Asymptotic electron energy flux equations for hot-carrier transport simulation

In isothermal device simulations, the Bernoulli function has to be computed carefully to avoid potential numerical difficulties. Problems may arise when the difference in discretized potential values between two nodes is sufficiently small. In nonisothermal hot-carrier transport, additional asymptotic cases can arise depending on the difference in the electron temperature values. In this letter, all possible limiting expressions for the electron energy flux are presented. A parallel treatment will lead to the corresponding equations for current densities.