Conductivity response of nonthermal hot carriers photoexcited by subpicosecond pulses in GaAs

A simplified formulation of the problem of calculating transient electrical conductivity σ(t) for nonequilibrium carriers excited by a subpicosecond laser pulse in semiconductors such as GaAs is presented. The Boltzmann equations for the distribution function of various types of hot carriers in the valence and conduction bands are set up in the presence of an electric field, and solved in the weak-field approximation. For assumed low-density excitations, the dynamics of the excited carriers is dominated by the LO-phonon emission via the strong Fröhlich interaction. The energy relaxation due to this interaction is treated within the model of ‘‘cascade emission’’ of LO phonons. The other slower relevant scattering processes are approximated by an effective relaxation time, for simplicity. The initial photoexcitation of carriers, by a laser beam of a short-time duration T, is taken to occur in a sufficiently narrow range of energy 2Δ. The time dependence of σ(t) arising from the conduction electrons and the holes in the two valence bands is calculated explicitly as a function of excitation energies ${\varepsilon }_0$ of these carriers (measured from the extrema of the appropriate bands), the initial energy spread 2Δ, generating laser pulse width T, the polarization state of the laser beam, and the effective quasielastic relaxation time ${\tau }_1$.

It is found that at sufficiently short times, σ(t) is a strong function of the initial carrier excitation energies. The conductivity rapidly decreases and becomes negative for initial conduction-electron excitation energy ɛ${̃}_0$, measured in units of the long-wavelength LO-phonon energy ħ${\omega }_{\mathrm{LO}}$, close to an integer m. For such special values of ɛ${̃}_0$, σ(t) shows a pronounced negative dip initially, before saturating to the usual positive value determined by the relaxation time ${\tau }_1$. For other ɛ${̃}_0$, not close to an integer, the conductivity steadily rises in time to saturate again at the value determined by ${\tau }_1$. The contribution of electrons excited from the light-hole band to σ(t) is found to be appreciable but insufficient to offset the -σ(t) effect. The hot holes have only a small contribution. The polarization of the laser beam is found to have a noticeable quantitative effect on the size of the negative dip in σ(t).