Questions about semiconductors

[wwonderboy]

Question 1:

Homework Statement

If E_f=E_v find the probability of a state being empty at E=E_v-KT

F(E)=1 Divided by 1+(exp(E-E_f)/KT)
k=8.62*10^-5 eV/k

Homework Equations

The Attempt at a Solution

when i used this equation to find the probability:
F(E)=1 Divided by 1+(exp(E-E_f)/KT) the final answer was wrong and the model answer used F(E)=1- [1 Divided by 1+(exp(E-E_f)/KT)]
why?

Question 2:

Homework Statement

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-E_f)/KT)]
F(E)=0.01
E-E_f=-0.03 eV
k=8.62*10^-5 eV/k

Homework Equations

The Attempt at a Solution

F(E)=1- [1 Divided by 1+(exp(E-E_f)/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:

Homework Statement

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: E_g=0.66 eV, GaAs:E_g=1.42 eV)

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

Homework Equations

The Attempt at a Solution

i just want to know how to get E and E_f for every element to calculate the probability

Question 4:

Homework Statement

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 n_i)=9.65*10⁹ atoms/cm³. the ionisation energy for phosphorus in Si 0.045eV )

n=n_i exp(E_f-E_i)/KT
p=n_i exp(E_i-E_f)/KT

Homework Equations

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=n_i exp(E_f-E_i)/KT
and what should i do to check if the assumption of complete ionisation is justified for each doping?

Question 5:

Homework Statement

For n-type silicon sample with 10¹⁶ phosphorus atoms/cm³ donor impurities and a donor level at E_D= 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.

Homework Equations

The Attempt at a Solution

i don't know how to find the ratio of the neutral donor density

 

[eljose79]

to the ionised donor density at 77 K.

Regarding your first question, the reason why the model answer used F(E)=1-[1 Divided by 1+(exp(E-Ef)/KT)] is because this equation represents the probability of the state being occupied by an electron, which is the opposite of being empty (1- probability of being occupied = probability of being empty).

For your second question, you are on the right track. You have correctly set up the equation and solved for KT. To find the temperature, you can rearrange the equation to solve for T. Also, make sure to convert all units to eV before plugging them into the equation.

For your third question, to calculate the probability for each element, you will first need to find the Fermi energy level (Ef) for each element. This can be done using the equation Ef=(Eg/2)+Ei, where Eg is the band gap energy and Ei is the ionization energy. Once you have Ef, you can plug it into the equation F(E)=1 Divided by 1+(exp(E-Ef)/KT) to find the probability for each element.

For your fourth question, the numbers 1015, 1017, and 1019 refer to the different doping levels, not different doping times. So the first doping level is with 1015 phosphorus atoms/cm3, the second with 1017 atoms/cm3, and the third with 1019 atoms/cm3. To check if the assumption of complete ionisation is justified, you can compare the calculated Fermi level to the ionization energy. If the Fermi level is significantly lower than the ionization energy, then the assumption of complete ionisation is justified.

For your fifth question, you can use the equation n/Nd=exp(Ef-ED)/KT to find the ratio of the neutral donor density to the ionized donor density. Nd is the donor concentration, Ef is the Fermi level, and ED is the donor level. Make sure to convert all units to eV before plugging them into the equation.

I hope this helps answer your questions. Good luck with your research!