Biaxial Relaxation Coefficient in Group-III Nitride Quantum Wells and Thin Films |
S.P. Lepkowski, Abdur-Rehman Anwar
Institute of High Pressure Physics - Unipress, Polish Academy of Sciences, SokoĊowska 29/37, 01-142 Warszawa, Poland |
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We apply the third-order elasticity theory to study the biaxial relaxation coefficient (the RB coefficient) in group-III nitride quantum wells and thin films. The RB coefficient determines the ratio between the out-of-plane and in-plane strain components in these strained layers. We show that the RB 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 RB 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 RB 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 RB coefficient on strain for GaN compared to InN and AlN. |
DOI:10.12693/APhysPolA.141.130 topics: third-order elasticity, biaxial relaxation coefficient, group-III nitrides, thin films |