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Semiconductor physics is the branch of solid state physics that focuses on specific properties of semiconductors. It studies dynamics of different perturbations (mainly electrons and holes) in the semiconductor crystal and the ways to harness it in electrical circuits.
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Physics behind depletion region?
In a general sense both of your questions ask "Why is the arrangement of free and bound charges in a PN junction in equilibrium different from $X$?", where $X$ is one of the alternative arrangements y …
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Accepted
Why does the depletion layer of a p-n junction diode decrease in width upon forward biasing?
The absence of free carriers in the depletion region (DR) produces charge separation. This is because the n-type material in the DR contains positively charged donor dopant atoms with no electrons to …
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Energy Band of pn junction in thermal equilibrium (Zero bias)
In the first figure it is important to note that the junction between the two materials has a region of negative charge density (in light blue below) and positive charge density (in light red below):
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Diffusion current in semiconductor while applying an electric field
You are right that the absence of a diffusion current implies no statistical trend in the carrier density from point to point. This however does not exclude the possibility of a non zero expectation f …