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We calculated the elastic strain relaxation in wurtzite GaN–AlN–GaN semiconductor–insulator–semiconductor (SIS) structures. Elastic strain tensor components, elastic energy, the density of the misfit dislocations, and the other parameters of the system were obtained as functions of the AlN layer thickness. Theoretical values of the elastic strain relaxation are in satisfactory agreement with experimental data extracted from the capacitance‐voltage (C‐V) characteristics of GaN–AlN–GaN SIS structures. Our results confirm that the gradual relaxation process starts from 30 Å AlN film thickness. The uniform contributions to the elastic strain tensor components decrease by approximately an order of magnitude when the film thickness increases from 30 to 100 Å. Commensurate with this decrease is an increase in a nonuniform contribution of the misfit dislocations. The dislocation interactions lead to redistribution of dislocations within the 30–60 Å range of AlN film thicknesses. © 1995 American Institute of Physics.