Drift is the movement of carriers due to an applied electric field ($\mathcal{E}$). While the field accelerates carriers, they constantly scatter due to collisions with the lattice (phonons) and impurities.
The concentration of carriers is governed by the Fermi-Dirac distribution function, $f(E)$, which describes the probability that an energy state is occupied by an electron. A critical parameter is the , the energy level where the probability of occupation is 50%. semiconductor physics and devices neamen pdf
"When the p-n junction is formed, electrons from the n-side diffuse into the p-side, leaving behind positively charged donor ions. A built-in potential barrier is established." Drift is the movement of carriers due to