Current-induced step bunching at vicinal surfaces during crystal sublimation

The limits of the applicability of the generalized BCF model of electromigration-affected sublimation are discussed in detail. Only in surface-diffusion limited sublimation are the steps boundaries, effectively separating the transport processes at neighbouring terraces. In the opposite case of high surface mobility and slow exchange between the 2D gas of mobile adatoms and the crystal, many atoms simply cross the steps, spending some time in an intermediate state of adsorption at the step edge, but never becoming “crystal atoms”. In this regime of sublimation the steps are no longer boundaries. Therefore, one cannot analyze diffusion and desorption on one separate terrace (as in the generalized BCF model) since the coupling between the adatom concentration fields on neighbouring terraces cannot be neglected. A relevant model for this regime of electromigration-affected sublimation is proposed in this paper. This model manifests step buching at the step-up direction of the adatom electromigration. The central result of the mathematical treatment is the formula (x₂−x₁)^{n + 2}=(4kT/F) l^{n + 1}₀, relating the interstep distance x₂−x₁ in a stable pair of steps with the electromigration inducing force F. Here n and l₀ determine the form and the magnitude of the step-step interaction. The formula obtained for x₂−x₁ provides a gound to evaluate n and l₀ from a set of experimental data on sublimation by combined DC and radiative heating.     

Adatom ascending at step edges and faceting on fcc metal (110) surfaces

Using first-principles total-energy calculations, we show that an adatom can easily climb up at monatomic-layer-high steps on several representative fcc metal (110) surfaces via a place exchange mechanism. Inclusion of such novel adatom ascending processes in kinetic Monte Carlo simulations of Al(110) homoepitaxy as a prototypical model system can lead to the existence of an intriguing faceting instability, whose dynamical evolution and kinetic nature are explored in comparison with experimental observations.     

Scattering of surface states at step edges in nanostripe arrays

Surface states of noble metal surfaces split into Ag-like and Cu-like subbands in stepped Ag/Cu nanostripe arrays. The latter self-assemble by depositing Ag on vicinal Cu(111). Ag-like states scatter at nude step edges in Ag stripes, leading to umklapp bands, quantum size effects, and peak broadening. By contrast, Ag stripe boundaries become transparent to Cu-like states, which display band dispersion as in flat Cu(111). We find a linear relationship between the quantum size shift and peak broadening that applies in a variety of stepped systems, revealing the complex nature of step barrier potentials.     

Curvature forces at crystal surfaces

The influence on thermal roughening of interactions beyond nearest neighbor sites on a surface is examined. In addition to the classical gradient term a novel dependence upon curvature appears in the surface energy. For interactions oscillatory with distance the curvature term can be dominant. The short range correlation function is then linear, it crosses over to the usual logarithmic behavior at large distances. This formalism can explain experimental results in disagreement with existing models. The non-trivial influence of finite size effects in anisotropic systems is also studied.     

NMR at single crystal surfaces

15 sites on 1 cm². To overcome this for the important class of alkali adsorbates on metals and semiconductors, two methods are presented. Common to both is the preparation of a highly nuclear spin-polarized atomic beam of ⁶Li in the one case and ⁸Li in the other. The latter isotope is radioactive and undergoes a β-decay with a half-life of 0.84 s. Li adsorbed on the close-packed Ru(001) surface is investigated. The longitudinal relaxation time, T₁, is the main observable and is used to deduce the local electronic density of states [LDOS(E_F,r=0)] and Li diffusion barriers. The second experiment uses ⁶Li as an adsorbate, also studied on Ru(001). The nuclear polarization is measured by beam foil spectroscopy. A novel particle detected (photon counting) Fourier transform NMR technique is demonstrated. This is done by observing the time-dependent flux of circularly polarized light emitted behind the foil after a 90° pulse has been employed at the surface. Electric field gradients and transverse relaxation times, T₂, are thus determined. A large difference between T₁ and T₂ is traced to the dimensionality of the system. Received: 21 March 1997/Accepted: 12 August 1997     

Force constants at crystal surfaces

In the vicinity of surfaces the coupling constants for lattice vibrations are changed. There have been some attempts to calculate these changes, but apparently there are no numerical results. We propose a new method for the calculation of force constant changes near surfaces, starting with the electronic correlation function. A simple model is discussed which allows for some numerical results.     

Coarsening dynamics at unstable crystal surfaces

In this paper we focus on crystal surfaces led out of equilibrium by a growth or erosion process. As a consequence of that, the surface may undergo morphological instabilities and develop a distinct structure: undulations, mounds or pyramids, bunches of steps, ripples. The typical size of the emergent pattern may be fixed or it may increase over time through a coarsening process that in turn may last forever or it may be interrupted at some relevant length scale. We study dynamics in three different cases, stressing the main physical ingredients and the main features of coarsening: a kinetic instability, an energetic instability, and an athermal instability.     

Electron attenuation anisotropy at crystal surfaces from LEED

Dynamical theory of electron scattering is used to describe the electron transport in the surface regions of crystals. The angle resolved attenuation length of electrons is derived from the transmitted LEED electron current decay. Electron attenuation length energy dependence and anisotropy in polar angle are found for crystalline Cu(1 1 1) for two high symmetry azimuths. Pronounced anisotropy in polar angle distributions of attenuation lengths is found to be in qualitative agreement with the results obtained from the photoelectron diffraction. Comparison with the attenuation lengths obtained from semiclassical simulations for amorphous copper is given. This comparison demonstrates that simple transfers of the smoothly behaving surface sensitivity from amorphous materials oversimplifies the electron attenuation process and can lead to incorrect results in quantitative analyses of crystalline surfaces.     

非常偏振光在单轴晶体表面的全反射分析

利用透射波函数和由菲涅尔公式求解反射相位差并对其求导的方法,分析了非常偏振光在单轴晶体表面发生的全反射现象,求解出晶体光轴在入射面内时,非常偏振光从各向同性介质入射到晶体和从晶体出射到各向同性介质两种情况的隐失波穿透深度和Goos-Hnchen位移的一般表达式。通过计算机模拟给出了单轴晶体为方解石和水晶情况时的穿透深度和Goos-Hnchen位移图像。结果表明,对于不同的晶体,光轴的取向对穿透深度和Goos-Hnchen位移的影响是明显不同的,若选取合适的晶体、光轴取向和入射角,可以得到较大的隐失波穿透深度和Goos-Hnchen位移。     

The structure and dynamics of crystal surfaces at high temperatures

After a brief review of the historical evolution of the understanding of crystal surfaces at high temperatures in general the subject is narrowed down to fcc metal surfaces, in particular to (110) surfaces. The recent work on these surfaces is reviewed, with emphasis on Pb, and the interpretation of the results in terms of various kinds of disordering such as surface melting, surface roughening, anharmonic vibrations and other processes is critically examined. While some of the results are now well established, others are contradictory, so that no unambiguous picture of metal surfaces at high temperatures can be given at present.     

Anisotropy of the angle resolved electron attenuation at crystal surfaces

Photoemission multiple scattering theory is used to describe the electron transport in the surface region of a crystal. Intensities of photoemission from core levels of atoms situated in subsurface atomic layers are calculated as a function of the emitter distance from the surface. The electron angle resolved attenuation length (ARAL) is extracted from the exponential fitting of the intensity decays of photoemission into different directions. Substantial anisotropy of the electron ARAL is found for the Cu(1 1 1) surface in Mg Kα photoexcitation of Cu 2p_3/2 levels and correlated with the orientation of highly packed atomic rows. Enhanced photoemission contributions from specific subsurface layers, caused by electron forward focusing effects, are reported.