Here, we report a new nanoantenna for surface-enhanced infrared absorption (SEIRA) detection, consisting of a fan-shaped Au structure positioned at a well-specified distance above a reflective plane with an intervening silica spacer layer. We examine how to optimize both the antenna dimensions and the spacer layer for optimal SEIRA enhancement of the CH stretching mode. This tunable 3D geometry yields a theoretical SEIRA enhancement factor of 105, corresponding to the experimental detection of 20200 zeptomoles of octadecanethiol, using a standard commercial FTIR spectrometer. Experimental studies illustrate the sensitivity of the observed SEIRA signal to the gap dimensions. The optimized antenna structure exhibits an order of magnitude greater SEIRA sensitivity than previous record-setting designs.