Relaxation of deep levels in semiconductors is studied through capacitance transients. We explore the temperature‐time duality relationship which is inherent in such thermal relaxation processes. Using duality considerations we show the existence of four distinct spectroscopies. We demonstrate that the techniques for spectroscopic evaluation of capacitance transients are based on differential operators and provide a novel interpretation to spectroscopy. We extend this approach to higher order spectroscopy. Two families of higher order spectroscopy are analyzed using the formalism of temperature‐time duality and differential operators. From duality considerations we have suggested a novel deep level spectroscopy as well as various improvements in line shapes and spectroscopic quality of existing techniques. ©1995 American Institute of Physics.