According to what I understand, diffusion current is caused by the change in concentration of charge carriers in semiconductor (free electrons and holes) from higher concentration region to lower concentration region due to thermal energy. However, I'm still unsure that if the diffusion current always exist inside crystal. As the concentration drop in higher region and increase in lower region, finally, the concentration in the whole crystal will be equal so no concentration change. Will the diffusion current still exist after that.
Moreover, in non-doping semiconductor (ex: pure Si) the density/amounts of holes and electrons the same so is there diffusion current. Suppose that the diffusion is only 1 dimensional and 1 direction. The charge carriers which diffuse contain both hole and electron then the total charge movement is zero that make the current zero, is it true?