Liliana Restuccia
In memory of H. Brezis, an expert in Nonlinear Analysis
Abstract. In this paper, in the framework of rational extended irreversible thermodynamics with internal variables, a model for doped semiconductor crystals with dislocations is worked out, where a dislocation tensor and its gradient are introduced in the set of independent variables to describe these defect lines influencing the mechanical, thermal, electric transport properties of these media. The main equations of the model are introduced and the entropy inequality is analyzed by Liu’s theorem, deriving the equations of state for the constitutive variables, the affinities, the dissipation inequality and other relations. Applying Wang’s and Smith’s theorems the constitutive theory and the expressions for the sources of the rate equations are carried out. According to the extended thermodynamics, a generalized Maxwell- Cattaneo-Vernotte equation for the heat flux and transport equations for the defects and charges fluxes present a relaxation time and a finite velocity for the disturbance propagation. The obtained results may have applications in several technological sectors, such as applied computer science, integrated circuits VLSI and nanotechnology (where high-frequency processes and the construction of sophisticated new materials with particular thermal properties are studied).
Keywords: rational extended irreversible thermodynamics, internal variables, extrinsic semiconductors, materials with defects of dislocation.
MSC: 74A15, 74A20.
DOI 10.56082/annalsarscimath.2025.1.253
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics on Its Application, Volume 17 no 1, 2025
