Controlled phase separation in epitaxial (Ge2)x(GaAs)1-x films: designed quasi-periodic Ge/GaAs stripe architectures and composition-dependent film structure

Banerjee, Kroemer, and Chung (Materials Letters, 1984) showed that molecular-beam-epitaxy growth of the isoelectronic heterovalent alloy $(Ge_{2})_{x}(GaAs)_{1-x}$ on GaAs(110), GaAs(211), and Ge(211) at 550-610 degrees C produces spontaneous phase separation into Ge-rich domains of order 100 Angstrom embedded in a continuous GaAs-rich matrix, with a {110}-faceted, cross-hatched morphology, and left four follow-up directions open: (1) controlled fabrication of a quasi-periodic, parallel stripe architecture of alternating Ge-rich and GaAs-rich regions with designed widths near 100 Angstrom, intended to confine electrons to one dimension; (2) the quantitative lattice-parameter relation $a(x)$; (3) the mechanism of the dependence of domain size and shape on composition, substrate orientation, and growth temperature; (4) the use of single-phase alloys to probe the proposed zincblende-to-diamond order-disorder transition. Directions (2), (4), and the mechanism question in (3) have been substantially addressed by the 1985-2003 literature on (III-V)1-x(IV2)x alloys: single-phase films were grown, the transition was probed and reinterpreted as growth-kinetic rather than bulk-thermodynamic with quantified measurement artifacts, lattice parameters were measured with Vegard deviations tied to nonstoichiometry, and morphology control was traced to growth-surface kinetics. The surviving open problem is direction (1): to fabricate and demonstrate, by kinetic control of the phase separation, a designed quasi-periodic Ge/GaAs stripe architecture, which no work known to date demonstrates or rules out, although the alloy system remains actively pursued for infrared optoelectronics, thermoelectric nanostructuring, and photovoltaics.

Background

Germanium and gallium arsenide are nearly perfectly lattice matched (cubic lattice constants $a ≈ 5.658$ Angstrom for Ge and $5.653$ Angstrom for GaAs), so the pseudo-binary notation $(Ge_{2})_{x}(GaAs)_{1-x}$ denotes an isoelectronic heterovalent alloy in which two Ge atoms (group IV, four valence electrons each) replace one Ga-As pair (three plus five electrons), preserving the octet electron count at every composition $x$. Molecular beam epitaxy (MBE) grows such films by co-evaporating elemental beams -- here Ga, Ge, and an arsenic flux -- in ultrahigh vacuum onto a heated crystalline substrate; its low growth temperatures can kinetically trap compositions that equilibrium forbids. Equilibrium is indeed hostile: the Ge-GaAs pseudo-binary phase diagram shows a wide miscibility gap (a composition-temperature region in which the solid separates into two phases) with mutual solubilities of only a few mole percent (Takeda, Hirai, and Hirao, 1965), so any homogeneous alloy is metastable and thermodynamically driven to decompose. Before 1984, single-crystal metastable Ge-GaAs alloys had been made by sputter deposition (film growth by condensing atoms knocked from a target by ion bombardment) and characterized optically (Barnett et al., 1982).

Two crystal structures compete in this system. In the zincblende structure of GaAs, two interpenetrating face-centered-cubic sublattices carry different atoms (Ga on one, As on the other), so the crystal lacks inversion symmetry; in the diamond structure of Ge both sublattices carry identical atoms and the structure is centrosymmetric. A random alloy would distribute all three species over both sublattices, giving a 'diamond-like' average structure. Newman and Dow (1983) proposed that with increasing $x$ the alloy passes through a zincblende-to-diamond order-disorder transition -- an ordered phase in which Ga and As prefer opposite sublattices giving way to a disordered phase with statistically equal sublattice occupations -- and connected it to the strongly V-shaped, negative bowing (deviation of the alloy's band gap from the linear interpolation between the end-member gaps) of the direct optical gap measured in sputtered metastable films (Newman et al., 1983).

Banerjee, Kroemer, and Chung (1984) grew $(Ge_{2})_{x}(GaAs)_{1-x}$ films by MBE on GaAs(110), GaAs(211), and Ge(211) substrates at substrate temperatures of 550-610 degrees C and examined them by transmission electron microscopy (TEM) under two-beam bright- and dark-field diffraction contrast, by transmission electron diffraction (TED), by convergent-beam electron diffraction (CBED, a focused-probe diffraction method sensitive to local point symmetry), and by reflection high-energy electron diffraction (RHEED) monitored during growth. The films were single-crystalline and free of dislocations, stacking faults, antiphase boundaries (interfaces across which the Ga and As sublattices are interchanged), and secondary Ge-As compounds, but in every case they had phase-separated compositionally into Ge-rich domains of order $10^{2}$ Angstrom (range 50-300 Angstrom) embedded in a continuous GaAs-rich matrix. Domain boundaries preferred {110} crystallographic planes, giving elongated-hexagonal domain cross sections. The authors had deliberately tried to nucleate an ordered array of parallel Ge-rich and GaAs-rich stripes -- pre-depositing sub-monolayer or about 100 Angstrom Ge 'priming' layers and using the highly anisotropic (110) and (211) substrate orientations -- aiming at a self-assembled structure that would confine electrons to one-dimensional motion; instead the domains formed a cross-hatched morphology with no preferred subset of {110} planes, and higher growth temperatures made the domains more randomly distributed. A systematic lattice-parameter-versus-composition study was indicated as unfinished, and whether single-phase material suitable for probing the order-disorder transition could be obtained under comparable growth conditions was left open. (Vegard's law, referenced below, is the assumption that an alloy's lattice parameter varies linearly with composition between the end-member values.)

Problem Statement

The problem, as posed by the 1984 study, is to turn the spontaneous phase separation of epitaxially grown $(Ge_{2})_{x}(GaAs)_{1-x}$ from an uncontrolled, cross-hatched morphology into a controlled and quantitatively characterized structure. Its four linked parts share one objective -- making this nearly lattice-matched heterovalent decomposition a usable materials-design tool: (1) specify, by kinetic control of the phase separation, a route to a quasi-periodic, parallel, stripe-like architecture of alternating Ge-rich and GaAs-rich regions with designed widths near 100 Angstrom (a self-assembled quantum-wire array: parallel wires that would confine electrons to one-dimensional motion), and argue and predict -- without executing the growth or microscopy -- that this route yields a stripe architecture that is genuinely quasi-periodic (parallel, with a single preferred in-plane orientation and a regular spatial period near 200 Angstrom, twice the ~100 Angstrom designed stripe width, rather than the cross-hatched morphology) and reproducible across nominally identical growth runs, together with the structural and compositional microscopy signature expected to verify it; (2) determine the quantitative lattice parameter $a(x)$ of the films across the composition range, including deviations from Vegard's law; (3) establish the mechanism controlling domain size and shape as a function of nominal composition $x$, substrate orientation, and substrate temperature -- whether temperature-driven coarsening or substrate surface chemistry dominates; (4) determine whether these growth conditions can produce single-phase alloys suitable for realizing and probing the proposed zincblende-to-diamond order-disorder transition. Parts (2) and (4) and the mechanism question of (3) have been substantially addressed by later literature; the surviving open core is part (1): whether kinetic control of the phase separation can produce designed, quasi-periodic Ge/GaAs stripe architectures. The question prescribes the target structure -- regular, parallel, alternating Ge-rich and GaAs-rich stripes of designed widths near 100 Angstrom in this alloy system -- but not the growth technique, substrate, composition window, or control pathway, any of which an answer may choose.

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