  We grow AlN/4H-SiC and AlN/6H-SiC heterostructures by physical vapor
deposition and characterize the heterointerface with nanoscale resolution.
Furthermore, we investigate the spatial stress and strain distribution in these
heterostructures using confocal Raman spectroscopy. We measure the spectral
shifts of various vibrational Raman modes across the heterointerface and along
the entire depth of the 4H- and 6H-SiC layers. Using the earlier experimental
prediction for the phonon-deformation potential constants, we determine the
stress tensor components in SiC as a function of the distance from the AlN/SiC
heterointerface. In spite that the lattice parameter of SiC is smaller than
that of AlN, the SiC layers are compressively strained at the heterointerface.
This counterintuitive behavior is explained by different coefficients of
thermal expansion of SiC and AlN when the heterostructures are cooled from
growth to room temperature. The compressive stress values are maximum at the
heterointerface, approaching one GPa, and relaxes to the equilibrium value on
the scale of several tens of microns from the heterointerface.
