Cooling dynamics of photoexcited carriers in Si studied using optical pump and terahertz probe spectroscopy

We investigated the photoexcited carrier dynamics in Si by using optical pump and terahertz probe spectroscopy in an energy range between 2 and 25 meV. The formation dynamics of excitons from unbound $e$-$h$ pairs was studied through the emergence of the 1$s$-2$p$ transition of excitons at 12 meV (3 THz). We revealed the thermalization mechanism of the photoinjected hot carriers (electrons and holes) in the low-temperature lattice system by taking account of the interband and intraband scattering of carriers with acoustic and optical phonons. The overall cooling rate of electrons and holes was numerically calculated on the basis of a microscopic analysis of the phonon scattering processes, and the results well account for the experimentally observed carrier cooling dynamics. The long formation time of excitons in Si after the above-gap photoexcitation is reasonably accounted for by the thermalization process of photoexcited carriers.

Figure 1

Photoinduced change of dielectric function (left-hand side) and conductivity (right-hand side) at lattice temperature $T_L$, (a) 30 K and (b) 60 K, for the excitation density of $I_p=17$ $\mu \text{J}/{\text{cm}}^2$ and for the indicated pump-probe delays $\Delta t$. The solid lines in each panel show the Drude model fitted to the low-energy region.

Figure 2

The temporal change of the free $e$-$h$ pair density $N_{\mathit{eh}}$ obtained from the fitting in Fig. 1.

Figure 3

Photoinduced change in dielectric function (left-hand side) and conductivity (right-hand side) for the excitation density of 17 $\mu \text{J}/{\text{cm}}^2$ at various lattice temperatures. The solid lines in each panel show the Drude model fitted to the low-energy region.

Figure 4

The lattice temperature dependence of the free-carrier density $N_{\mathit{eh}}$. The dots show the experimentally obtained $N_{\mathit{eh}}$. The solid line shows the prediction of the Saha equation.

Figure 5

The temporal change in carrier temperature $T_C(t)$. The dots show the experimental data obtained from the results in Fig. 2 and the Saha equation. The solid lines show the calculated thermodynamics considering the carrier-phonon interaction.

Figure 6

The interband scattering processes in Si. $g$ scattering means scattering to the opposite band, and $f$ scattering means a transition to one of the remaining four bands.

Figure 7

Calculated cooling rate per electron, $-{\mathit{dT}}_e/\mathit{dt}$, for a thermal (Maxwell-Boltzmann) distribution with electron temperature $T_e$. The lattice temperature $T_L$ is fixed to 30 K. Cooling rates owing to different interband scatterings are shown in (a), where each line denotes the following processes. g-LO: $g$ scattering with longitudinal optical phonons; f-LA: $f$ scattering with longitudinal acoustic phonons; f-LO: $f$ scattering with longitudinal optical phonons. Inter: The sum of above three contributions. A comparison of cooling rates between interband scattering and intraband acoustic phonon scattering is shown in (b), where each line denotes the following contribution. Inter: The sum of interband scatterings [corresponding to Inter in (a)]. Intra: Intraband deformation scattering by acoustic phonons. Total: The sum of all scatterings.

Figure 8

Calculated cooling rate per light hole (a) and heavy hole (b), $-{\mathit{dT}}_i/\mathit{dt}$, for a thermal (Maxwell-Boltzmann) distribution with light- and heavy-hole temperatures $T_i$. The lattice temperature $T_L$ is fixed to 30 K. Each line denotes the following scatterings. NOP: Nonpolar-optical phonon scattering, AC: acoustic-phonon scattering, Total: The sum of these two scatterings.