Bessel Decomposition of Temperature Profiles in Film Deposition Reactors

Among the three process pillars of adding, patterning, and removing actions in the fabrications of semiconductor devices, film deposition takes up the central position in the construction flow of structure formation. Film uniformity of the deposition processes has significant impacts on the distributions of the electrical functions of the fabricated devices. Achieving good final uniformity of the film thickness depends critically on profiles of the thermal fields inside the film deposition chambers. Constructing simple, efficient, and yet accurate enough models of the temperature fields is therefore crucial in effective fault detection and eventually, for film thickness uniformity controls. Instead of solving systems of nonlinear partial differential field equations or conducting large-scale simulation runs, we explored one decomposition method of the temperature fields using a zeroth order Bessel function of the first kind for applications of fault detection and classification.