The selective-sublimation processing is a technique for deposition of nanosized thin films aimed at controlling the composition of the film and hence its properties. The method consists of the deposition of a solid solution of a mixed-metal oxide with the sublimation temperature of one of the pure metal oxide being rather low. Proper thermal treatment allows to selectively sublimate the most volatile metal oxide. In this paper we first model the thermal processing undergone by the films under the assumption that the thickness of the layer is constant. The problem is formalized as an initial-boundary value problem for a one-dimensional diffusion equation with fixed boundary. We construct an explicit solution for the problem relying on a set of observable physical quantities that can be profitably used in experiments, i.e., the sublimation rate of the most volatile oxide and the diffusion coefficient. Conversely, we discuss the problem of determining such coefficients from an additional measurement and provide error estimates. Finally, we propose a more general model taking into account the thinning of the film due to sublimation. It results in a free-boundary value problem at the sublimation surface of the film, which is solved by successive approximations.
On a diffusion problem arising in nanophased thin films
CORLI, Andrea;
2008
Abstract
The selective-sublimation processing is a technique for deposition of nanosized thin films aimed at controlling the composition of the film and hence its properties. The method consists of the deposition of a solid solution of a mixed-metal oxide with the sublimation temperature of one of the pure metal oxide being rather low. Proper thermal treatment allows to selectively sublimate the most volatile metal oxide. In this paper we first model the thermal processing undergone by the films under the assumption that the thickness of the layer is constant. The problem is formalized as an initial-boundary value problem for a one-dimensional diffusion equation with fixed boundary. We construct an explicit solution for the problem relying on a set of observable physical quantities that can be profitably used in experiments, i.e., the sublimation rate of the most volatile oxide and the diffusion coefficient. Conversely, we discuss the problem of determining such coefficients from an additional measurement and provide error estimates. Finally, we propose a more general model taking into account the thinning of the film due to sublimation. It results in a free-boundary value problem at the sublimation surface of the film, which is solved by successive approximations.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
