Strain Related Phenomena in GaN Thin Films
Photoluminescence (PL), Raman spectroscopy, and x-ray diffraction are employed to demonstrate the co-existence of a biaxial and a hydrostatic strain that can be present in GaN thin films. The biaxial strain originates from growth on lattice-mismatched substrates and from post-growth cooling. An additional hydrostatic strain is shown to be introduced by the presence of point defects. A consistent description of the experimental results is derived within the limits of the linear and isotropic elastic theory using a Poisson ratio nu =0.23+/-0.06 and a bulk modulus B=200+/-20 GPa. These isotropic elastic constants help to judge the validity of published anisotropic elastic constants that vary greatly. Calibration constants for strain-induced shifts of the near-band-edge PL lines with respect to the E2 Raman mode are given for strain-free, biaxially strained, and hydrostatically contracted or expanded thin films. They allow us to extract differences between hydrostatic and biaxial stress components if present. In particular, we determine that a biaxial stress of one GPa would shift the near-band-edge PL lines by 27+/-2 meV and the E2 Raman mode by 4.2+/-0.3 cm-1 by use of the listed isotropic elastic constants. It is expected from the analyses that stoichiometric variations in the GaN thin films together with the design of specific buffer layers can be utilized to strain engineer the material to an extent that greatly exceeds the possibilities known from other semiconductor systems because of the largely different covalent radii of the Ga and the N atom.