Poisson Equation
In equilibrium, there is one independent variable only out of the three variables: 
If one of them is known to us, the rest can be obtained from equations stated above. We can take this independent variable to be potential.
The analysis problem in equilibrium is thus the determination of potential or equivalently, energy band diagram of semiconductor device.
This is the reason why we begin discussions of all the semiconductor devices with a sketch of its energy band diagram in the equilibrium state.
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