Magnetotransport and photoluminescence of two-dimensional hole gases in Si/${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ge}}_{\mathit{x}}$/Si heterostructures

The electrical and optical properties of Si/${\mathrm{Si}}_{0.8}$ ${\mathrm{Ge}}_{0.2}$/Si p-type modulation-doped heterostructures grown on (001) Si using low-pressure chemical-vapor deposition are investigated by a variety of techniques. The thickness of the ${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ge}}_{\mathit{x}}$ quantum well was about 15 nm and the modulation-doping effect has been obtained by two remote boron-doped ∼10-nm-thick Si layers. We found a mobility enhancement at low temperatures in all modulation-doped heterostructures. Clear Shubnikov–de Haas oscillations and quantum Hall plateaus confirm the presence of a two-dimensional hole gas. From the Hall-effect measurements a hole mobility of 6870 ${\mathrm{cm}}^2$/V s at a sheet-hole concentration of 4.5×${10}^{11}$ ${\mathrm{cm}}^{\mathrm{-}2}$ at 50 mK was obtained, which is comparable with the best published values for x=0.2. The experimental results were compared with self-consistent calculations of the valence-band diagram and hole concentration. The values for the effective mass used for the calculations were obtained by solving the 6×6 Luttinger-Kohn Hamiltonian. The photoluminescence from the ${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ge}}_{\mathit{x}}$ quantum well shows excitonic behavior according to its variation with excitation power. A general trend of increasing photoluminescence intensity with the mobility of the two-dimensional hole gas was observed. The high hole mobility and strong photoluminescence reflect the good interfacial quality of the Si/${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ge}}_{\mathit{x}}$/Si heterointerfaces grown by low-pressure chemical-vapor deposition.