Graded Index Silicon Geranium on Lattice Matched Silicon Geranium Semiconductor Alloy

A lattice matched silicon germanium (SiGe) semiconductive alloy is formed when a {111} crystal plane of a cubic diamond structure SiGe is grown on the {0001} C-plane of a single crystalline Al2O3 substrate such that a <110> orientation of the cubic diamond structure SiGe is aligned with a <1,0,-1,0> orientation of the {0001} C-plane. A lattice match between the substrate and the SiGe is achieved by using a SiGe composition that is 0.7223 atomic percent silicon and 0.2777 atomic percent germanium. A layer of Si(1-x), ,Ge(x) is formed on the cubic diamond structure SiGe. The value of X (i) defines an atomic percent of germanium satisfying 0.2277