In a forward-biased PN junction, the potential barrier decreases, allowing more majority carriers from one side to diffuse to the other side where they are minority carriers. After they cross the potential barrier, they form a diffusion current, the drift current of minority carriers is insignificant, then they recombine with majority carriers and form a drift current under the effect of the applied electric field.
Why do minority carriers form a diffusion current not a drift current after they cross the potential barrier? It is counter-intuitive that the main current is diffusion when there is an applied electric field.
This is according to all the microelectronics book I'm currently reading. There is one which says this can be proved but without providing anything. Can someone please provide a proof for this.