Serpentine superlattices (SSLs) grown by molecular beam epitaxy on vicinal substrates realize arrays of laterally modulated quantum wires. In the only antimonide report — Wong, Krishnamurthy, Brar, Yi, Kroemer, and English, Appl. Phys. Lett. 63, 1211 (1993) — GaSb/AlSb SSLs showed excellent lateral uniformity, 13–15 meV photoluminescence linewidths, roughly 60% linearly polarized emission, and a preliminary estimate of the lateral aluminum segregation, Δx≈0.35\Delta x\approx 0.35, far exceeding the arsenide-SSL value near 0.1; the polarization spectra were slightly redshifted relative to the photoluminescence intensity maximum for reasons the paper left open. The preliminary segregation rests on a first-order bulk-alloy mapping that neglects both carrier quantum confinement in the ~10 nm parabolic lateral potential and the energetic proximity of the Γ\Gamma and LL conduction valleys in the GaSb/AlSb system. No follow-up on antimonide SSLs is known to date, and the arsenide SSL methodology that solved the analogous composition-extraction problem has not been applied to this system. The problem is to determine the true lateral Al segregation (with a stated uncertainty) through modeling that includes confinement and Γ\Gamma–LL intervalley physics, to establish the mapping from measured PL transition energies to local alloy composition in this system, and to identify the physical origin of the polarization redshift.

Background

Semiconductor quantum wires — structures that confine electrons and holes in two spatial dimensions so that motion is effectively one-dimensional — were pursued in the late 1980s and early 1990s as a route to sharper density of states and stronger optical gain. One fabrication route avoided lithography entirely: molecular beam epitaxy (MBE, an ultrahigh-vacuum technique that deposits elemental beams monolayer by monolayer) on a vicinal substrate, i.e. a substrate miscut by one or two degrees from a low-index plane. A vicinal (001) surface breaks into a staircase of terraces, typically 5–15 nm wide, separated by atomic steps, and under step-flow conditions each deposited monolayer nucleates at the steps and advances across one terrace at a time. If the two deposited compounds are alternated on a timescale shorter than one terrace completion, adjacent terraces acquire different compositions, producing a lateral (in-plane) composition modulation whose period equals the terrace width. Growth with a fixed fractional step coverage per cycle produces a tilted superlattice (TSL), also called a fractional-layer superlattice; deliberately sweeping the step coverage around unity each cycle produces a serpentine superlattice (SSL), whose lateral wells bend into parabolic, snake-like shapes and whose geometry is insensitive to small step-coverage errors.

In the (Al,Ga)As system this program was carried through quantitatively. Miller, Pryor, Weman, Samoska, Kroemer, and Petroff introduced the SSL concept (J. Cryst. Growth 111, 323, 1991), Pryor computed the electronic structure and optical matrix elements of SSL quantum-wire arrays (Phys. Rev. B 44, 12912, 1991), and Miller et al. (Phys. Rev. Lett. 68, 3464, 1992) showed that three independent polarization measurements, an energy shift, and the light-hole–heavy-hole splitting (the energy difference between the two topmost valence subbands of a quantum well), all compared with theory, are jointly explained by lateral wells of Al fraction x=0.12x=0.12 and barriers of x=0.21x=0.21 — a lateral composition difference Δx≈0.09\Delta x\approx 0.09 that quantifies the intermixing (segregation saturation) limiting arsenide lateral superlattices. Weman et al. (Phys. Rev. B 48, 8047, 1993) extended this to a comprehensive optical study, comparing the measured luminescence polarization anisotropy with calculations as a function of intermixing; the arsenide line continued through 1995 (temperature-dependent polarization, Weman et al., Superlattices Microstruct. 17, 61, 1995; nanowire-array lasers, Hu et al., IEEE J. Quantum Electron. 31, 1380, 1995) and then ended.

The GaSb/AlSb system belongs to the lattice-matched ~6.1 Å family (InAs, GaSb, AlSb; reviewed by Kroemer, Physica E 20, 196, 2004). GaSb is a narrow-gap direct semiconductor whose two lowest conduction-band valleys are unusually close together: the LL-point valley lies only about 0.1 eV above the band-edge Γ\Gamma valley, so quantum confinement in narrow GaSb wells pushes Γ\Gamma-derived subbands up toward the LL valley. In narrow GaSb/AlSb (100) quantum wells, the same group observed recombination that becomes only 'quasi-direct' — nominally indirect in momentum space, but partially allowed through Γ\Gamma–LL mixing — as a direct consequence of this proximity (Brar, Kroemer, and English, J. Cryst. Growth 127, 752, 1993). This Γ\Gamma–LL subtlety is what makes converting antimonide optical transition energies into alloy compositions harder than in the arsenide case.

The source paper (Wong et al., 1993) grew GaSb/AlSb SSLs by MBE on vicinal GaAs and GaSb substrates (about 120 deposition cycles, nominally 40% AlSb and 60% GaSb per cycle, step coverage swept from 0.8 to 1.2). Cross-sectional transmission electron microscopy (TEM, imaging of an electron-transparent cross-section at near-atomic resolution) confirmed uniform parabolic crescents with crisp Ga-rich/Al-rich contrast. Low-temperature photoluminescence (PL, optical emission after above-gap excitation) showed an SSL-related peak of full width at half maximum 13–15 meV, and polarization-resolved PL, measured with a photoelastic modulator (an optical element that periodically switches the measured polarization axis so that both field components are recorded), gave a normalized linear polarization Pz=(I∥−I⊥)/(I∥+I⊥)≈60%P_z=(I_\parallel-I_\perp)/(I_\parallel+I_\perp)\approx 60\% — where I∥I_\parallel and I⊥I_\perp are the emitted intensities with the electric field parallel and perpendicular to the wire axis — the strongest reported for SSL structures. A first-order estimate converts the ~1.22 eV SSL peak energy into a bulk alloy composition and, enforcing the fixed average composition Al0.4Ga0.6Sb\mathrm{Al}_{0.4}\mathrm{Ga}_{0.6}\mathrm{Sb}, yields a preliminary aluminum segregation Δx=xb−xw≈0.35\Delta x=x_b-x_w\approx 0.35 between the Al-rich (barrier, xbx_b) and Ga-rich (well, xwx_w) lateral regions — far better than the arsenide value — but this estimate neglects quantum confinement of the carriers in the ~9.5 nm-period parabolic lateral potential and the Γ\Gamma–LL intervalley structure. The paper further reports that the polarization spectra show a slight redshift relative to the PL intensity maximum, and leaves the physical origin of this redshift open. The composition determination has not been independently corroborated.

Problem Statement

For MBE-grown GaSb/AlSb serpentine superlattices of the kind realized by Wong et al. (1993) — nominal average composition Al0.4Ga0.6Sb\mathrm{Al}_{0.4}\mathrm{Ga}_{0.6}\mathrm{Sb}, lateral period set by the vicinal terrace width (about 9.5 nm in the reported samples), parabolic lateral wells and barriers, SSL photoluminescence peak near 1.22 eV with 13–15 meV linewidth, and normalized linear polarization Pz≈60%P_z\approx 60\% — determine the true lateral aluminum segregation Δx=xb−xw\Delta x=x_b-x_w (equivalently the well and barrier Al fractions xwx_w, xbx_b under the fixed average composition), with a stated uncertainty, replacing the preliminary estimate Δx≈0.35\Delta x\approx 0.35 obtained from a first-order bulk-alloy mapping.

The determination must rest on a model of the SSL electronic structure that (i) includes quantum confinement of electrons and holes in the parabolic lateral potential at the ~10 nm scale, and (ii) treats the energetic proximity of the Γ\Gamma and LL conduction valleys in the GaSb/AlSb system, identifying which valley(s) the observed recombination involves. Within the same model, establish the quantitative mapping from measured PL transition energies to local alloy composition in this material system, including how the peak energy and its linewidth translate into the well composition and its lateral variation.

Additionally, identify the physical origin of the slight redshift of the polarization-resolved PL spectrum relative to the PL intensity maximum, and account for it quantitatively — since an unexplained systematic displacement between the polarized component and the total emission bears directly on how the transition energies used in the composition mapping should be interpreted.

Determine Δx\Delta x, xwx_w, and xbx_b consistently with all available observables of the SSLs (PL peak energy, linewidth, and polarization), identify which conduction valley(s) the observed recombination involves, establish the quantitative mapping from measured PL transition energies to local alloy composition, and account quantitatively for the physical origin of the polarization redshift.

References

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