Question 1:
1. The problem statement, all variables and given/known data
If Ef=Ev find the probability of a state being empty at E=Ev-KT

F(E)=1 Divided by 1+(exp(E-Ef)/KT)
k=8.62*10-5 eV/k
2. Relevant equations

3. The attempt at a solution
when i used this equation to find the probability:
F(E)=1 Divided by 1+(exp(E-Ef)/KT) the final answer was wrong and the model answer used F(E)=1- [1 Divided by 1+(exp(E-Ef)/KT)]
why?

Question 2:
1. The problem statement, all variables and given/known data
Calculate the temperature at which there is a 1 percent probability that a state 0.30 eV below the fermi level will be empty of an electron

F(E)=1- [1 Divided by 1+(exp(E-Ef)/KT)]
F(E)=0.01
E-Ef=-0.03 eV
k=8.62*10-5 eV/k

2. Relevant equations

3. The attempt at a solution
F(E)=1- [1 Divided by 1+(exp(E-Ef)/KT)]
0.01=1- [1 Divided by 1+(exp(-0.03)/KT)]
1.01=1 Divided by 1+(exp(-0.03)/KT)
100/101=1+(exp(-0.03)/KT)
-1/101=(exp(-0.03)/KT)
ln(-1/101)=-0.03/KT

so i stopped here and didn't know what to do

Question 3:
1. The problem statement, all variables and given/known data
Assume the fermi energy level is exactly in the centre of the band gap energy of a semiconductor at T=300 K (a)calculate the probability that an energy state in the bottom of the conduction band is occupied by an electron for Si, Ge and GaAs. (b) calculate the probability that an energy state in the top of the valence band is empty for Si, Ge and GaAs (Ge: Eg=0.66 eV, GaAs:Eg=1.42 eV)

F(E)=1 Divided by 1+(exp(E-Ef)/KT)

2. Relevant equations

3. The attempt at a solution
i just wanna know how to get E and Ef for every element to calculate the probability

Question 4:
1. The problem statement, all variables and given/known data
calculate the fermi level of silicon doped with 1015, 1017 and 1019 phosphorus atoms/cm3 at room temperature assuming complete ionisation. From the calculated fermi level, check if the assumption of complete ionisation is justified for each doping.
(Use ni)=9.65*109 atoms/cm3. the ionisation energy for phosphorus in Si 0.045eV )

n=ni exp(Ef-Ei)/KT
p=ni exp(Ei-Ef)/KT

2. Relevant equations

3. The attempt at a solution
what did he mean with 1015, 1017 and 1019 phosphorus atoms/cm3 does he mean first time doping with1015 phosphorus atoms/cm3 and the second time with 1017 phosphorus atoms/cm3
and the last time with 1019 phosphorus atoms/cm3 ?? and each time calculate electron concentration then holes concentration and then the fermi level with n=ni exp(Ef-Ei)/KT
and what should i do to check if the assumption of complete ionisation is justified for each doping?

Question 5:
1. The problem statement, all variables and given/known data
For n-type silicon sample with 1016 phosphorus atoms/cm3 donor impurities and a donor level at ED= 0.045 eV, find the ratio of the neutral donor density to the ionised donor density at 77 K where the fermi level is 0.0459 below the bottom of the conduction band.

2. Relevant equations

3. The attempt at a solution
i don't know how to find the ratio of the neutral donor density
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