Intersubband lifetimes in $p\text{−}\mathrm{Si}∕\mathrm{Si}\mathrm{Ge}$ terahertz quantum cascade heterostructures

Time-resolved studies of the dynamics of intersubband transitions are reported in three different strain symmetrized $p\text{−}\mathrm{Si}∕\mathrm{Si}\mathrm{Ge}$ multiple-quantum-well and quantum cascade structures in the far-infrared wavelength range (where the photon energy is less than the optical phonon energy), utilizing the FELIX free-electron laser. The calculated rates for optical and acoustic phonon scattering, alloy disorder scattering, and carrier-carrier scattering have been included in a self-consistent energy balance model of the transient far-infrared intersubband absorption, and show good agreement with our degenerate pump-probe spectroscopy measurements in which, after an initial rise time determined by the resolution of our measurement, we determine decay times ranging from $\sim 2\text{to}\sim 25\mathrm{ps}$ depending on the design of the structure. In all three samples the lifetimes for the transition from the first light hole subband to the first heavy hole subband are found to be approximately constant in the temperature range $4–100\mathrm{K}$.

Figure 1

Confinement potentials and calculated subband (or miniband) edge energies for the three samples studied: (a) SQW2, (b) QCL6, and (c) QCL10. The full and dashed curves show the confinement potentials for heavy and light holes respectively. In (a), one period of the ten-period structure is shown, and the suffixes (W) and (S) denote subbands localized in the quantum well and the adjacent spacer layer, respectively. In (b) and (c), two periods of the superlatticelike structures are shown; the shaded regions indicate the extent of the heavy and light hole minibands.

Figure 2

Differential probe transmission vs optical delay for temperatures between 4 and $80\mathrm{K}$ at $\lambda =45\mu \mathrm{m}$ for sample SQW2.

Figure 3

Differential probe transmission vs optical delay for temperatures between 4 and $100\mathrm{K}$, at $\lambda =95\mu \mathrm{m}$ for sample QCL6.

Figure 4

Differential probe transmission vs optical delay for temperatures between 4 and $100\mathrm{K}$ at $\lambda =85\mu \mathrm{m}$ for sample QCL6.

Figure 5

Differential probe transmission vs optical delay at $4\mathrm{K}$ between 38 and $45\mu \mathrm{m}$ for sample QCL10.

Figure 6

Differential probe transmission vs optical delay at $42\mu \mathrm{m}$ between 4 and $150\mathrm{K}$ for sample QCL10.

Figure 7

Comparison of simulated transmission relaxation and hole population relaxation lifetimes for the QCL10 structure, as a function of lattice temperature $\left(T_{\mathrm{latt}}\right)$. The simulations were performed using the self-consistent energy balance method with the initial carrier temperature $\left(T_h\right)$ set equal to $T_{\mathrm{latt}}$ (full curves), and with the initial $T_h$ set $50\mathrm{K}$ above $T_{\mathrm{latt}}$ (dot-dashed curves). Simulations were also carried out without energy balance, keeping $T_h$ fixed throughout each simulation (long-dashed curves).

Figure 8

Simulated transmission relaxation and hole population relaxation lifetimes for QCL6, as a function of lattice temperature $\left(T_{\mathrm{latt}}\right)$. Key as for Fig. 7.

Figure 9

Differential probe transmission vs optical delay at $17\mu \mathrm{m}$, for temperatures from $4\text{to}300\mathrm{K}$, for sample QCL10.