Geometric modeling of homoepitaxial CVD diamond growth: I. The {100}{111}{110}{113} system

Plasma-assisted CVD homoepitaxial diamond growth is a process that must satisfy many stringent requirements to meet industrial applications, particularly in high-power electronics. Purity control and crystalline quality of the obtained samples are of paramount importance and their optimization is a subject of active research. In the process of such studies, we have obtained high purity CVD diamond monocrystals with unusual morphologies, namely with apparent {1 1 3} stable faces. This phenomenon has led us to examine the process of CVD diamond growth and build up a 3D geometrical model, presented here, describing the film growth as a function of time. The model has been able to successfully describe the morphology of our obtained crystals and can be used as a predictive tool to predetermine the shape and size of a diamond crystal grown in a given process configuration. This renders accessible control of desirable properties such as largest usable diamond surface area and/or film thickness, before the cutting and polishing manufacture steps take place. The two latter steps are more sensitive to the geometry of the growth sectors, which will be addressed in a companion paper. Our model, applicable to the growth of any cubic lattice material, establishes a complete mapping of the final morphology state of growing diamond, as a function of the growth rates of the crystalline planes considered, namely {1 0 0}, {1 1 1}, {1 1 0}, and {1 1 3} planes, all of which have been observed experimentally in diamond films. The model makes no claim as to the stability of the obtained faces, such as the occurrence of non-epitaxial crystallites or twinning. It is also possible to deduce transient behavior of the crystal morphology as growth time is increased. The model conclusions are presented in the form of a series of diagrams, which trace the existence (and dominance) boundaries of each face type, in presence of the others, and where each boundary crossing represent a topology change in terms of number of faces, edges and vertices. We validate the model by matching it against crystals published in the literature and illustrate its predictive value by suggesting ways to increase usable surface area of the diamond film.