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Quantum oscillations in adsorption energetics of atomic oxygen on Pb(111) ultrathin films: A density-functional theory study

Using first-principles calculations, we have systematically studied the quantum size effects of ultrathin Pb(111) films on the adsorption energies and diffusion energy barriers of oxygen atoms. For the on-surface adsorption of oxygen atoms at different coverages, all the adsorption energies are found to show bilayer oscillation behaviors. It is also found that the work function of Pb(111) films still keeps the bilayer-oscillation behavior after the adsorption of oxygen atoms, with the values being enlarged by 2.10 to 2.62 eV. For the diffusion and penetration of the adsorbed oxygen atoms, it is found that the most energetically favored paths are the same on different Pb(111) films. And because of the modulation of quantum size effects, the corresponding energy barriers are all oscillating with a bilayer period on different Pb(111) films. Our studies indicate that the quantum size effect in ultrathin metal films can modulate a lot of processes during surface oxidation.


I. INTRODUCTION
Because of the well-defined simple geometry, thin metal films that are nanometers thick provides an ideal system to study the quantum behaviors of electrons in reduced dimensions.
Many researches have been carried out to investigate the corresponding quantum size effect (QSE) [i.e., the dependence on the film thickness] on electronic properties of metal films. According to the "particle-in-a-box" model, the itinerant electrons confined in metal films are quantized into discrete energy levels along the z direction perpendicular to the film surface, giving rise to the so-called quantum well states (QWS) [1,2,3,4,5,6,7,8], while the energy dispersion in the xy direction remains parabolic, forming a series of energy subbands. As the thickness of the metal film increases, these subbands sequentially cross the Fermi level, and make the physical properties of metal film oscillate periodically. Among all the metal species, ultrathin Pb(111) films have attracted vast attentions. By employing the epitaxy depositing methods, atomically flat Pb(111) films can be perfectly fabricated on both metal [9] and semiconductor [10,11] substrates. Moreover, extensive knowledge of the electronic properties and crystallite shape have been attained through systematical investigations.
Promimently, it has been found that the electron Fermi wavelength of Pb is nearly four times the lattice spacing along the [111] direction, so most physical properties of Pb(111) films such as the thermal stability, surface energy and work function, all oscillate with the thickness in a quasi-bilayer period [8,10,12]. The quantum effect of ultrathin Pb(111) films can also result in a spectacular oscillatory superconductivity transition temperature, by modulating the electron density of states near the Fermi level and the electron-phonon coupling [13]. Based on these previous results, it is easily understood that besides these intrinsic physical properties, QWS of ultrathin Pb(111) films will also affect the surface reactions such as oxidation.
In fact, a lot of researches have been carried out recently to study QSE on surface reactivities. Most of these studies are for applications in catalysis, corrosion, and gas sensing.
For example, the lifetime of negative N 2 ions physisorbed on Ag(111) films [14] and the desorption temperature of CO on Cu(100) films [15] are both found to be modulated by the film thickness. Apart from other reactivities, the oxidation of metal surfaces needs special concerns since the formed metal oxide layers have dominated many crucial properties of metals in industrial applications [16,17]. Previous experimental studies have already revealed that the initial oxidation rate of Mg(0001) [18] and Pb(111) films [19] depends on the film thickness in an oscillatory way. So it is of high interests to theoretically investigate the specific mechanisms of the oxidation processes and how QSE influences the initial oxidation rate. For the Mg(0001) system, unfortunately, present theoretical studies have failed to explain its surface oxidation process. The most notable is the long-term enigma of low initial sticking probability of thermal O 2 molecules at Mg(0001), which has been measured by many independent experiments [18,20] but cannot be reproduced by adiabatic state-of-the-art density functional theory (DFT) calculations [21]. The central problem is that the adiabatic DFT calculations were unable to find any sizeable barriers on the adiabatic potential energy surface (PES), whose presence, however, is essential for explanation of the experimental finding. This has led to speculations that nonadiabatic effects may play an important role in the oxygen dissociation process on the Mg(0001) surface. For the Pb(111) system, fortunately however, the oxygen dissociation process can be reasonably understood based on the adiabatic DFT calculations. In fact, our previous studies have already revealed that there are precursor adsorption states for molecular O 2 , and the molecular adsorption energy of O 2 shows a bilayer oscillation QSE with the thickness of Pb(111) films [22]. Moreover, we have also studied the adsorption properties for atomic O both at surface and subsurface sites systematically [23].
Based on these results, we further study the QSE on the adsorption energies and diffusion energy barriers of oxygen atoms on Pb(111) films in this work. The rest of the paper is arranged as follows. In Sec. II we give details of the first-principles total energy calculations, which is followed in Sec. III by our results of QSE on the adsorption energy for on-surface and subsurface adsorption of oxygen atoms. In Sec. IV, the QSE on the diffusion and penetration of oxygen atoms on Pb(111) films is discussed. And finally, we give our conclusions in Sec.

II. COMPUTATIONAL METHOD
The DFT total energy calculations are carried out using the Vienna ab initio simulation package [24]. The generalized gradient approximation (GGA) of Perdew et al. [25] and the projector-augmented-wave (PAW) potentials [26] are employed to describe the exchangecorrelation energy and the electron-ion interaction, respectively. The so-called "repeated slab" geometries [27] are employed to model the clean Pb(111) films ranging from 3 to 25 monolayers (ML). A vacuum layer of 20Å is adopted to separate the Pb(111) slabs in two adjacent cells, which is found to be sufficiently convergent from our test calculations.
The oxygen atoms are placed on both sides of the slabs in a symmetric way. During our calculations, the positions of all lead layers as well as the O atoms are allowed to relax until the forces on them are less than 0.02 eV/Å. The plane-wave energy cutoff is set to 400 eV. A Fermi broadening [28] of 0.1 eV is chosen to smear the occupation of the bands around E F by a finite-T Fermi function and extrapolating to T =0 K. Integration over the Brillouin zone is done using the Monkhorst-Pack scheme [29] with 21 × 21 × 1 grid points at Θ=1.0 coverage and 13 × 13 × 1 grid points at Θ=0.25 coverage. The calculated lattice constant of bulk Pb is 5.03Å, in good agreement with the experimental value of 4.95Å [30]. Furthermore, the nudged elastic band (NEB) method [31] is used to find the minimum energy path and the transition state for O atoms to penetrate or diffuse on ultrathin Pb(111) films.
One central quantity tailored for the present study is the average binding energy of the adsorbed oxygen atom defined as With this choice of adsorption energy, then a positive value indicates that the dissociative adsorption of O 2 is an exothermic process, while a negative value indicates that it is endothermic and that it is energetically more favorable for oxygen to be in the gas phase as is fully consistent with previous first-principles report [8], thus suggesting that the present calculation is reliable and accurate.
Formally, there are four high symmetry sites for surface adsorption, i.e., the top, bridge (bri), hcp, and fcc sites, which are schematically shown in Fig. 1(a). In our previous study [23], we have found that the top site is notably less favorable than the fcc and hcp hollow sites. When the O atom is placed on the bridge site, it always moves to the fcc hollow site after relaxation. Actually, Fig. 6 [33].
In our calculations, we see that the bilayer oscillation persists for films as thick as 21 MLs.
Between adsorbate and substrate, many physical properties such as binding (adsorption) energy, amount of charge transfer, and work function of the adsorption system change significantly with coverage. So studying the change of these quantities at different coverage has become one hot point. In this paper, our focus is to explore the QSE modulating the is located directly below a first-layer metal atom. From the calculated adsorption energies, we reveal that the most preferred adsorption site for the oxygen atom is the tetra-II site, in a wide coverage range [23]. In fact, the adsorption state at the tetra-II site is also found to be the most stable one in both surface and subsurface adsorption states [23]. Therefore, to study the QSE on the adsorption energy of the tetra-II adsorption state is very meaningful.
Similar to the surface adsorption, the subsurface adsorption energy for atomic oxygen is also larger at a higher coverage [23]. So we here focus on the QSE for the 1 ML subsurface adsorption of oxygen atoms.
The result of the adsorption energy for subsurface oxygen is shown in Fig. 5 as a function of the thickness of Pb(111) films, from which one can clearly see a bilayer oscillation fashion.
The oscillation is interrupted respectively at the 7 and 16 MLs, proving the existence of the 9-ML beating envelope. Although the bilayer oscillation and the beating envelope are normal characters for a lot of electronic properties of Pb(111) films, our calculational results are in fact a little fortuitous, because the unconfined p x and p y states of Pb also take part in the electronic interactions with O atoms [23]. And we are not surprised that the beating behavior for the subsurface adsorption of oxygen atoms does not accord well with that observed in surface oxidation [19]. During the subsurface adsorption of O atoms, the work function of Pb(111) films is found to be lowered down by about 0.65 ∼ 1.04 eV.

IV. QUANTUM SIZE EFFECT ON THE DIFFUSION AND PENETRATION OF ATOMIC OXYGEN
Diffusion of oxygen atoms after dissociation is also an elementary process during the whole surface oxidation process. Understanding the diffusion process is also very important for many important catalytic reactions such as oxidation of CO and hydrocarbons. So we here present first-principles calculations to study the QSE on the diffusion energy barriers of oxygen atoms on different Pb(111) films. In our previous work, we have reported that the the diffusion energy barrier is always larger for higher coverages adsorption of oxygen atoms [23]. And so we here mainly focus on the QSE on the diffusion of surface oxygen atoms with coverage of 1 ML. As shown in Fig. 6(a), the energy barrier for an adsorbed oxygen atom to diffuse from the hcp (fcc) to the fcc (hcp) hollow site is denoted as ∆E 1 (∆E 2 ). The calculated energy barriers for the diffusion of an adsorbed oxygen atom on different Pb (111) films are shown in Fig. 6(b). One can see that ∆E 1 is always smaller than ∆E 2 , indicating that the adsorption state at the surface fcc hollow site is more stable than the one at hcp hollow site for all Pb(111) films. The bilayer oscillation behavior can be clearly seen from