Patent ID: 7906358

Claim:
A method of forming a hetero-epitaxial crystal structure of a group IV, group III-V or group II-VI alloy on the basal (0001) plane of a trigonal crystal or hexagonal crystal substrate so as to minimize crystalline dislocation defects between the hetero-epitaxial crystal structure of the group IV, group III-V or group II-VI alloy and the trigonal crystal or hexagonal crystal substrate, said method comprising: (a) if said alloy is a type in which the trigonal arrangement of atomic sites of the {111} plane of said alloy crystal directly meets the hexagonal or trigonal coincidence lattice of atomic sites in the basal plane of said substrate without any rotation, calculating a target lattice constant (L target ) as 2/√3*basal plane lattice constant of the substrate (a tri/hex ); (b) if said alloy is of a type in which the trigonal arrangement of atomics sites of the {111} plane of said alloy crystal meets the hexagonal or trigonal coincidence lattice of atomic sites in the basal plane of said substrate with a 30° rotation, calculating L target as 4/3*basal plane lattice constant of the substrate (a tri/hex ); (c) if said alloy is of a type in which the trigonal arrangement of atomic sites of the {111} plane of said alloy crystal directly meets the inner vertices of the hexagonal or trigonal coincidence lattice of atomic sites in the basal plane of said substrate without any rotation, calculating a target lattice constant (L target ) as 4/(3*√3)*basal plane lattice constant of the substrate (a tri/hex ); (d) if said alloy to be of a type in which the trigonal arrangement of atomic sites of the {111} plane of said alloy crystal meets the inner vertices of the hexagonal or trigonal coincidence lattice of atomic sites in the basal plane of said substrate with a 30° rotation, calculating L target as ⅔*basal plane lattice constant of the substrate (a tri/hex ); (e) determining the respective proportions of the group IV, group III-V or group II-VI elements in said alloy by approximating L target as a linear function of the individual lattice constants for the constituent group IV, group III-V or group II-VI elements weighted in accordance with said proportions and a Bowing Parameter, and solving for said proportions; and (f) growing the group IV, group III-V or group II-VI alloy on the basal (0001) plane of the trigonal crystal or hexagonal crystal substrate in the determined respective proportions to thereby form the hetero-epitaxial crystal structure on the trigonal crystal or hexagonal crystal substrate so as to minimize crystalline dislocation defects between the hetero-epitaxial crystal structure of the group IV, group III-V or group II-VI alloy and the trigonal crystal or hexagonal crystal substrate.