Density-functional theory approach to ultrafast laser excitation of semiconductors: Application to theA1phonon in tellurium

Calculations of the $A_1$ phonon frequency in photoexcited tellurium are presented. The phonon frequency as a function of photoexcited carrier density and phonon amplitude is determined, including anharmonic effects. The sensitivity of the $A_1$ mode to photoexcitation is related to the Peierls mechanism for stabilizing the α-Te structure. The assumptions of slow and fast carrier recombination are investigated and it is found that the two regimes give qualitatively different predictions for the excitation dependence of the phonon frequency. Recent pump-probe experiments are compared with the calculations. The predictions based on fast carrier recombination are not in agreement with experiment. The reflectivity oscillations expected to occur in pump-probe experiments are simulated, including the coupled effects of optical absorption, carrier diffusion, and phonon dynamics. Using the calculated dependence of phonon frequency on carrier density (assuming slow carrier recombination) and experimental values for the optical dielectric constants, the derivative of the frequency peak for reflectivity oscillations with respect to pump fluence is found to be $-0.085\hspace{0.5em}\mathrm{}\mathrm{THz}$ per ${\mathrm{m}\mathrm{J}/\mathrm{c}\mathrm{m}}^2,$ compared to an experimental value of $-0.07\hspace{0.5em}\mathrm{THz}$ per ${\mathrm{m}\mathrm{J}/\mathrm{c}\mathrm{m}}^2$ in the low-fluence regime. The ambipolar diffusion constant for the optically excited carriers is estimated to be 10 ${\mathrm{cm}}^2/\mathrm{s},$ substantially smaller than its equilibrium value. The effects of carrier diffusion are found to be more important than phonon anharmonicity in the observed changes of phonon frequency within the first few cycles of motion after laser excitation. Greatly increased damping of the reflectivity oscillations at high pump fluences, which was reported in recent experiments, is not found in the simulations.