Semiconductor doping - doping concentration is 0?

[orangeincup]

Homework Statement

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

Homework Equations

No*Np=ni^2
Nv=Nv*(T/300)^3/2
Nc=Nc*(T/300)^3/2
ni^2=Nv*Nc exp(Ns)

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 = Ncni=((((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

 

[mfb]

Nv=Nv*(T/300)^3/2
Nc=Nc*(T/300)^3/2

Those equations don't make sense.

 

[orangeincup]

Those equations don't make sense.

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

 

[mfb]

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.

 

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

2.8x10^19

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

 

[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?