Parallel Transport in Low-Dimensional Semiconductor Structures

D.K. Maude    Grenoble High Magnetic Field Laboratory MPI-FKF and CNRS Grenoble, France

J.C. Portal    Grenoble High Magnetic Field Laboratory MPI-FKF and CNRS Grenoble, France
Institut National Des Sciences Appliquées Complexe Scientlfioue Toulouse, France

I Introduction

In this chapter we review the properties of two-dimensional (2D) electrons and holes in the presence of high magnetic fields applied perpendicular to the 2D layer. Historically, two types of systems have been investigated: electrons on the surface of liquid helium (Williams et al., 1971; Grimes, 1978) and electrons (or holes) in semiconductor structures. For hydrostatic pressure investigations, only the semiconducting system is relevant. Early work concentrated on the metal-oxide semiconductor (MOS) structures based on the Si-SiO2 system (for a review see Ando et al., 1982), which resulted in the discovery of the integer quantum Hall effect (IQHE) (von Klitzing et al., 1980).

The development of growth techniques such as molecular beam epitaxy allowed the realization of high-mobility (μ > 106 cm2/V-1 s-1) modulation-doped heterojunctions or quantum wells based on III–V semiconductors. The most commonly investigated system is the GaAs/AlGaAs heterojunction. Due to the different bandgaps of the two semiconducting materials, a two-dimensional electron gas (2DEG) is formed at the interface, usually due to charge transfer from a remote doping layer (Fig. 1). High mobility results from both the atomically flat interfaces and the greatly reduced ionized impurity scattering due to the inclusion of an undoped spacer layer (~ 100 nm) that spatially separates the electrons from the ionized donor impurities. It was in such a GaAs/AlGaAs heterojunction system that the fractional quantum Hall effect (FQHE) was discovered (Tsui et al., 1982).

High hydrostatic pressure has been recognized as a powerful tool in the study of semiconductor physics and, during the last decade, particularly in the field of low-dimensional systems studied in parallel tansport.

The direct effect of applying hydrostatic pressure to semiconductors is to decrease the interatomic distance. Pioneering pressure studies by William Paul showed that even if the decrease of lattice constant is not large (generally of the order of 1% at 10 kbar), it is sufficient to produce the following effects:

1. Pronounced, significant shifts in the electronic states. Deep electronic levels are created by impurity dopant or any defects and consequently change the charge carriers transferred to the quantum well.

2. A change in the energy of the band structure of each semiconductor and therefore the band-structure offset at the interface between the two components of the heterostructure. The electronic transport effects are more pronounced in type II heterostructures (Beerens et al., 1987a,b) with both electrons and holes (InAs/GaSb heterostructures) in comparison with type I heterostructures with only electrons or holes (AlGaAs/GaAs heterostructures). High pressure induces a phase transition from a semimetal to a semiconductor.

3. A change in the quantum effect observed in the oscillatory behavior of the resistivity, such as the magnetophonon resonance (MPR), in which the dependence of the effective mass, the scattering, the electron–phonon interaction, and 2D screening effects have been studied with hydrostatic pressure.

4. Reduction of the magnitude of the Landé spin g-factor, change the relative strengths of the different fractions of the quantum Hall effect, and the energy gap in the first composite fermion hierarchy.

Unlike other perturbations applied to study low-dimensional structures, such as electric and magnetic fields, alloying, or uniaxial stress, hydrostatic pressure preserves both the crystal symmetry and the atomic order.

In heterojunctions the electrons (or holes) have quantized energy levels in one spatial dimension but are free to move in two spatial dimensions. The system is not strictly two-dimensional due to the finite spatial extent of the wave function and the penetration of the wave function into the barrier. In addition, the applied magnetic field is not confined to the plane of the 2DEG, which has important consequences for Zeeman and orbital energies, which depend, respectively, on the total and the perpendicular component of the magnetic field.

An applied magnetic field quantizes the electron or hole motion into Landau levels, and the induced gaps in the density of states lead to new effects and fascinating new physics, such as the integer and fractional quantum Hall effects. Hydrostatic pressure, which can be used to vary the bandgap of the semiconducting material and hence tune the Landé g-factor through the spin–orbit interaction, is an extremely powerful tool for probing both the integer and fractional quantum Hall effects.

The main advantages of high-pressure applications in complementary study of gated microstructures are the possibility of tuning the 2D carrier concentration without a change in the band-structure parameters and of tuning just the band structure of low-dimensional systems.

Thus, the application of high pressure for systematic and controllable tuning of the electronic states seems ideally suited to fundamental studies of the electronic structure of low-dimensional systems and devices.

II The Effect of Pressure

1 PRESSURE EFFECTS ON 2D ELECTRONIC PROPERTIES OF SEMICONDUCTOR STRUCTURES

Hydrostatic pressure coupled with a high magnetic field is commonly used in studies of magnetotransport effects such as Shubnikov–de Haas oscillations (Shubnikov and de Haas, 1930) and classical and quantum Hall effects. This technique was applied to the GaAs/AlGaAs system, where it was found to cause a strong linear decrease in 2D carrier concentration.

The effect of hydrostatic pressure on 2D systems is a reduction of 2D carrier concentration. Nevertheless, depending on the heterojunction components and the nature of the doping impurities, different pressure effects are predominant for different heterostructures under study (Dmowski and Portal, 1989; Grégoris et al., 1987a).

The observed decrease of 2D carrier concentration can be related either to the deeping of the donor levels in the doped layer of modulation-doped heterostructures and consequent electron transfer from the quantum well to the localized donor states (Beerens et al., 1988) or to the reduction of the band-structure discontinuity and intrinsic charge transfer between the two components of undoped heterostructures (Beerens et al., 1987a; Gauthier et al., 1987).

a Pressure Dependence of Donor Levels in the Barrier and Control Process of Carrier Concentration in the Quantum Well

In GaAs/AlGaAs and GaInAs/AlInAs modulation-doped heterostructures in which a silicon impurity is used as a dopant, a deep electronic level in the barrier of the AlGaAs and AlInAs doped layers is created, which moves down into the gap relative to the Г minimum when pressure is applied. Therefore the free-electron concentration in the doped layer, and consequently the charge transfer to the quantum well (GaAs and GaInAs), is reduced. Beerens et al. (1988) have developed a very useful model that enables one to account for the case in which both the quantum well and the doped layer conduct (e.g., high-temperature measurements). Such parallel conduction is particularly large in AlInAs doped layers and can strongly effect magnetotransport measurements and lead to mistaken characterization of the 2D electron gas by the classical Hall effect.

Figure 2 shows as a function of pressure both the Hall concentration of a GaAs/AlGaAs heterostructure and the 2DEG concentration in a quantum well measured by Shubnikov–de Haas following a typical recording reported in Fig. 3. Pressure induces a decrease in both the 2DEG concentration and the 3D free-electron concentration in the doped layer. At sufficiently high pressures the parallel conduction through the doped layer becomes negligible compared with the contribution of the 2DEG. Thus, pressure allows one to eliminate parallel conduction and to verify whether the model used to discriminate the two components is correct (Grégoris et al. 1987b).