Roughness-induced piezoelectric charges in wurtzite group-III-nitride heterostructures

Abstract

We present a theoretical study of the disorder effect due to interface roughness on piezoelectricity in wurtzite group-III-nitride heterostructures, e.g., $\mathrm{Al}\mathrm{Ga}\mathrm{N}∕\mathrm{Ga}\mathrm{N}$. We have proved that interface roughness gives rise to random nonuniform fluctuations in the piezoelectric polarization. As a result, besides the uniform density of sheet piezoelectric (and spontaneous) polarization-induced charges on the interface, reported in the existing literature, there must exist fluctuating densities of bulk piezoelectric charges inside of both the strained and relaxed layers as well as a fluctuating density of sheet piezoelectric charges on the interface. The densities of these charges and their electric field were generally found to be high. The maximal rms density of roughness-induced bulk charges may be so large as ${10}^{21}\phantom{\rule{0.3em}{0ex}}e∕{\mathrm{cm}}^{3}$, while the rms density of roughness-induced sheet charges may be of the order of magnitude of the uniform density of sheet piezoelectric charges, up to ${10}^{13}\phantom{\rule{0.3em}{0ex}}e∕{\mathrm{cm}}^{2}$. Thus, the effects of piezoelectric polarization on the conductivity in actual wurtzite group-III-nitride heterostructures turn out to be counteracting, namely as a source of making up the two-dimensional electron gas, but also as a source of their scattering.