Stationary temperature field of dielectric films and substrates in the field of a continuous ion beam

The influence of temperature dependence of thermal conductivity and degree of blackness of sample-substrate system on formation of temperature field of dielectric and substrate films under irradiation by a continuous ion beam has been theoretically investigated. The case has been considered when the mean free path of ions is less than the thickness of the sample. Thus, an artificial separation of sample into two parts have been carried out, and for the film-substrate system under consideration, a system of three nonlinear heat conduction equations has been written. It has been supposed that the sample is attached to a massive substrate, the second surface of which has been immersed in water, and irradiation has been carried out in the air. The temperature dependence of coefficient of thermal conductivity and the degree of blackness of samples has been adopted in a linear form by means of thermal coefficients of these quantities. Analytic expressions for temperature field of sample and the substrate have been obtained, as well as a system of interrelated nonlinear algebraic equations for the characteristic temperatures. By a numerical solution of a system of nonlinear algebraic equations, the dependences of temperature of the irradiated surface of the sample-substrate system on parameters of incident ion beam for various types of substrates have been defined. It has been found that these dependences are nonlinear. It has been found that heating of the sample, including its irradiated surface, decreases substantially with increasing thermal conductivity of the substrate. (author)