Solving Doping Concentration: Temperature for 10% Hole Concentration

[brad sue]

Homework Statement

Silicon is doped with 10^16 phosphorus atoms/cm^3.
At what temperature would the hole concentration be equal to 10% of the ionized impurity concentration?

2. Homework Equations
I am very confused with the equation I have .

The translation of the question is I believe p=0.1(Nd+), where p is the hole concentration.

I think I can use the equation for Nd+= Nd x e(-(Ef-Ed)/KT),
where Nd+ is the ionized donor concentration, Nd is the donor concentration, Ef the fermi level, Ed the donor energy.

The Attempt at a Solution

First I am not sure I am using gthe good equation, then I don't know how to find the Ef and Ed . i was not able to find or don't understand how to get the Ev and Ec...

Homework Equations

Please can I have some guidance at least for the equations?

Thank you
brad

 

[mark726]

ley

Dear Bradley,

Thank you for your question. The equation you have mentioned is indeed the correct one to use in this scenario. As you have correctly stated, we are looking for the temperature at which the hole concentration (p) is equal to 10% of the ionized impurity concentration (Nd+). This can be written as p = 0.1Nd+.

To solve for the temperature, we need to rearrange the equation you have mentioned to solve for the Fermi level (Ef). This can be done by taking the natural logarithm of both sides of the equation and rearranging the terms. The resulting equation is:

Ef = Ed + (kT/ln(Nd+/Nd))

Now, to find the value of Ef, we need to know the values of Ed, Nd and Nd+. The donor energy (Ed) can be found in reference books or online databases for different impurities in silicon. The donor concentration (Nd) can be determined from the given information in the question, which is 10^16 phosphorus atoms/cm^3. Finally, the ionized donor concentration (Nd+) can be calculated by multiplying the donor concentration (Nd) with the Boltzmann distribution factor, which is given by e(-(Ef-Ed)/kT).

Once you have all these values, you can substitute them into the equation for Ef and solve for the temperature (T). This will give you the temperature at which the hole concentration will be equal to 10% of the ionized impurity concentration.

I hope this helps. If you have any further questions, please do not hesitate to ask.