We present a theoretical study of the disorder effect due to interface roughness on piezoelectricity in wurtzite group-III-nitride heterostructures, e.g., AlGaN / GaN. 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 spontaneous͒ 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 roughnessinduced bulk charges may be so large as 10 21 e /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 /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.

We work out a theory of piezoelectricity in an actual semiconductor heterostructure which is composed of a lattice-mismatched zinc-blende layer grown on a [001]-oriented substrate. In contrast to earlier theories, we predict a large density of fixed bulk piezoelectric charges, which are induced by strain fluctuations connected with interface roughness. The piezoelectric charges create a high electric field. The random piezoelectric field presents a conceptually new important scattering mechanism. The system of charge carriers in such a heterostructure becomes strongly disordered and includes generally both free electron-hole pairs near the interface and excitons far from it.

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A theory is developed of the density of states (DOS) of the two-dimensional electron gas (2D EG) in semiconductor heterostructures, taking into account the effect of disorder caused by some random field existing in the sample. For a smooth random field, the calculation is carried out within its Gaussian statistics and a semiclassical approach. A simple closed expression thus obtained includes the classical DOS and its quantum correction as well, which describe the DOS of the 2D EG in explicit dependence on the rms of the potential and of the force of the random field. The disorder effect is found to smear out the step-like singularity of the DOS at an unperturbed band edge of the ideal 2D EG into a tail deep below the band edge. A detailed treatment is given of the case when the disorder is due to remote ionized impurities, which are distributed randomly or correlated in the sample.Doan Nhat Quang and Nguyen Huyen Tung: Electron Gas in 2D SC Structures

A theory is given of the density of states (DOS) in the low-energy tail for the disordered twodimensional electron gas (2D EG) in a semiconductor heterostructure subjected to Gaussian random fields of any origin (especially of short range). The calculation is carried out by means of a path-integral technique within the approximation based on a non-local harmonic modelled action and that of the ground-state contribution. A simple analytic expression for the 2D DOS and different variational equations for the curvature of the trial well are then obtained, which describe the DOS tail in explicit dependence on the potential correlator, i.e., on the disorder origin as well as the geometry of the realistic 2D EG. An interpolation scheme for obtaining the 2D DOS over the whole energy region is proposed. The DOS in the deep tail is found to roughly go as a decreasing exponential function whose exponent is proportional to jEj n with n varying from 1 to 2 for very short-and long-range potential correlations, respectively. The case of a Gaussian potential correlator is thoroughly examined.