Stoyan Stoyanov

Mechanisms of epitaxial growth

Abstract ‘Epitaxy’ means order in the relative orientation of identical crystals nucleated and grown on a large single-crystal face. Every crystal of the deposited material is oriented in such a way that there is coincidence of some vectors of its reciprocal lattice with vectors of the reciprocal lattice of the substrate surface. Depending on the length of the coincident vectors, one distinguishes between epitaxy of first order (coincidence of basis vectors), second order, and so on. In this paper, selected epitaxial systems (metals on metal, semiconductor and insulator substrates, semiconductors on semiconductors) are used to illustrate the influence of the lattice mismatch, interatomic forces and experimental parameters on the mode of film growth. The interaction across the epitaxial interface induces homogeneous strain in ultra-thin films and inhomogeneous strain in thicker deposits. The periodic strain is usually described in terms of misfit dislocations or static distortion waves, which are mobile at...

Classical and atomistic models of electrolytic nucleation: Comparison with experimental data

Abstract Some recent experimental results on the steady state nucleation rate have been analyzed in detail. It has been established that the qualitative agreement between the experimental data and either the classical or the atomistic model cannot be considered as a reliable criterion for the validity of either of the two theoretical concepts. The quantitative treatment of the experimental data indicates the use of the atomistic model of nucleation to be more correct in the cases under consideration. Nevertheless the classical theory equations appear to be applicable, at least formally, to an interpretation of the experimental results.

On some probabilistic aspects of the nucleation process

Abstract Nucleation is a random phenomenon. The analysis of the expressions giving the time-dependence of the probability of formation of at least one (P⩾1), two (P⩾2), etc, nuclei makes it possible to assess the role of transient effects in nucleation kinetics as well as to evaluate the parameters of the process. Experiments on the electrolytic nucleation of mercury and cadmium on platinum are carried out by means of the double pulse potentiostatic technique ensuring reproducible working conditions and a precise control of the factors governing the deposition process. It is shown that the distribution of the number of the deposited nuclei as well as the P⩾m(t) plots (t = time) obtained are in good agreement with formal probabilistic considerations. The P⩾1(t) functions are S-shaped over the whole interval of variation of the overvoltage (equivalent to the supersaturation) which is an important indication of the non-steady state character of the process of electrolytic nucleation within the studied time intervals. A semianalytical procedure is developed to calculate stationary nucleation rates and induction times (in the sense of Zeldovich) from the experimental results. The outlined probabilistic approach may prove very useful in situations in which the time-dependence of the mean number of the nuclei formed at constant supersaturation is not available experimentally.

On the theory of epitaxial growth

Abstract It is well known that the three modes of growth (layer, island and Stranski-Krastanov growth) correspond to three qualitatively different types of the μ(n) dependence — the chemical potential as a function of the film thickness (in monolayers). This paper shows that μ(n) is not a universal function of the misfit between the crystal lattices of the film and the substrate. The physical ground for the μ(n) dependence is the substrate-induced strain of the film which is orientation dependent. Hence, the problem of calculating the μ(n) dependence cannot be separated from the problem of the epitaxial orientation of the film. The treatment is based on the expression U = φ0 + ΣGΣG′φGδG,G′ for the average energy of interaction between the substrate and an unmodulated monolayer. Here φG are Fourier coefficients of the substrate-deposit interaction potential, { G } and { G′ } are the sets of reciprocal lattice vectors of the substrate surface and the monolayer. A classification scheme of epitaxy is proposed relating the order of epitaxy to the hierarchy of the coinciding reciprocal lattice vectors — first-order epitaxy occurs when the coincidence involves basis vectors, higher-order epitaxy is connected to coincidence of longer vectors. High-order epitaxy can be expected only when it requires negligible strain and, therefore, negligible strain energy. In some deposit-substrate pairs the first-order epitaxy could only be thermodynamically favoured for mono- or bi-layer film, because of the strain energy, which increases with the film thickness. If a minimum free energy for thicker films is provided by higher-order epitaxy then a rotation must occur during film growth. This phenomenon could be expected, for instance, in a deposition of Pd, Au and Ni on (110) W under high-temperature annealing of a film of appropriate thickness. The transition from first-order epitaxy to higher-order epitaxy during film growth leads to a strong decrease of the strain energy and, thererefore, to a strong decrease of the chemical potential.

A direction of easy diffusion on the (001) face of Ge, Si and III-V semiconductor crystals — How to verify its existence?

Abstract The four-fold symmetry breaking at the (001) face of the semiconductor crystals results in a non-equivalence of the surface diffusion in [110] and [110] directions. Appropriate RHEED experiments are proposed and theoretical expressions for their interpretation are derived in order to quantitatively study the anisotropy of the surface diffusion. A dimerization of the monoatomic steps (running in [110] direction) during the growth of vicinal faces of Si and Ge is predicted to occur as a consequence of the existence of an easy diffusion direction on (001) surface.

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=(4kTF) ln + 10, 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.

Scaling properties of step bunches induced by sublimation and related mechanisms

This work provides a ground for a quantitative interpretation of experiments on step bunching during sublimation of crystals with a pronounced Ehrlich-Schwoebel (ES) barrier in the regime of weak desorption. A strong step bunching instability takes place when the kinetic length is larger than the average distance between the steps on the vicinal surface. In the opposite limit the instability is weak and step bunching can occur only when the magnitude of step-step repulsion is small. The central result are power law relations of the between the width, the height, and the minimum interstep distance of a bunch. These relations are obtained from a continuum evolution equation for the surface profile, which is derived from the discrete step dynamical equations for. The analysis of the continuum equation reveals the existence of two types of stationary bunch profiles with different scaling properties. Through a mathematical equivalence on the level of the discrete step equations as well as on the continuum level, our results carry over to the problems of step bunching induced by growth with a strong inverse ES effect, and by electromigration in the attachment/detachment limited regime. Thus our work provides support for the existence of universality classes of step bunching instabilities [A. Pimpinelli et al., Phys. Rev. Lett. 88, 206103 (2002)], but some aspects of the universality scenario need to be revised.

Layer growth of epitaxial films and superlattices

Abstract Thermodynamic analysis of a film consisting of three-dimensional crystals that coexist with a monolayer on a strongly attractive substrate results in a simple expression for the compression in the monolayer and an estimation of the related enhancement of its melting temperature. A kinetic criterion for the stability of layer growth is derived by considering the surface diffusion of adatoms from the homogeneously strained to unstrained parts of the film. An exactly solvable model for layer-by-layer growth is proposed and the amplitude of step density oscillations is found as a function of the substrate temperature and the deposition rate. The results are compared with experimental data for the growth mode of Ge x Si 1−x on silicon as well as with the RHEED intensity oscillations during molecular beam epitaxy of Si.

Non-steady state effects in MBE: oscillations of the step density at the crystal surface

Abstract An analysis of the microscopic processes (surface diffusion, nucleation) at the crystal surface during MBE provides a comparatively simple expression for the temperature dependence of the amplitude of the step density oscillations at a two-level and a three-level growth front. The time evolution of the terrace areas (in the case of complete condensation) is found to be temperature independent which leads to a temperature independent amplitude of the RHEED intensity oscillations when they originate from the interference of beams scattered by different terraces. The evolution of the growth front (the increase of its thickness) is found to depend only on the number of atoms in the critical nucleus. This provides the underlying physics for an understanding of the damping of the oscillations. When the RHEED intensity changes originate from diffuse scattering from the step edges, the oscillation amplitudes observed at different temperatures are expected to be essentially different, but the damped oscillations should coincide after appropriate scaling.

Nucleation on point defects

The real nucleation rate is practically an unobservable quantity because of the small size of the nuclei. It is the maximum slope of the Nv(t) curve that has been interpreted as the nucleation rate. In some cases, however, the dependence of the visible cluster density Nv on the deposition time t reflects cluster growth processes rather than nucleation. A theory describing observable quantities has been developed. It was shown that the random location of point defects is the most important factor in determining the cluster size distribution and the character of the Nv(t) dependence.