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.     

Adsorption and diffusion of Si adatom near single-layer steps on Si surface

By use of the empirical tight-binding （ETB） method, the adsorption and diffusion behaviours ot single sllmon adatom on the reconstructed Si（100） surface with single-layer steps are simulated. The adsorption energies around the SA step, nonrebonded SB step, rebonded SB step, and rough SB step with a kink structure are specially mapped out in this paper, from which the favourable binding sites and several possible diffusion paths are achieved. Because of the rebonded and kink structures, the SB step is more ~uitable for the attachment of Si adatom than the SA step or defective surface.     

Continuum model for low temperature relaxation of crystal steps

High and low temperature relaxation of crystal steps are described in a unified picture, using a continuum model based on a modified expression of the step-free energy. Results are in agreement with experiments and Monte Carlo simulations of step fluctuations and monolayer cluster diffusion and relaxation. In an extended model where mass exchange with neighboring terraces is allowed, step transparency and a low temperature regime for unstable step meandering are found.     

Finding polymorphic structures during vicinal surface growth

A hybrid scheme is developed to describe vicinal surface growth during epitaxy on two different time and length scales. For this purpose this algorithm combines two modules based on a continuum and an atomistic approach. The continuum module is realized by a phase-field-model which traces back to the Burton–Cabrera–Frank theory, the atomistic module is based on the anisotropic Ising model which is mapped onto a lattice-gas model. The latter provides thermal density fluctuations resulting in adatom clustering. With increasing temperature the probability for island nucleation on the terraces decreases according to 1-p where p is an Arrhenius-type activation probability which prevents clusters from becoming islands. Within this framework it is possible to find the transition from a rough surface at low temperatures to an evenly stepped surface at high temperatures where slight step meandering is observed. Furthermore two competing mechanisms of step bunching are investigated within this scale bridging algorithm: alternating anisotropic diffusion and different Ehrlich–Schwoebel barriers at the step edges. It is shown that a simulation of step bunching displaying the full variety of phenomena observed in experiments can only be achieved by the consideration of different time and length scales.     

Impact of the growth on the stability–instability transition at Si (111) during step bunching induced by electromigration

The central result of this work is the definite proof that the mechanisms of the direct current induced step bunching in the middle and high temperature domains are different. We used the recently developed technique for reflection electron microscopy (REM) observation of Si surfaces during equilibrium and during crystal growth to document the impact of the growth on the process of step bunching induced by direct current heating of an Si crystal. We found completely different effects of crystal growth on the stability of the vicinal surfaces in the two temperature domains 1160–1240°C and 1260–1320°C. In the high temperature domain step bunching takes place at step-down direction of the electric current during sublimation, equilibrium and growth; whereas in the 1160–1240°C domain bunching takes place at step-up current during sublimation and at step-down current during growth. These findings support the concept of local mass transport in the high temperature domain — the surface migration of adatoms is effectively interrupted at each step by a high rate exchange between the adlayer and the crystal phase. At 1160–1240°C the mass transport is global — adatoms easily cross the steps without taking part in the crystal–adlayer exchange. Since earlier studies of other researchers support the concept of local mass transport in the low temperature domain, 900–1050°C, a difficult question arises — why do the properties of the steps, with respect to the mass transport over the crystal surface, have a temperature dependence which is not monotonous? To explain the transition from local mass transport in the low temperature domain to global mass transport in the middle temperature domain we advance a hypothesis for a transition from a low temperature state of adsorption (Takayanagi-like adatoms, existing above the (7×7)↔(1×1) transition) to a high temperature state of adsorption (adatom with three dangling bonds) with much lower activation energy for desorption.     

A two-region diffusion model for current-induced instabilities of step patterns on vicinal Si(1 1 1) surfaces

We study current-induced step bunching and wandering instabilities with subsequent pattern formations on vicinal surfaces. A novel two-region diffusion model is developed, where we assume that there are different diffusion rates on terraces and in a small region around a step, generally arising from local differences in surface reconstruction. We determine the steady state solutions for a uniform train of straight steps, from which step bunching and in-phase wandering instabilities are deduced. The physically suggestive parameters of the two-region model are then mapped to the effective parameters in the usual sharp step models. Interestingly, a negative kinetic coefficient results when the diffusion in the step region is faster than on terraces. A consistent physical picture of current-induced instabilities on Si(1 1 1) is suggested based on the results of linear stability analysis. In this picture the step wandering instability is driven by step edge diffusion and is not of the Mullins–Sekerka type. Step bunching and wandering patterns at longer times are determined numerically by solving a set of coupled equations relating the velocity of a step to local properties of the step and its neighbors. We use a geometric representation of the step to derive a nonlinear evolution equation describing step wandering, which can explain experimental results where the peaks of the wandering steps align with the direction of the driving field.     

Steps,facets and nanostructures: investigations of Cu (11n) surfaces

Step structure and dynamics and adsorbate-induced reconstruction of stepped surfaces are useful features for investigating fundamental surface phenomena and their practical consequences. In this respect, vicinal Cu (11n) surfaces with n=3, 5 and 9 were studied by scanning tunneling microscopy (STM) at 300 K. While the regular monoatomic steps fluctuate for Cu (119), they are apparently stabilized for n≤5 by their strong repulsive interaction and this leads to a very low kink activity. In addition to the regular steps, the formation of double steps was observed as a particular phenomenon on those surfaces. These double steps determine the dynamic behavior at room temperature. By applying existing models for the fluctuations of the step positions in space and time, the formation energy for kinks at these double steps was determined to be 0.16 eV for Cu (115). According to this evaluation, diffusion along step edges is the dominating mass-transport mechanism. A model for the structure of the double steps and for the atomic displacement processes necessary for kink migration at these steps is presented. Complete faceting is observed for these surfaces upon oxygen adsorption at elevated temperatures (around 500 K) and was studied in detail for n=5 and 9. Both surfaces reconstruct into two types of {104} facets and a third facet, the orientation of which is determined by the macroscopic crystal orientation. The facet size is governed by the formation kinetics and can be controlled by varying the crystal temperature or the oxygen partial pressure. The formation kinetics is discussed as a nucleation and growth process and the relevant parameters are given. Facets within a range of size between 5 nm and 100 nm could thus be produced. They remained stable at ambient atmosphere, up to about 620 K, and also if covered by additional metal layers such as Ni. Received: 1 June 2001 / Accepted: 23 July 2001 / Published online: 3 April 2002     

The return of the kink

We present a simple theory for the statistics of subsequent passages of kinks at a particular position along a fluctuating step on a crystal surface. Two situations are treated, namely one where the waiting time until the next passage is measured starting from the previous passage of a kink at the observation point, and one where the waiting time is measured starting from a random instant in time. In both cases the waiting time distribution is shown not to obey simple Poisson statistics. Monte Carlo simulations of kink motion show that Poisson statistics emerges for longer waiting times only when the creation and annihilation of kink-antikink pairs are explicitly included. Together, the theory and simulations provide an alternative interpretation of experimental results obtained by Giesen et al. with Scanning Tunneling Microscopy [M. Giesen-Seibert, H. Ibach, Surf. Sci. 316 (1994) 205].     

The strictly attractive 1/l interaction between steps of crystal surfaces

Using SSH model for the step structure of crystal surfaces, a strictly attractive 1/l² energy, which originates from the quantum effect of surface atoms’ collective relaxation, was obtained for the first time and shown to generally exist between steps. The repulsive 1/l step interaction was confirmed to come from the surface electrons’ interaction. These results are crucial for understanding the dynamics of steps and for reconciling the dilemma associated with the equilibrium crystal shape of gold crystallites.     

Effect of reduced cooperativity on growth-induced polarity formation: a comparison between different growth models

We investigate the influence of the growth process on macroscopic polarity formation in molecular crystals consisting of polar molecules with two directional states. Specifically, layer-by-layer growth is compared with growth along surface steps, and growth at kink sites. Idealized models for these growth processes are presented, being characterized by the thermal equilibrium formation of a domain of molecules on the surface, ranging from an entire adlayer to a single molecule only (reduced cooperativity). Longitudinal and lateral Ising-type nearest neighbour interactions are taken into account. Formerly attached and thermalized molecules are kept frozen upon growth and therefore, bulk polarity results. Growth models are studied by means of Monte Carlo simulations. Results show that a reduced cooperativity between neighbouring molecules on the crystal surface increases the probability of orientational disorder. However, in the asymptotic limit of infinite growth and for sufficiently strong longitudinal couplings, phenomenologically, evolution of polarity for step and kink growth remains the same as for layer-by-layer growth, being mainly a thermodynamically driven process. Despite their strong out-of-equilibrium character, step and kink growth processes feature a continuous phase transition as layer-by-layer growth and are reasonably well described by an effective lateral coordination number within a mean field approach.     

Initial surface roughening in Ge/Si(001) heteroepitaxy driven by step-vacancy line interaction

The initial surface roughening during Ge epitaxy on Si(001) is shown to arise from an effective repulsion between S(A) surface steps and dimer vacancy lines (VLs). This step-VL interaction gradually inactivates a substantial fraction of adatom attachment sites at the growth front, causing a rapid increase in the rate of two-dimensional island nucleation. The mutual repulsion hinders the crossing of S(A) surface steps over VLs in the second layer, thus organizing the developing surface roughness into a periodic array of anisotropic 2D terraces. Isolated (105) facets forming at specific sites on this ordered template mediate the assembly of first 3D Ge islands.     

Enhanced terrace stability for preparation of step-free Si(001)-(2 x 1) surfaces

We show that depositing Si while annealing patterned Si(001)-(2 x 1) substrates at sublimation temperatures enhances terrace stability, permitting larger step-free areas to be produced in a given time than possible by annealing alone. We confirm this enhanced terrace stability using real-time low-energy electron microscopy observations, and quantitative microscopic modeling of step dynamics. Our measurements can be used to estimate the lateral variation in adatom concentration across large terraces, and to estimate an adatom diffusion length lambda approximately 10-30 microm at 1000 degrees C.     

Temperature-driven change in the unstable growth mode on patterned GaAs(001)

We observe a dramatic change in the unstable growth mode during GaAs molecular beam epitaxy on patterned GaAs(001) as the temperature is lowered through approximately 540 degrees C, roughly coincident with the preroughening temperature. Observations of the As2 flux dependence, however, rule out thermodynamic preroughening as driving the growth mode change. Similar observations rule out the change in surface reconstruction as the cause. Instead, we find evidence that the change in the unstable growth mode can be explained by a competition between the decreased adatom collection rate on small terraces and a small anisotropic barrier to adatom diffusion downward across step bunches.     

Glancing-angle ion enhanced surface diffusion on gaAs(001) during molecular beam epitaxy

We describe the effects of glancing incidence 3-4 keV Ar ion bombardment on homoepitaxial growth on vicinal GaAs(001). The average adatom lifetime on surface terraces, measured during growth using specular ion scattering, decreased monotonically with increasing ion current density. The results indicated that surface diffusivity was increased by the ions. The ion beam also suppressed growth oscillations and decreased the film surface roughness. This indicates a change from two-dimensional island nucleation to step-flow growth due to increased adatom surface diffusivity. A simple model, involving direct momentum transfer from ions to adatoms, is shown to be consistent with the measured enhanced diffusion.     

Localized spin modes on the insulating antiferromagnetic stepped surface model

We present a numerical method to calculate the spin fluctuation dynamics on a stepped surface. The model discussed here consists of an extended antiferromagnetic surface step at the surface boundary of an insulating antiferromagnetic substrate. The stepped surface is formed by two straight steps dropped randomly and the spins moments of the steps and the substrate are considered as local with no electronic effects. The full magnetic problem arising from the absence of translational symmetry due to the presence of a magnetic surface and steps is considered and studied. The calculations concern in particular the energies of localized spin-wave modes near the surface steps and employ the matching procedure in the random-phase approximation and mean field approximation. Only the nearest-neighbor exchange interactions are considered between the spins in the model. The analytical formalism presented here is adapted from an earlier work on the vibrational spectra of two isolated steps, a structure that can be considered as a low dimensional system and solved for the three dimensional evanescent crystal spin field in the bulk and the surface domains around the steps. This spin field arises from the breakdown of the magnetic translation symmetry of the system. The results are used to calculate the spin mode energies associated with the steps and surface terraces. We show the presence of localized acoustic and optical spin wave modes propagating along the surface and the steps as well as the interface surface-steps, their fields are also described as evanescent in the plane normal to the surface step layers and depend on the nature of the exchange interaction near the steps.Received: 9 March 2004, Published online: 30 September 2004PACS: 75.70.Ak Magnetic properties of monolayers and thin films - 75.50.Ee Antiferromagnetics - 75.30.Ds Spin waves - 76.70.Hb Optically detected magnetic resonance (ODMR)     

Crystallographic anisotropy in chemisorption: Nitrogen on tungsten single crystal planes

A molecular beam technique for the determination of sticking probabilities and surface coverages was used in earlier work to investigate the adsorption of nitrogen on tungsten {110}, {111} and {100} single crystal planes. In the present paper these studies have been extended to the {310}, {320} and {411} planes. Absolute sticking probabilities and adatom surface coverages are reported for crystal temperatures between 90 K and 960 K. Crystallographic anisotropy in this system is exemplified by zero coverage sticking probabilities with the crystal at room temperature: {110}, 1̃0^?2; {111}, 0.08; {411}, 0.4; {100}, 0.59; {310}, 0.72; {320}, 0.73. Results for planes on the [001] zone are quantitatively described by a general model developed for adsorption on stepped planes as an extension to the precursor-state order-disorder model for adsorption kinetics of King and Wells. It is shown that nitrogen dissociation only takes place at vacant pairs of {100} sites, but that subsequently the chemisorbed adatoms so formed may migrate out onto {110} terraces. The results are critically analysed in terms of the available LEED and work function data for nitrogen on tungsten single crystal planes, and the general model developed by Adams and Germer.     

Exchange processes in interlayer diffusion – kinks, corners and the growth mode

Interlayer diffusion, i.e. mass transport between different terraces, is known to be an essential process for obtaining layer-by-layer growth, avoiding formation of three-dimensional (3D) islands when growing thin films. We present experimental results for the growth of cobalt on Pt (111), which demonstrate the importance of kinks and corners for interlayer diffusion. We show that Co grows two-dimensionally as long as strain caused by the Pt-Co interface keeps the step edges rough, with a high kink density, and then transforms to 3D growth with straight steps. The results for growth with adsorbed carbon monoxide show that CO acts as a surfactant, causing two-dimensional growth unless heterogeneous nucleation occurs. Again, this process is related to roughening of the steps, being a new mechanism for the action of a surfactant. A scanning tunneling microscopy study at the atomic scale confirms the fact that step descent happens only at kinks and (concave) corners, and in conjunction with simulations allows us to identify some of the relevant atomic-exchange processes. We finally argue that the dependence of the growth mode on the step morphology, together with straightening of the steps by step–step interaction, can lead to an instability of the growth mode. Received: 27 March 2000 / Accepted: 4 September 2000 / Published online: 7 March 2001     

Near molecular-scale growth of natural minerals: Experimental methods and errors in length-dependent step speeds with scanning probe microscopy

Experimental observation of step (i.e., a linear discontinuity in a surface) growth on calcium carbonate and barium sulfate surfaces was performed using in situ scanning probe microscopy (SPM) in aqueous solutions. Step speeds at very short step lengths (<300 nm) were found to increase with step length, but scatter in the data precluded comparison of different theoretical models with regard to the experimental data. Analysis of experimental errors revealed that the data scatter was not unusual and further suggested that significant experimental bias in the determination of step properties such as the step free energy and kinetics of kink propagation and nucleation are introduced if the instrument bandwidth is not appropriate for the specific dynamics of the step. In light of step growth models based on either equilibrium assumptions or non-equilibrium assumptions, these biases tend to favor one model over the other.     

Adatom mobility on the surface planes of a simple metal

An approach using the Density Functional Approximation, which had in an earlier paper been applied to the binding of an adatom to a jellium metal (r_s = 4a₀), has been extended to a partially structured metal surface by introducing a layer of surface atoms to replace an equivalent layer of jellium. The model has been used to estimate the adatom motion energies over several quite close packed planes for a simple surface. An important preliminary step was to determine the general electron density contours for each surface by a simple variational method. The ensuing shielding charge distributions have an important bearing on the adatom motion energy. Adatom energies were calculated at three positions: (1) A above a surface atom, (2) B above a bridge position between two surface atoms and (3) C above a central position between three or four neighboring atoms. The motion energy was taken to be E_B ? E_C. As might have been expected this quantity was larger for the less closely packed planes, although it was always quite small due to the nature of the metal — large r_S, small ion core and typical s-p binding. To a rather surprising degree the strength of the shielding charge, the energies and the positions of the adatoms proved to be quite smooth functions of a parameter chosen to measure the close packing of the surface, namely the square of the interplanar distance divided by the surface area per atom.     

KDP晶体台阶生长动力学的激光干涉实验研究

采用迈克尔逊干涉技术 ,通过测量KDP晶体生长的法向速率和台阶斜率来研究其台阶生长的动力学系数、台阶自由能、溶质在边界层内的扩散特征以及激发晶体生长台阶的位错活性 .实验表明 ,KDP中不同活性位错的台阶动力学系数差异较大 ,例如高活性和低活性台阶动力学系数分别为 10 .3× 10 -2 和 5 .2 1× 10 -2 cm/s,位错源在晶体表面的形状、面积的变化 ,以及Burgers矢量的变化是造成晶体生长动力学测量数据重复性差的主要原因