Abstract In a recent paper, I have shown that the electric field at the surface of a charged conducting sphere evaluates to half the field discontinuity across the surface of the sphere. This exact result has been found by solving an improper integral, which has been criticized by Assad in a very recent paper in this journal [6]. In this note, I present a simpler approach that yields a proper integral for that field. This integral also evaluates to exactly half the field discontinuity, contrarily to Assad's objections.

The results of an accurate theoretical study on the effects of non-abrupt doping and interfacial profiles on the electron sheet density in one-side modulation-doped wurtzite GaN/AlGaN single quantum wells at low temperatures are presented. We solve coupled Schrödinger and Poisson equations self-consistently via the finite difference method. By employing a proper discretization on a nonuniform grid and taking into account the strong piezoelectric and spontaneous polarization fields exhibited by the wurtzite III-nitride heterostructures, a substantial increase in the 2DEG density is predicted with the increase of the donor diffusion length and the reduction of the spacer thickness.

The low-temperature electron mobility is investigated here for electrons confined in modulation-doped In0.53Ga0.47As/InP single symmetric quantum wells. The subband structure calculation is developed via variational method, both Schrödinger and Poisson equations being solved simultaneously with adequate heterointerface matching conditions. With this in hands, the main electron scattering rates are computed, namely alloy disorder, remote ionized impurity, and interface roughness. As a result, interesting interchanges in these scattering rates were found by varying the well width and the spacer width, which show that some scattering mechanisms can surpass the alloy disorder scattering rate and come to limit the electron mobility, a behavior not reported in the literature.