The depletion layer in a p-n junction is the region where mobile charge carriers (electrons and holes) are depleted. The thickness of the depletion region depends on the applied voltage and the material properties. Typically, in a p-n junction, the depletion layer is very thin and typically of the order of micrometers (\( \mu m \)).
Thus, the thickness of the depletion layer on either side of the p-n junction is of the order of \( \mu m \).
Thus, the correct answer is: \(\boxed{\mu m}\).