Strain and piezoelectric fields in embedded quantum wire arrays

Utilizing a recently developed exact closed-form solution for a single polygonal quantum wire (QWR) inclusion problem, we theoretically investigate the elastic strain and electric fields induced by QWR arrays embedded in GaAs. We consider arrays ranging from 1×1 to 7×7 QWRs embedded in infinite substrates and up to 4×7 QWRs in half space substrates where the wires are near a surface. Our results for the infinite substrate indicate that although the elastic fields within any single QWR are similar to the fields in the other wires with only a weak dependence on the number of QWRs, the electric fields (both inside and outside the QWRs) can be significantly different for different array sizes. Due to the existence of the free surface, the half space solutions show that the elastic and electric fields both inside of and outside of the QWRs depend significantly on the number of QWRs, again with the electric field having the stronger dependence. A detailed analysis of the strain and electric fields for embedded QWR arrays is presented and the results could impact the design of proposed strain-modulated electronic devices.