Step 1: Compare the options
Drift under an applied field and thermal excitation are not the origin of the region, and nothing is physically removed during manufacturing.
Step 2: Why the other options fail
Option (A) mentions an applied field, but the region exists even with no bias. Options (B) and (D) are not the physical cause.
Step 3: Answer
Only option (C) explains the formation of the depletion layer.
Final Answer:
Option (C) is correct.
\[ \boxed{\text{(C) }\text{diffusion of majority carriers across the junction immediately after formation, leaving behind fixed immobile ions.}} \]