The correct answer is A. Increases.
As the source-drain voltage increases, the channel depth increases. This is because the electric field between the source and drain terminals increases, which causes the inversion layer to become thicker. The inversion layer is a layer of charge carriers (electrons or holes) that forms at the interface between the semiconductor material and the insulator material. The thickness of the inversion layer determines the conductivity of the channel, and therefore the current that flows through the device.
Option B is incorrect because the channel depth decreases as the source-drain voltage decreases. This is because the electric field between the source and drain terminals decreases, which causes the inversion layer to become thinner.
Option C is incorrect because the channel depth does not logarithmically increase as the source-drain voltage increases.
Option D is incorrect because the channel depth does not exponentially increase as the source-drain voltage increases.