An integrated silicon-based vapor sensor is realized with a ZnO-on-Si surface-acoustic-wave (SAW) oscillator containing an absorptive polymer located on a thinned, membrane region of the device. If the membrane thickness is comparable with or smaller than a SAW wavelength, wave energy is present at both membrane surfaces. Thus the SAW transducers and associated amplifiers can be protected by an enclosure, leaving only the polymer exposed to the ambient atmosphere. Experiments on a 30 MHz, ZnO-on-silicon thin-membrane temperature-compensated SAW oscillator for vapor sensing are described. The use of the multi-channel device for solubility parameter sensing is discussed.