Critical layer thickness in compositionally-graded semiconductor layers with non-zero interfacial mismatch

Abstract

The critical layer thicknesses for the glide of misfit dislocations have been determined for compositionally-graded semiconductor layers with non-zero interfacial mismatch. Two cases have been considered: the case for which the interfacial mismatch (or ‘pre overshoot’) has the same sign as the grading coefficient (referred to as ‘jump graded’) and the case in which the signs are opposite (called ‘retro graded’). A force-balance approach was used, and it was assumed that threading dislocations would glide to create misfit dislocations if the glide force exceeded the line tension. We find that for a jump-graded structure with a particular value of interfacial mismatch, the critical layer thickness decreases monotonically with the absolute value of the grading coefficient. Retro-graded structures exhibit more complicated behavior; for a particular combination of interfacial mismatch and grading coefficient, there may be three different thicknesses for which the line tension and glide force of the dislocation are equal, denoted hc1, hc2 and hc3. Lattice relaxation by glide of grown-in dislocations is favorable for thicknesses in the range hc1 < h < hc2. Lattice relaxation by glide of the dislocations in the opposite sense can occur if h > hc3. This complicated behavior must be considered when modeling the strain relaxation and dislocation dynamics in retro-graded buffer structures.