Analysis of electrorefractive index change in Ge/SiGe coupled quantum well for low-voltage silicon-based optical modulators

A Ge/SiGe coupled quantum well (CQW) for optical modulators based on phase modulation has been proposed and studied theoretically. First we analyze quantized energies and wavefunctions of electrons and holes, and valence band dispersions for holes by solving the Schrödinger equation using the propagation matrix method and the k·p perturbation theory with the 4×4 Luttinger–Kohn Hamiltonian. The Ge/SiGe CQW is expected to exhibit unique quantum-confined Stark effect (QCSE) and polarization-independent large electrorefractive index change in transparent wavelength range. In addition, we calculated the driving voltage of a phase modulator with the multiple Ge/SiGe CQW. The product of a half-wave voltage and a phase shifter length VπLp is estimated to be about 0.31 V cm. The proposed CQW structure is a promising candidate for Si-based optoelectronic devices such as the Mach–Zehnder interferometer optical modulators and switches.