I. Introduction (Preface, Nanostructures in Si Inversion Layers, Nanostructures in GaAs-AlGaAs Heterostructures, Basic Properties). 
II. Diffusive and Quasi-Ballistic Transport (Classical Size Effects, Weak Localization, Conductance Fluctuations, Aharonov-Bohm Effect, Electron-Electron Interactions, Quantum Size Effects, Periodic Potential). 
III. Ballistic Transport (Conduction as a Transmission Problem, Quantum Point Contacts, Coherent Electron Focusing, Collimation, Junction Scattering, Tunneling). 
IV. Adiabatic Transport (Edge Channels and the Quantum Hall Effect, Selective Population and Detection of Edge Channels, Fractional Quantum Hall Effect, Aharonov-Bohm Effect in Strong Magnetic Fields, Magnetically Induced Band Structure).

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Quantum Transport in Semiconductor Nanostructures

Publisher Summary Quantum transport is conveniently studied in a two-dimensional electron gas (2DEG) because of the combination of a large Fermi wavelength and large mean free path. Semiconductor nanostructures are unique in offering the possibility of studying quantum transport in an artificial potential landscape. This is the regime of ballistic transport in which scattering with impurities are neglected. The chapter presents a self-contained account of these three novel transport regimes in semiconductor nanostructures. The study of quantum transport in semiconductor nanostructures is motivated by more than scientific interest. The fabrication of nanostructures relies on sophisticated crystal growth and lithographic techniques that exist because of the industrial effort toward the miniaturization of transistors. Conventional transistors operate in the regime of classical diffusive transport, which breaks down on short length scales. The discovery of novel transport regimes in semiconductor nanostructures provides options for the development of innovative future devices.

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Silicon-based heterostructures have come a long way from the discovery of strain as a new and essential parameter for band structure engineering to the present state of electron and hole mobilities, which surpass those achieved in the traditional material combination by more than an order of magnitude and are rapidly approaching the best III - V heteromaterials. It is the purpose of this article to report on the most recent developments, and the performance level achieved to date in this material system, in a concise and critical manner. The first part of this review is concerned with the structural and electronic properties of the lattice-mismatched Si/SiGe heterostructure. Emphases are put on the effects of strain both on the band structure and on the band offsets, as well as on means to actually control the strain in a stack of heteroepitaxial layers. The second part is dedicated to the transport properties of low-dimensional carrier systems in Si/SiGe and Ge/SiGe heterostructures. The prospects and limitations of the different layer concepts are discussed in terms of scattering mechanisms and experimental results. This part also reviews the most recent magneto-transport experiments on quantum wires and quantum point contacts, which became possible by the enhanced mean free paths in these materials. The third part covers the device aspects of these high-mobility materials, which is of special interest, because silicon-based heterostructures can significantly enhance the performance level of contemporary Si devices without sacrificing the essential compatibility with standard Si technologies. The recent achievements in this application-driven research field, but also the foreseeable problems and limitations, are discussed, and an assessment of the possible role of such heterodevices in future microelectronic circuits is given.

http://iopscience.iop.org/article/10.1088/0268-1242/12/12/001/pdf

High-mobility Si and Ge structures

In this review, we discuss the results of recent experimental studies of the low-temperature electron dephasing time (τφ) in metal and semiconductor mesoscopic structures. A major focus of this review is on the use of weak localization, and other quantum-interference-related phenomena, to determine the value of τφ in systems of different dimensionality and with different levels of disorder. Significant attention is devoted to a discussion of three-dimensional metal films, in which dephasing is found to predominantly arise from the influence of electron–phonon (e–ph) scattering. Both the temperature and electron mean free path dependences of τφ that result from this scattering mechanism are found to be sensitive to the microscopic quality and degree of disorder in the sample. The results of these studies are compared with the predictions of recent theories for the e–ph interaction. We conclude that, in spite of progress in the theory for this scattering mechanism, our understanding of the e–ph interaction remains incomplete. We also discuss the origins of decoherence in low-diffusivity metal films, close to the metal–insulator transition, in which evidence for a crossover of the inelastic scattering, from e–ph to ‘critical’ electron–electron (e–e) scattering, is observed. Electron– electron scattering is also found to be the dominant source of dephasing in experimental studies of semiconductor quantum wires, in which the effects of both large- and small-energy-transfer scattering must be taken into account. The latter, Nyquist, mechanism is the stronger effect at a few kelvins, and may be viewed as arising from fluctuations in the electromagnetic background, generated by the thermal motion of electrons. At higher temperatures, however, a crossover to inelastic e–e scattering typically occurs; and evidence for this large-energy-transfer process has been found at temperatures as high as 30 K. Electron–electron interactions are also thought to play an important role in dephasing in ballistic quantum dots, and the results of recent experiments in this area are reviewed. A common feature of experiments, in both dirty metals 3 Authors to whom any correspondence should be addressed.

https://iopscience.iop.org/article/10.1088/0953-8984/14/18/201/pdf

Recent experimental studies of electron dephasing in metal and semiconductor mesoscopic structures

Reduction of quantized conductance at low temperatures observed in 2 to 10 μm-long quantum wires

We present an experimental and theoretical study of quantum ballistic transport in single quantum point contacts (QPC's), defined in the two-dimensional electron gas (2DEG) of a high-mobility GaAs/${\mathrm{Al}}_{0.33}$${\mathrm{Ga}}_{0.67}$As heterojunction. In zero magnetic field the conductance of quantum point contacts shows the formation of quantized plateaus at multiples of 2${\mathit{e}}^{2}$/h. The experimental results are explained with a simple model. Deviations from ideal quantization are discussed. The experimental results are compared with model calculations. Energy averaging of the conductance has been studied, both as a function of temperature and voltage across the device. The application of a magnetic field leads to the magnetic depopulation of the one-dimensional subbands in the QPC. It is shown that the zero-field quantization and quantization in high magnetic fields are two limiting cases of a more general quantization phenomenon. We use quantum point contacts to study the high-magnetic-field transport in a 2DEG. Quantum point contacts are used to selectively populate and detect edge channels. The experiments show that scattering between adjacent edge channels can be very weak, under certain circumstances even on length scales longer than 200 \ensuremath{\mu}m. This adiabatic transport has resulted in the observation of an anomalous integer quantum Hall effect, in which the quantization of the Hall conductance is not determined by the number of Landau levels in the bulk 2DEG, but by the number of Landau levels in the QPC's instead. Related effects are the anomalous quantization of the longitudinal resistance and the adiabatic transport through QPC's in series. A theoretical description for transport in the presence of Shubnikov--de Haas (SdH) backscattering is given. This model explains the experimentally observed suppression of the SdH oscillations due to the selective population or detection of edge channels. Finally, we demonstrate that the combination of a QPC and a bulk Ohmic contact can act as a controllable edge-channel mixer.

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Quantum ballistic and adiabatic electron transport studied with quantum point contacts

The Hall conductance of a wide two-dimensional electron gas has been measured in a geometry in which two quantum point contacts form controllable current and voltage probes, separated by less than the transport mean free path. Adjustable barriers in the point contacts allow selective population and detection of Landau levels. The quantization of the Hall conductance is determined by the number of quantum channels in the point contacts and is independent of the number of occupied bulk Landau levels. A theoretical description based on the Landauer-B\"uttiker formalism is given.

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Anomalous integer quantum Hall effect in the ballistic regime with quantum point contacts.

The Shubnikov–de Haas resistance oscillations of a wide two-dimensional electron gas are suppressed dramatically when current is injected with a quantum point contact which does not populate the upper Landau level. A similar suppression is observed when a quantum point contact is used as a voltage probe which does not detect the upper Landau level. The results are explained with a model in which the Shubnikov–de Haas oscillations arise from backscattering of electrons in the upper Landau level. It is shown that quantum ballistic transport in high magnetic fields can occur on length scales larger than 200 µm.

Suppression of Shubnikov–de Haas resistance oscillations due to selective population or detection of Landau levels: Absence of inter-Landau-level scattering on macroscopic length scales

E.M.M. Willems

Papers

Quantum ballistic and adiabatic electron transport studied with quantum point contacts

Anomalous integer quantum Hall effect in the ballistic regime with quantum point contacts.

Suppression of Shubnikov–de Haas resistance oscillations due to selective population or detection of Landau levels: Absence of inter-Landau-level scattering on macroscopic length scales

Quantum Wires and Ballistic Point Contacts