The use of a foreign metallic cold source (CS) has recently been proposed as a promising approach toward the steep-slope field-effect-transistor (FET). In addition to the selection of source material with desired density of states-energy relation (D(E)), engineering the source: channel interface for gate-tunable channel-barrier is crucial to a CS-FET. However, conventional metal: semiconductor (MS)-interfaces generally suffer from strong Fermi-level-pinning due to the inevitable chemical disorder and defect-induced gap states, precluding the gate-tunability of the barriers. By comprehensive materials and device modeling at the atomic-scale, we report that the two-dimensional (2D)-van der Waals (vdW)-MS-interfaces, with their atomic sharpness and cleanness, can be considered as general ingredients for CS-FETs. As test cases, InSe-based n-type FETs are studied. It is found that graphene can be spontaneously p-type doped along with slightly opened bandgap around the Dirac-point by interfacing with InSe, resulting in super-exponentially decaying hot carrier density with increasing n-type channel-barrier. Moreover, the D(E) relations suggest that 2Dtransition-metal-dichalcogenides and 2D-transition-metal-carbides are rich libraries of CS materials. Both graphene and H-TaTe2 CSs lead to subthreshold swing below 60 mV/decade. This work broadens the application potentials of 2D-vdW-MSheterostructures and serves as a springboard for more studies on low-power electronics based on 2D materials.