Free-space time domain THz spectroscopy accesses electrodynamic
responses in a frequency regime ideally matched to interacting condensed
matter systems. However, THz spectroscopy is challenging when samples
are physically smaller than the diffraction limit of ∼0.5 mm,
as is typical, for example, in van der Waals materials and heterostructures.
Here, we present an on-chip, time-domain THz spectrometer based on
semiconducting photoconductive switches with a bandwidth of 200 to
750 GHz. We measure the optical conductivity of a 7.5-μm wide
NbN film across the superconducting transition, demonstrating spectroscopic
signatures of the superconducting gap in a sample smaller than 2%
of the Rayleigh diffraction limit. Our spectrometer features an interchangeable
sample architecture, making it ideal for probing superconductivity,
magnetism, and charge order in strongly correlated van der Waals materials.