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

Abstract

The growth of an arbitrary multicomponent crystal via the Burton–Cabrera–Frank mechanism due to chemical reaction is studied. The rates of advancement of a single step, a group of equidistant steps, and a step formed by a screw dislocation on a surface are analyzed for three cases: growth of a single-component crystal via chemical reaction; growth of a multicomponent crystal from its vapors; growth of a multicomponent crystal due to chemical reaction. It is shown that the cases are very similar to the single-component case of crystal growth from its vapor and can be described by the same formulas as derived in classical paper of Burton–Cabrera–Frank, while in the multicomponent case the diffusion coefficient and incorporation rate are dependent on properties of individual components of the crystal, and mean free paths of adatoms are dependent on the rate of reverse chemical reaction. Some effects taking place in multicomponent systems with chemical reactions, such as dependence of the growth rate at given supersaturation on the reaction rate and nucleation of pure components at terraces, are discussed.

Dynamic Interaction of Steps and Nanoislands during Growth of a Multicomponent Crystal

“…This work continues the cycle of papers on the growth of crystals and pores in multicomponent systems − developed by the authors. Its primary goal is to study the growth mode of an arbitrary multicomponent crystal when islands of pure components nucleate on its surface.…”

“…Let us consider the multicomponent crystal growing from vapors of its own components. In general, the reaction can be written as , where A i are the initial components in the gaseous phase, C (s) is a solid multicomponent crystalline phase, and ν i are the stoichiometric coefficients of reaction . N is the number of the components.…”

“…If the multicomponent supersaturation ξ is high , then the crystal growth occurs via nucleation of multicomponent islands on the surface. If ξ ≥ 0 is sufficiently small (but still greater than 0), then the main growth mechanism is a step-flow or spiral growth, which is considered in detail in ref . Within such step-flow growth, the velocity of a group of equidistant steps ϑ ∞ gr can be written as where 1/ n C0 is the area occupied by a crystalline cell of the multicomponent crystal C (s) , is the averaged diffusion coefficient, is the averaged incorporation coefficient of adatoms into a multicomponent step, is the diffusion length of the adatom of the i th component, and D i , β i , V i , n i 0 , τ i are the diffusion and incorporation coefficients, atomic volume, equilibrium surface concentration, and desorption time of the i th component (in the context of multicomponent growth), respectively.…”

Особенности зарождения и роста нитевидных нанокристаллов InGaN на подложках SiC/Si методом хлорид-гидридной эпитаксии

“…Образование V -дефектов в слое GaN, как показано в [15], связано с образованием малоугловых границ зерен, приводящих к упругим деформациям, нарушению стехиометрического состава адатомов, из ансамбля которых растет пленка GaN, и формированию дислокации. Впоследствии в этом месте реализуется слоисто-спиральный рост [16] GaN, что хорошо видно по частично незаросшему верхнему слою, а само зарождение ННК происходит непосредственно возле или в ядре дислокации. Средняя длина ленточных нанокристаллов составляет 30−60 µm.…”

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.…”