بسم الله الرحمن الرحيم
If one finds wetness on his private part after getting up and he remembers that he had discharged semen then ghusl will be wajib. If no wetness or spot is seen on the cloth then the cloth will not be termed impure. However, in case of doubt it is better to wash in case of surety it is compulsory to wash.
Allah knows Best!
Darul Uloom Deoband
This answer was collected from the official ifta website of Darul Uloom Deoband in India.