A new, versatile substrate design for surface-enhanced Raman spectroscopy (SERS) is introduced that provides better illumination and collection efficiency than other solid substrates. It uses sheets of 5 nm diameter gold nanoparticles that are draped by drying-mediated self-assembly onto 100 nm thick silicon nitride membranes. During laser illumination, partial in-situ sintering of the nanoparticles into larger structures with tiny gaps (≈2 nm) greatly increases the SERS enhancement factor. The detection of 1 pM of p-mercaptoaniline and 1 fg of 2,4-dinitrotoluene is demonstrated. The use of self-assembled nanoparticle sheets furthermore makes it possible to perform SERS detection in situ on top of a probe solution droplet.