Diffusion and Drift of Charge Carriers in a Semiconductor

A p-n junction is a basis for all transistor. It is formed in a single crystal silicon (Si) by doping the n-side with phosphorus (P) atoms and the p-side with boron (B) atoms.

The doping can be achieved by diffusing atoms from a liquid, solid or gaseous source of dopants atoms known as a precursor. We can use ion implantation method, in which dopant atoms are incorporated using high-energy ion beams or another method like thermally diffusing dopant atoms. Now, each phosphorus atom contributes an extra electron and each boron atom contributes to an extra hole.  Consider that the diffusion of the species is initiated by the concentration gradient and temperature and then the external electric and magnetic field can initiate the drift of carriers. Assume the temperature is 300K.

Firstly, we know that the concentration of electrons on the n-side (n_n) is greater than that in the p-side (n_p) and vice versa. We also have a small concentration of electrons (n_p) on the p-side, because bonds of silicon atoms break due to thermal energy resulting in the creation of electron-hole pairs. Hence, due to the concentration gradient, electrons in the n-side (n_n) will diffuse into the p-side and vice versa. Notice that across the p-n junction there is a concentration gradient of P and B atoms as well. But, these atoms, which now become ions after donating and accepting electrons, do not diffuse since the temperature of 300K is too low.

As electrons diffuse from n-side to p-side, a portion of the n-side crystal becomes positively charged since the positively charged P ion is left behind. The same thing happens to the portion of the p-side crystal. As more and more holes try to diffuse from p-side to n-side, they encounter the positively charged P ion and their motion is resisted. Thus, always remember that the diffusion of electrons and holes in a p-n junction does not continue until the concentration of electrons and holes become equal, unlike the situation of two different glass partitioned in a box. To prevent the equalization of electron and hole concentrations, an internal electric field (E_x) sets up over a width W and the resultant voltage is called contact potential (V_o).

Thus, this internal electric field causes the electrons from p-side drift to n-side. Take note that here we are using the word drift, not diffuse, because the movement of electrons and holes now is due to the electric field. Thus, the flow of electrons due to diffusion and drift is in the opposite direction. The same goes for the holes. Hence, the electrical current due to diffusion and drift of each type of carrier cancels out. As a result, a p-n junction under equilibrium does not carry a net current.