Question

Consider an open-circuited p-n junction in thermal equilibrium. Let \[{{\text{J}}_{\text{p,drift}}}\] and \[{{\text{J}}_{\text{p,diff}}}\] be the hole drift and diffusion current densities, respectively, and let \[{{\text{J}}_{\text{n,drift}}}\] and \[{{\text{J}}_{\text{n,diff}}}\] be the corresponding electron current densities. Of the following equalities, mark false, at all points in the p-n junction structure.
A) \[{{{J}}_{{n,drift}}}+{{{J}}_{{p,drift}}} = -{{{J}}_{{n,diff}}}-{{{J}}_{{p,diff}}}\]
B) \[{{{J}}_{{n,drift}}}+{{{J}}_{{n,diff}}} = {{{J}}_{{p,drift}}}+{{{J}}_{{p,diff}}}\]
C) \[{{\text{J}}_{\text{n,drift}}}={{\text{J}}_{\text{n,diff}}}\] and \[{{\text{J}}_{\text{p,drift}}}={{\text{J}}_{\text{p,diff}}}\]
D) \[{{{J}}_{{n,drift}}}+{{{J}}_{{p,diff}}}=-{{{J}}_{{n,drift}}}-{{{J}}_{{p,diff}}}\]

Answer 1

Hint: There are two types of current through a semiconducting material – one is drift current and the other is diffusion current. The mechanism of drift current is similar to the flow of charge in a conductor. In semiconducting material, when a heavy concentration of carrier is introduced to some region, the heavy concentrations of carriers distribute themselves evenly through the material by the process of diffusion. We have to choose the option that stands for all points in the p-n junction structures.

Complete step by step solution:
In the case of a conductor when a voltage is applied across the material, the electrons are drawn to the positive end. Similar is the case in a semiconductor. However, the movement of the charge carriers may be erratic due to collisions with other atoms, ions and carriers. So, the net result is a drift of carriers to the positive end. It should be remembered that there is no source of energy as required for drift current.

The electron diffusion and drift current densities are not equal in a p-n junction structure at any point and the same holds for the drift and the diffusion current densities for holes.

Hence option (C) is the correct answer.

Note: Some students get confused here and try to use the drift-diffusion equation for electrons, which is the wrong approach. The drift-diffusion equation states that \[\overrightarrow{{{J}_{n}}}={{\text{J}}_{\text{n,drift}}}+{{\text{J}}_{\text{n,diff}}}\] where \[\overrightarrow{{{J}_{n}}}\] is the overall current density. This is not applicable in all cases because if a strong electric field is applied, then drift current dominates the overall current density.