Applications of molecular dynamics methods to low energy ion beams and film deposition processes

Abstract

Molecular dynamics methods are used to model the impingement of low energy ions onto crystalline targets, and the effects of these beams on thin film deposition. Simulations of the deposition of silicon films show that the structure of deposits can often be improved by the use of low energy ion beams instead of the conventional thermal beam. We examine the influence of beam energy on the formation of amorphous or crystalline deposits. The influence of ion beams on surface diffusion rates and the interdiffusion between atomic layers near the surface are also considered. Cluster deposition is treated, and the results suggest that cluster beams would be effective for depositing smooth films of materials that do not wet the substrate. We discuss the use of special purpose computers and signal processing boards to extend the time scales of molecular dynamics simulations. Rapid advances in computer hardware, algorithms, and the development of accurate interatomic potentials are dramatically increasing the power of these simulations.     

利用Keating模型计算Si（1-x）Gex及非晶硅的拉曼频移

利用Keating模型计算了Si_（1-x）Ge_x合金中Si—Si,Ge—Ge和Si—Ge三种振动模态的拉曼频移,计算分别获得Ge浓度为01,05和09时,Si—Ge的振动拉曼频移分别为40275,41339和38815 cm^-1,这些结果与文献的实验结果符合,证明了Keating模型建立的关于原子振动模型是有效的,并可以利用拉伸压缩和相邻原子键之间弹性系数变化获得处于应变状态的拉曼光谱频率.利用Kea 关键词： Keating模型 拉曼光谱 （1-x）Ge_x')" href="#">Si_（1-x）Ge_x 非晶硅     

Discrete and continuum models for calculating the phonon spectra of carbon nanotubes

The vibration spectrum of perfect carbon nanotubes is studied using a two-parametric potential which includes pairwise and three-particle interatomic interactions. This potential was proposed by Keating and allows one to take into account the elasticity of pairwise interatomic bonds and the elasticity associated with a change in the angle between directional interatomic bonds in covalent crystals. Using the Keating potential, the vibration spectrum of a graphite monolayer is calculated and fitted to the vibration spectrum of crystalline graphite, thereby determining the parameters of the potential. With these parameters, the phonon spectra of perfect monolayer graphite nanotubes are calculated. A continuum model, in which a monolayer nanotube is represented as an elastic cylindrical shell of a finite thickness, is also discussed. Within this model, the vibration spectrum of a nanotube is calculated numerically in the long-wavelength limit as a function of the radius and thickness of the nanotube.     

Molecular effect on interatomic potentials

Abstract

In the low energy atomic collision of ε ≤ 0.1, the energy dissipation of projectile ion is mainly by the nuclear stopping. In this energy range Z-oscillation appears on ranges and range stragglings. In order to explain this osciallation from the viewpoint of molecular effect on interatomic potentials, an extended Hückel method is adopted for potential calculation. The Z-dependence on interatomic potentials to describe respective atomic collisions is similar to that of Z ₁-range oscillation. It suggests a possibility of molecular effect on the Z ₁-range oscillation.     

Statistical mechanical models for liquid and amorphous structure in covalently bonded systems

Summary Considerable effort has been given for some years to developing models of interatomic forces aimed at accounting for bond directionality in liquid and amorphous state calculations. Models involving three-body potentials have been especially useful for computer simulation studies of liquid and amorphous states in elemental semiconductors and binary chalcogenides of group-IV elements, starting with the work of Stillinger and Weber on silicon. However, pair potential models that may still account for the main effects of angular dependences of the effective interatomic forces, though at a primitive level, are desirable from the viewpoint of liquid structure theory. Developments in this direction are briefly reviewed, with particular emphasis on bond particle models for the structure of liquid and amorphous germanium. We also discuss the relation between liquid structure in a bond-particle model and crystallization accompanied by electron localization and volume expansion, as observed in elemental and III-V polar semiconductors. Paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1–3 May, 1989.     

利用电子结构数据拟合H2分子的电子壳模型势函数参数

电子壳模型势函数在离子晶体的原子级计算机模拟中有广泛应用,其势参数主要通过拟合晶体的实验数据或电子结构数据得到.提出了通过拟合双原子分子的量子化学从头计算电子结构数据来获得该势函数的方法,并由H₂分子的电子结构数据建立了H原子间的电子壳模型势函数.此外,还应用该势函数对H⁺₂分子离子进行了计算.该势函数拟合方案更适合于共价键型的分子. 关键词： 电子壳模型势 参数拟合 共价键 2分子')" href="#">H₂分子     

利用电子结构数据拟合H2分子的电子壳模型势函数参数

电子壳模型势函数在离子晶体的原子级计算机模拟中有广泛应用,其势参数主要通过拟合晶体的实验数据或电子结构数据得到.提出了通过拟合双原子分子的量子化学从头计算电子结构数据来获得该势函数的方法,并由H2分子的电子结构数据建立了H原子间的电子壳模型势函数.此外,还应用该势函数对H+2分子离子进行了计算.该势函数拟合方案更适合于共价键型的分子.     

Surface disorder in c-Si induced by swift heavy ions

The disorders induced in crystalline silicon (c-Si) through the process of electronic energy loss in the swift heavy ion irradiation were investigated. A number of silicon <1 0 0> samples were irradiated with 65 MeV oxygen ions at different fluences, 1×10¹³ to 1.5×10¹⁴ ions/cm², and characterized by the Raman spectroscopy, the optical reflectivity, the X-ray reflectivity, the atomic force microscopy (AFM) and the X-ray diffraction (XRD) techniques. The intensity, redshift, phonon coherence length and asymmetric broadening associated with the Raman peaks reveal that stressed and disordered lattice zones are produced in the surface region of the irradiated silicon. The average crystallite size, obtained by analyzing Raman spectrum with the phonon confinement model, was very large in the virgin silicon but decreased to<100 nm dimension in the ion irradiated silicon. The results of the X-ray reflectivity, AFM and optical reflectivity of 200–700 nm radiation indicate that the roughness of the silicon surface has enhanced substantially after ion irradiation. The diffusion of oxygen in silicon surface during ion irradiation is evident from the oscillation in the X-ray reflectivity spectrum and the sharp decrease in the reflectivity of 200–400 nm radiation. The rise in temperature, estimated from the heat spike model, was high enough to melt the local silicon surface. The results of XRD indicate that lattice defects have been induced and a new plane <2 1 1> has been formed in the silicon <1 0 0>after ion irradiation. The results of the present study show that the energy deposited in crystalline silicon through the process of electronic energy loss ～0.944 keV/nm per ion is sufficient to induce disorders of appreciable magnitude in the silicon surface even at a fluence of ～10¹³ ions/cm².     

Keating改良模型的硅纳米梁动态特性

提出一种用于分析硅纳米梁动态特性的改良型半连续体模型,对比传统的连续体理论,这种新模型使用了Keating势,并考虑了纳米梁在宽厚两个维度的分立特性。依据Sun-Zhang模型思想和能量守恒定律,建立了改良型Keating模型,并进行了双端固支梁的基频计算。在这个过程中,对一些表面效应也进行系统分析。结果表明,该改良模型一方面在纳米尺度下与Material StudioTM软件仿真结果较为符合,另一方面也能在微观尺度下较好的接近连续体模型的计算数据。同时,该模型还反映了基频随纳米梁宽度变化的特性,这也符合一些实际实验。     

Evaluation of repeated single-point diamond turning on the deformation behavior of monocrystalline silicon via molecular dynamic simulations

A three-dimensional molecular dynamics simulation study is conducted to investigate repeated single-point turnings of a monocrystalline silicon specimen with diamond tools at nanometric scale. Morse potential energy function and Tersoff potential energy function are applied to model the silicon/diamond and silicon/silicon interactions, respectively. As repeated nano-cutting process on surfaces often involve the interactions between the consequent machining processes, repeated single-point diamond turnings are employed to investigate the phase transformation in the successive nano-cutting processes. The simulation results show that a layer of the damaged residual amorphous silicon remained beneath the surface after the first-time nano-cutting process. The amorphous phase silicon deforms and removes differently in the second nano-cutting process. By considering the coordination number (CN) of silicon atoms in the specimen, it is observed that there is an increase of atoms with six nearest neighbors during the second nano-cutting process. It suggests that the recovery of the crystalline phase from the amorphous phase occurred. Moreover, the instantaneous temperature distributions in the specimen are analyzed. Although the tangential force (F _X ) and the thrust force (F _Y ) become much smaller in the second cutting process, the material resistance rate is larger than the first cutting process. The larger resistance also induces the increase of local temperature between the cutting tool and the amorphous layer in the second cutting process.     

Effects of vacancy defects and axial strain on thermal conductivity of silicon nanowires: A reverse nonequilibrium molecular dynamics simulation

Thermal conductivity of silicon nanowires (SiNWs) is evaluated using the reverse nonequilibrium molecular dynamics simulation. The Stillinger–Weber (SW) and Tersoff interatomic potentials are employed to simulate thermal conductivity of SiNWs. In this work, the influence of random vacancy defects, axial strain, temperature and length on thermal conductivity and effective mean free path of SiNWs is investigated. It is found that by raising the percent of random vacancy defects, thermal conductivity of SiNWs decreases linearly for the results obtained form SW potential and nonlinearly for those obtained from Tersoff interatomic potential. Dependence of the thermal conductivity on axial strain is also studied. Results show that thermal conductivity increases as compressive strain increases and decreases as tensile strain increases. Influence of temperature is also predicted. It is found that the thermal conductivity of SiNWs decreases with increasing the mean temperature. Most of the simulations are performed for 4 UC×4 UC×40 UC silicon nanowires using ssp boundary condition.     

硅纳米晶体薄膜热膨胀性质的分子动力学研究

基于Stillinger-Weber势对硅纳米晶体薄膜的热膨胀性质进行了分子动力学模拟。研究表明,硅纳米晶体薄膜表面层原子的二聚现象引起薄膜收缩,而原子之间的非和谐势能引起薄膜膨胀;在约400K以下的低温段,由于硅纳米晶体薄膜表面层原子发生二聚的原子数目随温度的升高而明显增多,而原子间非和谐势能很小,故此时二聚主导热膨胀性质,热膨胀系数为负;在高温段（约400K以上）,由于发生二聚的原子数目随温度升高不再显著地增加并渐趋于稳定,而原子间非和谐势能逐渐显著并主导热膨胀性质,故热膨胀系数为正。     

Phase nucleation and stability in irradiated metal-silicon systems

Amorphization, or crystalline structure development in metal-silicon systems undergoing ion mixing, or ion implantation are interpreted by an atomistic model. Energy spike formation and evolution within the irradiated target provide the conditions necessary to develop composition variations at the spike-lattice interface, where one component preferentially migrates. As a consequence of local non-equilibrium compositional conditions, interatomic interactions, schematized via charge transfer events, occur, and give rise to formation of glassy, or crystalline nuclei. Qualitative differences are found between the surface behaviour of amorphous and respectively crystalline silicides.     

Tests of the empirical potential structure refinement method and a new method of application to neutron diffraction data on water

Empirical potential structure refinement (EPSR) is a method for developing a structural model of a liquid for which diffraction measurements are available. The EPSR technique involves refining a starting interatomic potential energy function in a way that produces the best possible agreement between the simulated and measured site-site partial structure factors. Here a series of test simulations are performed to establish how well the EPSR method can recover the interatomic potential for a single component fluid of Lennard-Jones particles, and for a binary fluid consisting of charged atoms interacting at short range by a Lennard-Jones potential. Special attention is given to the problem of developing an accurate interatomic potential for water using these procedures. An alternative method for perturbing the starting potential is used to obtain the best possible fit to the diffraction data. The resulting parametrization of the water potential is in contrast to many existing effective potentials for water, and indicates that water molecules in the liquid at ambient conditions are highly polarized, as has been suggested in recent ‘first-principles’ simulations of water. Three-body correlation functions and spatial density functions derived from the EPSR simulations show excellent agreement with those obtained with the model potential simulations. However, the potentials extracted by EPSR are found to depend on the constraints applied to the hardness of the core potential and the energy and pressure of the simulation, even when the fits to the data are equally good. It is concluded that performing EPSR on diffraction data can be used as a good test for interatomic potentials and to derive reliable many-body structures in the liquid state, but cannot on its own be used to derive a reliable set of site-site pair potentials for a particular system.     

From nuclear stopping to interatomic potential via the power law formalism

A general method for inverting the energy-dependent nuclear stopping cross sections S_n(?) to derive the interatomic potential V(x) is described. A correspondence between ? and x is derived for mapping S_n(?) to V(x) and vice versa. The method is illustrated by using the recent range-energy data of keV indium and xenon ions in amorphous silicon to self-consistently deduce the In-Si and Xe-Si potentials.     

Short-range order, atomic structure, and dynamics of the amorphous alloy Ni80Zr20

The method of molecular dynamics with pair-interaction potentials calculated in terms of pseudopotential theory is used to model the rapid quenching process and to study the atomic structure and lattice dynamics of the alloy Ni₈₀Zr₂₀ in the amorphous state. The total and partial atomic radial distribution functions and the densities of vibrational states are calculated, and the nearest-neighbor interatomic distances and coordination numbers are determined. Fiz. Tverd. Tela (St. Petersburg) 39, 961–963 (June 1997)     

Phenomenological interatomic potentials for silicon, germanium and their binary alloy

A phenomenological potential is constructed for silicon, germanium, and their binary alloy. As in the modified embedded atom model (MEAM), the interatomic interactions are assumed to arise from the overlap of the electron wave functions. However, the calculation of energy is quite different in the two models. The proposed potential has seven adjustable parameters in contrast to ten or more in MEAM but gives perfect fit with the measured values of seven most important quantities for characterizing strained silicon: cohesive energy, equilibrium lattice constant, vacancy formation energy, Raman frequency, and the three elastic constants. The potential should be suitable for lattice statics calculations on strained silicon.     

State equations and properties of various polymorphous modifications of silicon and germanium

The state equations and the pressure dependences of the lattice properties have been obtained for various polymorphous modifications of silicon and germanium using the Mie–Lennard-Jones pair interatomic potential and the Einstein crystal model. It is shown that the elastic-type interatomic potential gives the best results for the semiconductor phase and the plastic-type interatomic potential for the metalized phases whose potential well depth is significantly smaller. The pressure dependences of the lattice properties are calculated along isotherm 300 K and the jumps of the properties during the phase transition from the diamond structure to the β-Sn phase are evaluated for both silicon and germanium. The calculated results agree well with the experimental data.     

Construction of embedded-atom-method interatomic potentials for alkaline metals （Li,Na,and K） by lattice inversion

The lattice-inversion embedded-atom-method interatomic potential developed previously by us is extended to alkaline metals including Li,Na,and K.It is found that considering interatomic interactions between neighboring atoms of an appropriate distance is a matter of great significance in constructing accurate embedded-atom-method interatomic potentials,especially for the prediction of surface energy.The lattice-inversion embedded-atom-method interatomic potentials for Li,Na,and K are successfully constructed by taking the fourth-neighbor atoms into consideration.These angular-independent potentials markedly promote the accuracy of predicted surface energies,which agree well with experimental results.In addition,the predicted structural stability,elastic constants,formation and migration energies of vacancy,and activation energy of vacancy diffusion are in good agreement with available experimental data and first-principles calculations,and the equilibrium condition is satisfied.     

Depth control of a silicon structure fabricated by 100q keV Ar ion beam lithography

Ion beam lithography of a silicon surface using an Ar ion beam with an ion energy in the order of hundreds of keV is demonstrated in this study. A specially designed ion irradiation facility was employed that enabled generation and irradiation with a highly accelerated and highly charged Ar ion beam. An ion-beam-induced amorphous layer on a silicon substrate can be selectively etched in hydrofluoric acid, whereas, a non-irradiated area is scarcely etched and, consequently, a concave structure can be fabricated on the irradiated area. To control the depth of the structure, parameters for dependence of the depth on ion irradiation were investigated. As a result, the depth of irradiated area can be controlled by the ion energy that is adjusted by the acceleration voltage and the ion charge. In addition, the etch resistance of the irradiated area increases with an increase in ion energy due to the crystalline layer formed on the surface. Simulation results reveal that the depth is strongly related to the defect distribution induced by ion irradiation. These results indicate the potential use of this method for novel three-dimensional lithography.