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

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 ${10}^{21}e∕{\mathrm{cm}}^3$, 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 ${10}^{13}e∕{\mathrm{cm}}^2$. 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.

Figure 1

Maximal rms densities of roughness-induced piezoelectric charges vs Al content $x$ in the $\mathrm{Al}\mathrm{Ga}\mathrm{N}∕\mathrm{Ga}\mathrm{N}$ heterostructure with a Gaussian interface profile of $\Delta =6.5\mathrm{\AA }$ and $\Lambda =15\mathrm{\AA }$. The solid, dashed, and dotted lines labeled $b$, $w$, and $s$ correspond to the densities: bulk in the barrier, bulk in the well, and sheet on the interface, respectively. The dotted line labeled $\sigma$ corresponds to the flat-interface density of sheet piezoelectric charges.

Figure 2

Rms piezoelectric field strengths vs distance $z$ in the $\mathrm{Al}\mathrm{Ga}\mathrm{N}∕\mathrm{Ga}\mathrm{N}$ heterostructure with an Al content $x=0.25$, a barrier thickness $L=300\mathrm{\AA }$, and a Gaussian interface profile of $\Delta =6.5\mathrm{\AA }$, $\Lambda =15\mathrm{\AA }$, for: (a) the in-plane and (b) the normal components. The interpretation is the same as in Fig. 1.