Temperature dependence of the direct interband transitions of a Ge/SiGe multiple-quantum-well structure with Ge-rich barriers

Temperature-dependent piezoreflectance (PzR) measurements were used to study the direct-gap–related optical transitions in a strain-compensated Ge/SiGe multiple-quantum-well (MQW) structure with Ge-rich SiGe barriers in the temperature range between 20 and 375 K. The PzR spectra revealed a wide range of possible optical transitions in the MQW structure. Detailed line-shape fits to the PzR spectra and comparison to a theoretical calculation based on the envelope-function approximation led to the identification of various interband transitions. In addition, the parameters that describe the temperature dependence of the excitonic transition energies [E(T)] and broadening parameters [Γ(T)] were evaluated and compared to those of the polar systems. In agreement with polar materials, [E(T)] values of the MQW structure were found to be similar to the constituent bulk well material. On the other hand, no significant dimensionality dependence of [Γ(T)] was observed, in contrast to polar systems.

Figure 1

Schematic diagram of the Ge/Si${}_{0.15}$Ge${}_{0.85}$ MQW structure deposited on virtual substrate.

Figure 2

The experimental PzR spectra (dashed curves) at (a) 300 and (b) 20 K of the Ge/Si${}_{0.15}$Ge${}_{0.85}$ MQW structure. The solid curves are the least-squares fits to Eq. (1). The arrows indicate all the transition energies resulting from the fits. Error bars are indicated.

Figure 3

The lineup of various relevant bands at the Γ point in a strain-compensated structure of a Ge well between Si${}_{0.15}$Ge${}_{0.85}$ barriers on a Si${}_{0.10}$Ge${}_{0.90}$ strain-relaxed virtual substrate.

Figure 4

The dashed curves are the experimental PzR spectra at various temperatures in the region of interband transitions of a Ge/Si${}_{0.15}$Ge${}_{0.85}$ MQW structure. The solid curves are least-squares fits to Eq. (1), yielding the energies indicated by arrows. For clarity, the zero of energy is the energy of the 11 H transition at each temperature. Error bars are indicated.

Figure 5

Temperature dependence of various interband excitonic transition energies for a Ge/Si${}_{0.15}$Ge${}_{0.85}$ MQW structure. The dashed lines and solid lines are the least-squares fits to Eqs. (2) and (3), respectively. Representative error bars are indicated.

Figure 6

Temperature-dependent broadening parameters Γ(T) of 11H (closed circles) and 11L (closed squares) features for a Ge/Si${}_{0.15}$Ge${}_{0.85}$ MQW structure. The solid lines are the least-squares fits to Eq. (4) with the dominant longitudinal acoustic phonons energy E${}_{\mathrm{LA}}$ $=$ 28 meV. Error bars are indicated.