First-principles calculations by Li, Zhang and Chan (Physica B 390, 225 (2007)) predict that the binding energy of atomic hydrogen adsorbed on free-standing Mg(0001) thin films oscillates with film thickness with a period of about eight monolayers, in phase with quantum well states crossing the Fermi level and with the predicted oscillations of the surface energy, work function and interlayer relaxation. The authors proposed an experimental test: measure the hydrogen coverage as a function of Mg(0001) film thickness for films grown on Si(111) or W(110), systems in which the quantum well states were already accessible. Later work experimentally established thickness-oscillatory adsorption reactivity for oxygen — on Mg(0001)/W(110) (photoemission microscopy, 2004), on Pb mesas/Si(111) (scanning tunneling microscopy, 2007) and on Mg(0001)/Si(111) (chemicurrents, 2014) — and refined the theory of quantum size effects in Mg films, but no measurement of hydrogen adsorption or coverage versus Mg film thickness exists. The problem is to determine experimentally whether atomic hydrogen adsorption on Mg(0001) ultrathin films exhibits the predicted quantum size effect, including whether the free-standing-film period survives on substrate-supported films; a null result bounding the oscillation amplitude would also settle the question.

Background

When a metal film is only a few nanometers thick, electrons are confined between its two boundaries, and their allowed energies split into discrete subbands. The resulting standing-wave states are called quantum well states (QWS). In the phase-accumulation model, a QWS obeys 2k⊥Nd+2Φ=2πn2k_\perp Nd+2\Phi=2\pi n, where NN is the number of atomic layers (monolayers, ML), dd the interlayer spacing, k⊥k_\perp the electron wave-vector component perpendicular to the film and Φ\Phi the phase shift upon reflection at the film boundaries. Each time a QWS crosses the Fermi level EFE_F (the highest occupied electron energy), film properties oscillate with thickness — a quantum size effect (QSE), known experimentally mainly from Pb films on Si(111).

Magnesium is a nearly-free-electron hexagonal-close-packed metal, and epitaxial Mg(0001) films — crystalline films grown in registry with a substrate — can be grown with well-defined QWS: angle-resolved photoemission spectroscopy (ARPES) on Mg(0001)/Si(111) shows new QWS peaks at thickness intervals of about 8 ML (Aballe, Rogero and Horn, 2002), and the electronic structure of Mg(0001) films from monolayers to bulk was measured on W(110) (Schiller et al., 2004). The confinement also modulates chemical reactivity: Aballe et al. (2004) showed that the oxidation rate of Mg(0001)/W(110) films oscillates with thickness, peaking when a QWS crosses EFE_F — 'tuning surface reactivity via electron quantum confinement'.

Hydrogen on Mg(0001) is a benchmark adsorption system, relevant because Mg/MgH2_2 is a model hydrogen-storage couple. On the semi-infinite surface, atomic H chemisorbs in the fcc hollow site (the three-fold hollow position above a triplet of surface atoms with face-centred-cubic stacking continuity), and density-functional theory (DFT) studies map the coverage dependence from isolated adatoms through hydride-like H–Mg–H structures (Li, Zhang, Sun, Yang and Wei, 2009); molecular H2_2 dissociation on clean Mg(0001) is strongly activated, so experiments with atomic hydrogen are the natural route.

In this context, Li, Zhang and Chan (2007) performed DFT slab calculations of free-standing Mg(0001) films of 2–30 ML. They found that a QWS crosses EFE_F every ~8 ML, and that the surface energy, work function, interlayer relaxation (the deviation of the spacing between adjacent atomic layers from the bulk value) and the binding energy of an atomic-H monolayer all oscillate with that same period, the adsorption-energy oscillation being damped as thickness grows. They proposed that 'the calculated quantum size effect in H adsorption can be verified by observing the dependence of H coverage on the thickness of Mg(0001) thin films grown on Si(111) or W(110) substrate'. Subsequent experiments confirmed thickness-oscillatory reactivity for oxygen on Mg(0001)/W(110) (Aballe et al., 2004), on Pb mesas/Si(111) by scanning tunneling microscopy (Ma et al., 2007) and on Mg(0001)/Si(111) epilayers via chemicurrents — hot-electron currents in a Schottky diode (a metal–semiconductor junction) generated by non-adiabatic steps of a surface reaction (Hagemann and Nienhaus, 2014), with rate enhancements above a factor of two near 9 and 13 ML correlated with the photoemission intensity at EFE_F. Theory attributed the oxygen effect to the thickness-modulated density of states and its vacuum decay length at EFE_F (Binggeli and Altarelli, 2006, 2008). For hydrogen, however, no experiment measuring adsorption or coverage versus Mg film thickness has been reported, and later theoretical work on Mg films addressed clean films, Mg adatoms or oxygen adsorbates — not hydrogen.

Problem Statement

Determine experimentally whether the adsorption of atomic hydrogen on Mg(0001) ultrathin films exhibits a quantum size effect: does the hydrogen adsorption energy — and hence the equilibrium hydrogen coverage attained under controlled atomic-hydrogen dosing — oscillate with film thickness in correlation with quantum well states crossing the Fermi level, with a period of order eight monolayers as predicted for free-standing films? The test proposed by the source is to grow Mg(0001) films of controlled, layer-resolved thickness on Si(111) or W(110), dose atomic hydrogen under conditions that keep the system in the chemisorbed-monolayer regime (avoiding hydride formation), and measure the hydrogen coverage or adsorption/desorption energetics as a function of film thickness over a range spanning at least one full predicted oscillation period, with the films' quantum well states characterized independently (for example by angle-resolved photoemission). The question includes whether the oscillation predicted for free-standing films survives the substrate-modified electron confinement of supported films, since the interface changes the reflection phase shifts that set the period and amplitude. A null result that bounds the oscillation amplitude below a stated detection threshold would answer the question negatively; the stated detection threshold must itself lie below the predicted (Li, Zhang and Chan, 2007) oscillation amplitude over the probed thickness range, so that the null result excludes the predicted effect. Extensions the source mentioned — other adsorbates, other coverages, other substrates — are follow-up directions beyond this completion boundary.

References

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