Calculating Fermi Level in Doped Silicon at Room Temperature and 0K

[andarr]

Homework Statement

(a)If a silicon crystal is doped with 10^15 cm−3 phosphorus atoms, find out the electron
concentrations and hole concentrations in the silicon at room temperature. Find
out the Fermi level.
(b)Repeat at temperature = 0K

Homework Equations

n*p=ni^2
n=2(2pi(n*)kT)^(3/2)exp-[(Ec-Ef)/(kT)] where (n*) = electron effective mass

The Attempt at a Solution

I have calculated the hole concentration p = 10^15 per cm^3
and the electron concentration n = 1.96*10^5 electrons per cm^3

but I am not sure where to begin for calculating the fermi level. I don't know what to plug in for Ec the conduction band edge energy. For part (b) I am also unable to find ni, the intrinsic carrier concentration of silicon at T = 0K. Any suggestions or insight would be appreciated, thanks in advance.

 

[hagopbul]

Ef=[(Ec+Ev)/2]+((KT/2))ln(Nc/Nv):if n=p=ni

and i think that you can use Eqs:
Ef==KT*ln{[(1/4)*[e^(Ed/KT)]*([(1+(8Nd/Nc)e^(deltaEd/KT))^(1/2)]-1)}

 

[piercas]

I would suggest starting by reviewing the equations and concepts related to the Fermi level in doped semiconductors. The Fermi level is a measure of the energy level at which electrons have a 50% probability of being occupied in a material. In doped semiconductors, the Fermi level is typically located closer to the conduction band edge for n-type doping and closer to the valence band edge for p-type doping.

For part (a), you have correctly calculated the electron and hole concentrations using the equation n*p=ni^2. To calculate the Fermi level, you will need to use the equation Ef=Ec+(kT)ln(n/Nc), where Nc is the effective density of states in the conduction band and T is the temperature in Kelvin. Nc can be calculated using the equation Nc=2(2pi(m*)kT)^(3/2), where (m*) is the effective mass of the electrons in the conduction band. You will also need to know the energy level of the conduction band edge, Ec, which can be found in a table or by using a band structure diagram for silicon.

For part (b), at T=0K, the intrinsic carrier concentration ni is equal to the product of the effective density of states in the conduction band, Nc, and the effective density of states in the valence band, Nv. This can be written as ni^2=Nc*Nv. You can use the equations mentioned above to calculate Nc and Nv, and then solve for ni.

Overall, it is important to carefully review the equations and concepts related to the Fermi level in doped semiconductors and make sure all the necessary values are known or can be calculated. Additionally, it may be helpful to consult with a professor or colleague for further clarification or guidance.