# Why is the energy-band diagram affected by nonuniform doping?

In Semiconductor Physics and Devices by Donald A. Naemen (pg. 176) the following figure appears:

The donor concentration is a decreasing function of x.

My question: why are the energies of the conduction and valence band ($E_c$ and $E_v$) a function of the concentration? Why is the Fermi-level the only value in the figure that is not affected by the non-uniform distribution of donors?

• $E_{fi}$ is the intrinsic Fermi energy at mid gap. $E_{f}$ is the result of varying the doping. To be in equilibrium the Fermi energy is constant across the material. So, what is your confusion more specifically? Jun 4 '17 at 21:01
• I understand why $E_f$ is constant, and why $E_{fi}$ varies. I don't understand why $E_c$ and $E_v$ vary with donor concentrations.
– YoA
Jun 5 '17 at 11:44
• Because in equilibrium the Fermi energy has to be constant across the material. What does the band diagram look like across a $pn$ junction? The Fermi energy is constant, the conduction and valence bands bend. Jun 5 '17 at 12:41
• How do we know that the material is in equilibrium? Dec 28 '20 at 8:09

• Thank you , so $E_i$ bends because its defined to be at the middle of $Ec$ and $Ev$? Dec 28 '20 at 7:52