Biaxial Relaxation Coefficient in Group-III Nitride Quantum Wells and Thin Films

We apply the third-order elasticity theory to study the biaxial relaxation coefficient (the R-B coefficient) in group-III nitride quantum wells and thin films. The R-B coefficient determines the ratio between the out-of-plane and in-plane strain components in these strained layers. We show that the R-B coefficient in four material systems, i.e., AlN thin films grown on AlxGa1-xN substrates, GaN quantum wells grown on AlxGa1-xN substrates, GaN thin films grown on InxGa1-xN virtual substrates, and InN quantum wells grown on InxGa1-xN virtual substrates, to a large extent, depends on the in-plane strain arising from the lattice misfit between the strained layers and the substrates. This phenomenon cannot be described by the linear theory of elasticity. We also find that the R-B coefficient in most of the quantum wells and thin films made of InxGa1-xN and AlxGa1-xN alloys significantly depends on the in-plane strain, which is reflected by the observed discrepancies between the results obtained using third-order elasticity and linear elasticity. These discrepancies are proportional to the magnitude of the in-plane strain for AlxGa1-xN thin films and InxGa1-xN quantum wells grown on GaN substrates and they vanish when Al or In contents are smaller than 0.2. For AlxGa1-xN the quantum wells grown on AlN substrates and InxGa1-xN thin films grown on InN substrates, we find that the discrepancies between the results obtained using third-order elasticity and linear elasticity are not proportional to the in-plane strain. Unusual behaviour of the R-B coefficient in group-III nitride alloys originates from the different values of the elastic constants for the binary nitride semiconductors, causing the opposite dependences of the R-B coefficient on strain for GaN compared to InN and AlN.

Automated summary

We applied the third-order elasticity theory to study the biaxial relaxation coefficient in III nitride quantum wells and thin films. The results showed that the coefficient largely depends on the in-plane strain arising from the lattice misfit between the strained layers and the substrates. In most cases, the R-B coefficient in quantum wells and thin films made of InxGa1-xN and AlxGa1-xN alloys significantly depends on the in-plane strain, and the discrepancies between the results obtained using third-order elasticity and linear elasticity are proportional to the magnitude of the in-plane strain. However, for certain systems, such as AlxGa1-xN quantum wells on AlN substrates and InxGa1-xN thin films on InN substrates, the discrepancies are not proportional to the in-plane strain.