Direct and indirect band gaps in Ge under biaxial tensile strain investigated by photoluminescence and photoreflectance studies

Germanium is an indirect semiconductor which attracts particular interest as an electronics and photonics material due to low indirect-to-direct band separation. In this work we bend the bands of Ge by means of biaxial tensile strain in order to achieve a direct band gap. Strain is applied by growth of Ge on a lattice mismatched InGaAs buffer layer with variable In content. Band structure is studied by photoluminescence and photoreflectance, giving the indirect and direct bands of the material. Obtained experimental energy band values are compared with a $\mathbf{k}·\mathbf{p}$ simulation. Photoreflectance spectra are also simulated and compared with the experiment. The obtained results indicate direct band structure obtained for a Ge sample with $1.94\%$ strain applied, with preferable $\mathrm{\Gamma }$ valley to heavy hole transition.

Figure 1

(a) Photoluminescence spectra of Ge/AlAs (sample A) under $\varepsilon =0\%$ biaxial tensile strain depending on temperature; (b) experimental (circles) and calculated (triangles) peak energy (black line) and normalized integrated intensity (red line) versus temperature.

Figure 2

(a) Photoluminescence spectra of $\mathrm{GaAs}/\mathrm{Ge}/{\mathrm{In}}_{0.16}{\mathrm{Ga}}_{0.84}\mathrm{As}/\mathrm{GaAs}$ (sample C) under $\varepsilon =0.95\%$ biaxial tensile strain depending on temperature; (b) experimental (circles) and calculated (triangles) peak energy (black line) and normalized integrated intensity (red line) versus temperature.

Figure 3

(a) Photoluminescence spectra of $\mathrm{Ge}/\mathrm{I}{\mathrm{n}}_{0.24}\mathrm{G}{\mathrm{a}}_{0.76}\mathrm{As}$ (sample E) under $\varepsilon =1.6\%$ biaxial tensile strain depending on temperature; (b) experimental (circles) and calculated (triangles) peak energy (black line) and normalized integrated intensity (red line) versus temperature.

Figure 4

(a) Photoluminescence spectra of $\mathrm{InGaAs}/\mathrm{Ge}/\mathrm{I}{\mathrm{n}}_{0.29}\mathrm{G}{\mathrm{a}}_{0.71}\mathrm{As}/\mathrm{GaAs}$ (sample F) under $\varepsilon =1.94\%$ biaxial tensile strain depending on temperature; (b) experimental (circles) and calculated (triangles) peak energy (black line) and normalized integrated intensity (red line) versus temperature.

Figure 5

PL spectra at different biaxial tensile strain (samples A, C, E, F) at 80 K.

Figure 6

Photoreflectance spectrum of Ge under $\varepsilon$: (a) sample A, $0\%$; (b) sample B, $0.82\%$; (c) sample D, $1.11\%$; (d) sample E, $1.6\%$ biaxial tensile strain at 80 K, fitted with two TDLS functions. Open circles correspond to the experimental data, red lines are the fit including two TDLSs, depicted in green and blue, respectively.

Figure 7

Photoreflectance spectrum of Ge under $\varepsilon$: (a) $0\%$, (b) $0.82\%$, (c) $1.11\%$, (d) $1.6\%$ biaxial tensile strain at 80 K, fitted with two Airy functions. Dotted lines correspond to the experimental data, red lines are the fit including two Airy functions, depicted in green and blue, respectively.

Figure 8

Theoretical band-gap-strain dependence for Ge calculated using a $30\times 30\mathbf{k}·\mathbf{p}$ model taking into account quantization-induced band-gap enhancement at decreased ε-Ge layer thicknesses for 40-, 30-, and 15-nm quantum wells. Experimental peaks given by PL and PR data are shown as circles over theoretically predicted transitions from $\mathrm{\Gamma }$ and $L$ valley to light (lh) and heavy (hh) holes.

Figure 9

Full photoreflectance spectra simulation on the top of experimental data for (a) unstrained sample; (b) $\varepsilon =0.82\%$ model over sample D spectra; (c) $\varepsilon =1.11\%$ model over sample E spectra. $\mathrm{\Gamma }$-lh, $\mathrm{\Gamma }$-hh, and split-off subband transition energies are depicted as vertical dashes.

Figure 10

Photoluminescence spectra of $\mathrm{Ge}/\mathrm{I}{\mathrm{n}}_{0.24}\mathrm{G}{\mathrm{a}}_{0.76}\mathrm{As}/\mathrm{GaAs}$ (sample E) and $\mathrm{InGaAs}/\mathrm{Ge}/\mathrm{I}{\mathrm{n}}_{0.24}\mathrm{G}{\mathrm{a}}_{0.76}\mathrm{As}/\mathrm{GaAs}$ (sample E capped) under $\varepsilon =1.6\%$ biaxial tensile strain at 8 K.

Figure 11

$\mathbf{k}·\mathbf{p}$ calculations of electron-hole wave-function coupling and density of states (DOS) for subband transition energies in (a) 40-nm Ge quantum well with $\varepsilon =0.82\%$ biaxial tensile strain; (b) 30-nm Ge quantum well with $\varepsilon =1.11\%$ biaxial tensile strain.

Figure 12

Calculated (a) $\alpha$ and (b) $\beta$ Seraphin-Bottka coefficients in Ge at 80 K and at $0\%,0.8\%$, and $1.1\%$ biaxial tensile strain.