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This chapter uses a case study of two-dimensional electron gases in heterostructures to illustrate the theoretical concepts put forward in Chapters 7 and 8. The electrostatics and the field effect in these structures are worked out, and the capacitance between the electron gas and a top-gate is determined. Quantum mechanics is introduced in the approximation of the Fang–Howard variational approach. The theory of linear screening in two-dimensional electron gases is discussed in detail, including the Thomas–Fermi approximation, and the appearance of Friedel oscillations in the electron density. Spin-orbit interaction effects in two-dimensional electron gases are discussed, and finally, the characteristic quantities of two-dimensional electron gases are summarized.

During the 1970s, III-V compounds and epitaxial crystal growth provided the basis for low dimensional structures (or nanostructures). The best known example is a GaAs quantum well within AlGaAs barriers, electrons, and holes being confined in well defined energy levels that determine the optical properties. Quantum wires and dots are also described. The quantum well laser and the vertical cavity laser (VCSEL) show considerable advantages over their heterostructure predecessor. Another exciting development was that of the two-dimensional electron gas (2DEG) at an interface between semiconductors with different band gaps. By doping only the wide gap material so as to separate the doping atoms from the resulting free electrons, ionised impurity scattering can be minimised and extremely high electron mobilities achieved. Such samples led to the discovery of the fractional quantum Hall effect and to high mobility FETs (HEMTs) for microwave applications. Mesoscopic systems and heterojunction bipolar transistors (HBTs) are also described.

Low-dimensional structures consisting of semiconductor heterostructures of thickness down to a very few atomic monolayers were grown ideally by MBE and resulted in a surge of interest in MBE itself. Short period superlattices, doping superlattices, quantum wells, wires and dots and two-dimensional electron gases (2DEGs) all proved of significance from scientific and commercial viewpoints. Superlattices and quantum wells showed negative electrical resistance, doping superlattices provided tuneable energy gaps, and quantum wells, quantum wires and quantum dots were characterised by confined energy states which offered photon energies tuneable by varying their dimensions. They also demonstrated increasingly sharp density of state functions, of interest for semiconductor lasers. 2DEGs showed very high electron mobilities by minimising ionised impurity scattering. The 2D localisation in 2DEGs resulted in discovery of the quantum Hall effect and fractional quantum Hall effect.

This chapter discusses the basic properties of two-dimensional electron gas (2DEG). Topics covered include different structures supporting 2DEG, basic properties of a 2DEG, subband structures for holes, self-consistent solutions, subbands in multivalley semiconductors, different types of band alignments, type I-II crossover, and modified scattering of 2D systems. Exercises are provided at the end of the chapter.

This chapter describes investigations of the interaction of phonons with magnetically quantized two-dimensional (2-D) electron systems including the quantum Hall states, with particular attention to work using acoustic phonons as probes. This includes studies of phonon emission from the two diagonally opposite ‘hot spots’ of a Hall bar where the current enters and leaves. One study detected the phonons using bolometers placed opposite the corners and, in another, the temperature increases at the ‘hot spots’ were indicated by the thickness of superfluid helium film covering the Hall bar. Information has also been obtained on the frequency spectrum of the emitted phonons. Studies have been made of the location and frequency dependence of the absorption of phonons in the integer states. Phonon absorption studies of the fractional quantum Hall state provide support for the magnetoroton picture, and the fruitful studies of the quantum Hall states using surface acoustic waves are reviewed in detail.

This chapter discusses a variety of device concepts that are based on the conductive interface between LaAlO₃ and SrTiO₃. The interface between these two insulating oxides spontaneously forms a high mobility, two dimensional electron gas when the LaAlO₃ thickness exceeds a critical value. At the critical thickness, the insulator-metal transition can be reversibly controlled using externally applied fields, and furthermore can be defined on the extreme nanoscale using a conducting AFM probe. After an initial discussion of macroscopic field effects at this interface, the chapter describes the use of conducting AFM lithography to fabricate nanoscale devices. Nanoscale wires, diodes, transistors, and photodetectors can be created, modified, and erased. Possible future integration with silicon-based electronics is discussed, along with possible applications in the fields of spintronics, quantum information processing, and quantum simulation.

Thermoelectric energy conversion technology to convert waste heat into electricity has received much attention. In addition, metal oxides have recently been considered as thermoelectric power generation materials that can operate at high temperatures on the basis of their potential advantages over heavy metallic alloys in chemical and thermal robustness. This chapter fabricates high quality epitaxial films composed of oxide thermoelectric materials, which are suitable for clarifying the intrinsic properties. It focuses on the thermoelectric properties of two representative oxide epitaxial films, p-type Ca₃Co₄O₉ and n-type SrTiO₃, which exhibit the best thermoelectric figures of merit, ZT(=S ²·σT·κ^-1, S: Seebeck coefficient, σ: electrical conductivity, κ: thermal conductivity, and T: absolute temperature) among oxide thermoelectric materials reported to date. In addition, it introduces the recently discovered giant S of two-dimensional electrons confined within a unit cell layer thickness (~0.4 nm) of SrTiO₃.

This chapter presents a review of quantum dots in two-dimensional electron gases. The spin qubits realized in these systems are strongly affected by the surrounding nuclear spins. An elegant demonstration is given that the nuclear spin bath is not as irreversible as one might think. Echo sequences can efficiently undo the dephasing of the qubitbrought about by the motion of nuclear spins.