Infrared transitions in strained-layer Ge<i>x</i>Si1−<i>x</i>/Si

Abstract

We present a detailed procedure for calculating confined energy levels of strained-layer GexSi1−x/Si valence-band quantum wells as a function of Ge concentration x and well width L. The method assumes noncoupled wells and takes into account strain and spin-orbit-induced band shifts and splitting. We illustrate the method and find the heavy-hole (hh), light-hole (lh), and spin-orbit split-off (so) subband energy levels for wells deposited on Si(001) and Si(111) oriented substrates. We show results for L=40 Å and Ge concentrations between x=0.0 and x=0.8, and for composition x=0.25 and well widths between L=0.0 and L=100 Å. We plot (x,L) sets which give transition wavelengths between 10 and 11 μm, the central region of an atmospheric transmission window of interest to infrared detector applications. We find that hh ground to excited-state transitions are more sensitive to well width variations, whereas hh to lh or hh to so transitions are more composition dependent. There are (x,L) combinations which permit both hh ground to excited state and hh to lh transitions. Such regions may possess strong absorption cross sections both for excitation at normal incidence and for illumination at an angle. Energy levels for the two substrate orientations are qualitatively similar, but for Si(111) the corresponding transitions occur at smaller x and L. The smaller L minimizes strain relaxation effects.