Table of contents

Today the fractional quantum Hall effect (FQHE) is well understood as the condensation of two-dimensional electrons in a high magnetic field into a sequence of quantum liquids. Thus far the relationship between the different liquids has been viewed as a hierarchy in which higher-order fractional states develop from the condensation of the elementary excitation of the next fewer-order fractional state. Recent theory has shed a new light on these relationships and provided us with a new framework for the FQHE. The central ingredients of this new picture are bizarre new particles, often termed composite fermions. This paper reviews our recent experimental evidence for the existence of such objects.

A recent theory of a compressible Fermi-liquid-like state at Landau level filling factors nu =1/q or 1-1/q, q even, is reviewed, with emphasis on the basic physical concepts.

Recent resonant inelastic light scattering experiments in the fractional quantum Hall regime highlight the power of the method in studies of election-electron interactions in semiconductors of reduced dimensions. We review here light scattering experiments that determine gap excitations in the regimes of the integer and fractional quantum Hall effects. At integer values of the Landau level filling factor we consider inter-Landau level excitations. In the fractional quantum Hall regime we discuss the determination of long-wavelength gap excitations and spin waves in the incompressible quantum fluid at filling factor 1/3.

We discuss various aspects of electron-electron and electron-phonon interaction in electron transport in submicrometre structures. We show that it is only above a certain critical Fermi velocity that the acoustic phonons can significantly influence the electron states in a quasi-one-dimensional quantum wire. We predict a characteristic temperature dependence of the plateaus in the linear conductance as a function of a magnetic field which should be experimentally observable. When the mean distance between Coulombically interacting electrons in a quantum dot is comparable to or larger than the Bohr radius their excitation spectrum shows fine structure which is related to the formation of a localized charge distribution, a Wigner molecule. We demonstrate that the excitations can be understood in terms of vibrational and tunnelling modes. Nonlinear transport of confined interacting electrons coupled to semi-infinite leads yields detailed information about the excitation spectrum. We present results including the degrees of freedom that were obtained from a master equation approach, and demonstrate that the correlations between the electrons lead to negative differential resistances that are related to spin selection rules.

A general formulation will be given of the loss of phase coherence between two partial waves, leading to the dephasing of their interference. This is due to inelastic scattering from the 'environment' (which is a different set of degrees of freedom that the waves are coupled with). For a conduction electron, the other electrons ('Fermi sea') are often the dominant environment of this type. Coulomb interactions with the latter are, especially at lower dimensions, the most important dephasing mechanism. It will be shown how this picture yields rather straightforwardly the very non-trivial results of Altshuler, Aronov and Khmelnitskii in one and two dimensions, in the diffusive case. Subtleties associated with divergences that have to be subtracted will be discussed. These results are known to agree well with experiments. As a new application of the above ideas, the dephasing in a zero-dimensional quantum dot will be briefly considered. This will lead to stringent conditions for observing the discrete spectrum of such a dot, in agreement with recent experiments. The crossover at low temperatures in small wires from one- to zero-dimensional behaviour will be shown to 'rescue' the Landau Fermi-liquid theory from being violated because of the T^2/3 behaviour of the 1D dephasing rate. After clarifying the relationship between the e-e scattering rate and the dephasing rate, the connection with the former will be made, including the ballistic regime.

Lateral transport through a quantum dot defined by the split-gate technique in a two-dimensional electron gas is investigated as a function of backgate voltage and emitter-collector bias voltage. This measurement technique allows us to identify the regimes of single-electron tunnelling. Within these regimes, excited states of the electron system in the quantum dot provide additional transport channels which can be classified as being opened in resonance with the Fermi level of either the emitter or the collector. The method of transport spectroscopy is discussed. When performing spectroscopy in a magnetic field, one has to take into account that the magnetic field affects not only the electronic states of the quantum dot but also the electronic states in the electrodes surrounding the quantum dot.

We report measurements of universal-like conductance fluctuations in a quasiballistic approximately 2 mu m² GaAs/AlGaAs quantum dot with adjustable point contact leads. Measurements cover a range of conductance G from nearly isolated, (G) approximately 0.1e²/h, to several modes in each lead, (G) approximately 5e²/h. The characteristic magnetic field scale of the fluctuations is found to increase with increasing mean conductance through the dot, consistent with a semiclassical picture of escape through the leads, and provides a means of estimating the phase breaking time tau _phi for electrons inside the dot. The fluctuation amplitude is found to increase with increasing dot conductance, then begins to saturate once a few conducting channels are open.

We show that chaos and nonlinear resonances are clearly reflected in the magnetotransport of lateral surface superlattices and thereby explain a series of magnetoresistance peaks observed in antidot arrays on semiconductor heterojunctions. For small magnetic fields we find the counterintuitive result that electrons move in the opposite direction to the free-electron E*B drift when subject to a two-dimensional periodic potential. We show that this phenomenon arises from chaotic channelling trajectories, and by a subtle mechanism leads to a negative value of the Hall resistivity for small magnetic fields. For a quantum mechanical description of Bloch electrons in magnetic fields Harper's equation has been studied extensively; this is integrable in the classical limit and thus fails for lateral surface superlattices where chaotic trajectories prevail near the classical limit. We therefore derive a new model, which is exact under the most general conditions, study the influence of classical chaos on the fractal spectrum known as Hofstadter's butterfly, and make predictions on its observability in lateral surface superlattices.

The classical dynamics of electrons in antidot superlattices subject to a perpendicular magnetic field is known to be chaotic. The quantum aspects of this system are investigated by calculating the magnetotransport properties and by studying the level statistics. We obtain quantitative agreement with experimental data for the longitudinal and Hall resistances and find distributions of level separations which, depending on the magnetic wavevector, show level repulsion as a signature of quantum chaos.

Electron tunnelling through donor-related states is discussed. This tunnelling process, which occurs well below the threshold voltage for conventional resonant tunnelling into the two-dimensional continuum states of the quantum well, reveals a new type of Fermi edge singularity effect which arises from the Coulomb interaction between the tunnelling electron on the localized site and the Fermi sea of electrons in the emitter layer. A new means of forming laterally confined resonant tunnelling devices is also described. By studying the effect of an applied magnetic field, the additional structure that appears in the current-voltage characteristics of these devices can be unambiguously associated with a lateral quantum mechanical confinement effect.

Nanometre-scale fabrication techniques, combined with epitaxial resonant tunnelling structures, now routinely allow the study of quasi-0D confined electron systems. In addition to energy level separations that are tunable by the confining potentials, these systems can also exhibit Coulomb blockade. Surprisingly similar effects are also observed for conventional, unconfined resonant tunnelling devices. We have recently discovered that the turn-on characteristics of nearly all resonant tunnelling devices exhibit sharp peaks in conductance, attributable to tunnelling through single quantum well donor states. These unintentional donor states are distributed in energy, depending on position in the quantum well. We have performed electronic spectroscopy of these states, and consistently find binding energies approximately 10 meV greater than expected for a single quantum well donor due to quantum well fluctuations. We present detailed measurements of single-electron tunnelling through a single donor bound state utilizing simple non-confined heterostructures.

We have studied tunnelling processes between a multiple quantum dot (MQD) system and a two-dimensional electron gas (2DEG) system, which are realized on a GaAs-AlGaAs-GaAs heterostructure. Using a transfer Hamiltonian formalism. It is shown that the tunnelling probability for transitions between a zero-dimensional (0D) and a two-dimensional (2D) state strongly depends on the quantum dot potential profile. In the case of a square well potential, only the resonance of the ground state is pronounced significantly, whereas for a cosine-shaped quantum dot potential profile a multitude of resonance structures is caused by each 0D state. From our experimental results we conclude that the potential of the quantum dots is best described by a cosine-shaped profile. In addition, the subband spacings and the extent of the wavefunctions of the individual subbands are also determined directly.

We have used the molecular beam growth technique, which we call cleaved edge overgrowth, to fabricate highly efficient lasers that operate in the 1D quantum limit. The active region of our laser consists of atomically precise quantum wires that form at the T-shaped intersections of 7 nm wide GaAs quantum wells grown along the (001) and, after an in situ cleave, along the (110) crystal axis. The origin of the quantum mechanical bound state is the relaxation of quantum well confinement at this intersection, which leads to an expansion of the electron and hole wavefunction into the larger available volume at the T-junction. The high degree of structural perfection achievable in this way allows the observation of stimulated optical emission from the lowest exciton state in optically pumped devices. The interpretation that the observed quantum wire response is due to exciton recombination is based on the near spectral constancy of the emission over almost three orders of magnitude in excitation power from low-power luminescence to a single-mode lasing line. The implied absence of bandgap renormalization effects suggests that the Mott density is never reached and indicates interesting new behaviour of excitons in 1D. In contrast, the quantum well photoluminescence peak indeed shifts to lower energies consistent with the notion that the 2D excitons ionize and a free electron-hole plasma forms.

We present a detailed and systematic investigation of carrier capture, relaxation, cooling and radiative recombination in a one-dimensional semiconductor quantum wire of high structural perfection and optical quality over a large range of excitation (carrier) densities. Experimental evidence for a complete lack of 1D bandgap renormalization is found. Even up to high carrier densities, >10⁶ cm^-1, where strong band filling is already present and directly visible in the luminescence, no shift of bandgap to low energy is found. The carrier cooling in 1D is appreciably slower than in comparable 2D structures, thus leading to high carrier temperatures. This confirms theoretical predictions of reduced phonon scattering probability in one-dimensional structures. The temperature dependence of the radiative lifetime of the 1D carriers is investigated. The theoretically predicted T dependence is not found. On the contrary an empirical tau _rad=0.02 T ns K^-1 law is fulfilled.

Interdigitated gates are employed on heterostructure surfaces to induce strong and tunable lateral superlattice potentials of type II, i.e. of purely field-effect origin. The design of the heterostructures is optimized in a way that avoids statistical potential fluctuations even at very low electron densities where screening of carriers is ineffective. Single-particle electron states confined to one-dimensional electron wires are investigated with capacitance spectroscopy. The precise control of the potential as well as the homogeneity of the potential allow us to investigate 'true' quantum wire arrays, i.e. wires in which only the lowest one-dimensional subband is occupied. Furthermore, we employ interdigitated gates to investigate the optical properties of quantum wells in a type II potential superlattice. The lateral fields are sufficiently high to field-ionize optically excited electron-hole pairs. Absorption spectra of the quantum well under such strong lateral fields show the typical signatures of the Franz-Keldysh effect.

In this paper we review some recent optical studies on CdTe-based nanostructures fabricated either by etching two-dimensional structures or by direct growth by molecular beam epitaxy. Photoluminescence can be observed on as-etched wires for sizes as small as 40 nm, due to the combined effect of exciton trapping on radiative centers and low surface damage. It is found that electrodynamic effects are very strong in gratings of wires for grating periods of about the photoluminescence wavelength.

The coherent excitation of excitonic wavepackets in AlGaAs/GaAs superlattices is investigated in a comparative study employing three different time-resolved optical techniques. The experimental results obtained in time-resolved four-wave mixing (PWM), THz emission spectroscopy and transmissive electro-optic sampling (TEOS) provide the final proof of the existence of Bloch oscillations in the THz range. Each of these measurements provides complementary information on these oscillations. As a result, Bloch oscillations appear as a special case of quantum interference involving the coherent superposition of Wannier-Stark states.

The coherent dynamics of exciton wavepackets in (GaIn)As/GaAs as well as (GaIn)As/Ga(PAs) multiple quantum well structures is studied by means of transient four-wave mixing (FWM) experiments. The wavepackets are generated by simultaneous excitation of several exciton transitions with laser pulses of about 100 fs duration. The time-integrated FWM signals exhibit a pronounced modulation superimposed on the overall decay which can be attributed to the quantum interference of the different eigenstates. In the time-resolved FWM signals this interference is not present, reflecting the interplay between many-body Coulomb effects and inhomogeneous broadening. This experimental technique is then employed to extract the exciton binding energies in pseudomorphic symmetrically strained (GaIn)As/GaIPAs) with various In contents.

Time-resolved luminescence, absorption and four-wave-mixing spectroscopy in the picosecond and femtosecond regimes are currently the most efficient experimental methods for studying energy and phase relaxation rates of highly excited charge carriers in solids. Here most of the effort concerns semiconductors, as these relaxation rates will determine and limit the efficiency of future generations of ultrafast electronic and optoelectronic devices. The following survey describes some attempts at a detailed analysis of recent experimental luminescence and absorption data covering a representative range of materials, spectral regimes and excitation densities. In spite of the fact that nanostructures are at the focus of present-day technological developments our discussion is limited to experiments on unstructured semiconductors, because the much simpler electronic structure of bulk materials will make it easier to realize the essentials of an extremely transient generation and relaxation dynamics of charge carriers and its description by appropriate Monte Carlo or quantum transport techniques.

The study of semiconductor carriers excited by femtosecond laser excitation has proved to be one of the most effective methods of characterization of semiconductors, as well as providing a probe for new physical effects. On the femtosecond time-scale, however, it is not expected that the semiclassical Boltzmann equation will be correct, and a more basic quantum mechanical formulation is required. The formulation of equivalent transport equations from the Schrodinger equation and its variants will be briefly reviewed. Results, using an ensemble Monte Carlo method, for electron-electron and electron-phonon interactions will be presented to show how these studies can be used to investigate the strength of the electron-phonon interaction and how the finite collision duration affects such studies.

We report optical experiments on electric-field-tunable GaAs/AlAs coupled quantum well structures in the regime of the electric-field-induced Gamma -X transition. The formation of real- and k-space indirect excitons causes a huge increase of the exciton lifetime, which is the basis for the phenomena discussed here. We first use the energetically tunable X-point state in the AlAs layer as an internal energy spectrometer to prove the existence of natural quantum dots in the neighbouring GaAs quantum well. Secondly we report on low-temperature CW and time-resolved magneto-optical experiments in the purely indirect regime, designed to search for condensation phenomena of indirect excitons in k-space.

The energy spectrum of electrons in semiconductor superlattices consists of Bloch-like miniband states and localized impurity states. Optical transitions between these states are investigated by infrared spectroscopy. The inter-miniband absorption spectrum is dominated by the van Hove singularities of the quasi one-dimensional joint density of states. The detailed shape of the absorption can be understood in terms of the relevant transition matrix elements and the electron concentration, i.e. it depends on whether the first miniband is full or half-filled. We show that this has implications for intra-miniband absorption and the optical sum rules. In addition, a transition between the states localized at the lower edge of the minibands occurs, which can be traced back to the 1s-2p_z hydrogenic donor transition in the low-doping limit. Finally, we discuss the relevance of our observations for the study of the metal-insulator transition in superlattices.

Electroreflectance measurements have been carried out in order to investigate Stark-ladder transitions in a GaAs (40 AA)/AlGaAs (20 AA) superlattice under various uniform electric fields, and compared with the transition energies calculated on the basis of a microscopic tight-binding theory. The observed electroreflectance spectra over a wide range of photon energies (1.5-2.2 eV) shift in proportion to an applied electric field. The signals in a higher photon energy region (1.4-2.2 eV) indicate the existence of a transition from the spin-orbit split-off band in the valence band to the Wannier-Stark localization states in the conduction band. The assignment is supported by the tight-binding calculation. Resonant coupling between the localized states is also observed.

We show that the use of circularly polarized light for the excitation in optical experiments (optical pumping) such as excitation spectroscopy or photoluminescence gives a better optical resolution as well as a much more reliable interpretation of the results when confined systems are investigated. We present an investigation of pseudomorphic strained InGaAs/GaAs and InGaAs/AlGaAs structures by means of optical pumping and give the conduction band offsets obtained from these experiments. We show that by applying a transverse magnetic field the circular polarization of the luminescence is decreased. By analysing such experiments in combination with time-resolved spectroscopy we determine the excitonic spin relaxation times and the excitonic g-factors. From these results we see that details of the confinement and strain conditions enter into these quantities. Finally we demonstrate that the spin of electrons is conserved during the tunnelling process through the barriers of tunnel structures when the barrier thickness is below a critical value. From our results we conclude that the interface quality determines the spin relaxation in heterostructures much more strongly than any other property.

The era of integrated circuits based on SiGe heterojunction bipolar transistors arrived with the announcement of a 12-bit digital to analogue converter (DAC) fabricated using an analogue optimization of IBM's SiGe HBT technology. Medium-scale integration was employed, the circuit consisting of approximately 3000 transistors and 2000 passive elements (resistor and capacitors). Operable at 1 GHz, this converter consumes approximately 0.75 W, thus yielding power-delay performance a decade superior to prior devices. It is significant that this DAC was fabricated employing the same technology and toolset as found on a standard silicon-based CMOS product line. In addition to the CMOS toolset, only one unique tool is required to support this technology, a commercial (Leybold-AG) ultrahigh vacuum chemical vapour deposition system for SiGe deposition. It is of interest to note, however, that the processing of these integrated circuits was no different from that employed in fabricating high-performance SiGe high electron mobility transistors (HEMTs), as well as the first N-type SiGe-based resonant tunnelling devices (RTDs), all functional at room temperature. This enables one to combine a wafer-scale manufacturable SiGe-based heterojunction technology with devices that utilize quantum phenomena, made accessible by the use of band offsets and strain-induced band splitting in the Si/SiGe materials system. This new ability to incorporate leading edge developments in SiGe device physics into a standard technology line opens up a host of new areas for exploration.

Interband optical transitions have been studied in a variety of short-period Si/Ge superlattice structures by means of photocurrent spectroscopy, infrared absorption, photo- and electroluminescence. Furthermore, the bandgap photoluminescence from strain-adjusted Si_mGe_n (m=9, 6, 3; n=6, 4, 2) superlattices was studied under applied hydrostatic pressure. The strain adjustment was achieved by a thick, step-graded Si_1-xGe_x buffer layer resulting in an improved quality of the superlattice with respect to dislocation density. The hydrostatic pressure dependence was modelled using an approach based on deformation potentials and effective-mass theory. In samples annealed at 500 degrees C and higher, a systematic shift of the bandgap was observed which is discussed in terms of a process involving interdiffusion of the Si and Ge atoms. Bandgap-related electroluminescence was observed in mesa diodes at room temperature, whereas the photoluminescence disappeared at about 40 K. The electroluminescence from samples based on different buffer-layer concepts is compared. Apart from the strain-symmetrized Si/Ge superlattices, another structure that has been proposed to act as an efficient, light-emitting device in the Si-based systems is an ultrathin Ge layer (1-2 monolayers) embedded in bulk Si. We report on the electroluminescence spectra at various temperatures from a sample based on this concept, namely a layer sequence consisting of two periods of Si₁₇Ge₂ grown pseudomorphically on an n⁺ Si substrate. A very intensive, well resolved electroluminescence was obtained at 55 K from the QW.

Luminescence properties associated with strain-induced band modification in SiGe/Si heterostructures such as quantum wells (QWS) and quantum wires (QWRS) are reviewed. Among several issues concerning formation of highly luminescent SiGe materials, surface segregation is shown to be the main cause of deteriorating interface integrity. To resolve the problem, a new technique called segregant-assisted growth (SAG) is proposed. SAG and gas-source MBE (GSMBE), which is considered to be quasi-SAG, are shown to provide high-quality SiGe/Si heterostructures with abrupt interfaces. Highly efficient band edge emissions are observed in not only type-1 but also spatially indirect type-2 QWS. The energy shift in QWS is discussed based upon the band modification due to surface segregation during growth. The ratio between the no-phonon (NP) peak and its phonon replica (TO) in the edge emission reflects the nature of the QWS formed with alloy materials. The coupling of QWS and evolution of superlattices are well understood based on the effective-mass approximation by precisely taking into account the band alignment. QWRS are well fabricated on V-groove patterned substrates and luminescent properties very different from those of QWS are observed. These findings indicate the high potential of SiGe/Si heterostructures, not only in scientific areas but also in device applications.

Optical microresonators can now be fabricated with dimensions of the order of half a wavelength on a side. For semiconductor microresonators this results in only a few optical modes interacting with the emitting material in the cavity. In this limit the threshold lasing characteristics are dramatically modified. Semiconductor microdisc experiments will be described where as much as 20% of the spontaneous emission is captured into the single lasing mode. This strong coupling of the radiation field with the resonant mode can cause anomalous laser linewidths and fluctuation phenomena. These experiments provide a good test of detailed models of dense, non-equilibrium electron-hole gases. Extensions of optical microcavities to a broad range of material systems will also be discussed.