The Equation of Backward Diffusion and Negative Diffusivity

Up to now, all the diffusion theories have shown that the direction of diffusion flux is from high concentration area to lower concentration area (forward diffusion) and diffusivity is positive. In some research on simultaneous diffusion of boron and point defects in Si, the results show that the diffusivity of interstitials can be negative and diffusion process can be backward diffusion. In backward diffusion process, the direction of diffusion flux is from low concentration area to higher concentration area. The phenomenon of backward diffusion and negative diffusivity should be explained. Based on thermodynamic theory, the equation of backward diffusion and negative diffusivity are presented and discussed.