Inelastic electron-exciton scattering in bulk germanium

We investigate the destructive inelastic as well as the elastic scattering of a hot electron-hole plasma with an incoherent exciton population in bulk Ge by means of optical pump-terahertz probe spectroscopy. An incoherent exciton population evolves from a first optical pulse while a delayed second optical pulse creates the electron-hole plasma. The interaction of the plasma with the exciton population is monitored via the intraexcitonic transitions by a probing terahertz pulse. Analyzing the density-dependent decay of the intraexcitonic transitions after the arrival of the second optical pulse yields an inelastic scattering rate of $2.0\times {10}^{-4}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$. An analysis of the corresponding linewidth of the $1s-2p$ transition yields a total scattering rate of $3.7\times {10}^{-4}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$. This allows us to experimentally distinguish between elastic and inelastic scattering and we obtain an elastic scattering rate of $1.7\times {10}^{-4}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$.

Figure 1

(a) The linear absorption of the sample (blue) is plotted together with the spectrum of the optical excitation pulse (red). (b) Schematic of the excitation process and the indirect band structure of Ge. (c) A schematic of the experimental optical pump-THz probe setup. The THz section is purged with dry nitrogen gas to avoid THz absorption by water vapor.

Figure 2

Contour plots of the THz absorption for a constant photon density of the first excitation pulse $P_1$ of $9.8\times {10}^{13}\mathrm{photons}/{\mathrm{cm}}^2$ and photon densities of (a) $2.9\times {10}^{13}\mathrm{photons}/{\mathrm{cm}}^2$, (b) $5.9\times {10}^{13}\mathrm{photons}/{\mathrm{cm}}^2$, and (c) $1.0\times {10}^{14}\mathrm{photons}/{\mathrm{cm}}^2$ for the second optical pulse $P_2$. The second pulse is delayed by 6.7 ns with respect to the first optical pulse. A time delay of zero between the second optical pulse and the THz pulse is set to 10 ps on the time axis to allow for a logarithmic representation. Before the second optical pulse excites the sample, all graphs show a pronounced intraexcitonic resonance at 3.2 meV. With the excitation from the second optical pulse at 10 ps, the amplitude of the resonance decreases on a time scale of tens of picoseconds, while simultaneously the absorption increases at low energies. This process occurs more rapidly with increasing photon density of the second pulse. It takes a few hundred picoseconds for the intraexcitonic resonance to build up again and about 3 ns to reach a similar level as before the excitation of the second pulse.

Figure 3

(a) Intraexcitonic oscillator strength for a photon density of $9.8\times {10}^{13}\mathrm{photons}/{\mathrm{cm}}^2$ from the first optical pulse and five different densities of the second pulse. For the sake of clarity, the data points have been provided with an offset. A biexponential fit (black) yields the decay as well as the reformation times. (b) Fit of a Drude-Lorentz model to the intraexcitonic $1s-2p$ transition 10 ps before and 3 ps after the second optical pulse injects an electron-hole plasma. The borders of the fit are marked by vertical gray dashed lines. (c) Decay times ${\tau }_1$ (black data points) from the biexponential fit are plotted together with the additional dephasing due to electron-exciton scattering $T_{2,\mathrm{scat}}$ (red data points), which is calculated via Eq. (7), for photon densities of $9.8\times {10}^{13}\mathrm{photons}/{\mathrm{cm}}^2$ (squares) and $2.8\times {10}^{14}\mathrm{photons}/{\mathrm{cm}}^2$ (circles) of the first excitation pulse. (d) The corresponding inelastic and total scattering rates together with the respective median of the data.