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We present a theory of the band-bending effects on two-dimensional 2D carriers confined in a modulationdoped square quantum well. We develop a tractable variational evaluation of several physical quantities that are important in the theory of 2D systems. Analytic expressions of the envelope wave function and the 2D screening form factor allow us to compute various electronic properties such as electrical mobility, density of states in the presence or in the absence of magnetic fields, and Landau level broadening. We prove that in the case of the interface roughness scattering, the band-bending effects lead to a peak in the channel-width dependence of the mobility and a minimum in the Landau level broadening. Our modeling explains recent measurements for a 2D hole gas.

A theory is given of the mobility of a two-dimensional hole gas (2DHG) at low temperature in narrow square $\mathrm{Si}∕{\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}∕\mathrm{Si}$ quantum wells at high Ge content. Different from the previous treatment, we have carried out a proper calculation of the misfit deformation potential and 2DHG screening. As a result, the scattering mechanisms due to surface roughness, misfit deformation potential, and alloy disorder are found to dominate the 2DHG mobility. Our theory enables a very good quantitative description of recently measured data about the dependence of the $8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ mobility of holes in a $\mathrm{Si}∕{\mathrm{Si}}_{0.2}{\mathrm{Ge}}_{0.8}∕\mathrm{Si}$ quantum well on the channel width varying from $25--70\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$. Further, this provides evidence in favor of screening of short-range interactions such as alloy disorder.

A theory is presented of the quantum and transport lifetimes of the two-dimensional electron gas (2DEG) at low temperature in a uniformly doped wurtzite group-III-nitride single heterostructure. In the calculation, besides the well-known scattering mechanisms, we took into account the roughness-induced scatterings, viz. misfit piezoelectric charges and misfit deformation potential. We proved that these exhibit important scattering sources for the 2DEG in wurtzite group-III-nitride heterostructures, in particular, the piezoelectric charges and alloy disorder dominate the transport and quantum lifetimes in a high-density regime (e.g., ${n}_{s}=2\ifmmode\times\else\texttimes\fi{}{10}^{12}--10\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$). Further, it is found that because of uniform doping, the electron distribution may be remarkably shifted far away from the key scattering sources, thus increasing the lifetimes. Our theory is able to provide a good quantitative explanation of the recent experimental data about the 2DEG lifetimes in a background-doped ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}∕\mathrm{Ga}\mathrm{N}$ heterostructure. The theory may reproduce not only the magnitude but also the nonmonotonic (bell-shaped) dependencies on the carrier density of both the transport and quantum lifetimes as well as their ratio, which could not be understood if starting merely from the scattering mechanisms known so far.

We present a theory of the low-temperature mobility of the two-dimensional electron gas 2DEG in wurtzite group-III-nitride heterostructures, e.g., AlGaN/ GaN, taking adequate account of the roughness-induced scattering mechanisms and the effect due to sheet polarization charges. The squeeze of the electron distribution in the quantum well by positive piezoelectric and spontaneous polarization-induced charges on the interface is calculated in an analytic form. Thus, we obtained simple expressions describing the squeeze-related enhancement of the 2DEG screening and the unscreened potentials for different scattering sources. Altogether, their screened potentials may be strongly enhanced, so that the 2DEG mobility may be remarkably reduced by sheet polarization charges. Moreover, we proved that the roughness-induced piezoelectric charges and the roughnessinduced deformation potential exhibit new important scattering mechanisms governing the 2DEG transport in wurtzite III-nitride heterostructures. The partial 2DEG mobilities limited by them may be of the order of or less than 10 3 cm 2 / V s. Our theory turns out to be successful in the quantitative explanation of recent experimental data about the high-density 2DEG mobility, e.g., its nonmonotonic dependence on carrier density and its enhancement in the double heterostructure, which have not been understood starting merely from the conventional scattering mechanisms.

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 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 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.

A theoretical study is presented of effects from strain fluctuations in a surface quantum well (SQW), which is composed of a strained zinc-blende-structure layer grown on a (001) substrate. It is found that in analogy to a zinc-blende quantum well (QW) with buried interfaces there always exist in the SQW a large fluctuating density of bulk piezoelectric charges and a high random piezoelectric field. However, in contrast to the buried QW case, roughness at a free surface of the SQW causes random fluctuations in the dilatation, which give rise to perturbing deformation potentials. The piezoelectric field and deformation potentials supply strong disorder interactions as new important scattering mechanisms for confined charge carriers in SQW's. A comparison of their effects in a SQW and the QW under equal conditions is given.

A theory is given of the electronic properties of modulation-doped quantum wires which undergo a thermal treatment, taking into account the Coulomb interaction among ionized impurities in the sample preparation. It is pointed out that the correlation among impurities weakens their field and is enhanced when elevating the doping level, lowering the freezing temperature for impurity diffusion, and reducing the size of the impurity system. The screening of the ionic correlation by charge carriers in the sample growth is of minor importance. In the limiting case of a one-dimensional impurity system, the correlation may totally suppress the random field at any doping level, so that a finite electron mobility is governed by other scattering mechanisms than impurity doping, e.g., interface roughness and alloying. It is found that the ionic correlation changes the electron mobility of quantum wires as regards not only its magnitude but its dependence on the doping conditions as well. For impurity systems of a small size, the mobility may be increased by up to more than one order of magnitude at a doping level of ${10}^{6}{\mathrm{cm}}^{\ensuremath{-}1}.$