Define and derive the quasi-fermi energy and potential for

Question

1. If the above sample is n-type and the electron concentration at the location x₁ is N(x₁)=10¹⁶cm^-3, what is the drift current density in A/cm²? What is the concentration gradient at this point, dN(x₁)/dx?

2. Define and derive the quasi-Fermi energy and potential for a species of ions.

3. Define and derive the quasi-Fermi energy and potential for a species of neutral atoms.