Theory of nonlinear optical absorption associated with free carriers in semiconductors

We present calculations of the intensity dependence of the free-carrier absorption in semiconductors by high-intensity light with a wavelength near 10 μm. The paper is divided into two sections. The first section examines the nonlinear absorptive and dispersive properties associated with free-hole transitions in semiconductors, and the second section presents calculations of the nonlinear absorption associated with free-electron intraband transitions in germanium. The dominant free-hole absorption of CO
2
laser light for most p-type semiconductors with a diamond or zinc-blende crystal structure is direct intervalence-band transitions where a hole in the heavy- (or light-) hole band absorbs a photon and makes a direct transition to another band within the valence band structure. The absorption coefficient due to this mechanism is found to decrease with increasing intensity in a manner closely approximated by an inhomogeneously broadened two-level model. We present detailed results for the saturation behavior of germanium as a function of temperature, wavelength, and doping density. Calculated values for the intensity dependence of the index of refraction and low-frequency conductivity are presented. Calculated values of the saturation intensity are also given for most of the other Groups IV and III-V semiconductors. In several n-type semiconductors, the dominant absorption of 10 μm light is free-electron intraband transitions where an electron absorbs a photon and is excited to a state in the same band. The interaction of the electron distribution with the high-intensity light increases the average energy of the electrons and leads to an increase in the free-carrier cross section. For sufficiently high intensities, a significant fraction of the electron density in the interaction region can have an energy greater than the bandgap (relative to the conduction band minimum) by successive one-photon intraband transitions. These hot electrons can relax by creating an electron-hole pair by an impact ionization process. This can lead to the formation of an optically induced plasma and an abrupt increase in the absorption coefficient for light well below the bandgap of the material. Calculated threshold values for the formation of a laser-induced plasma by this impact ionization process are presented for germanium as a function of the lattice temperature and wavelength of the CO
2
laser light.