On integral forms of the balance laws for deformable semiconductors

Abstract

The general nonlinear differential equations describing the interaction of finitely deformable, polarizable, heat conducting intrinsic n-type semiconductors with the quasi-static electric field are transformed from the unknown present coordinate description to the known reference coordinate description, which is the form needed in the treatment of problems. For the differential form of each balance equation in the reference coordinate description, the associated integral form is obtained. The resulting integral forms turn out as expected with the exception of the one due to the balance of linear momentum for the semiconducting fluid, in which an important change in and simplification from the form used heretofore is introduced. More importantly, the previous existing integral form of the equation of the balance of energy in the present coordinate description is transformed to a different form, which is equivalent to the original form only when the field variables are differentiable. The revised integral form in the present coordinate description is then transformed to the reference coordinate description, from which an energetic jump condition across a moving non-material surface of discontinuity is obtained which is consistent with all the other jump conditions obtained from the other integral forms. In addition, the expression for the quasi-static electric Poynting vector in the reference coordinate description is determined.