# Space charge width pn junction

• MorrowUoN
In summary, The task is to calculate the width of the space charge region in a silicon pn junction at T=300K with doping concentrations of Na=10^16 cm^-3 and Nd=10^15 cm-3, when a reverse biased voltage of 5V is applied. The formula for calculating the width is W=((2Ef(Vbi+Vr)/e)((Na+Nd)/((Na*Nd))))^1/2 and the in-built potential was found to be 0.635V. The formula does not involve the Fermi energy and epsilon is the permittivity of the material.
MorrowUoN

## Homework Statement

Calculate the width of the space charge region in a pn junction when a reverse biased voltage is applied. Consider a silicon pn junction at T=300K with doping concentrations of Na=10^16 cm^-3 and Nd=10^15 cm-3. Assume that Ni=1.5*10^10 cm-3 and VR=5V

## Homework Equations

W=((2Ef(Vbi+Vr)/e)((Na+Nd)/((Na*Nd))))^1/2

## The Attempt at a Solution

I correctly calculated the in built potential to be 0.635V however, I do not know how to calculate the fermi energy

Check that formula again. It does not involve the Fermi energy.

phyzguy said:
Check that formula again. It does not involve the Fermi energy.

What is the value of epsilon in the formula attached?

#### Attachments

• f05651bb2afeca1e83a68bd340cc6fbb.png
1.6 KB · Views: 514
It's the permittivity of the material.

As a scientist, it is important to have a solid understanding of the concepts and equations involved in your calculations. The Fermi energy, denoted by Ef, is a measure of the highest energy state occupied by electrons at absolute zero temperature. It is typically used to describe the energy level at which the probability of finding an electron is 50%. In the context of a pn junction, the Fermi energy is used to determine the width of the space charge region.

To calculate the Fermi energy, you will need to use the equation: Ef = kTln(N/Ni), where k is the Boltzmann constant, T is the temperature in Kelvin, N is the number of dopant atoms, and Ni is the intrinsic carrier concentration. In this case, N = Na + Nd, so you will need to substitute the given values for Na, Nd, and Ni into the equation to solve for Ef.

Once you have calculated the Fermi energy, you can then use the equation W = ((2Ef(Vbi+Vr)/e)((Na+Nd)/((Na*Nd))))^1/2 to determine the width of the space charge region. Make sure to double check your calculations and units to ensure accuracy.

## 1. What is the space charge width in a pn junction?

The space charge width in a pn junction is the region between the p-type and n-type materials where there is an excess of either positive or negative charges due to the diffusion of charge carriers. This region is also known as the depletion region.

## 2. How is the space charge width determined?

The space charge width is determined by the doping concentrations of the p-type and n-type materials, as well as the applied voltage across the junction. A higher doping concentration results in a narrower space charge width, while a lower doping concentration results in a wider space charge width.

## 3. What is the significance of the space charge width in a pn junction?

The space charge width is important because it creates a built-in electric field that prevents further diffusion of charge carriers, creating a barrier that allows the pn junction to function as a diode. It also affects the breakdown voltage and forward bias characteristics of the junction.

## 4. How does temperature affect the space charge width in a pn junction?

As temperature increases, the space charge width in a pn junction also increases. This is because higher temperatures increase the number of thermally generated charge carriers, leading to a wider depletion region. This can affect the performance of the pn junction, especially in high-temperature applications.

## 5. Can the space charge width be controlled in a pn junction?

Yes, the space charge width can be controlled by adjusting the doping concentrations of the p-type and n-type materials. Additionally, the space charge width can also be manipulated by applying an external voltage across the junction, which changes the size of the depletion region and therefore, the space charge width.

• Electrical Engineering
Replies
1
Views
1K
• Electrical Engineering
Replies
3
Views
2K
Replies
7
Views
1K
Replies
2
Views
3K
Replies
1
Views
2K
• Engineering and Comp Sci Homework Help
Replies
3
Views
1K
• Electrical Engineering
Replies
12
Views
1K
Replies
1
Views
2K