Question

to ion 3-okular x Week3HW S15 Solut 副ee 1 30-spo8.mti-so Χ-aurirs..* ㄨ 2. The probability of a state being filled at Ec kT is equal to the probability of a state being empty at Ec 3kT. Where is the Fermi level located? Use a graphical method to solve the problem! 3. The photo shows a piece of a semiconductor wafer with small integrated circuits. What can you tell about the bandgap energy and why.

can you explain this two problem step by step?

Answer 1

Question 2

If the probabilities are equal, then:

$f(E_{c}+kT)=1-f(E_{c}+3kT)$

or

$\frac{1}{1+e^{(E_{c}+kT-E_{f})/kT}}=1-\frac{1}{1+e^{(E_{c}+3kT-E_{f})/kT}}$

The equation above can be written as:

$1+e^{(E_{c}+3kT-E_{f})/kT}=e^{(E_{c}+kT-E_{f})/kT}+e^{(2E_{c}+4kT-2E_{f})/kT}$

or

$e^{2E_{c}+4kT-2E_{f}}=1$

This can be written as:

$e^{2E_{c}+4kT-2E_{f}}=e^{0}$

or

$2E_{c}+4kT-2E_{f}=0$

Therefore:

${\color{Blue} E_{f}=E_{c}+2kT}$