{e}}_2$ by the randomization of the Cu and In atoms positions on the cation sublattice (b).

Figure 5

MT spectra measured at 20 T for ${\sigma }^{-}$ (a) and ${\sigma }^{+}$ (b) polarizations (solid lines). The symbols show calculated energies of diamagnetic excitons comprising an electron (from level $n$) and holes from level $l=n-M+\frac{1}{2}$, with $M=\pm 1/2,\pm 3/2$ (upper sign “+” for ${\sigma }^{+}$ and lower sign “−“ for ${\sigma }^{-}$ spectra), $\lambda =\pm 3/2$ for the heavy hole (□ and ○), and $\lambda =\pm 1/2$ for the light hole (Δ and $x$), respectively.

Figure 6

The relative difference of the spectral energies of two excitons, comprising a hole (with number $l$) and two different electrons, with Landau level numbers $n+1$ and $n-1$ for magnetic fields of 15 and 20 T plotted on a $\hslash {\omega }_0\left(2n+1\right)$ scale (c). The relative difference of the spectral energies of two excitons, comprising an electron (with number $n$) and two different holes, with Landau level numbers $l-1$ and $l+1$, for magnetic fields of 20 T plotted on a $\hslash {\omega }_0\left(2l+1\right)$ scale (d).