In 1985, Uppal and Kroemer grew antiphase-domain-free GaAs on Si(211) by molecular beam epitaxy and found that unintentionally doped n-type layers (n≈2×1016 cm−3n\approx2\times10^{16}\,\mathrm{cm}^{-3} by capacitance-voltage profiling) on lightly doped p-type Si substrates show a Hall sheet charge of 7×1012 cm−27\times10^{12}\,\mathrm{cm}^{-2}, roughly five times the charge contained in the epilayer, with a mobility near 1100 cm2/Vs1100\,\mathrm{cm^2/Vs} characteristic of silicon rather than GaAs. They proposed that most of the conducting electrons reside in a quasi-two-dimensional electron gas on the Si side of the interface, confined by a conduction-band discontinuity then estimated at about 0.5 0.5\,eV, but left this interpretation unconfirmed. The problem is to determine the GaAs/Si(211) heterojunction band lineup, the spatial distribution of the conducting electrons between the epilayer and the Si substrate, and the microscopic origin of the anomalous sheet charge (interface states, unintentional doping, or band bending), thereby validating or refuting the quasi-2DEG interpretation, and to clarify how the near-interface misfit dislocations and any associated interface states bear on this carrier distribution. The band lineup of this (211) interface and the spatial distribution of the conducting electrons have not been determined directly.

Background

Integrating III-V compound semiconductors (materials with one element from group III and one from group V of the periodic table, such as GaAs) on silicon substrates has long been pursued to combine III-V optoelectronic performance with silicon's cost, size, and processing advantages. Molecular beam epitaxy (MBE) is an ultrahigh-vacuum growth technique in which elemental beams (here Ga, and arsenic supplied as As2) deposit the film atom layer by atom layer. A fundamental difficulty of growing a III-V film on an elemental group-IV substrate is the polar-on-nonpolar problem: the film has two possible sublattice allocations (Ga-on-As versus As-on-Ga), and a mixture produces antiphase domains (APDs), regions of opposite sublattice ordering separated by boundaries that act as electrical defects. The (211) surface orientation was predicted to allow electrically neutral interfaces and suppress APD formation; Uppal and Kroemer's 1985 MBE experiments (a one-page summary abstract in J. Vac. Sci. Technol. B and a companion full paper in J. Appl. Phys.) demonstrated APD-free GaAs and GaP layers on Si(211), confirmed by etch-pit analysis and transmission electron microscopy, with strong 4 K photoluminescence and rectifying, photosensitive n-GaAs/p-Si and n-GaP/p-Si diodes.

The GaAs/Si system is, however, highly lattice mismatched (about 4.1%, versus 0.4% for GaP/Si), so the interface contains a dense network of misfit dislocations (dislocations introduced to absorb the mismatch between the two crystal lattices at their common boundary). This matters for the electrical characterization. In the Hall effect, a current-carrying sample in a perpendicular magnetic field develops a transverse voltage; for a thin conducting layer it yields a sheet carrier density (number of mobile carriers per unit area) and a Hall mobility. Capacitance-voltage (C-V) profiling instead measures, on a Schottky or junction diode, the depth distribution of the volumetric carrier density from the bias dependence of the depletion capacitance. For the unintentionally doped GaAs layers on Si(211), C-V profiling gave n≈2×1016 cm−3n\approx2\times10^{16}\,\mathrm{cm}^{-3}, while Hall measurements on layers grown on lightly doped p-type ('low-p') Si substrates gave a sheet charge of 7×1012 cm−27\times10^{12}\,\mathrm{cm}^{-2} with a Hall mobility of roughly 1100 cm2/Vs1100\,\mathrm{cm^2/Vs}. Two features made this anomalous: the sheet charge corresponds to about five times more electrons than the whole epilayer contains at the C-V density, and the mobility is close to values typical of electrons in silicon, well below what good GaAs layers achieve.

The authors' interpretation was that the majority of the mobile electrons seen by the Hall measurement do not conduct in the GaAs epilayer at all, but in a quasi-two-dimensional electron gas (2DEG: carriers confined to a thin interfacial channel, moving freely only parallel to the interface) located on the silicon side of the heterojunction. In a heterojunction (a junction between two different semiconductors), the band edges on the two sides are offset; the relative placement of the conduction-band minima is the conduction-band offset, and the full edge placement is the band lineup. If the GaAs conduction band were substantially above the Si conduction band - the 1985 papers quoted an estimate of about 0.5 0.5\,eV, from then-current literature rather than their own measurement - electrons from the n-GaAs would spill into a conduction-band notch on the Si side, where band bending at the n-GaAs/p-Si junction (an anisotype junction: n-type on p-type) would additionally invert the p-Si surface and confine them. Notably, the simple electron-affinity rule (aligning the vacuum levels using tabulated electron affinities of 4.07 eV for GaAs and 4.05 eV for Si) predicts a conduction-band offset of only about 0.02 eV and a valence-band offset of about 0.3 eV for this material pair, already in tension with the 0.5 eV estimate.

What the 1985 papers could not do is measure where the carriers actually are. Hall and C-V data average over all parallel conduction paths and cannot by themselves decide between a Si-side confined channel, an anomalously doped near-interface GaAs region (for example from autodoping, i.e. contamination of the growing layer by atoms from the substrate), or some combination. The papers therefore left open: the precise GaAs/Si band lineup, the spatial distribution of the conducting electrons, and the microscopic origin of the large sheet charge and its relation to interface states associated with the polar/nonpolar, dislocated boundary. These questions define the problem addressed here.

Problem Statement

Establish the interfacial electronic structure of the MBE-grown GaAs/Si(211) heterojunction of Uppal and Kroemer and settle the interpretation of its electrical anomaly, whose common scientific objective is to determine where the conducting electrons reside and why. Concretely: (i) determine the GaAs/Si conduction-band offset (band lineup) relevant to this interface - the value assumed in 1985 was about 0.5 0.5\,eV; (ii) determine directly the spatial distribution of the conducting electrons responsible for the reported Hall sheet charge of 7×1012 cm−27\times10^{12}\,\mathrm{cm}^{-2} with a Hall mobility of roughly 1100 cm2V−1s−11100\,\mathrm{cm}^2\mathrm{V}^{-1}\mathrm{s}^{-1}, specifically what fraction resides in a confined channel on the Si side of the interface versus in the GaAs epilayer including its near-interface region; and (iii) identify the microscopic origin of the anomalous sheet charge - conduction-band discontinuity and junction band bending, interface states associated with the polar/nonpolar boundary, or unintentional doping such as Si autodoping of the GaAs. The verdict on the quasi-two-dimensional-electron-gas interpretation follows from these sub-results.

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