Vladimir G. Mokerov

Kinetic model for molecular beam epitaxial growth on a singular surface

Abstract We present a new kinetic model for molecular beam epitaxial growth on a singular surface which combines the modified rate equations approach with a concept of a feeding zone. The model involves irreversible nucleation, growth and coalescence of 2D islands in each layer and consists of an infinite set of coupled differential equations for adatom and 2D island densities and coverage in successive growing layers. It is shown that in the complete condensation regime and in the absence of step edge barriers, the homoepitaxial growth mode is fully determined by a single dimensionless parameter which is proportional to the ratio of the surface diffusion coefficient and the deposition flux. With decreasing this parameter, the growth mechanism crosses over from smooth 2D layer-by-layer growth to rough multilayer growth and eventually to very rough Poisson random deposition growth with time-divergent rms roughness. The extension of the model to the case of the heteroepitaxy by introducing different coefficients in the first and the next layers is presented as well.

Rate equations model for layer epitaxial growth kinetics

Abstract Recently, we have proposed a simple kinetic model for layer epitaxial growth, which combines the rate equations approach and a feeding zone that allows accounting for the interlayer adatoms diffusion. With this model it has clearly been demonstrated how with decreasing surface adatom diffusivity and/or increasing the repulsive Ehrlich–Schwoebel (ES) barrier height growth, mode crosses over from atomically smooth layer-by-layer growth to a smooth multilayer growth and finally to a rough 3D growth, and corresponding ‘phase diagram’ of the growth mode in parametric space has been constructed. In this paper the role of the growing island collisions in the epitaxial growth is analyzed. To that end the comparative studies of the growth kinetics and morphology evolution in two extreme cases of the island collision process behaviour: impingement and coalescence are performed by numerical integration of the rate equations. It is shown that the character of the island collision process weakly affects on the location of demarcating lines in the phase diagram of the growth mode, which is determined by the growth parameters characterizing the surface adatoms diffusivity (μ) and the ES barrier (ω). It is found that in addition to these growth parameters, there exists important internal parameter, the critical coverage for the next layer nucleation, its magnitude uniquely determines the onset of a growth mode transition irrespective of μ and ω thus remaining constant along a demarcating line. The growing island collisions significantly influence on the nucleation kinetics in successive layers and its scaling with growth parameters μ and ω and corresponding scaling exponents are determined.

Epitaxial growth kinetics in the presence of an Ehrlich-Schwoebel barrier: comparative analysis of different models

In the last years, much theoretical effort has been devoted to the effects of the Ehrlich–Schwoebel (ES) step-edge barrier to interlayer diffusion on epitaxial growth. In a number of models, in a frame of the rate equation approach the expressions for critical island size for second-layer nucleation have been derived and various growth mode transitions, induced by the ES barrier, have been revealed, and corresponding ‘phase diagrams’ of the growth mode in a parameter space have been constructed. The application of these models to the experimental data has been shown to result in the reasonable estimates of the ES barrier. However, in just published papers by employing kinetic MC simulations and theory, based on a concept of the residence time of an adatom on top of an island and simple statistical arguments, the expressions for critical island size and nucleation rate differing from that of the rate equation approach, have been obtained and it has been remarked that the applicability of mean field rate equations to the confined geometry on top of a small island is not obvious. This article presents a comparative analysis and reconsideration of the rate equation-based models in view of these critical comments that shows that these models are valid at least in a range of weak ES barriers where the most interesting growth phenomena are developed.

Homoepitaxial growth kinetics in the presence of a Schwoebel barrier

Nowadays it is well-recognized that the additional barrier to downhill adatom diffusion at the step edge plays an important role in the epitaxial growth. Very recently we have developed a simple model for homoepitaxial layer growth kinetics which allows to take into account the Schwoebel barrier impact on adatoms interlayer diffusion by using the concept of a feeding zone, as we have proposed earlier. This paper is devoted to further refinement and extension of the model to the cases of an arbitrary nucleus size and coalescence behaviour of growing islands. The model consists of an infinite set of coupled non-linear rate equations for adatom and 2D island surface densities and coverage in each successive growing layer. These equations in combination with an integral condition determining the new layer formation onset fully describe homoepitaxial growth kinetics at predetermined five model parameters, characterizing adatoms diffusion rate, critical nucleus size and stability, Schwoebel barrier effect, and coalescence. The growth mechanisms and kinetics in a wide range of parameter values are studied and growth mechanism phase diagrams in various parameter spaces are constructed and discussed.

Growth mode transitions and scaling behaviour at successive stages of molecular beam epitaxy

Recently developed kinetic model for homoepitaxial growth is extended to the case of heteroepitaxy (without lattice mismatch) by introducing different adatom surface mobilities in the first layer (heterodiffusion) and in all the next layers (self-diffusion). With this model the effect of two adatom mobilities as a function of the Schwoebel step-edge barrier is studied with an emphasis on the growth mode transitions. It is shown that the difference between homo- and heteroepitaxy is confined to the first few monolayers and is crucially sensitive to the ratio between the hetero- and self-diffusion coefficients: lower heterodiffusion coefficient with respect to that of self-diffusion improves essentially epitaxial growth and vice-versa. This is important for growing smooth ultrathin layers needed in modern nanotechnology. Island density kinetics in successive growing layers is studied and it is found that in smooth growth regime it acquires eventually (after deposition approx. 10 monolayers) a universal scaling form and corresponding scaling exponents have been determined.

Investigation of the structural properties of GaAs layers grown by molecular-beam epitaxy at low temperatures

The results of an investigation of the structural perfection of GaAs epitaxial films grown by molecular-beam epitaxy at low growth temperatures (240–300 °C) and various As/Ga flux ratios (from 3 to 13) are presented. Diffraction reflection curves display characteristic features for the samples before and after annealing in the temperature range from 300 to 800 °C. Hypotheses which account for these features are advanced. The range of variation of the arsenic/gallium flux ratio, in which low-temperature growth takes place under nearly stoichiometric conditions, is established.

Kinetic Model for Layer-By-Layer Homoepitaxial Growth

The new kinetic model for homoepitaxial growth on a singular surface is presented. The model combines a familiar rate equations approach and a concept of a feeding zone that allows to connect the growth processes in neighbouring monolayers. The model involves the irreversible 2D nucleation, growth and coalescence of the islands in each growing monolayer and consists of an infinite set of coupled rate equations for the adatom and island densities and coverage in successive monolayers. With using this model the temporal evolution of the surface morphology (rms roughness and RHEED intensity) is studied. It is shown that the growth mode is fully determined by a single dimensionless parameter μ = D/J where D and J are the normalized surface diffusion coefficient and deposition flux, respectively. There exist five regions of m corresponding different growth regimes varying from smooth 2D layer-by-layer growth at sufficiently high values of μ (>10 8 ) to very rough Poisson-like random deposition growth at μ −4 . The extension of the model to the case of heteroepitaxy is also discussed.