Kinetic Monte Carlo simulation of thin film growth

A three-dimensional kinetic Monte Carlo technique has been developed for simulating growth of thin Cu films. The model involves incident atom attachment, diffusion of the atoms on the growing surface, and detachment of the atoms from the growing surface. The related effect by surface atom diffusion was taken into account. A great improvement was made on calculation of the activation energy for atom diffusion based on a reasonable assumtion of interaction potential between atoms. The surface roughness and the relative density of the films were simulated as the functions of growth substrate temperature and film thickness. The results showed that there exists an optimum growth temperatureT _opt at a given deposition rate. When the substrate temperature approaches toT _opt, the growing surface becomes smoothing and the relative density of the films increases. The surface roughness minimizes and the relative density saturates atT _opt. The surface roughness increases with an increment of substrate, temperature when the temperature is higher thanT _opt.T _opt is a function of the deposition rate and the influence of the deposition rate on the surface roughness depends on the substrate temperatures. The simulation results also showed that the relative density decreases with the increasing of the deposition rate and the average thickness of the film.     

薄膜外延生长的计算机模拟

以Cu膜为例，用Monte-Carlo算法模拟了薄膜生长的随机过程，并提出了更加完善的模型.在合理选择原子间相互作用计算方法的基础上，考虑了原子的吸附、在生长表面的迁移及迁移所引起的近邻原子连带效应、从生长表面的脱附等过程.模拟计算了薄膜的早期成核情况以及表面粗糙度和相对密度.结果表明，随着衬底温度的升高或入射率的降低，沉积在衬底上的原子逐步由离散型分布向聚集状态过渡形成一些岛核，并且逐步由二维岛核向三维岛核过渡.在一定的原子入射率下，存在三个优化温度，成核率最高时的最大成核温度Tn、薄膜的表面粗糙度最低 关键词： Monte-Carlo算法 计算机模拟 薄膜生长     

Theoretical study on diffusion mechanism of fluorine atom adsorbed on Si(111) reconstructed surface

We study diffusion mechanisms of fluorine atom adsorbed on Si(111) reconstructed surface by means of the first-principles density functional calculation. Recently, it was revealed experimentally that the fluorine diffusion is assisted by extra silicon atoms diffusing freely on the surface, whereas the detailed mechanism of the Si assist has not been understood. We first investigate F atom adsorption structures with and without a Si atom and find that extra Si atoms do not affect them. Next, we investigate the diffusion mechanism, considering four models in which extra silicon atoms act a different role, and find that SiF-complex diffusion model with activation energy of 1.34 eV is appropriate to explain the experiment. In this model, the Si–F bond is kept during diffusion, while in the others, it repeats breaking and re-bonding. This diffusion mechanism is also understood as the Si diffusion with carrying an F atom. We analyze why this diffusion mechanism is preferable to the others and find that two important features play roles. One is the strong Si-F bond that favors to keep the complex form, and the other is the existence of an extra silicon atom, which takes over the adatom position to passivate dangling bonds left behind after the SiF-complex removal.     

Surface diffusion of lead on tungsten

Field electron microscopy is used to study the surface diffusion of lead on tungsten. A simple method to measure rough values of the diffusion coefficient and its dependence on sub-monolayer coverage is described and tested. In the region around (001) the displacement energy found is about 1.30 eV/atom up to 10¹⁵ atoms/cm² where it decreases to 0.78 eV/atom. In the residual region except (110) this energy at 1.5×10¹⁴ atoms/cm² is 1.22 eV/atom, it decreases at 4 × 10¹⁴ atoms/cm² to 0.61 eV/atom and increases at 10¹⁵ atoms/cm² to 0.78 eV/atom. Corresponding values of the diffusion coefficient D and of the preexponential D₀ are given. The dependence of D on submonolayer coverage is discussed.     

Surfactant properties of cesium in molecular beam epitaxy of GaAs(100)

The experimental and ab initio investigations of the effect of a decrease in the binding energy of surface arsenic atoms under the cesium adsorption on an As-stabilized GaAs(001)-(2 × 4) surface have been performed. The cesium-induced redistribution of the charge on the surface atoms reduces the electron density in the As-Ga bond of the upper layer of the GaAs(001) surface; thus, the As-Ga binding energy decreases and, as a result, the diffusion activation energy, as well as the arsenic atom desorption, decreases. An increase in the diffusion coefficient of surface atoms, along with the property of Cs to segregate on the surface of a growing semiconductor film, makes it possible to use cesium as a surfactant in the low-temperature growth of GaAs by molecular beam epitaxy.     

Quantum chemical calculations on Al-CVD using DMEAA: surface reaction mechanism of AlH3 on Al(111)

An investigation has been made of the elementary surface reactions of alane and its surface dissociation products using density functional theory and a cluster model to elucidate the reaction mechanism of the deposition of aluminium in aluminium chemical vapour deposition (Al-CVD) using dimethylethylamine alane (DMEAA). Molecular structures, potential energies, and normal mode frequencies of the reactants, the products, and the transition states were calculated for each of the surface elementary reactions. Based on transition state theory, rate constants were estimated from the calculation results. The proposed reaction mechanism is the following. DMEAA is adsorbed onto an aluminium surface without any dissociation in the gas phase; DMEAA dissociates into dimethylethylamine (DMEA) and alane on the surface; DMEA is desorbed and alane remains adsorbed; the adsorbed alane molecules dissociate to AlH₂, AlH, and H on the surface; hydrogen molecules to be desorbed are produced from the hydrogen atoms of AlH whose aluminium atoms form a quasi-aluminium surface on the original surface. The cluster size and structure dependence in quantum chemical calculations has also been considered using model clusters.     

Influence of the Si(111)-7×7 surface reconstruction on the diffusion of strontium atoms

The diffusion of strontium atoms on the Si(111) surface at room temperature has been investigated using scanning tunnel microscopy and simulation carried out in terms of the density functional theory and the Monte Carlo method. It has been found that the reconstruction of a clean silicon surface with a 7 × 7 structure has a profound effect on the diffusion process. The average velocity of motion of a strontium atom in a unit cell of the 7 × 7 structure has been calculated. The main diffusion paths of a strontium atom and the corresponding activation energies have been determined. It has been demonstrated that the formation of scanning tunnel microscope images of the Si(111)-7 × 7 surface with adsorbed strontium atoms is significantly affected by the shift of the electron density from the strontium atom to the nearest neighbor silicon adatoms in the 7 × 7 structure.     

Surface diffusion during decay of nano-island on Si(1 0 0) at high temperature

Surface diffusion during decay of a two-dimensional nano-island formed on Si(1 0 0) surface at 750-800 K is studied using STM and a kinetic Monte Carlo simulation. From a surface diffusion point of view, decay proceeds so that the total diffusion rate of atoms on a surface decreases. Atoms at step edges move more frequently than terrace atoms, which results in decay from step edges of the island. In addition, a terrace atom takes part in surface diffusion in the same way as an atom from steps of the island once it hops up on a terrace leaving a vacancy. The mass transport is not a specific atom process but terrace atoms and vacancies on the terrace are involved. Repeated upward and downward hops of atoms and their difference are combined with surface diffusion, which leads to the mass transport. Some tracks of atom using simulation show random walk with preferential diffusion along step edges, re-entering to the island, exchange of diffusing atom and filling in a vacancy on the terrace. The motion of the center of the island to the upper side of the terrace observed by STM is also well reproduced in the simulation.     

Coarse-grained kinetic scheme-based simulation framework for solution growth of ZnO nanowires

Kinetic Monte Carlo (KMC)-based stochastic model is used to understand the growth of zinc oxide nanowires from aqueous solution containing chemical precursors and capping agent. Through a hydrothermal growth mechanism, the average diameter of zinc oxide wires obtained is around 300 nm, whereas the length is order of several micrometers. Our Monte Carlo algorithm is based on the continuous-time Monte Carlo algorithm of Bortz, Kalos and Lebowitz (BKL) methodology. Both reactions and diffusion mechanisms assigning stochastic probabilities have been simulated. In algorithm, the ZnO atoms were treated as individual particles which diffuse in solution substrate and interact with other type of atoms. Once attached with growing nanowires, the diffusion rate of ZnO atom is considerably reduced. Since in a KMC algorithm each atom can be represented individually therefore, internal noise is automatically incorporated.     

Kinetics of the diffusion of an impurity atom on a fcc(111) surface

An analytical study of the migration of an embedded impurity atom over a solid surface under the influence of the diffusion of vacancies is performed. The case of small surface coverages of both vacancies and impurity atoms is considered. It is shown that the realization of multiple collisions of a single impurity atom with vacancies imparts a Brownian character to its motion. At long times, the dependence of the mean square displacement on the time differs little from the linear, whereas the spatial density distribution is close to the Gaussian, features that makes it possible to introduce a diffusion coefficient. For the latter, an analytical expression is derived, which differs from the product of the diffusion coefficient of vacancies and their relative concentration only by a numerical factor. The dependence of the diffusion coefficient of an impurity atom on the ratio of the frequency of its jumps to the frequency of jumps of vacancies is analyzed. In the kinetic mode, when the frequency of jump ω of the imurity atom is small, the diffusion coefficient of the impurity depends linearly on ω, whereas in the opposite case, a saturation occur and its dependence on the frequency of jumps of the impurity atom disappears.     

Fluctuations and scaling in models for particle aggregation

We consider two sequential models of deposition and aggregation for particles. The first model (No Diffusion) simulates surface diffusion through a deterministic capture area, while the second (Sequential Diffusion) allows the atoms to diffuse up to ? steps. Therefore the second model incorporates more fluctuations than the first, but still less than usual (Full Diffusion) models of deposition and diffusion on a crystal surface. We study the time dependence of the average densities of atoms and islands and the island size distribution. The Sequential Diffusion model displays a nontrivial steady-state regime where the island density increases and the island size distribution obeys scaling, much in the same way as the standard Full Diffusion model for epitaxial growth. Our results also allow to gain insight into the role of different types of fluctuations.     

Dynamics of molybdenum nano structure formation on the TiO2(1 1 0) surface: A kinetic Monte Carlo approach

The rutile TiO₂(1 1 0) surface is a highly anisotropic surface exhibiting “channels” delimited by oxygen rows. In previous experimental and theoretical DFT works we could identify the molybdenum adsorption sites. They are located inside the channels. Moreover, experimental studies have shown that during subsequent annealing after deposition, special molybdenum nano structures can be formed, especially two monolayer high pyramidal chains of atoms.In order to better understand the dynamics of nano structure formation, we present a kinetic Monte Carlo study on diffusion and adsorption of molybdenum atoms on a TiO₂(1 1 0) surface. A quasi one-dimensional lattice gas model has been used which describes the possible adsorption sites of a Mo atom in a single channel of the surface. The atomic positions of a 1.5 monolayer thick Mo film formed of pyramidal chains define the lattice sites of the model. Thereby the formation of three-dimensional clusters could be studied. Here we have studied the cluster formation as a function of parameters that can be controlled in a growth experiment by physical vapor deposition: deposition and annealing temperature, flux and total amount of deposited Mo. Good qualitative agreement with recent experiments is obtained.     

SiH4/H2等离子体气相生长硅薄膜的动力学模型

在化学气相沉积微晶硅薄膜过程中,为了降低成本,必须提高生长速率,但薄膜的微观结构和光电性能则随之降低,原因是成膜先驱物在薄膜表面上的扩散长度降低了. 本文利用量子化学的反应动力学理论建立有关成膜先驱物SiH₃和H的反应平衡方程,求解薄膜生长速率和成膜先驱物的扩散长度,并找出影响生长速率与扩散长度的微观参数,发现生长速率不仅与流向衬底的SiH₃的通量密度有关,而且与H的通量密度有关;SiH₃的扩散长度与衬底温度和薄膜表面的硅氢键的形态有关,当     

Kinetics of the diffusion of an impurity atom on a square lattice

An analytical study of the migration of an embedded impurity atom over a solid surface under the influence of the diffusion of vacancies is presented. The case of small surface coverages of both vacancies ϑ _v and impurity atoms ϑ _i , with ϑ _i ≪ ϑ _v ≪ 1, is considered. It is shown that the realization of multiple collisions of a single impurity atom with vacancies imparts a Brownian character to its motion. At long times, the dependence of the mean square displacement on the time differs little from the linear, whereas the spatial density distribution is close to the Gaussian, features that makes it possible to introduce a diffusion coefficient. For the latter, an analytical expression is derived, which differs from the product of the diffusion coefficient of vacancies and their relative concentration only by a numerical factor η. The dependence of the diffusion coefficient of an impurity atom on the ratio of the frequency of its jumps to the frequency of jumps of vacancies is analyzed. In the kinetic mode, at ω ≪ 1, the diffusion coefficient of impurity atoms depends linearly on ω, whereas at ω ≫ 1, a saturation is observed; i.e., the dependence on the frequency of jumps of the impurity atom disappears. Nevertheless, the value of η remains less than unity, and no total entrainment of impurity atoms with vacancies occurs.     

Al原子在Pb基底上的沉积过程研究

利用分子动力学方法模拟了Al原子在Pb基底上的沉积过程. 对Al原子在Pb基底(001)面上沉积的形态与Pb原子在Al(001)基底上沉积的形态做了比较. 由于界面间势垒的不同, 两个体系界面间的形态有明显的差异. 分析了基底温度、基底晶面指向、沉积原子的入射动能对界面间原子混合的影响. 模拟结果显示: 随着基底温度升高, 基底原子的可移动性大大增加, 与沉积原子发生较大程度的混合; 入射能的改变对界面间原子的混合影响很小; 基底表面取不同的晶格指向时, 基底与沉积原子间的混合行为也有明显的不同. 利用径向分布函数分析了沉积原子的入射能对薄膜中原子排列有序性的影响. 较高入射能对应更有序的薄膜结构; 由径向分布函数的结构可以推测Al原子在Pb(001)基底表面沉积时界面间可能有金属间化合物生成. 关键词： Pb/Al体系 沉积过程 分子动力学 入射能     

动力学晶格蒙特卡洛方法模拟Cu薄膜生长

利用动力学晶格蒙特卡洛方法模拟了Cu薄膜在Cu(100)面上的三维生长过程。模型中考虑了四个动力学过程:原子沉积、增原子迁移、双原子迁移和台阶边缘原子迁移,各动力学过程发生的概率由多体势函数确定。讨论了基底温度、沉积速率及原子覆盖率对Cu原子迁移、成核和表面岛生长等微观生长机制的影响;获得了Cu薄膜的表面形貌图并计算了表面粗糙度。模拟结果表明,随基底温度升高或沉积速率下降,岛的平均尺寸增大,数目减少,形状更加规则。低温时,Cu薄膜表现为分形的离散生长,高温时,Cu原子迁移能力增强形成密集的岛。Cu薄膜表面粗糙度随着基底温度的升高而迅速减小;当基底温度低于某一临界温度时,表面粗糙度随原子覆盖率或沉积速率的增大而增大;当基底温度超过临界温度时,表面粗糙度随原子覆盖率或沉积速率的变化很小,基本趋于稳定。     

Origin of compressive residual stress in polycrystalline thin films

We present a model for compressive stress generation during thin film growth in which the driving force is an increase in the surface chemical potential caused by the deposition of atoms from the vapor. The increase in surface chemical potential induces atoms to flow into the grain boundary, creating a compressive stress in the film. We develop kinetic equations to describe the stress evolution and dependence on growth parameters. The model is used to explain measurements of relaxation when growth is terminated and the dependence of the steady-state stress on growth rate.     

Diffusion in a surface: the atomic slide puzzle

We review measurements performed using scanning tunneling microscopy of the motion of impurity atoms in the Cu (001) surface. Like several other elements, the impurity that we have introduced, In, tends to embed itself in the first atomic layer of this surface. Via the motion of the embedded In atoms, we obtain direct information on the motion of the Cu atoms in the surface. In other words, we employ the In atoms as tracer particles to investigate the intrinsic motion in the first Cu layer. The peculiar statistics of the two-dimensional In diffusion allows us to conclude that the motion is assisted by a rapidly diffusing entity, which we identify as a surface vacancy, i.e. a single missing Cu atom in the outermost Cu layer. A comparison with model calculations of the statistics of the vacancy-assisted motion of terrace atoms shows that there must be an attractive interaction between an embedded In atom and a vacancy, which makes the In atom somewhat more mobile than a Cu surface atom. Such an attraction is indeed found in embedded-atom-method calculations. Nevertheless, the temperature dependence of the indium motion provides an accurate estimation of the sum E_form+E_act, representing the sum of the formation energy of a vacancy and the activation energy for the motion of vacancies through a clean Cu (001) surface. Received: 30 April 2001 / Accepted: 23 July 2001 / Published online: 3 April 2002     

Broadening of Cr nanostructures in laser-focused atomic deposition

This paper presents the experimental progress of laser-focused Cr atomic deposition and the experimental condition.The result is an accurate array of lines with a periodicity of 212.8±0.2 nm and mean full-width at half maximum as approximately 95 nm.Surface growth in laser-focused Cr atomic deposition is modeled and studied by kinetic Monte Carlo simulation including two events:the one is that atom trajectories in laser standing wave are simulated with the semiclassical equations of motion to obtain the deposition position;the other is that adatom diffuses by considering two major diffusion processes,namely,terrace diffusion and step-edge descending.Comparing with experimental results(Anderson W R,Bradley C C,McClelland J J and Celotta R J 1999 Phys.Rev.A 59 2476),it finds that the simulated trend of dependence on feature width is in agreement with the power of standing wave,the other two simulated trends are the same in the initial stage.These results demonstrate that some surface diffusion processes play important role in feature width broadening.Numerical result also shows that high incoming beam flux of atoms deposited redounds to decrease the distance between adatoms which can diffuse to minimize the feature width and enhance the contrast.     

Effect of adsorbed Sn on Ge diffusivity on Si(111) surface

The effect of adsorbed Sn as a surfactant on Ge diffusion on a Si(111) surface has been studied by Low Energy Electron Diffraction and Auger Electron Spectroscopy. The experimental dependence of Ge diffusion coefficients on the Si(111) surface versus temperature in the presence of adsorbed Sn atoms has been measured in the range from 300 to 650°C. It has been shown that at a Sn coverage of about 1 monolayer the mobility of Ge atoms increases by several orders of magnitude.