Analytic scaling function for island-size distributions

Abstract

We obtain an explicit solution for the island-size distribution described by the rate equations for irreversible growth with the simplified capture rates of the form σ(s)(Θ)∝Θ(p)(a+s-1) for all s≥1, where s is the size and Θ is the time-dependent coverage. The intrinsic property of this solution is its scaling form in the continuum limit. The analytic scaling function depends on the two parameters a and p and is capable of describing very dissimilar distribution shapes, both monomodal and monotonically decreasing. The obtained results suggest that the scaling features of the size distributions are closely related to the size linearity of the capture rates. A simple analytic scaling is obtained rigorously here and helps to gain a better theoretical understanding of possible origins of the scaling behavior of the island-size distributions.

CdTe Nanowires by Au-Catalyzed Metalorganic Vapor Phase Epitaxy

“…From eq , the radius-independent growth rate requires that the diffusion flux j diff (0) is proportional to R 2 , that is, to the surface area of the nanowire base. Such a situation is typical for surface growth of point islands at high diffusivities where the neighboring islands compete for the diffusion flux. − On the other hand, the mean length of nanowires grown from the colloidal Au NPs at 507 °C with Δ t Te = 1 min is 912 nm and is reduced to only 219 nm when grown from thermally annealed Au film (Table ). This effect is not associated with a larger size of the Au colloids as the nanowire length is almost radius-independent (see Supporting Information).…”

Enhancement of island size by dynamic substrate disorder in simulations of graphene growth

“…This is not surprising given that dynamic roughness enhances both island cleaving and island growth, leading to a broader distribution. Since increasing the value of i* typically sharpens the peak of the scaled ISD and i* = 0 ISDs are typically monotonically decreasing, 26,28,36 this altered scaling form suggests that the effects due to a combination of dynamic roughness and annealing could not be captured in any standard irreversible aggregation picture.…”

“…The precise forms of ISDs have been discussed for many years. [26][27][28] Experimentally, one can use a technique such as scanning tunnelling microscopy (STM) to study island formation and growth with atomic-scale precision, normally quenching the sample after sub-ML growth and working ex situ. 1,25,29 Atomic resolution STM is well suited to ultra-high vacuum growth techniques, and can even be performed in situ.…”

Дисперсия Масштабно-Инвариантных Функций Распределения По Размерам

“…Если предположить, что данная зависимость справедлива абсолютно для всех, а не только для больших s, полученная при некоторых дополнительных предположениях в работе [10] СФ имеет вид…”

“…Для гомогенного роста двумерных островков данные параметры рас-шифрованы в [10]. Легко проверить, что СФ (4) удовлетворяет условиям нормировки (2) при любых a и b. В самое последнее время модели гетерогенного необратимого роста [11,12] стали применяться для моделирования ФР по длине III−V нитевидных нанокристаллов (ННК).…”