We report on the realization of a solid-state-based vacuum ultraviolet frequency comb, using multiharmonic generation in an external enhancement cavity. Optical conversions in such arrangements were so-far reported only using gaseous media. We present a theory that allows selecting the most suited solid generation medium for specific target harmonics by adapting the bandgap of the material. Consequently, we experimentally use a thin AlN film grown on a sapphire substrate to realize a compact frequency comb multi-harmonic source in the DUV/VUV spectral range. Extending our earlier VUV source [Opt. Exp. 26, 21900 (2018)] with the enhancement cavity, a sub-Watt level Ti:sapphire femtosecond frequency comb is enhanced to 24 W stored average power, its 3 rd , 5 th and 7 th harmonics are generated, and the target harmonic power at 160 nm increased by two orders of magnitude. The emerging non-linear effects in the solid medium together with suitable intra-cavity dispersion management support optimal enhancement and stable locking. To demonstrate the spectroscopic ability of the realized frequency comb, we report on the beat measurement between the 3 rd harmonic beam and a 266 nm CW laser reaching about 1 MHz accuracy.