# Calculating Fermi Level position in doped Silicon

• Benjammith
In summary, the Fermi level position EFn for a Si sample at room temperature with a donor concentration of 1015 cm-3 can be estimated using the equation EF=EC-kT ln(NC/n). However, the value of EC is not known and other approaches may be needed to find it. One possible solution is to assume Ec=0 eV, making the Fermi level reference to the conduction band edge and Ev = -Eg.
Benjammith
Estimate the Fermi level position EFn for a Si sample at room temperature that
is doped with 1015 shallow donors cm-3.

From coursework I've gatherred over the year I understand the equation needed is: EF=EC-kT ln(NC/n)
n, being equal to the donor concentration
EC is the conduction band energy.

my problem with the question is knowing the value of EC. I know the value of the bandgap for silicon but I can't relate it to EC without introducing EV, another variable I don't know. Any help with finding EC or another approach to the question would be great.

If you assume Ec=0 eV... then the Fermi level will be reference to the conduction band edge (Ev would then be -Eg, since Eg = Ec - Ev).

## What is the Fermi Level in doped Silicon?

The Fermi Level in doped Silicon is the energy level at which the probability of finding an electron is equal to 50%. It represents the energy at which the electron concentration is equal to the hole concentration, and therefore the material is electrically neutral.

## How is the Fermi Level calculated in doped Silicon?

The Fermi Level in doped Silicon can be calculated using the following equation:
EF = Ev + (kT/2)ln(NA/ni) - (kT/2)ln(nd/ni)
Where EF is the Fermi Level, Ev is the energy of the valence band, k is the Boltzmann constant, T is the temperature, NA is the acceptor concentration, ni is the intrinsic carrier concentration, and nd is the donor concentration.

## What factors affect the position of the Fermi Level in doped Silicon?

The position of the Fermi Level in doped Silicon is primarily affected by the doping concentration, temperature, and the presence of impurities or defects in the material. Changes in any of these factors can shift the Fermi Level up or down.

## Why is the Fermi Level important in doped Silicon?

The Fermi Level in doped Silicon is important because it determines the conductivity and electronic properties of the material. It also plays a crucial role in the operation of electronic devices such as transistors and solar cells.

## How does the Fermi Level change in doped Silicon compared to undoped Silicon?

In doped Silicon, the Fermi Level is shifted towards the valence or conduction band depending on the type of doping (p-type or n-type). In comparison, in undoped Silicon, the Fermi Level is located in the middle of the band gap, at the intrinsic level. Doping introduces impurities that can donate or accept electrons, thus changing the position of the Fermi Level.

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