Pseudomorphic ZnO‐based heterostructures: From polar through all semipolar to nonpolar orientations

We calculate the strain and stress state and the polarization in pseudomorphic wurtzite Mgx Zn1 − x O/ZnO and Cdx Zn1 − x O/ZnO heterostructures as a function of the polar angle θ between the c ‐axis and the epitaxial direction. (Cd,Zn)O/ZnO behaves qualitatively similar to the systems (In,Ga)N/GaN and (Al,Ga)N/GaN. (Mg,Zn)O/ZnO represents a unique case since the signs of the change of lattice constants ∂ a / ∂ x and ∂ c / ∂ x are opposite. Among the consequences are: (i) the epilayer strain energy has a minimum between 0 ∘ and 90 ∘ for semipolar growth plane close to ( 11 2 ‾ 2 ) ; (ii) for nonpolar growth ( θ = 90 ∘ ) the strain in the epitaxial direction is close to zero; and the in‐plane polarization is large (comparable to the polar case); and (iii) the piezoelectric polarization along the growth direction has only one zero (at θ = 90 ∘ ) between 0∘ and 180 ∘ . Also we give useful analytical formula within an isotropic approximation for the compliances. Elastic strain energy (in relative units) of pseudomorphic wurtzite (Mg,Zn)O/ZnO and (Cd,Zn)O/ZnO heterostructures as a function of the polar angle θ between interface normal and the c ‐axis