  Tunnel junctions, a well-established platform for high-resolution
spectroscopy of superconductors, require defect-free insulating barriers with
clean engagement to metals on both sides. Extending the range of materials
accessible to tunnel junction fabrication, beyond the limited selection which
allows high-quality oxide formation, requires the development of alternative
fabrication techniques. Here we show that van-der-Waals (vdW) tunnel barriers,
fabricated by stacking layered semiconductors on top of the transition metal
dichalcogenide (TMD) superconductor NbSe$_2$, sustain a stable, low noise
tunneling current, and exhibit strong suppression of sub-gap tunneling. We
utilize the technique to measure the spectra of bulk (20 nm) and ultrathin (3-
and 4-layer) devices at 70 mK. The spectra exhibit two distinct energy gaps,
the larger of which decreases monotonously with thickness and $T_C$, in
agreement with BCS theory. The spectra are analyzed using a two-band model
modified to account for depairing. We show that in the bulk, the smaller gap
exhibits strong depairing in an in-plane magnetic field, consistent with a high
Fermi velocity. In the few-layer devices, depairing of the large gap is
negligible, consistent with out-of-plane spin-locking due to Ising spin-orbit
coupling. Our results demonstrate the utility of vdW tunnel junctions in
mapping the intricate spectral evolution of TMD superconductors over a range of
magnetic fields.
