Measurement of the Band Alignment

There are a number of ways to measure the band alignment of a heterostructure, all of which are indirect (see chapters by several authors in Capasso and Margaritondo [34]). The reason for this situation will be discussed below. The result is that there remain significant uncertainties in the band alignments of many heterojunction systems. A comprehensive review of these issues has been prepared by Yu, McCaldin, and McGill [23], but the reader is cautioned to continue to consult the scientific literature on this subject, as further modifications to ``known'' band alignments are likely in the future.

One issue which arises in cases such as GaAs-AlGaAs, where it is technologically convenient to make junctions involving any of a range of compositions x, is the question of how the band alignment changes with the solid-solution composition. It is often convenient to assume that the band energies vary linearly with composition, and then the band discontinuities may be expressed as fractions of the total band discontinuity . However, it is well known that the band gaps of such solid solutions often display significant nonlinearities as a function of composition [35], so a simple linear interpolation is rather suspect. The GaAs-AlGaAs band lineup has been studied over a wide range of compositions by Batey and Wright [36], who found that the valence-band discontinuity varied linearly with composition.

The difficulties involved in determining the band alignment at heterojunctions is vividly illustrated by the history of measurements of the GaAs-AlGaAs junction, which is certainly the most intensively studied system over the past two decades. The development of high-quality heterostructures grown by molecular beam epitaxy permitted the fabrication of ``quantum wells'' in which the electron and hole energies were size-quantized by the heterojunction energy barriers, and these quantum states were measured spectroscopically by Dingle, Wiegmann, and Henry in 1974 [37]. Fitting the observed spectra to a simple square-well model suggested that most of the discontinuity occurred in the conduction band, with [38], and this value was widely accepted until 1984. At that time, similar measurements were made by Miller, Kleinman, and Gossard [39] on quantum wells which were fabricated so that the potential profile was parabolic. In this case, the quantized energy levels are more sensitive to the value of the band discontinuity than in the square-well case. The parabolic-well experiments produced a value of . The average value of more recent results is approximately [23].

Heterojunctions between Si and GeSi alloys have attracted a great deal of attention recently. Because the lattice mismatch between Si and Ge is large (greater than 4%), one or the other of the materials participating in the heterojunction is generally highly strained. The band alignment depends rather sensitively on the strain, and is also complicated by the fact that the strain causes a splitting of the degenerate states at both the valence and conduction band edges. Further information may be found in the chapter by King [4]. Kasper and Schäffler [40] have also reviewed the work on this system.