Two-Phonon Deformation Potential Coupling: Free-Carrier Absorption in InSb

We calculate the contribution of the free-carrier absorption due to scattering of electrons by two nonpolar optical phonons. An effective Hamiltonian is formulated for the interaction between the electrons and two phonons. Using the previously calculated values of the two-phonon effective deformation potential, we find that significant contributions to the absorption coefficient occur because of two-phonon processes. The absorption coefficient due to two nonpolar optical phonons varies with wavelength $\lambda$ of the incident radiation as ${\lambda }^{1.5}$. The resultant calculated absorption coefficient varies as ${\lambda }^{2.2}$ while the experimental value varies as ${\lambda }^2$. Thus the agreement between theory and experiment is improved if two-phonon processes are taken into account. The variation of the absorption coefficient with temperature is also calculated.