Spiral growth of a multicomponent crystal from vapor of its components

Development of Burton–Cabrera–Frank Theory for the Growth of a Non-Kossel Crystal via Chemical Reaction

“…To solve this complex problem and to find the distribution of components, their diffusion fluxes to the step; and thus, to calculate its rate of advancement on the surface of a multicomponent crystal, it is necessary first to consider some simpler subtasks: (1) The growth of a single-component crystal by the BCF mechanism due to a chemical reaction (e.g., epitaxy of silicon from an atmosphere of silane and hydrogen). 39 In this case, in reaction 1, phase C consists of atoms of only one type and the reagents A i(g) and B i(g) can be of any atomic composition. It should be noted that the formation of certain types of molecular crystals can also be attributed to this case if an entire molecule is being deposited onto the surface, which then diffuses as a whole and integrates entirely into the crystal.…”

“…(2) The growth of a multicomponent crystal from vapors of its components (e.g., the growth of gallium nitride via molecular-beam epitaxy from gallium and nitrogen flows). In this case, in reaction , phase C consists of L types of atoms, the same number L of initial reagents A i ( g ) participates in the reaction, and reaction products B i ( g ) are absent …”

“…So, assuming that the independent diffusion of adatoms of individual components of the crystal occurs on the surface and they react with each other only at the kinks, we can represent the process near the kinks in the following way: where L is the number of types of atoms that build up the crystal, C i is the type of the atom (e.g., Ga, N, Si etc. ), and ν s i is the stoichiometric coefficient of the i th atom type in the crystal.…”

“…There are a lot of valuable papers devoted to the growth of such multicomponent crystals 27−31 and to chemical reactions at the crystal surface; 32−34 however, as far as we know, there is no generalization which would allow one to describe the growth of an arbitrary multicomponent crystal due to chemical reaction. This work continues the series of papers 35−38 and develops conference papers 39,40 devoted to the growth and evolution of crystals and pores in one-and multicomponent systems by various mechanisms, and its primary goal is the development of the classical BCF theory to describe the growth of an arbitrary multicomponent non-Kossel crystal in the presence of chemical reactions, and obtaining expressions for the growth rate of the multicomponent crystal from vapors or a solution of chemical reagents. It should be noted that in a series of papers the BCF theory is applied to describe the growth of the non-Kossel crystals taking into account the properties of individual components and the intake of substances through chemical reactions, but most often specific growth methods and specific systems, for example, SiC, 41 and gallium nitride (GaN) 42,43 were studied.…”

Influence of Adatoms on the Vacancy Growth of Faceted Pores in a Crystal Under Mechanical Load

“…Since the process of growth of an ordinary crystal and a pore are similar, similarly to the effect of advacancies on the growth of a crystal, adatoms on the surface of a pore can affect the rate of its vacancy growth. This work is a continuation of a series of works devoted to the growth and evolution of crystals [11][12][13][25][26][27][28] and pores in single-and multicomponent systems due to various mechanisms, and its main goal is to analyze the effect of adatoms on the pore surface on its vacancy growth of the pore according to the Barton-Cabrera-Frank mechanism, and find an expression for the dependence of the pore growth rate on the applied mechanical load and the properties of the crystal.…”