Electron-phonon coupling in $n$-type Ge two-dimensional systems

Electron-optical phonon interaction is the dominant energy-loss mechanism in low-dimensional Ge/SiGe heterostructures and represents a key parameter for the design and realization of electronic and optoelectronic devices based on this material system compatible with the mainstream Si complementary metal-oxide semiconductor technology. Here we investigate the intersubband relaxation dynamics of $n$-type Ge/SiGe multiquantum wells with different symmetry and design by means of single-color pump-probe spectroscopy. By comparing the experimental differential transmittance data as a function of the pump-probe delay with numerical calculations based on an energy-balance rate-equation model, we could quantify an effective value for the optical phonon deformation potential describing the electron-phonon coupling in two-dimensional Ge-based systems. We found nonradiative relaxation times longer than 20 ps even in samples having intersubband energy separations larger than the optical phonon energy, evidencing the presence of a less effective electron-phonon coupling with respect to that estimated in bulk Ge.

Figure 1

(a), (b) Band-edge profiles, calculated electron energies, and squared envelope wave functions for the symmetric MQW S1 and the stepwise structure S2, respectively. The solid black and dashed red curves represent the $L$ and ${\mathrm{\Delta }}_2$ band profiles, respectively. The theoretical energy values corresponding to the $L_1\text{−}{L}_2$ transition are also indicated. (c, d) The corresponding experimental ISB absorption spectra measured by FTIR (red dots). The Lorentzian fits of the resonances centered at $E_{12,\mathrm{abs}}$ (dashed blue curve) and $E_{13,\mathrm{abs}}$ (dashed violet curve) are displayed. For S2, the dashed black curve is the sum of the blue and violet fit curves. (e), (f) The time-resolved pump-probe signals as defined in the text for (e) S1 and (f) S2, recorded at a lattice temperature $T_{\mathrm{L}}=4\mathrm{K}$. The red dots are the experimental relative differential transmission data. Theoretical results for the dynamics of the relative differential transmission are reported for different sets of the material parameters driving the electron-phonon scattering: taking into account all the elastic scattering channels and using the deformation potentials provided in Ref. [24] (black curve); switching off all the elastic channels and adopting the values for the deformation potentials provided in Ref. [24] (magenta curve); keeping active only the elastic scattering (cyan curve); considering all the scattering channels but using our best-fit values for the deformation potentials as discussed in the text (orange curve).

Figure 2

Differential transmission data for sample S3 and S4 at a lattice temperature $T_{\mathrm{L}}=4\mathrm{K}$. The experimental curve is shown as red dots. Theoretical results for the dynamics of the relative differential transmission are reported for different sets of the material parameters driving the electron-phonon scattering: taking into account all the elastic scattering channels and using the deformation potentials provided in Ref. [24] (black curve); keeping active only the elastic scattering (cyan curve); taking into account all the elastic scattering channels, switching off the intervalley OP channel, and using the intravalley deformation potentials of Ref. [24] (green curve); considering all the scattering channels but using our best-fit values for the deformation potentials as discussed in the text (orange curve); for sample S4, taking into account all the elastic scattering channels, switching off the intravalley OP channel, and using the intervalley deformation potential of Ref. [24] (dashed purple curve).

Figure 3

(left panels) The experimental ISB absorption spectra measured by FTIR (red dots) on symmetric MQWs (a) S5, (c) S6, and (e) S7. The dashed blue curve is a Lorentzian fit to the data. (Right panels) The corresponding time-resolved pump-probe signals, recorded at a lattice temperature $T_{\mathrm{L}}=4\mathrm{K}$. The red dots are the experimental relative differential transmission data. Theoretical results for the dynamics of the relative differential transmission are reported for different sets of the material parameters driving the electron-phonon scattering: taking into account all the elastic scattering channels and using the deformation potentials provided in Ref. [24] (black curve); keeping active only the elastic scattering (cyan curve); taking into account all the elastic scattering channels, switching off the intervalley OP channel, and using the intravalley deformation potentials of Ref. [24] (green curve); considering all the scattering channels but using our best-fit values for the deformation potentials as discussed in the text (orange curve).

Figure 4

The time-resolved pump-probe signals for sample S7, to be compared to Fig. 3. (a) Signal recorded at lower pump power (one order of magnitude less carrier is excited into $L_2$). (b) Signal recorded at higher lattice temperature $(T_{\mathrm{L}}=80\mathrm{K})$. The red dots are the experimental relative differential transmission data. Theoretical results for the dynamics of the relative differential transmission are reported for different sets of the material parameters driving the electron-phonon scattering: taking into account all the elastic scattering channels and using the deformation potentials provided in Ref. [24] (black curve); considering all the scattering channels but using our best-fit values for the deformation potentials as discussed in the text (orange curve).