Comprehensive computer experiments have been performed on various aspects of thin film deposition and growth in attempts to bridge the gap between theoretical predictions and experimental observations and to facilitate the development a realistic model for predictive purposes. The results enhance our understanding of the underlying physical processes and provide a vehicle for demonstrating relationships between fabrication conditions and subsequent film properties. Ultimately, we hope that this understanding will improve process reproducibility and promote our ability to produce desirable film properties. This paper comprehensively surveys the modeling of amorphous solids and, in the course of examining prior simulations of thin film deposition and growth, identifies areas that warrant particular attention.
In this study several recently developed theoretical models will be reported which help to understand some of the fundamental processes which occur at an atomic level during thin film growth. A simple stochastic lattice-gas model has been employed to reveal substrate temperature effects on columnar microstructure. Molecular-dynamics studies have been performed in order to elucidate the adatom-surface interaction and to simulate vapor, sputter and ion-assisted deposition. A collision cascade model for ion-assisted optical films has also been used and explains quantitatively the experimentally observed densification of optical films.
Efficient algorithms have been developed for both off-lattice and lattice models of ballistic deposition. These models allow large structures to be generated (particularly in two dimensions) which can be used to explore the fractal scaling relationships which describe their geometry. A series of lattice and off-lattice models have been used to explore the effects of simple restructuring mechanisms on deposit densities as well as the self-affine fractal geometry of their surfaces. Despite the fact that ballistic deposits are uniform on all but short length scales, the growth process and/or particle connectivity can be used to define a tree-like substructure with a power law distribution of tree sizes. This substructure exhibits universal scaling properties which are shared by a variety of ballistic deposition models as well as the Eden growth model.
Thin films deposited from the vapor or by molecular beam epitaxy exhibit a wide range of morphologies. Low temperature processes often lead to an irregular columnar structure, with numerous pores and voids throughout the film. At higher temperatures the structure is usually more compact, but the formation of a deposit of uniform thickness may be precluded by clustering. In this paper we consider model studies of the structure of thin films based on molecular dynamics calculations of the deposition process and of thin film stability. Although large scale simulations of vapor deposition in three dimensions are not feasible on realistic time scales, important information can be obtained by the use of stability arguments and elementary models. The morphologies corresponding to meatstable and equilibrium states are predicted from the potential energy surfaces. Kinetic effects on thin film structures are assessed by simulations of two-dimensional and simple three-dimensional systems.
Two macroscopic two-dimensional geometrical models have been developed to describe the cross-sectional morphology of thin films which exhibit columnar microstructure. Using simple geometrical assumptions and assumptions based on experimental results, these models trace the evolution of cone-like clusters from their point of nucleation within the film to their emergence at the top surface. The simulated films are then characterized by calculating their roughness as a function of film thickness for different input parameters.
We have modelled the microstructures that result from grain nucleation and growth-to-impingement in two dimensions, using various nucleation and growth conditions. Nucleation conditions include simultaneous nucleation at a fixed number of sites, continuous nucleation at a constant rate per unit of untransformed area, cases in which the nucleation rate declines with time, and cases in which nucleation is excluded in a zone surrounding each pre-existing grain. The growth rate for each grain is taken to be a simple function of the grain radius, either increasing with radius, decreasing with radius, or remaining constant. These different conditions result in markedly different structures, with different geometric and topological properties. We have also modelled the effect of grain boundary migration and grain growth following impingement.
The nature of the microstructure of physical vapor-deposited films depends sensitively on the substrate temperature during deposition. At low temperatures the microstructure is porous and ballistic aggregation-like, at intermediate temperatures the microstructure is columnar, and at elevated temperatures the grains are three dimensional. These different microstructural regimes are known as Zone I, II, and III, respectively. A theoretical analysis is presented in which the temporal evolution of the columnar micro-structure (Zone II) is studied. The columnar microstructure is shown to be a balance between shadowing (which results in Zone I microstructures) and surface diffusion (which tends to smooth the surface). In addition to predicting the proper microstructure, this analysis properly predicts the temperature at which the Zone II to Zone I microstructural transition occurs. Since bulk diffusion is negligible and surface diffusion controls the microstructure in Zone II, the microstructure in the bulk of the film, may be viewed as frozen and all microstructural evolution occurs at the current, or active, surface. A Monte Carlo computer simulation technique which models the microstructural evolution of the surface is presented. The simulation follows the temporal evolution of realistic three dimensional Zone II microstructures and accounts for growth competition between adjacent grains and the formation of film texture.
Structure zone models based on examinations of thin films using optical and scanning microcopy have provided useful guide-lines in categorizing general regimes of film growth behavior. However, many observations have been made since the original zone model for evaporated coatings was proposed by Movchan and Demichishin in 1962 and extended to magnetron sputtering in 1974. The purpose of this paper is to revisit the structure zone models and their physical interpretation in the light of recent experimental and computer simulation observations.
The recently developed microscopic approach to solid-state nucleation is applied to the case of monolayers. Using the previously defined stability factor, a criterion for nucleus stability is derived and used to analyze the stability of square nuclei on a two-dimensional square lattice. The nucleation behavior is found to be similar to that predicted by classical nucleation theories only when the binding energy is high or the temperature is low. Computer simulations indicate that this is also true for nuclei of random shapes.
Preliminary results of a modified thin-film-growth model are presented. The basic simulation is of the type first introduced by Henderson et al.1 The modification introduced is inclusion of a simple potential between the particles in the film and each incoming evaporant particle.
The nodule has been successfully simulated for vapor deposition techniques by a modified hard-disk model. The influence of model parameters on nodule growth is more thoroughly explored in this paper. Also, by making minor changes in the model, simulations of amorphous film and sputtered film are considered. The model is compared with experimental results.
The refractive index of an optical film composed of a mixture of more than one constituent is a function of the micro-structure of the film. Even films that are nominally of a single material have refractive index values that require interpretation on the basis of mixed component models because these values differ significantly from the values in equivalent bulk materials. In the latter case, the film is usually a mixture of bulk material and voids, or bulk material, voids, and adsorbed water. Many models have been used to explain the refractive indices of mixed component systems. The Lorentz-Lorenz model, the Drude model, and the effective media approximation (EMA or Bruggeman model) are the most common models used to estimate isotropic refractive indices of mixtures of isotropic materials. Films composed of anisotropic micro-structures, however, require other models such as the Bragg and Pippard model. One use of mixed component models would be to predict the porosity of optical films. Another would be to predict the refractive index of coevaporated films. However, no one model is applicable to all situations. Therefore, the prediction of refractive index becomes difficult. Usually, the model is chosen after the set of measurements has been done.
A thin-film growth simulation of the type first introduced by Henderson et. al.1 is applied to defect propagation in thin films. Film growth is simulated on substrates having sinusoidally varying surfaces. The surfaces of the simulated films are then characterized by their power spectrum and their correlation with the substrate surface. The effects of film thickness as well as substrate sinusoid variation period and amplitude are investigated.
The effects of coatings on the optical scatter and related surface microroughness of coated surfaces are examined. Experimental results indicate that coated surfaces, in some cases, are smoother than the bare substrate. A model for smoothing process is presented. The role of deposition mechanism and substrate morphology are discussed.
In-situ ellipsometry may be used to characterize thin films during growth. To interpret ellipsometric raw data, models must be assumed. The model for dielectrics is usually simple: a smooth, homogeneous, isotropic film of uniform thickness on a smooth substrate. This simple model causes index and thickness errors, especially in very thin films. More accurate models are required, and microstructure must be included in these models. Surface and bulk-like phenomena are caused by microstructure. As a result of surface roughness, light is scattered from the beam. At finite angles of incidence, s-polarized light is preferentially scattered. Furthermore, the microstructure breaks the film's inherent two-dimensional symmetry, and an isotropic bulk material becomes a birefringent thin film (form birefringence). Films with columnar microstructure on smooth substrates have been considered. As the films grow, the columnar microstructure develops. This leads to scattering and anisotropy in the films. Ellipsometer signals have been calculated using microstructure models. In CaF2 films, form birefringence appears to be the dominant effect.
This study addresses the question, "How can the optical properties of matter in ultrathin amorphous nonmetallic films in multilayers best be determined from reflectance (R) and transmission (T) measurements." A blue shift in the band gap of plasma CVD a-Si:H/a-SiN.:H multilayers was reported sev-eral years ago. It was suggested that the shift in the band gap, Eg, relative to bulk a-Si:H as given by the Tauc plot was due to quantum confinement effects. The purpose of this study is to evaluate the usefulness of various effective media theories (EMT) for determining the optical constants of materials in a multilayer and to explore to what extent a shift in band gap to higher energy may be an artifact of the method of optical analysis. Incoherent approaches are the most common methods of determining band gap from R and T. These do not require iteration to obtain optical constants from the optical data. The band gap determined by such methods was, however, generally 8% higher than the actual band gap when a suitable hypothetical case was investigated. Coherent effective media theory provides a noteworthy alternative to both incoherent EMT and fully coherent multilayer modeling, (which is accurate but is excessively com-plicated and poorly convergent). The accuracy of the band gap is at the limit, 2-3%, of what can be expected for graphical methods. A previously unappreciated source of optical artifacts was also identified. Dispersion, which is commonly ignored when Eg is determined graphically, is shown to distort, in certain cases, the anticipated straight line behavior of the aE vs. E plot.
A program was written to simulate the sputter deposition of amorphous rare earth-transition metal (RE-TM) thin films using a model based on the serial deposition of hard disks. Apart from permitting the simultaneous deposition of multi-component films, the model attempted to incorporate details of the deposition process by using realistic representations of the energy and trajectory distributions in the depositions stream. These were found to improve significantly the packing fraction of simulated films and reduced the pronounced columnar tilt observed in many previous simulations. A number of analytical techniques were employed which provided useful configurational information and some details of the short range ordering (SRO) of simulated films.
A real deposition of optical interference filters involves many, often interconnected parameters l, which may change from one run to the next; thus the performance of the resulting filters is, in general, non repeatable. We have developed a model for a thin film process2, using a Monte-Carlo technique that makes it possible to emulate the operator response to the optical monitor, the evaporation plant and the physical properties of materials as a function of the operating point during deposition, according to previous experimental data. Until now a visual estimation of the espectral response after several simulations is ussually done, providing a qualitative way to control some critical parameters. In this paper we show the correlation of the standard deviation of an evaluating factor of the performance of the filter. This quality factor and its uncertainty are convenient in estimating the reliability of certain experimental procedures in the real process, allowing the operator to control a given parameter which influences more dramatically the performance of the deposited filter. It is not simple to stablish a criterium for performance repeatability for an ideal filter with a single quality factor because, depending on the application, the spectral re-sponse requirements are different. We propose a general purpose criterium of repeatability as well as a discussion of the widely accepted definition of "ideal filter".
Thermal behavior of optical thin films subjected to laser irradiation is modeled by coupling the one-dimensional heat flow equations with the characteristic matrix formalism developed to describe the optical properties of thin-film multilayers. The heat flow has two major effects on multilayer behavior: first, differential expansion of adjacent layers can create stress and second, the temperature dependence of the refractive index can affect optical performance. We have chosen to test this model by simulating the thermally induced bistability of a Fabry-Perot etalon. The transmittance peak of such an etalon is extremely sensitive to the optical thickness of its spacer layer because the electric field of the incident light beam is maximized there. Such models can also be applied to studies of thermal- and laser-induced damage in optical materials and to other models dealing with the growth of coatings.
A deposition system for laser flash evaporation was assembled and used to deposit onto polycarbonate SiOxNy rugate filters with optical densities as high as 2.5 and band-widths as low as 6.8% of the rejection wavelength. When coupled with feedback loop closure, installation of a real-time index and thickness monitor should provide the necessary control to produce higher quality rugate filters with multiple rejection lines and optical densities greater than 4.
Metals were evaporated under vacuum and the metal atoms solvated by excess organic solvents at low temperature. Upon warming stable colloidal metal particles were formed by controlled metal atom clustering. The particles were stabilized toward flocculation by solvation and electrostatic effects. Upon solvent removal the colloidal particles grew to form thin films that were metallic in appearance, but showed higher resistivities than pure metallic films. Gold, palladium, platinium, and especially indium are discussed.
Simulation results are presented for some dynamical processes occurring in the growth of (100) layers of silver. The overlayer dynamics are evolved using a recently developed method that, in the regime where surface diffusion consists of discrete hops, yields classically exact dynamics for an arbitrary interatomic potential. The time-scale limitations of direct molecular dynamics simulations are thus overcome. The Ag/Ag(100) system is modeled using a sophisticated form of interaction potential, similar to the embedded atom method, in which the energy is given by a sum of pairwise interactions plus a term for each atom that depends on the local atomic density. This type of potential includes the many-body terms necessary to describe a variety of atomic environments, such as the perfect fcc metal, free surfaces, vacancies, interstitials, and even the diatomic molecule, but with the computational scaling of a simple pair potential. The present study focuses on some of the dynamics in a single layer of silver: the diffusion and dissociation of clusters of adatoms and vacancies. Some interesting features are observed, including a nonmonotonic decrease in diffusion constant with increasing cluster size, and a roughly constant mean square distance a cluster migrates before dissociation (ejection of a monomer).