pn junction - In band diagram, why the Fermi energy (EF) is constant along the device?

In band diagrams of PN/PIN junctions etc. the Fermi energy level ($E_F$) is drawn as constant along the device (see image).

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Why is it constant? What does it represent?

Answer

A gradient in the Fermi level is the driving force for carrier motion:

$$F_n = \frac{D_n}{k_BT} n \frac{\mathrm{d}E_F}{\mathrm{d}x}$$

In equilibrium (zero bias), $F_n = 0$ and therefore $E_F=\text{const}$.