Question

For \(\mathrm{p}-\mathrm{n}\) junction, which statement is incorrect (A) Donor atoms are depleted of their holes in junction (B) No net charge exists far from junction (C) Barrier potential \(\mathrm{V}_{\mathrm{B}}\) is generated (D) Energy \(\mathrm{V}_{\mathrm{B}}\) is to be surmounted before any charge can flow across junction

Short answer

The incorrect statement is (D): "Energy V_B is to be surmounted before any charge can flow across junction." The energy that must be surmounted is not equal to the barrier potential \(V_B\). External energy or voltage needs to be applied to counteract the barrier potential and allow charge carriers to cross the p-n junction.

Step-by-step solution

Understanding the p-n junction

A p-n junction is a boundary between two different types of semiconductor material, namely p-type and n-type. At the junction, electrons from the n-type material can recombine with holes from the p-type material, creating a region with no free charge carriers called the depletion layer. This process generates an electric potential called the barrier potential (V_B). With this background in mind, let's analyze each statement one by one.

Statement A

"Donor atoms are depleted of their holes in junction." This statement is correct. As mentioned before, the recombination of electrons and holes from n-type and p-type materials at the p-n junction leads to the creation of the depletion layer, where donor atoms are indeed depleted of their holes.

Statement B

"No net charge exists far from junction." This statement is also correct. Far from the junction, the charge density is approximately uniform and does not have an impact on the electric field.

Statement C

"Barrier potential V_B is generated." This statement is correct. Due to the diffusion of charge carriers and the recombination at the p-n junction, the resulting electric field creates the barrier potential (V_B). This potential opposes the further flow of charges across the junction.

Statement D

"Energy V_B is to be surmounted before any charge can flow across junction." This statement is incorrect. The energy that must be surmounted before any charge can flow across the junction is not equal to the barrier potential (V_B). External energy or voltage needs to be applied to counteract the barrier potential and allow charge carriers to cross the p-n junction. Hence, the answer is (D).