Determination of the critical thickness of misfit dislocation multiplication using in situ double-crystal x-ray diffraction

Two different kinds of critical thicknesses in the relaxation process were determined by means of in situ synchrotron double-crystal x-ray reflection topography and in situ synchrotron double-crystal x-ray diffractometry during the growth of an epilayer on a GaAs (001) substrate. The first critical thickness, derived from the in situ x-ray topographs, has been found to be in agreement with the Matthews and Blakeslee theory of misfit dislocation generation. We present measurements of the lattice constant perpendicular to the interface employing the rocking curves of the symmetric reflection and show that the deep drop in the plot of the lattice constant versus epilayer thickness may be related to misfit dislocation multiplication rather than to misfit dislocation generation processes. Our second critical thickness, derived from the in situ x-ray diffraction data has been found to be in reasonable agreement with recently published theories of misfit dislocation multiplication and substantial relaxation. .