Experiments on ultrathin Mg(0001) films grown on W(110) showed that the initial oxidation rate oscillates strongly with film thickness, peaking when a quantum-well state crosses the Fermi energy. Binggeli and Altarelli (2006) attributed this to a thickness oscillation of the vacuum decay length λ\lambda of the electronic density of states at the Fermi level — maximal when the highest occupied quantum-well state at Γˉ\bar{\Gamma} is closest to EFE_F — which exponentially modulates the tunneling electron-transfer rate believed to control the initial sticking of O2_2. Their density-functional calculations reproduce the oscillation but place the quantum-well crossing and the λ\lambda extrema about +2 monolayers away from the measured values, a shift they attribute to the commensurate, dislocation-free interface model. The open problem is to establish the mechanism quantitatively: compute the quantum-well spectrum and λ(L)\lambda(L) for the realistic, lattice-mismatched Mg/W(110) interface including strain relaxation and misfit dislocations; directly measure λ(L)\lambda(L) and the thickness dependence of the electron-transfer observables (terrace-resolved decay-length contrasts, transfer rates, negative-ion-state lifetimes); and test the robustness of the quantum-well level positions beyond the independent-electron description. Adjacent systems (Al/W(110), Pb mesas, Mg/Si(111) chemicurrents) support but do not settle the Mg/W(110) case.

Background

When a metal film a few atomic layers thick is grown epitaxially on a substrate that reflects its conduction electrons, standing waves — quantum-well states (QWS) — form in the film. As the film thickness LL increases, these discrete levels descend one by one through the Fermi energy EFE_F, so film properties oscillate with thickness with a period fixed by the Fermi wavevector along the confinement direction. This is the quantum-size effect (QSE); for Mg(0001) a Bohr–Sommerfeld phase-accumulation count gives a period of about 7.7 monolayers (ML) (Schiller et al., 2004).

The experimental puzzle comes from Aballe et al. (Phys. Rev. Lett. 93, 196103 (2004)), who grew atomically flat Mg(0001) films of up to 15 ML on W(110) and monitored their initial oxidation rate with X-ray photoemission electron microscopy (XPEEM, a full-field imaging form of photoemission). The initial oxidation rate showed pronounced oscillations with thickness, largest when a QWS crossed EFE_F in near-normal-incidence photoemission. Because the total density of states (DOS) at EFE_F necessarily grows monotonically with thickness, the oscillating reactivity could not be explained by the DOS alone.

Binggeli and Altarelli (Phys. Rev. Lett. 96, 036805 (2006)) proposed and tested, by density-functional theory (DFT) within the PBE functional, a specific mechanism. Outside a film, each state's local density of states (LDOS) decays into the vacuum as e−2αnze^{-2\alpha_n z}, with decay length 1/(2αn)1/(2\alpha_n) set by the binding energy of the highest occupied subband at Γˉ\bar{\Gamma} (k∣∣=0k_{||}=0); the LDOS at EFE_F therefore inherits a decay length λ\lambda that oscillates with LL, maximal whenever the highest occupied QWS at Γˉ\bar{\Gamma} is closest to EFE_F. Their slab calculations for Mg(0001) on W(110) (5–12 ML) gave λ≈0.46\lambda \approx 0.46–0.540.54 Å, i.e., an oscillation of about 10%. Through the electron-transfer picture of Hellman et al. (Surf. Sci. 532-535, 126 (2003)), in which the initial sticking of O2_2 on Mg is controlled by nonadiabatic tunneling charge transfer into the affinity level of the approaching molecule (a transient O2−_2^- negative-ion resonance), such a λ\lambda oscillation roughly doubles the transfer rate at physisorption distance (≈3.5\approx 3.5 Å), of the order of the measured rate changes. Independent support for the role of confined states in charge transfer came from layer-KKR (Korringa–Kohn–Rostoker, a multiple-scattering electronic-structure method) calculations by Rous (Phys. Rev. Lett. 83, 5086 (1999)), predicting that adsorbate negative-ion-state lifetimes should be controllable through coupling to film QWS — a prediction unmeasured at the time.

The catch is the interface. Mg(0001) on W(110) is heavily lattice-mismatched (about 1.6% along one in-plane axis and about 20% along the other), so the real interface must contain strained layers and misfit dislocations (line defects that absorb lattice mismatch at an interface). Ab initio supercells cannot accommodate the corresponding lateral dimensions, so the calculations used a commensurate, dislocation-free model with the W substrate laterally strained to the Mg lattice parameters. As a result, the calculated QWS crossing of EFE_F (at 8–9 ML) and the λ\lambda extrema were shifted by about +2 ML relative to experiment (the QWS enters the measured valence band at a nominal thickness of 6–7 ML). The authors stated that the λ\lambda changes should be observable by scanning tunneling microscopy (STM) near terrace steps on films with regions of different thicknesses, and that a more realistic description — beyond the independent-electron treatment, including electron interaction, atomic orbitals and bonds, surface states, and the presence of the substrate, all expected to influence λ\lambda — was clearly needed to confirm the robustness of the predicted behavior.

Problem Statement

Establish, quantitatively and directly, whether the quantum-size oscillation of the electronic density decay length — and the resulting exponential modulation of the tunneling electron-transfer rate — is the mechanism controlling the observed thickness-dependent initial oxidation reactivity of Mg(0001) ultrathin films on W(110). The common objective ties together three strands, all left open by the source work and jointly serving this one question:

  1. Interface-realistic theory. Model Mg(0001)/W(110) films with the realistic, lattice-mismatched interface — including strain relaxation and misfit dislocations — and compute the thickness dependence of the quantum-well spectrum at Γˉ\bar{\Gamma} and of the vacuum decay length λ(L)\lambda(L) of the LDOS at EFE_F. Does the realistic interface remove the ≈+2\approx +2 ML shift, i.e., does the highest occupied quantum-well state cross EFE_F at the experimentally observed nominal thickness (6–7 ML), and do the λ\lambda extrema coincide with the measured reactivity maxima?

  2. Direct experimental verification. Measure the predicted observables for this system — the vacuum decay-length contrast across terraces of different film thickness (e.g., by STM near terrace steps), the tunneling-mediated electron-transfer rate as a function of film thickness, and/or the lifetimes of negative ionic molecular states coupled to the film quantum-well states — and compare their thickness dependence (period and phase) with the calculated λ(L)\lambda(L) and with the measured reactivity oscillations.

  3. Robustness of the level structure. Assess, beyond the independent-electron PBE treatment, how many-body (quasiparticle) corrections and the pseudopotential and slab/substrate modeling choices shift the quantum-well level positions and modify the resonant-versus-localized character of the states crossing EFE_F, and hence how robust the predicted phase and amplitude of the λ(L)\lambda(L) oscillations are.

An answer resolving any strand within this common objective — for example, a dislocation-resolved calculation reproducing the measured crossing thickness, or a direct measurement of the decay-length or transfer-rate oscillation with the predicted period and phase — constitutes decisive progress on the problem; full resolution requires theory and experiment to agree on both the phase and the magnitude of the reactivity oscillations for this system.

References

  1. N. Binggeli and M. Altarelli, "Surface Reactivity and Quantum-Size effects on the Electronic Density Decay Length of ultrathin Metal Films", Phys. Rev. Lett. 96, 036805 (2006), DOI: 10.1103/PhysRevLett.96.036805, arXiv:cond-mat/0601364, https://doi.org/10.1103/PhysRevLett.96.036805
  2. L. Aballe, A. Barinov, A. Locatelli, S. Heun, and M. Kiskinova, "Tuning Surface Reactivity via Electron Quantum Confinement", Phys. Rev. Lett. 93, 196103 (2004), DOI: 10.1103/PhysRevLett.93.196103, https://doi.org/10.1103/PhysRevLett.93.196103
  3. N. Binggeli and M. Altarelli, "Quantum-size effects in ultrathin Mg films", Phys. Rev. B 78, 035438 (2008), DOI: 10.1103/PhysRevB.78.035438, https://doi.org/10.1103/PhysRevB.78.035438
  4. L. Aballe, A. Barinov, N. Stojić, N. Binggeli, T. O. Mentes, A. Locatelli, and M. Kiskinova, "The electron density decay length effect on surface reactivity", J. Phys.: Condens. Matter 22, 015001 (2010), DOI: 10.1088/0953-8984/22/1/015001, https://doi.org/10.1088/0953-8984/22/1/015001
  5. Xucun Ma, Peng Jiang, Yun Qi, Jinfeng Jia, Yu Yang, Wenhui Duan, Wei-Xue Li, Xinhe Bao, S. B. Zhang, and Qi-Kun Xue, "Experimental observation of quantum oscillation of surface chemical reactivities", Proc. Natl. Acad. Sci. USA 104, 9204–9208 (2007), DOI: 10.1073/pnas.0611024104, https://doi.org/10.1073/pnas.0611024104
  6. U. Hagemann and H. Nienhaus, "Quantum size effects in chemicurrent measurements during low-temperature oxidation of Mg(0001) epilayers", New J. Phys. 16, 113035 (2014), DOI: 10.1088/1367-2630/16/11/113035, https://doi.org/10.1088/1367-2630/16/11/113035
  7. M. Wiesenmayer, M. Bauer, S. Mathias, M. Wessendorf, E. V. Chulkov, V. M. Silkin, A. G. Borisov, J.-P. Gauyacq, P. M. Echenique, and M. Aeschlimann, "Lifetime of an adsorbate excitation modified by a tunable two-dimensional substrate", Phys. Rev. B 78, 245410 (2008), DOI: 10.1103/PhysRevB.78.245410, https://doi.org/10.1103/PhysRevB.78.245410
  8. N. A. Vinogradov, D. E. Marchenko, A. M. Shikin, V. K. Adamchuk, and O. Rader, "Size effects in ultrathin Mg/W(110) films: Quantum electronic states", Phys. Solid State 51, 179–188 (2009), DOI: 10.1134/S1063783409010235, https://doi.org/10.1134/S1063783409010235
  9. Xin Liu, S. B. Zhang, X. C. Ma, Jin-Feng Jia, Qi-Kun Xue, Xin-He Bao, and Wei-Xue Li, "Wavevector-dependent quantum-size effect in electron decay length at Pb thin film surfaces", Appl. Phys. Lett. 93, 093105 (2008), DOI: 10.1063/1.2977529, https://doi.org/10.1063/1.2977529
  10. Meng Li, Hong-Bo Jin, Jin-Ming Li, Qiang Sun, and Yu Jia, "Electronic Density Decay Lengths of Pb Films from First Principles Calculations", Chin. Phys. Lett. 28, 047302 (2011), DOI: 10.1088/0256-307X/28/4/047302, https://doi.org/10.1088/0256-307X/28/4/047302
  11. L. Aballe, A. Barinov, A. Locatelli, T. O. Mentes, and M. Kiskinova, "Initial stages of heteroepitaxial Mg growth on W(110): Early condensation, anisotropic strain, and self-organized patterns", Phys. Rev. B 75, 115411 (2007), DOI: 10.1103/PhysRevB.75.115411, https://doi.org/10.1103/PhysRevB.75.115411
  12. A. Hellman, B. Razaznejad, Y. Yourdshahyan, H. Ternow, I. Zorić, and B. I. Lundqvist, "Initial sticking of O2 modeled by nonadiabatic charge transfer", Surf. Sci. 532-535, 126–131 (2003), DOI: 10.1016/S0039-6028(03)00111-0, https://doi.org/10.1016/S0039-6028(03)00111-0
  13. P. J. Rous, "Controlling the Lifetime of Adsorbate Negative Ion States", Phys. Rev. Lett. 83, 5086–5089 (1999), DOI: 10.1103/PhysRevLett.83.5086, https://doi.org/10.1103/PhysRevLett.83.5086
  14. F. Schiller, M. Heber, V. D. P. Servedio, and C. Laubschat, "Electronic structure of Mg: From monolayers to bulk", Phys. Rev. B 70, 125106 (2004), DOI: 10.1103/PhysRevB.70.125106, https://doi.org/10.1103/PhysRevB.70.125106