We present a general theoretical treatment of ionized impurity scattering in semiconductor superlattices. Employing an extension of the quasi-two-dimensional calculations of Stern and Howard to multi-well structures, we explicitly account for nonuniformity of the wavefunction distribution function, arbitrary dispersion relations, scattering by impurities in neighboring periods, and screening by electrons in neighboring wells. Interperiod phenomena are found to be quite significant whenever the screening length is comparable to or longer than the distance between the quantum wells. Calculated results are compared with recent data for modulation-doped and setback-modulation-doped HgTe-CdTe superlattices. However, the discussion emphasizes general aspects of the problem rather than features specific to a particular system.

Presented here is a comprehensive, single-particle formalism for free-carrier transport in semiconductor superlattices with cylindrically symmetric energy dispersion. The spatial nonuniformity of the carrier population is accounted for by employing a scattering potential that is weighted by the wave-function distribution function. In the limit of large barrier-to-well thickness ratios, one regains the quasi-two-dimensional (2D) expressions derived previously. In the opposite limit of thin barriers and hence a nearly uniform wave-function distribution, transport in the superlattice becomes analogous to that in a 3D semiconductor with an anisotropic effective mass. Anisotropic relaxation times are obtained for acoustic-phonon, nonpolar-optical-phonon, polar-optical-phonon, and ionized-impurity scattering. Arbitrary energy dispersion relations are assumed, so that complex, numerically derived band structures may be straightforwardly incorporated. For the example of a HgTe-CdTe superlattice with weak hole dispersion but relatively strong electron dispersion in the growth direction, superlattice mobilities obtained using the present formalism are compared in detail with results for the quasi-2D and isotropic 3D limits.

We demonstrate that interface roughness is the dominant low-temperature scattering mechanism for electrons in HgTe-CdTe superlattices with thin wells. Not only do the experimental mobilities follow the expected d6W dependence, but the observed temperature dependence is accurately reproduced by theory when the treatment of interface roughness scattering is generalized for narrow-gap superlattices. The fits to data yield roughness correlation lengths in the range 60–200 Å.

We have investigated quantum oscillations in the magneto-transport properties of HgTe–CdTe superlattices grown by molecular-beam epitaxy. Modulation doping was achieved by incorporating either indium donors or arsenic acceptors into the CdTe barriers. In a p-type sample, quantized plateaus were observed in the Hall conductivity down to i=3 conduction channels. Since the structure contained 200 periods, this implies that the quantized holes populated only a small fraction of the total superlattice volume. A mixed conduction analysis of the nonoscillating component of magneto-transport data provided confirming evidence for the presence of a two-dimensional hole gas with the appropriate density in addition to the superlattice holes. Previous reports of the quantum Hall effect in HgTe–CdTe also yielded i far less than the total number of superlattice wells. In contrast, an n-type sample from the present study displayed a single quantum Hall plateau at i≊140, indicating that in this case most of the 200 superlattice periods contributed to the conduction. We argue that this represents the first observation of the quantum Hall effect associated with carriers distributed throughout the interior of a HgTe–CdTe superlattice.

We present results of the first detailed theory for electron and hole transport in HgTe-CdTe superlattices. The calculation incorporates the superlattice band structure in full generality, and also treats multi-well scattering and screening processes which have been ignored in previous theories. It is predicted that whereas the electron and hole mobilities should be nearly equal at low temperatures, the hole mobility falls far below the electron value at somewhat higher temperatures due to the extreme nonparabolicity of the valence band. This prediction is entirely consistent with experimental results reported previously. Excellent quantitative agreement with the data over a broad temperature range is achieved if interface roughness scattering is considered in addition to ionized impurity scattering, acoustic and optical phonon scattering, and electron–hole scattering. It is pointed out that low-temperature electron mobilities for a number of thin-well HgTe–CdTe superlattices follow the d6W dependence expected for the interface roughness mechanism.

We report a detailed magneto-transport investigation of HgTe-CdTe multiple quantum wells. The data yield the first experimental confirmation of a theoretically-predicted “negative-gap” semiconducting region in wide-well Hg-based heterostructures. Gaps of up to 19 meV are observed.