Integral equations are derived which describe free molecular flow and simultaneous film deposition in long rectangular trenches. The equations apply to flow in the absence of deposition and to both low-pressure chemical vapor deposition (LPCVD) and physical vapor deposition (PVD), i.e., over the full range of reactant sticking coefficient from zero to unity. A steady-state assumption is implicit in the formulation. In the absence of film deposition, the flux to the surface is spatially uniform. Analytical expressions are presented for the initial deposition profiles along the trench sides and bottom for PVD (unity sticking coefficient). Numerical inversion of the integral equations provides initial deposition profiles for LPCVD (low sticking coefficient). The calculated initial deposition profiles are consistent with empirical results which typically show poor uniformity in PVD and high uniformity in LPCVD, and also compare well with Monte Carlo based simulations of deposition processes.
Two models used for predicting film profile evolution during low pressure chemical vapor deposition in features on patterned substrates are compared; (i) a ballistic transport-reaction model (BTRM) in which transport between surfaces in a feature is "line of sight" and (it) a diffusion-reaction model (DRM) in which gas-phase transport is expressed in terms of concentration gradients and Knudsen diffusion. In order to compare the qualitative and quantitative predictions of the two models we use blanket tungsten deposition by the hydrogen reduction of tungsten hexafluoride in long (two-dimensional) rectangular trenches as an example. The two models are based on the same underlying assumptions: however, they differ in their treatment of molecular transport in features. For both models, film deposition occurs through heterogeneous gas-solid reactions, and profile evolution is two dimensional. The BTRM is formulated in terms of three-dimensional fluxes to the evolving film surface. These fluxes are expressed in terms of fluxes from all other points on the surface of the feature and from the source volume and are therefore "nonlocal." In the DRM, fluxes to the local surface are expressed in terms of local gas-phase concentrations. Because of the assumptions used to compute Knudsen diffusivity in the DRM, the transport occurs in one dimension. "Rules of thumb" relating qualitative changes in film conformality to changes in process conditions, derived using the governing equations of the two models, are the same and agree well with observed trends. Using a "relative reactant depletion criterion," both models predict the same ratio of partial pressures of reactants which maximizes film conformality. Quantitative step coverage predictions obtained from the BTRM simulations are consistently higher than those of the DRM.Process modeling is gaining importance in the microelectronics industry and has assumed multiple roles in process development, modification, and optimization. For example, low pressure chemical vapor deposited (LPCVD) process models are used to predict film conformality 1-9 as well as to develop novel process protocols to increase film cortformality and wafer throughput. 3,g Typical LPCVD systems are characterized by the presence of free molecular or Knudsen flow (high Knudsen numbers) within micronscale features and heterogeneous gas-solid reactions which lead to film growth. In recent years, two different physically based models of LPCVD processes have achieved reasonable success: (i) a "continuum-like" diffusion-reaction model (DRM), 14 and (it) a particle-based modified line-ofsight or ballistic transport-reaction model (BTRM). 44The BTRM has the advantage that its equations are derived from a strong fundamental basis; however, its application is restricted to low pressure processes. The advantage with the DRM is that it can be modified to simulate CVD processes at higher pressures (lower Knudsen numbers), in addition to the low pressure processes. Limitations of the DRM lie mainly in its treatment of mo...
The integro-differential equations which govern free molecular flow and low pressure chemical vapor deposition in long rectangular trenches are reviewed. The model equations are used to simulate the deposition of tungsten by hydrogen reduction of tungsten hexafluoride, with reactive sticking coefficients determined by local deposition conditions. Numerical solution of the governing equations provides film profiles and deposition rate profiles as a function of position in the trench at any time until the trench mouth closes. The impact of the operating conditions on step coverage is discussed in relation to reactive sticking factors. Calculated tungsten step coverages for three selected realistic initial trench shapes highlight the importance of establishing a consistent method for reporting step coverages. We introduce the percentage of feature fill as a measure of step coverage. To allow evaluation of the quantitative predictive ability of a model, cross-sectional scanning electron micrographs are required in general.
Conformality of SiO2 films from tetraethoxysilanesourced remote microwave plasmaenhanced chemical vapor deposition J. Vac. Sci. Technol. A 13, 676 (1995); 10.1116/1.579806Optical characteristics of SiO2 formed by plasmaenhanced chemicalvapor deposition of tetraethoxysilane Quantitative infrared analysis of the stretching peak of SiO2 films deposited from tetraethoxysilane plasmas EVOLVE, a low pressure deposition process simulator based on a fundamental model for free molecular transport and heterogeneous surface reactions in features, is used to predict the evolution of silicon dioxide film profiles during plasma enhanced chemical vapor deposition from mixtures of tetraethoxysilane (TEOS) and oxygen. The constitutive relationships required by EVOLVE are supplied by simple models for the plasma, the plasma sheath and the surface chemistry. The intrinsic kinetic model used in the simulations involves film growth by oxidative attack on adsorbed TEOS and/or TEOS fragments by both oxygen ions and oxygen atoms. Recombination of oxygen atoms on the surface of the growing film competes with TEOS oxidation by atoms. The plasma models are used to predict the fluxes of oxygen ions and oxygen atoms to the surface. The fluxes of all neutral species from the source and from all surfaces are assumed to obey cosine distribution functions. Oxygen ions are assumed to follow an exponential distribution; the standard deviation of the distribution is adjusted to match predicted film profiles with experimentally determined profiles. This combination of an almost directional component and an almost isotropic component allows the prediction of the experimental trends in deposition rate and film conformality with operating conditions. The constitutive models are used by EVOLVE to predict film profiles as a function of temperature, within their window of validity, for deposition in ideal rectangular trenches with an aspect ratio of 2. Film conformality decreases as temperature increases, even though deposition rate actually decreases. Film con formality decreases with increasing pressure and increases with increasing power. All of these predicted trends in conformality agree with our experimental results.
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