Step PN Junction - Energy Band Diagram

[metroplex]

A step pn junction diode is made in silicon with the n side having N'D = 2x10^16 cm^-3 and the p side having a net doping of N'A = 5x10^15 cm^-3.

1). Draw to scale the energy band diagram of the junction at equilibrium.
2). Find the built-in voltage, and compare with the value measured off your drawing in 1).

There are 9 parts to this question, but I cannot seem to find out how to start it off. I've tried for 3 hours and couldn't make any progress. The other parts are somewhat related.

 

[metroplex]

back to the top for the evening crew.

 

[quicknote]

I can provide a response to the content provided. To start, let's break down the problem and understand what is being asked.

1) Draw to scale the energy band diagram of the junction at equilibrium:
The first part of the question is asking for a visual representation of the energy band diagram for a step pn junction diode. This means we need to plot the energy levels of the n and p sides, as well as the energy levels at the junction. The junction is the interface between the n and p sides, where the two different types of doping come together.

To start, we need to understand the concept of energy bands. In a semiconductor, there are two main energy bands - the valence band and the conduction band. The valence band is the highest energy level that electrons can occupy in a material, and the conduction band is the lowest energy level that electrons can occupy to move freely through the material. In between these two bands is the bandgap, which is the energy range that electrons cannot occupy.

In a pn junction, the n side has an excess of electrons (due to the n-type doping) and the p side has a deficit of electrons (due to the p-type doping). This creates a built-in electric field at the junction, which causes the energy bands to bend. The n side's energy bands are shifted downwards, while the p side's energy bands are shifted upwards. This creates a depletion region at the junction, where there is a lack of free charge carriers.

To draw the energy band diagram, we need to plot the energy levels for the n and p sides, and then show the bending of the bands at the junction. The energy levels for the n side will be lower than the energy levels for the p side, due to the difference in doping concentrations. The depletion region will be represented by a gap between the two energy bands at the junction.

2) Find the built-in voltage, and compare with the value measured off your drawing in 1):
The built-in voltage is the voltage that is required to overcome the built-in electric field at the junction. This voltage can be calculated using the following equation: Vbi = (kT/q) * ln(Na * Nd / ni^2), where k is the Boltzmann constant, T is the temperature, q is the charge of an electron, Na is the acceptor doping concentration, Nd is the donor doping concentration, and ni is the intrinsic