Resonant scattering of phonons by adsorbates on clean silicon surfaces

We used Phonon Surface Scattering Spectroscopy (PSSS) to study excitations of adsorbates in the far infrared region from 100 eV up to 3 meV. We investigated the scattering of pulses of monochromatic phonons by thin films of H₂O, D₂O and Ne deposited in situ onto laserannealed Si(100)-surfaces. For all substances we observed a broad scattering at coverages below one monolayer and a strong resonant scattering at about 3 monolayers. The resonance frequency decreased with increasing coverage. The reasons for the resonances are discussed. Because of the lack of any observable isotope effect between H₂O and D₂O, the possibility of tunneling states in these layers can be excluded. Instead, we conclude that a lateral vibrational mode of the adlayer is responsible for the resonance effect. Corresponding calculations by means of continuum elasticity theory describe the scattering behaviour very well if similar elastic constants are used for all film substances.     

Quantum theory of atom-surface scattering: Incommensurate and fluid adsorbates

The problem of atomic scattering from adsorbate-covered surfaces, treated earlier for the case of commensurate overlayers, is considered again in the eikonal approximation for incommensurate lattice phases and for fluid phases. Stochastic methods are employed and for a specific model (hard bosses on a plane) it is shown how the statistical and geometric problems can be separately solved. In order to explain the meaning of the coherent and incoherent scattering contributions a time-dependent theory is introduced and it is shown that the incoherent “elastic” scattering is in fact weakly inelastic and (for classical diffusion with diffusion coefficient D) has an energy width of the order ?DQ², where Q is the parallel momentum transfer. The problem of the decay of substrate diffraction intensities when the coverage of random impurities is increased is also discussed.     

Comment on enhanced Raman scattering from adsorbates on semiconductor surfaces

A recently published model of surface enhanced Raman scattering from adsorbed molecules on semiconductor surfaces is compared to our experimental results for amorphous carbon on PbTe. The model fails to account for the major features of the observed scattering.     

Multiphonon atom-surface scattering from corrugated surfaces: derivation of the inelastic scattering spectrum for diffraction states

A strictly quantum mechanical derivation of the energy and parallel momentum resolved scattering spectrum formula that combines the effects of the diffraction of atoms from corrugated surfaces and multiple inelastic scattering by dispersive phonons is presented. The final result is expressed in the compact and numerically tractable form of a Fourier transform of a cumulant expansion in which each term embodies an interplay between the processes of projectile diffraction and multiphonon scattering to all orders in the respective interaction potentials. The Debye-Waller reduction of the intensities of diffraction peaks is explicitly formulated.     

Model calculations of atom-surface scattering

The elastic scattering of light mass, thermal-energy atoms from simple surfaces is investigated. The surface is represented by the model of a single planar square array of hard spheres. The effect of the surface potential well is treated semiclassically by simply shifting the energy of the incident atom ; furthermore a constant imaginary term is added to the energy to account for inelastic scattering and adsorption. As in the multiple scattering formalism of LEED the total scattering matrix of the lattice is expanded in terms of the individual gas atom-surface atom t-matrices. Propagation of the incident atom on the surface is described in terms of a one particle Green's function propagator with complex energy. The terms in the multiple scattering series are summed to all orders, by using standard matrix inversion techniques. The size of the matrix to be inverted limits to ten the total number of phase shifts that are included in the calculation. Thermal effects are included through angle dependent Debye-Waller factors.Model calculations have been performed to study the intensity of the specular and the diffracted beams as a function of the angles of incidence. The importance of surface temperature (introduced by the Debye-Waller factors), the incident energy and the depth of the potential well of the gas-surface interaction are discussed. The main feature of the results is the decrease of the intensity of the specular beam in going from glancing incidence to normal incidence and the presence of structure due to the appearance and disappearance of diffracted beams across the surface. The azimuthal behavior of the specular beam is in agreement with experimental observations.     

Debye-Waller effects in atom-surface scattering

The temperature sensitivity of helium atom reflection from NaF ranges from slight in the quantum regime (long wavelength, near-glancing incidence) to considerable in the classical regime (short wavelength, near-normal incidence). The latter is describable by the Debye-Waller theory only over a limited range of angles. In this range, no Beeby well-depth correction is required. The surface Debye temperature of the NaF is found to be 425 ± 20 K.     

Resonance theory in atom-surface scattering

We study the problem of analytic extension of the resolvent for Hamiltonians arising in scattering of atoms by a quantum surface. We prove that the resolvent extends holomorphically to some regions of the lower half plane with isolated singularities called Landau resonances which are branch points of the resolvent. We study also the effect of impurities on the singularities of the resolvent and show that the presence of impurities adds poles to the Landau resonances.     

Adsorption of oxygen on clean gaas surfaces investigated by ultraviolet photoemission

The adsorption of oxygen at exposures of up to 10⁵ L on differently oriented, ion-bombarded and annealed GaAs surfaces was investigated by UPS. Coverages θ_As for the clean surfaces and oxygen coverages for the oxygen exposed surfaces were estimated by additional SXPS measurements. It was concluded that at small exposures molecular and atomic adsorption are comparable in quantity and that atomic adsorption (oxidation) becomes maximum at θ_As, ≈ 0.2 for (111)Ga and (001) surfaces. Bonding of oxygen molecules should involve Ga sites. Specific bonding of oxygen atoms (O-Ga or O-As) was not indicated by the two stable UPS peaks as they occurred for arsenic coverages from 0 to 0.5 and did not shift their energy positions. They simply indicate the two states of the adsorbate atoms, single and double bonds, to substrate atoms. For the surfaces prepared here, monolayer coverage by oxygen was obtained at about 10¹⁰L. Likewise adsorption of H₂O was investigated.     

Elastic scattering of atoms from surfaces covered with adsorbates: Exact solution for the Einstein-model

The problem of atom scattering from surfaces covered with adsorbates is considered within the Einstein model for the adsorbate phonons. In this case the problem can be solved exactly by the use of a numerical method developed earlier by the present authors. In particular we investigate the temperature dependence of the elastic scattering. It turns out that the deviations from conventional Debye-Waller-factor theory occurring in neutron scattering and Mößbauer effect for single oscillators also show up in atom surface scattering: At higher momentum transfers the elastic scattering probability does not decrease monotonously with temperature but exhibits a maximum at non-zero temperature.     

Elementary resonance processes in atom-surface scattering

In atom-surface scattering, the resonance phenomenon is being very actively investigated. In this work, and within the closecoupling formalism, a systematic classification of the elementary resonance processes is proposed according to the different selective adsorption/desorption mechanisms which are thought to be the most important. In doing so, new mechanisms can be theoretically predicted and experimentally observed. As an extension, the processes of capture, trapping and sticking are also considered, and some operational definitions to calculate their respective probabilities are proposed.     

Phonon coupling in inelastic atom-surface scattering

Inelastic scattering of a thermal He beam from a LiF surface has been observed in terms of velocity and intensity distributions as a function of scattering angle. The results allow a correlation with theoretical predictions assuming single Rayleigh phonon coupling for both phonon creation and annihilation processes. A marked decrease of inelastic intensities with momentum or energy transfer is demonstrated, which depends strongly on the temperature of the scattering surface.     

Multipole contributions to atom-surface scattering potential

We calculate multipole corrections to the standard van der Waals (dipole) potential in atom-surface scattering. The quadru- and octupoles give at most a 15% deeper potential at relevant physisorption distances, and the degree of metal screening is shown to have very little effect on this conclusion.     

The extinction theorem in atom-surface scattering

We present a generalization of the extinction theorem of optics to treat atom-surface scattering. The method, which is valid for a wide class of atom-surface potentials, is not limited to the case of small roughness. Its connections with Rayleigh approximation are discussed.     

On the Debye-Waller factor for atom-surface scattering

The Debye-Waller factor in atom-surface scattering is considered. It is found that the equation suggested by Beeby is valid for soft potentials provided that (1) the attractive portion of the potential is stationary, (2) the repulsive portion of the potentials moves but does not distort, and (3) the effect of trajectories that reflect off the attractive well and multiply scatter from the repulsive wall is negligible.     

Brillouin scattering from supercooled adsorbates

Brillouin scattering is used as a sensitive probe of structural properties of gases adsorbed on porous glass. Evidence is seen for extensive supercooling behavior in both oxygen and nitrogen.     

Interpretation of selective adsorption in atom-surface scattering

The elastic theory for resonant atom-surface scattering is shown to explain simply the occurrence of both minima and maxima at resonance and the strength and shape of the absorption lines, on the assumption that the repulsive part of the potential is of the form V(z?ζ), where ζ is the surface corrugation and V can be regarded as a hard wall at the locus of turning points. Explicit formulae are obtained in the semiclassical limit. For a simple sinusoidal corrugatrion with rectangular symmetry, the signature of an isolated resonance is determined unambiguously by the parity of ¦m¦+¦m' ? m¦?¦m'¦+¦n¦+¦n' ?n¦$\text{}\text{?}$s|n'¦, where (m,n) is the resonant vector and (m',n') the scattering vector, in reciprocal lattice units. The predicted signatures of isolated resonances agree with experiments and more elaborate calculations for the systems He/LiF and He/Graphite. Calculated splittings in the surface band structure also show reasonably good agreement. An alternative formulation of resonant scattering, as suggested by Wolfe and Weare, can be based in an appropriate sorting of successive orders of distorted wave perturbation theory. For small corrugations there is good correspondence between the two approaches.     

Local models for the interaction of adsorbates with surfaces

Local models on the basis of the surface cluster approach have been applied extensively in the study of surface and adsorbate systems. The energetic details of the adsorbate-substrate interaction can be characterized in these models by the constrained space orbital variation (CSOV) method. This method allows a detailed study of adsorbate binding in different surface sites. Further, consequences of the chemisorptive interaction for adsorbate valence photoemission and vibrational properties of adsorbed molecules can be studied.     

Simple approach to refraction effects in atom-surface scattering

A simple method of calculating low energy atom-surface diffraction intensities is presented for the case in which the scattering is dominated by a single rainbow pattern. Good agreement is obtained when these calculations are compared with recent results for the scattering of He by a Pt(997) surface.