Modeling of the wafer bow in GaN-on-Si epiwafers employing GaN/AlN multilayer buffer structures

We built a calculation model for the wafer bow in GaN-on-Si epiwafers employing GaN/AlN multilayer (ML) buffer structures by extending Stoney's equation. The calculated bow and the derived strain in the epilayers were almost consistent with experimental results. The calculation quantitatively revealed that the ML buffers introduced an in-plane compressive stress in the epitaxial structures. Also, relationships between the epiwafer bow and the stress in the respective layers became clear to a certain extent. For instance, when considering the case where periodic structures with 20 nm thick GaN/5 nm thick AlN pairs were grown as ML buffers on 4-in.diameter and 525 mu m thick Si (111) substrates at a growth temperature (T-g) of 1125 degrees C, the stress in the MLs was derived to be 2.18 GPa in the in-plane compressive direction in the GaN layers and 5.89 GPa in the in-plane tensile direction in the AlN layers at T-g. Although magnitude of the in-plane stress in the GaN layers is obviously smaller than that in the AlN layers, the restoring force generated in the GaN layers becomes larger than that in the AlN layers, because the force is in proportion to the layer thickness rather than to just the stress. As a consequence, the generated stress in the MLs was considered to produce enough force to suppress the epiwafer bow. The calculation also demonstrated that GaN epilayers on GaN/AlN MLs were strained in the inplane compressive direction at T-g and almost strain-free at room temperature.