A two-dimensional hole gas (2DHG) can be formed without intentional acceptor doping in a GaSb quantum well (QW) by capping the AlSb/GaSb heterostructure with a thin InAs layer, whose surface Fermi-level pinning lies near or above the GaSb valence-band edge and thereby electrostatically induces holes. Makimoto, Brar, and Kroemer (J. Cryst. Growth 150, 883 (1995)) used this scheme to measure intrinsic 2D hole transport (sheet density 0.6-1.0e12 cm^-2, nearly temperature-independent; mobilities up to ~7000 cm^2/Vs at 80 K) and posed four open issues: which mechanisms dominate low-temperature scattering; whether and by how much mobility improves with defect reduction; the role of strain in band alignment, subband structure, and effective mass; and reconciliation of their extracted InAs-GaSb broken-gap energy (0.21+/-0.02 eV) with earlier ~0.15 eV determinations. Later literature has consolidated the band-alignment question (accepted unstrained InAs/GaSb overlap of ~150 meV with tens-of-meV strain and interface-composition shifts) and substantially quantified the strain question (hole effective masses, HH-LH splittings, and mobility-vs-strain are now measured across well widths and InSb fractions), and undoped low-temperature mobilities have risen to ~2e4 cm^2/Vs; however, the dominant low-temperature scattering mechanisms in state-of-the-art GaSb/AlSb 2DHGs are not yet quantitatively separated, nor is the mobility gain from further native-defect reduction yet bounded, and the latest dedicated papers state explicitly that these mechanisms are not fully characterized.

Background

The 6.1-angstrom antimonide family. The III-V semiconductors InAs, GaSb, and AlSb share nearly the same lattice constant (~6.1 Angstrom), so molecular beam epitaxy (MBE, an ultrahigh-vacuum growth technique depositing one atomic layer at a time) can combine them into strained-free or controllably strained heterostructures. A quantum well (QW) is a thin semiconductor layer sandwiched between layers of wider band gap, confining carriers to move freely only in the plane; when the confined carriers are holes (missing electrons acting as positive mobile charges), the system is a two-dimensional hole gas (2DHG), characterized by its sheet density p_s (holes per unit area) and Hall mobility mu (drift velocity per unit electric field, in cm^2/Vs; higher means fewer scattering events).

Doping problem and the InAs-cap solution. In GaAs/AlGaAs 2D gases, carriers are usually supplied by modulation doping, i.e., dopants placed in the barrier away from the channel so that ionized-dopant scattering of channel carriers is reduced. In the antimonides this is difficult on the p-type side: acceptor-doped AlSb or AlGaSb barriers tend to have the Fermi level in a position that leaves holes in the barrier or surface, causing parallel conduction that corrupts mobility measurements of the QW itself. InAs has the unusual property that its free surfaces pin the Fermi level about 0.08 eV above the InAs conduction-band minimum (Nguyen, Brar, Kroemer, J. Vac. Sci. Technol. B 11, 1706 (1993)); a thin InAs cap layer on top of an AlSb/GaSb QW therefore pins the whole heterostructure's bands such that holes accumulate in the GaSb well with no intentional doping at all. (Accumulation in this context means that carriers, here holes, are drawn into the well purely by electrostatic band bending.) Makimoto, Brar, and Kroemer (1995) applied this to GaSb and strained InGaSb wells, and measured hole transport versus top-barrier thickness d, well width Lw, temperature (300 K down to 10 K), and InSb mole fraction.

Band alignment. InAs/GaSb is a type-II broken-gap (also called type-III) junction: the InAs conduction-band minimum lies below the GaSb valence-band maximum, so their nominal band gap overlaps. (The broken-gap energy is the amount by which the GaSb valence-band edge exceeds the InAs conduction-band edge.) Their 1995 sample series, analyzed with a capacitor model of the layer stack, indicated a broken-gap energy of 0.21+/-0.02 eV, in tension with earlier ~0.15 eV determinations.

Scattering and mobility. The dominant scattering processes limiting low-temperature mobility in a QW are: (i) ionized-impurity or fixed-charge scattering, from residual charged centers either in the well (native defects) or in barriers and at surfaces (remote charges), which is stronger at lower carrier density and weaker the farther the charges sit from the well; (ii) interface-roughness scattering, from atomic-scale fluctuations of the well thickness, which grows as well width shrinks; and (iii) at higher temperature, phonon scattering. As-grown GaSb is usually p-type from native point defects (doubly charged Ga vacancies and Ga-on-Sb antisites acting as acceptors) at ~1e16-1e17 cm^-3 background concentrations, making background-charge scattering a plausible but unquantified limit for GaSb QWs. Interpreting mobility data requires care: Hall measurements average over all conducting channels, and hole bands have strong spin-orbit coupling, nonparabolicity, and heavy-hole/light-hole mixing, making mass and scattering-rate extraction harder than for electrons.

Status. Subsequent literature resolved the broken-gap question (unstrained overlap ~150 meV, with tens-of-meV dependence on interface composition and strain; Makimoto's higher value corresponds to a strained-stack-specific configuration) and substantially quantified the strain question (hole effective masses measured versus well width and InSb fraction; mobility rises up to ~2% strain; strain shifts of the InAs/GaSb alignment quantified). Undoped low-temperature mobilities have risen from ~7000 cm^2/Vs (1995) to ~2e4 cm^2/Vs (2019), while room-temperature values rose from ~650 to ~1500 cm^2/Vs under strain; GaAs/AlGaAs 2DHGs reach ~1e6-2e6 cm^2/Vs (peak 2.3e6 cm^2/Vs; Watson et al., Phys. Rev. B 85, 165301 (2012)), so the GaSb system remains roughly 50-100x below comparable GaAs hole gases, with no published quantitative account of why. The broken-gap alignment and the strain dependence of the subband structure and effective masses are treated as settled inputs and lie outside the scope of the transport problem posed below.

Problem Statement

Determine, quantitatively, which scattering mechanisms limit the low-temperature Hall mobility of undoped (InAs-cap-induced or gate-induced) two-dimensional hole gases in (In)GaSb/AlSb quantum wells over ranges of sheet density and well width, which are independent parameters in this scheme (the sheet density is set by the InAs cap or gate and the top-barrier thickness, not by the well width), with operating points chosen to resolve both the density dependence at fixed well width and the width dependence at fixed sheet density (low temperature here meaning the regime where phonon scattering no longer dominates, so that the mobility is set by temperature-independent mechanisms), testing the candidate mechanisms (a) native-defect-related background charged centers in the (In)GaSb channel (for example, Ga vacancies and Ga-on-Sb antisites), (b) interface roughness at the well/barrier interfaces, and (c) remote ionized charges, including surface-related charges, together with any further mechanism the analysis identifies, and separating the contributions of those that are significant; and establish quantitatively how much the two-dimensional hole mobility can be raised by reducing the native-defect/background-carrier concentration.

References

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