The current equation in strong electric fields

The paper theoretically investigates tie emergence:of:the. drift-diffusion current equation in electron transport in a semiconductor subjected to a strong electric field using a method applicable to other transport processes. The changes to the drift-diffusion equation are examined in two cases. First, if the electric field exhibits spatio-temporal variations, the corrections to-the drift velocity and diffusion tensor are derived to first order in the field derivatives. Second, it is shown that, over times shorter than the energy-relaxation time, drift and diffusion should be supplemented with 'paradiffusion' terms associated with non-Gaussian spreading. The work shows the limits of the drift-diffusion picture in designing or analysing semiconductor devices.