Two-photon magnetospectroscopy ofA-exciton states in CdS

Abstract

High-resolution spectra are obtained for the free $A$ excitons in CdS by two-photon absorption using photoconductivity techniques. At zero applied magnetic field the anisotropy splitting of the $2P$ and $3P$ exciton states is observed and interpreted with an anisotropic effective-mass Hamiltonian. The energies of these states are measured as a function of magnetic field up to $B\ensuremath{\simeq}$10 T. The magnetic field dependences are analyzed in terms of linear Zeeman splitting and diamagnetic interactions. At low fields the diamagnetic contribution gives the usual quadratic field dependence but deviates significantly at higher fields. At a given field, the deviation is found to increase dramatically with increasing quantum number $n$. This deviation is fitted by variational calculations developed by Larsen, which take into account the interaction of states through the diamagnetic term in the Hamiltonian. The magnetic field dependence of these states allow us to determine the masses as ${m}_{e}^{\ensuremath{\perp}}=(0.210\ifmmode\pm\else\textpm\fi{}0.003){m}_{0}$ and ${m}_{h}^{\ensuremath{\perp}}=(0.64\ifmmode\pm\else\textpm\fi{}0.2){m}_{0}$. At $B=0$ the narrow laser linewidths (0.05 meV) allow an accurate determination of the $A$-exciton binding energy of 27.4\ifmmode\pm\else\textpm\fi{}0.8 meV and the anisotropy parameter of 0.797\ifmmode\pm\else\textpm\fi{}0.013 from which the energy gap ${E}_{g}^{A}=2582.5\ifmmode\pm\else\textpm\fi{}0.2$ meV at $T=1.8$ K is calculated. Finally, the temperature dependence of the $A$ gap is determined.