Contact-induced change of the bandgap of semiconductors of the wurtzite structure

Progress in the synthesis of semiconductors of nanoscale structures has revived an interest in using semiconductors of different structures in the sensing of mechanical deformation through the change of photoluminescent characteristics under external stress/strain. In the heart of the deformation-induced change of photoluminescent characteristics is the deformation-induced change of the bandgap of semiconductors. In this work, we investigate the bandgap changes of bulk semiconductors of the wurtzite structure due to elastic indentation by a rigid, axisymmetric indenter. Using deformation potentials and the analytical solutions for the contact problems, we obtain closed-form solutions of the contact-induced change of the bandgaps for the elastic indentation by three different indenters of flat-ended, spherical, and conical shapes. For the elastic indentation by a flat-ended indenter, the bandgap changes are proportional to the indenter displacement/indentation load. For the elastic indentation by a spherical indenter, the bandgap changes are proportional to the cubic root of the indention load. For the elastic indentation by a conical indenter, the bandgap changes exhibit the characteristic of shape-similarity, independent of the indentation depth/load.