P1: FHF [RD1: JMS] KL958(A)-6528-99 August 1, 2000 9:45JOURNAL OF MATERIALS SCIENCE 35 (2000)5371– 5381Multi-length scale modeling of CVD of diamondPart IIA combined atomic-scale/grain-scale analysisM. GRUJICIC, S. G. LAIProgram in Materials Science and Engineering, Department of Mechanical Engineering,241 Fluor Daniel Building, Clemson University, Clemson, SC 29634-0921E-mail: [email protected] vapor deposition of polycrystalline diamond films is studied by combining anatomic-scale kinetic Monte Carlo model with two (one three-dimensional and onetwo-dimensional) grain-scale models. The atomic-scale model is used to determine thegrowth rates of (111)- and (100)-oriented surface facets, the surface morphology of thefacets and the extent of incorporation of the crystal defects. Using the atomic-scalemodeling predicted growth rates for the (111)- and (100)-oriented facets, grain-scalemodelling is carried out to determine the evolution of grain structure, surface morphologyand crystallographic texture in the polycrystalline diamond films. It is found that dependingon the relative growth rates of the (111)- and (100)-oriented facets, which can be controlledby selecting the CVD processing conditions, one can obtain either h110i-textured films witha relatively smooth faceted surface or h100i-textured films with a highly pronounced deepfacets. In both cases, however, the film surface is composed entirely of the h111i facets.This findings are found to be fully consistent with the available experimental results.C°2000Kluwer Academic Publishers1. IntroductionOver the last decade,chemicalvapor deposition (CVD)of the diamond films from a precursor gas mixture con-tainingasmallamountofhydrocarbon(e.g.CH4,C2H2,etc.) and H2as the carrier gas at pressures in the range1–200 Torr has become a commercially viable process[e.g. 1–3].In the CVD processthe gas mixture isheatedviahot filaments,plasmasor combustionflames, topro-mote dissociation of the molecular hydrogen (H2) intoatomic hydrogen (H) and formation of various hydro-carbon radicals. While under the typical CVD process-ing conditionsgraphite is thermodynamically moresta-ble than diamond, H atoms bond with and passivate thesurface carbon atoms by converting the graphite-typesp2-bonding into the diamond-type sp3-bonding [2, 3].It is well-established that CVD of the diamond oc-curs by incorporation of the chemisorbed hydrocar-bon radicals. However, the mechanism of the diamondgrowth is still not well understood, primarily becausethe atomic-scale events which lead to diamond growthare difficult to study in situ. Consequently, computermodeling/simulations and/or interpretation of the exsitu experimental results are the main means of elu-cidating the mechanisms of diamond growth. A varietyof modeling techniques have been employed to date.In a number of these models [e.g. 4, 5], the CVD pro-cess is analyzed at the reactor scale by solving the ap-propriate continuum reactive-gas fluid-dynamics/heat-transfer boundary value problem. While such modelsare quite useful in the design of CVD reactors and typ-ically predict reasonably well the average film-growthrate, they can not account for the effect of surface mor-phology on the growth rate or be used to predict for-mation of the crystal defects during film deposition. Inother classes of models, the CVD process is analyzedat the atomic scale. Among these models some dealwith the surface energetics [6, 7], determination of ki-netic parameters for individual surface reactions [7–9]and the analysis of stability of various surface configu-rations [10–16]. In addition, molecular dynamics [e.g.17] and Monte Carlo [e.g. 18, 19] methods are utilizedto carry out the three-dimensional atomic-scale simu-lations of CVD of the diamond single-crystalline films.The atomic-scale models, while being very instrumen-tal in predicting the generation of crystal defects, andthe effectof surface morphology on the film-depositionrate, can not be used to study the evolution of grainstructure, surface morphology and texture in polycrys-talline diamond films. While the latter phenomena canbe analyzed using one of the grain-scale models such asthe model proposed by Van der Drift [20], these modelshave not yet been applied to CVD of the polycrystallinediamond films.In the present paper, which is Part II of a two-part paper, a multi-length scale approach is used tostudy CVD of the polycrystalline diamond films. InPart I [21], the CVD process is analyzed by cou-plinga reactor-scalemodel withinwhichan appropriatereactor-scale continuum-type boundary value problemfor reactive-gas mixture interacting with the depositionsurfaceis combined with a kinetic Monte Carloatomic-scale model. The coupling between the two models0022–2461C°2000 Kluwer Academic Publishers 5371P1: FHF [RD1: JMS] KL958(A)-6528-99 August 1, 2000 9:45is accomplished by: (a) using the species concentra-tions at the deposition surface obtained via the reactor-scalemodelingtodefinetheboundaryconditionsfortheatomic-scale modeling and; (b) using the atomic-scalemodelling results to identify which surface reactionsgovern CVD of the diamond single crystals of differentcrystallographic orientations and feed this informationback into the reactor-scale model to ensure self consis-tency. In this paper, the atomic scale model developedin Part I [21], is coupled with two grain-scale models tostudy the evolution of surface morphology, grain struc-ture and crystallographicand morphological texturesinthe polycrystalline diamond films.The organization of the paper is as following: InSection II, a detailed description is given of the atomic-scale kinetic Monte Carlo method and of the resultsobtained by applying this method to CVD of the (111)-and (100)-oriented diamond single crystals. A simplethree-dimensional and a two-dimensional grain-scalemodels for the evolution of grain-structure and filmtexture are developed and applied to study CVDof the polycrystalline diamond films in Section III.Main conclusions resulting from the present work aresummarized in Section IV.2. Atomic-scale modeling of CVD2.1. General considerationThe growth of (111)- and (100)-oriented diamondfilms by the CVD has been modeled at the atomicscale using rigid diamond-type lattices. In other words,the atomic relaxations and vibrations are not consid-ered. In the case of (111)-oriented films, the orienta-tion of the lattice is defined as: x =[11¯2], y =[1¯10]and z =[111] while in the case