Dynamic Piezo-Optic Study of Exciton and Polaron States in AgBr

Abstract

A recently developed piezo-optic technique has been used to study the indirect absorption edge of AgBr. Appreciable structure has been detected. From the variation of the piezo-optic signal as a function of the direction in which the modulating force was applied, it was deduced that the maxima of the valence band are along 111>. From the same data, it was deduced that the $1s$ indirect exciton is split by the valley-orbit interaction into a group of states whose symmetry assignment is $2(\ensuremath{\Gamma}_{4}^{}{}_{}{}^{\ensuremath{-}}+\ensuremath{\Gamma}_{5}^{}{}_{}{}^{\ensuremath{-}})$ and a group of states whose symmetry assignment is $2\ensuremath{\Gamma}_{3}^{}{}_{}{}^{\ensuremath{-}}$. The energy splitting is 3.8 meV. The exciton series limit is 16.4\ifmmode\pm\else\textpm\fi{}0.5 meV above its ground state. From the relative magnitudes of the piezo-optic signal assigned go the $1s$ exciton states, the magnitudes of the shear deformation potentials of both the phonons and the indirect gap are evaluated as, respectively, -0.58\ifmmode\pm\else\textpm\fi{}0.12 and 4.3\ifmmode\pm\else\textpm\fi{}0.8 eV. The selection rules for the creation of indirect excitons are discussed. It is observed that the exciton series is repeated whenever the incident photon has an energy that is sufficient to create an exciton whose center of mass has a kinetic energy that is equal to that of the LO phonon at $k=0$. The measured energy of the LO phonon is 17.4\ifmmode\pm\else\textpm\fi{}0.5 meV. The exciton series is repeated again whenever the energy of the incident photon is sufficient to create an exciton in which one or both of the constituting polarons may be excited to the edge of their respective polarization wells. The polaron coupling constants of the electron and hole are, respectively, ${\ensuremath{\alpha}}_{e}=1.68\ifmmode\pm\else\textpm\fi{}0.02$ and ${\ensuremath{\alpha}}_{h}=3.0\ifmmode\pm\else\textpm\fi{}0.3$. An average of the undressed hole's effective mass that is likely to be close to the value of its transverse mass is $(0.56\ifmmode\pm\else\textpm\fi{}0.06){m}_{0}$.