A field effect transistor (FET) includes a nanosheet stack having first and second stacked semiconductor channel layers. The first channel layer defines a channel region of a tunnel FET, and the second channel layer defines a channel region of a thermionic FET. Source and drain regions are provided on opposite sides of the nanosheet stack such that the first and second channel layers extend therebetween. A first portion of the source region adjacent the first channel layer and a second portion of the source region adjacent the second channel layer have opposite semiconductor conductivity types. Related fabrication and operating methods are also discussed.