Ivan Markov

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...

Screening action and growth kinetics of electrodeposited mercury droplets

Abstract Electrolytically growing new phase centres exert a certain screening action in their near vicinity manifested in the formation of spatial zones around them where the nucleation process is practically arrested. This phenomenon, resembling similar effects in non-electrical crystallization processes, is due to the redistribution of the ohmic drop within the solution during the electrodeposition process. A triple-pulse technique is developed to visualize the screening action of single mercury droplets deposited on to platinum electrodes from Hg 2 (NO 3 ) 2 solution and to measure the screening zone radii as a function of the growth parameters. Detailed measurements pertaining to the growth kinetics of mercury are presented showing that the electrolytic growth under the experimental conditions employed is governed by the ohmic resistance of the solution. A quantitative treatment of the experimental data is outlined based on an expression for the screening zone radius derived. The significance of the results obtained for the kinetics of the overall electrodeposition process prior to the formation of continuous layers is discussed.

Nucleation on active centres: I. General theory

Abstract The process of nucleation in a supersaturated system containing a finite number of active centres of various potencies with respect to the nucleus formation is studied. The effect of screening zones appearing around the growing nuclei in which practically no nucleus formation occurs is accounted for. General equations are derived for the time dependence of the number of nuclei in both cases of discrete and continuous centre activity distribution. It is shown that the results of Kolmogoroff, Avrami and Kaischew and Mutaftschiev can be obtained as limiting cases of the theory presented.

Saturation nucleus density in the electrodeposition of metals onto inert electrodes II. Experimental

Abstract The number of nuclei grown as a function of time, overpotential and eletrolyte concentration have been investigated experimentally during the electrodeposition of Hg from an aqueous solution of Hg 2 (NO 3 ) 2 onto a plane structureless platinum electrode and a hemispherical single-crystal electrode. It has been established that: (i) at constant overpotential after an induction period the number of nuclei grows linearly with time and reaches a saturation value after a sufficient time has elapsed; (ii) the higher the overpotential the shorter the induction period and the higher both the steady state nucleation rate and the saturation nucleus density; (iii) the smaller the electrolyte concentration the lower the nucleation rate, the longer the induction period and the larger the saturation nucleus density. It is shown that the time dependence of the number of nuclei can be described by an equation derived by assuming that nuclei are formed on active energetically preferred sites on the electrode surface, and that the saturation nucleus density is determined by the deactivation of the active centres by overlapping nucleation exclusion zones. Experimental data confirming the idea of Mutaftschiew and Toschev that the active centres are defects in the oxide layer covering the platinum are presented.

The influence of surface diffusion processes on the kinetics of heterogeneous nucleation

Abstract The screening effect of the process of surface diffusion of adatoms towards the growing nuclei on the kinetics of heterogeneous nucleation is studied. A zone around every growing nucleus is formed, in which the probability of nucleation is practically zero. The saturation nucleus density depends on the correlation between the nucleation and the zone spreading rates. The analysis of the diffusion processes onto the substrate in both cases of sufficiently low and high substrate temperatures permits the derivation of the definitive equality which determines the radius of the diffusion zone. A solution of the problem treating the time dependence of the number of nuclei is suggested for the case of sufficiently high substrate temperatures. The form of the results permits a direct experimental determination of the spreading law of diffusion zones, the surface diffusion coefficient as well as the nucleation rate as a function of the nucleation parameters.

Coherent Stranski-Krastanov growth in 1¿1 dimensions with anharmonic interactions: An equilibrium study

The formation of coherently strained three-dimensional islands on top of the wetting layer in Stranski-Krastanov mode of growth is considered in a model in 1+1 dimensions accounting for the anharmonicity and non-convexity of the real interatomic forces. It is shown that coherent 3D islands can be expected to form in compressed rather than in expanded overlayers beyond a critical lattice misfit. In the latter case the classical Stranski-Krastanov growth is expected to occur because the misfit dislocations can become energetically favored at smaller island sizes. The thermodynamic reason for coherent 3D islanding is the incomplete wetting owing to the weaker adhesion of the edge atoms. Monolayer height islands with a critical size appear as necessary precursors of the 3D islands. The latter explains the experimentally observed narrow size distribution of the 3D islands. The 2D-3D transformation takes place by consecutive rearrangements of mono- to bilayer, bi- to trilayer islands, etc., after exceeding the corresponding critical sizes. The rearrangements are initiated by nucleation events each next one requiring to overcome a lower energetic barrier. The model is in good qualitative agreement with available experimental observations.

Saturation nucleus density in the electrodeposition of metals onto inert electrodes I. Theory

Abstract On the basis of the general theory of the kinetics of nucleation at active centres developed by Markov and Kashchiev, the particular case of the electrolytic formation of metallic nuclei under potentiostatic conditions on the surface of inert ideally polarisable electrodes is considered. The influence of the electrolyte concentration on the induction period, the steady state nucleation rate and the saturation nucleus density is analysed in the two timiting cases where the saturation nucleus density is determined by (i) the number of energetically preferred active centres on the electrode surface and (ii) the overlapping of nucleation exclusion zones.

The effect of anharmonicity in epitaxial interfaces: II. Equilibrium structure of thin epitaxial films

Abstract The influence-of anharmonicity on the equilibrium structure of thin epitaxial films is studied in the framework of the theoretical model, introduced in Part I. Using the conventional Frank and van der Merwe model as a reference basis, it is shown that allowing for anharmonicity of the interatomic forces leads to qualitatively new effects, such as: (i) a significant asymmetry of dislocation length, strains in the deposit, activation energy for surface diffusion of epitaxial islands with respect to the sign of natural misfit between substrate and deposit; (ii) a split of the critical stability limits for pseudomorphic growth as well as for spontaneous generation of misfit dislocations whereby the limits corresponding to negative misfit rapidly increase whereas the positive misfit limits decrease (in absolute terms) with growing degree of anharmonicity. Experimental evidence, concerning the pseudomorphic growth of metals, semiconductors and ferromagnetic garnets, is shown to agree favourably with these theoretical results. A dependence of structural properties of the overlayer, such as critical thickness of pseudomorphic growth, density of dislocations beyond the critical thickness and preferred epitaxial orientation, not only on absolute value but also on sign of the natural misfit is predicted. It appears important as a guideline for material research in the field of epitaxial growth.

Electrolytic nucleation of cadmium

Abstract A method is described which makes it possible to determine directly the probability of the electrolytic formation of a single nucleus of cadmium on platinum and its variance with time and overvoltage. It is shown that the nucleation times are dispersed around median values characteristic for a given overvoltage according to the Gauss distribution law. The median times are related to the overvoltage as predicted by the nucleation theory. However, difficulties arise in the quantitative interpretation of the results on the basis of the classical liquid drop model for heterogeneous nucleation.

The role of active centers in the kinetics of new phase formation

Abstract A general equation for the time dependence of the number of nuclei is derived in the case of a nucleation process limited by the finite number of active centers and by the existence of zones around the growing nuclei forbidden for nucleation. The particular case of nucleation onto substrate from the vapour phase is considered. A method for determinating the number of active centers and the forbidden zone spreading rate constant with the help of an experimentally-found nucleation rate, a saturation nucleus density and a saturation time is developed.