# Homework Help: Semiconductor doping - doping concentration is 0?

1. Oct 11, 2015

### orangeincup

1. The problem statement, all variables and given/known data
A sample of germaium has an acceptor concentration of Na=10^17 and a donor concentration of Nd=0. Calculate the intrinsic carrier concentration, majority carrier concentration, and Ef-Efi. Use T=400

2. Relevant equations
No*Np=ni^2
Nv=Nv*(T/300)^3/2
Nc=Nc*(T/300)^3/2
ni^2=Nv*Nc exp(Ns)
3. The attempt at a solution
1.04*10^19 * (400/300)^3/2 = 1.23*10^19 =Nv
6*10^18 * (400/300)^3/2=7.11*10^18 = Nc

ni=((((1.04*10^19*6*10^18)^2exp(-.66/(2*400*8.6*10^-6)))^1/2

ni=9.21*10^16

10^17/2+sqrt((10^17/2)^2+(9.21*10^16)^2)=1.55*10^17

Does this look correct? I feel like the ni value is wrong

Last edited: Oct 11, 2015
2. Oct 11, 2015

### Staff: Mentor

Those equations don't make sense.

3. Oct 11, 2015

### orangeincup

Isn't the new Nv different at different temperatures? Are you saying it doesn't make sense because I put Nv=Nv, or because I shouldn't use it?

I wasn't sure if I had to re-calculate a new value of Nv and Nc or not, the calculations I did below that used the original values and not the ones I calculated above

4. Oct 11, 2015

### Staff: Mentor

What is new, what is old?
Your equations could be "solved" to give T=300. If you want to indicate two different things with Nv, then use different labels.
If you use numbers not given in the problem statement, it would help to explain where they come from (I made this comment before).
Also, for long formulas it is useful to write it in terms of variables first, and then plug in numbers. A large collection of numbers is hard to decrypt, and even harder if the origin of those numbers is unclear.

5. Oct 11, 2015

### orangeincup

Nvi=Nvf*(T/300)^3/2

Effective density of states(valence, Nv T=300 K )
Nvf is the new calculated density of states(valence, Nv T=400 K )

The Nc is the same, but for the conduction band

Effective density of states
(conduction, Nc T=300 K )

2.8x10^19

source https://www.el-cat.com/silicon-properties.htm

6. Oct 13, 2015

### orangeincup

x^2=((1.04*10^19*6*10^18)*(400/300)^3exp(-.66/(400*8.62*10^-5))
=8.50*10^14, does this look more correct? I fixed errors in my last post

My calculated ni for 300k is off by a bit though... it's suppose to be 2.4*10^13 but I calculated 2.2*10^13 using the same method above. Did I make a mistake?