Simulation of morphological instabilities during diamond chemical vapor deposition

Abstract

The diamond chemical vapor deposition (CVD) process has been investigated theoretically and the morphological instabilities associated with the growth of diamond films have been examined with a model based on the continuum species conservation equation coupled to surface reaction kinetics. A linear stability analysis and numerical calculations have been carried out to determine critical parameters affecting the diamond deposition layer morphology. A two-dimensional model describes the evolution of the gas-solid interface. The dynamic behavior of the interface depends on the reactants' diffusivity and surface kinetics. These factors depend upon the reactant material properties and film growth conditions such as the reactor temperature and pressure. From the analyses, it has been found that the ratio (2/k) of gas phase diffusivity (9) to the surface reaction rate constant (k) plays the critical role in promoting diamond morphological instabilities because the film morphology stabilizing processes of surface diffusion and re-evaporation are absent or negligible during diamond CVD. It is found that the film nonuniformity increases as the ratio (2/k) decreases. Increasing growth rates also result in increasing morphological instability. leading to rough surfaces. It is shown that increasing reactor pressure and decreasing gas-phase temperature and/or substrate temperature promote deposition layer nonuniformity.An approach to avoiding these instabilities is proposed. 0 1997 Elsevier Science S.A.

A Simple Index to Restrain Abnormal Protrusions in Films Fabricated Using CVD under Diffusion‐Limited Conditions

“…These factors, however, are of limited importance for simulating protrusion growth in CVD processes in the continuum regime. [21,30] Although we did not include these factors in our 1D model, here we discuss the effect of these factors. Capillarity tends to stabilize the growth of protrusions.…”

“…According to the result of linear stability analysis in a 2D model [28,30], when stabilizing factors (e.g., surface diffusion, capillarity) can be neglected, the growth of protrusion can be expressed as…”

“…In addition to instabilities caused by concentration gradients, these models also include stabilizing effects due to capillarity and to surface diffusion, which for simulating the growth of micrometer-sized protrusions, are less important than diffusion-limited growth. Among the theoretical studies, only in the work by Mahalingam and Dandy [30] has there been an attempt to determine a simple theoretical description by modeling, in a 2D analysis, the protrusion growth due only to a concentration gradient. They then proposed an index for protrusion growth, namely, the Damköhler number, and finally, based on theory, they predicted the conditions at which protrusion-free films of diamond can be fabricated.…”

“…They then proposed an index for protrusion growth, namely, the Damköhler number, and finally, based on theory, they predicted the conditions at which protrusion-free films of diamond can be fabricated. [30] Development and validation of a simple analytical model for simulating the growth of abnormal protrusions is crucial. A simple model should only include the mechanisms needed for simulating the growth of such protrusions.…”

Nonlinear stability analysis of the growth surface during diamond chemical vapor deposition

“…The onset of morphological instability in the chemical vapor deposition ͑CVD͒ process and the critical properties that cause an initially planar interface to break down have been predicted by means of linear perturbation analyses. [1][2][3][4][5][6][7][8][9] In general, CVD constitutes a free-boundary problem for which the interface shape and position are unknown, and therefore the temperature and concentration fields at the gassolid interface are also unspecified. If the amplitude of the interface shape perturbation can be assumed to be infinitesimal, linear perturbation analysis may be applied to study the onset of interface instability.…”