Two-dimensional transition metal dichalcogenide (2D TMD) semiconductors allow facile integration of p- and n-type materials without a lattice mismatch. Here, we demonstrate gate-tunable n- and p-type junctions based on vertical heterostructures of MoS2 and WSe2 using van der Waals (vdW) contacts. The p-n junction shows negative differential resistance (NDR) due to Fowler-Nordheim (F-N) tunneling through the triangular barrier formed by applying a global back-gate bias (VGS). We also show that the integration of hexagonal boron nitride (h-BN) as an insulating tunnel barrier between MoS2 and WSe2 leads to the formation of sharp band edges and unintentional inelastic tunnelling current. The devices based on vdW contacts, global VGS, and h-BN tunnel barriers exhibit NDR with a peak current (Ipeak) of 315 μA, suggesting that the approach may be useful for applications.