Microscopic origin of the reduced transition energies of few-monolayer InAs/AlSb quantum wells

In 1993, Brar, Kroemer, Ibbetson and English reported strong, monolayer-resolved photoluminescence from InAs quantum wells as thin as two monolayers (ML) between AlSb barriers, and found that standard $\Gamma$-valley envelope-function calculations reproduce the measured transition energies only for wells wider than about 4 ML; the 2–3 ML wells emit at substantially lower energies, an effect the authors attributed to the influence of the AlSb $X$-valley barrier on the conduction-band states. Later work established that InSb-like versus AlAs-like interface bonding shifts the emission by roughly 100 meV, that In–Sb-bond Tamm interface states (localized states bound to the interface bonds) exist, and, through a ten-band tight-binding calculation, that $\Gamma$–$X$ mixing plausibly lowers the conduction states of the thinnest wells. However, no study has combined conduction- and valence-band physics, realistic interface chemistry, strain, and nonparabolicity to quantitatively reproduce the monolayer-series energies and decompose the mechanisms, and the required InAs $X$-valley parameters still lack direct experimental determination. The surviving open problem is a quantitative, experimentally validated microscopic account of these transition energies and of the dominant mechanism or mechanism combination responsible for the reduction below the $\Gamma$-valley envelope-function predictions.

Background

The 6.1 Å III-V heterosystem InAs/AlSb combines a narrow-gap semiconductor (InAs, band gap about 0.41 eV at low temperature, electron effective mass $m^*_{\Gamma}\approx0.023m_0$) with an indirect-gap barrier (AlSb, whose lowest conduction-band minimum lies at the $X$ point of the Brillouin zone, with a gap near 1.6 eV). The two binaries are nearly lattice matched (mismatch about 1.3%) and the band alignment is staggered ("type-II"): the InAs $\Gamma$ conduction-band minimum lies roughly 2.2 eV below the AlSb $\Gamma$ conduction band, while the InAs valence-band maximum lies only about 0.1 eV below that of AlSb. In a quantum well — a thin semiconductor layer confined between higher-gap barriers, here with thickness counted in monolayers (ML; one atomic bilayer, about 0.3 nm) — electrons are therefore strongly confined in InAs, while heavy holes reside in the AlSb barriers, so the lowest interband transition is spatially indirect. Photoluminescence (PL) measures these transition energies directly. In early transport work, undoped AlSb/InAs/AlSb wells showed high electron densities attributed to a deep donor in the AlSb barriers (Tuttle, Kroemer and English, 1989), establishing the electronic baseline of the system.

Brar, Kroemer, Ibbetson and English (1993) grew InAs/AlSb multi-quantum-well structures with wells of nominal thickness from 1 to 8 ML and observed strong, clearly resolved PL peaks that they assigned to wells of 2–8 ML; cross-sectional transmission electron microscopy (TEM) showed structurally well-defined layers, including the 1 ML wells, although a 1 ML PL peak was absent. They compared the measured energies with a standard quantum-well calculation based on the envelope-function approximation (EFA) — the effective-mass treatment in which confined states are described by slowly varying $\Gamma$-valley envelopes with continuity conditions at the interfaces — including the strong nonparabolicity of narrow-gap InAs (energy-dependent effective mass) but neglecting strain. For wells wider than about 4 ML the calculation reproduced the data; for the narrowest wells (2–3 ML) the measured transition energies were significantly lower than the $\Gamma$-based prediction. The authors attributed this to the AlSb $X$ barrier: under such extreme quantization the confined electron level rises to within a few tenths of an eV of the AlSb $X$ conduction band, and possibly near the InAs $X$ minima as well.

Several microscopic mechanisms could lower the transition energies: (i) the electron ground state could become $X$-like under quantization, so that electrons are effectively confined by the AlSb $X$ barrier rather than the $\Gamma$ barrier (a "quasi-direct" transition); (ii) mixing (hybridization) between InAs $\Gamma$ states and AlSb $X$ states could depress the well ground state as it approaches the $X$ continuum; (iii) valence-band Tamm-type interface states — localized states that arise, in a no-common-anion system like InAs/AlSb where both the cation and the anion change across each interface, from the interfacial In–Sb or Al–As bonds — could lower the valence-band ground state through interactions between the two interfaces; or (iv) the envelope-function approximation itself could break down at the monolayer scale. Additional complications are known: the lattice mismatch puts the InAs wells under tensile strain; the interface chemistry (InSb-like versus AlAs-like bonding, selectable by molecular-beam-epitaxy shutter sequences) shifts optical transition energies by about 100 meV; and growth may proceed by island nucleation rather than layer-by-layer growth, producing roughness that could also redshift the PL. A persistent obstacle is that the InAs $X$-valley energy position and effective masses — needed to quantify any of these mechanisms — have no direct experimental determination: first-principles and tight-binding estimates place the InAs $X$ minima roughly 1.4–1.9 eV above the InAs $\Gamma$ minimum, and the InAs/AlSb valence-band offset is known only at the tens-of-meV level.

Problem Statement

Determine quantitatively, and with experimental validation, which microscopic mechanism or combination of mechanisms is responsible for the interband transition energies of few-monolayer InAs/AlSb quantum wells — in particular the reduction of the 2–3 ML (monolayer; one atomic bilayer, about 0.3 nm) well energies below the predictions of $\Gamma$-valley envelope-function calculations (the effective-mass treatment of confined states by slowly varying zone-center wave functions). The candidate mechanisms to be discriminated are: confinement-driven $X$-like character of the electron ground state, where $X$ denotes the indirect conduction-band minima near the Brillouin-zone edge and $\Gamma$ the direct zone-center minimum (confinement by the AlSb $X$ barrier rather than the $\Gamma$ barrier); $\Gamma$–$X$ mixing between InAs well states and AlSb $X$-barrier states; valence-band Tamm-interface-state interactions (Tamm states being localized electronic states arising from the interface-specific chemical bonds, here the interfacial In–Sb or Al–As bonds) associated with InSb-like or AlAs-like interface bonding; breakdown of the envelope-function approximation at the monolayer scale in this no-common-anion system; tensile strain from the ~1.3% lattice mismatch; and extrinsic growth effects (islanding, interface roughness, intermixing). Resolving this requires accounting for the AlSb $X$ barrier, realistic interface chemistry, nonparabolicity, and strain, computing the spatially indirect interband transition energies across the monolayer-width series, quantitatively reproducing the measured photoluminescence energies, and identifying the dominant mechanism or mechanism combination. The candidate mechanisms need not each be individually ruled in or out; identifying the dominant mechanism or mechanism combination, supported by the quantitative reproduction of the measured energies, is what resolves the problem. The optically silent 1 ML well (no distinct 1 ML photoluminescence peak despite 1 ML layers visible in transmission electron microscopy, TEM) belongs to the same experimental series and may be addressed within such an account; the experimentally undetermined InAs $X$-valley parameters and the tens-of-meV InAs/AlSb band-offset uncertainty are obstacles for any such model rather than separate mandatory deliverables.

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