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).

Key concepts

Depletion Layer

The p-n junction is a fascinating area in semiconductor devices, where two distinct types of materials meet: p-type and n-type. An important feature that forms in this area is called the depletion layer. When electrons from the n-type material fill up the holes in the p-type material, they create this zone devoid of mobile charge carriers.
This region is sans free electrons and holes, which results from the recombination process that occurs when the junction forms.
It acts like an insulator, preventing further movement of charge carriers across the junction by forming an electric barrier. The depletion layer essentially creates a buffer that separates the positive and negative sides, enabling the p-n junction to control the flow of electric current in a semiconductor device, making it crucial in the functioning of diodes.
Key points about the depletion layer:

• Depletion layer is charge-free and acts as an insulator.
• Results from electrons and holes recombining at the junction.
• Forms a barrier that inhibits further charge migration.

Barrier Potential

Once the depletion layer forms, it naturally gives rise to another critical concept known as the barrier potential. This potential forms because of the internal electric field created within the depletion layer due to the separation of charges. It represents the inherent voltage difference across the junction.
This electric potential occurs as a result of the difference in concentration of charge carriers between the p-type and n-type materials.
It prevents further recombination because it builds an electric field that opposes the movement of further electrons and holes. Understanding barrier potential is vital as it plays an essential role in the operation of electronic devices:

• Acts against the diffusion of charge carriers across the depletion region.
• The barrier must be overcome for current to flow across the junction.
• Influences the forward-biasing and reverse-biasing behaviors of diodes.

This barrier potential is what one usually refers to when discussing the voltage required to "switch on" a diode.

Donor Atoms

Donor atoms are a key component in n-type semiconductor materials. These atoms are intentionally added to the semiconductor to increase its conductivity by providing extra electrons.
In n-type materials, donor atoms usually have one more electron than the semiconductor's intrinsic atoms, allowing them to easily donate an electron to the conduction band, where it can move freely and contribute to an electric current.
When a p-n junction is formed, the electrons from these donor atoms flow towards the p-type material, filling the holes there and becoming part of the depletion layer. Important considerations about donor atoms include:

• They provide electrons, enhancing the conductivity of n-type semiconductors.
• Integral in creating the electric potential across the junction by donating excess electrons.
• Critical in the formation and expansion of the depletion layer.

This explains why donor atoms are essential to the creation and function of p-n junctions, as they help establish the necessary electronic infrastructure.

Charge Flow Across Junction

The flow of charge across a p-n junction is central to its operation in semiconductor devices like diodes and transistors. Initially, due to the inherent barrier potential, charge cannot freely move across the junction.
This barrier must be overcome to allow current to flow, which is fundamental for the device to conduct electricity. For current to start flowing, an external voltage must be applied that surpasses the barrier potential. Key aspects of charge flow across the junction include:

• Adequate external voltage helps charges overcome the barrier potential.
• Under forward bias, the depletion layer narrows, allowing charges to flow.
• Under reverse bias, the depletion layer widens, restricting charge flow.

Understanding charge flow across a p-n junction is pivotal for grasping how diodes function, as it dictates when and how the diode can conduct current in a circuit.