A comparative analyze of fundamental noise in cantilever sensors based on lateral and longitudinal displacement: case of thermal infrared detectors

The performance of novel cantilever-based sensors approaches the limit posed by thermo-mechanical fluctuations, which is the currently accepted fundamental detection barrier for micro- and nanomechanical sensors. At the same time, the sensitivity of a high-level measurement techniques used for readout of the cantilever displacement nears the value of 10⁻¹⁴ m/Hz^½. However, the thermo-mechanical noise of some cantilever sensors based on bimaterial structures is considerably higher than imposed by the fundamental limit. Moreover, the signal-to-noise ratio of some sensors based on contemporary MEMS technologies falls behind the characteristics of older types of mechanical sensors, fabricated using macroscopic production technologies. To investigate the cause of this situation, we perform a comparative analysis of the performance limits for two classes of cantilever sensors: the bimaterial cantilevers where the output signal is the transversal (lateral) displacement of the cantilever tip and the simple cantilever sensors where the signal is the longitudinal displacement along the cantilever axis. As a starting point of our analysis we established a correspondence between the parameters of a bimaterial cantilever and the simple cantilever. In a general case these two structures are not directly comparable, since the deformation of the bimaterial cantilever depends on 14 variables, while the longitudinal elongation of the simple cantilever depends on seven parameters only. However, under certain conditions analyzed in this paper a partial correspondence between the parameters of these two structures can be established. Our analysis shows that in certain applications a cantilever with longitudinal elongation has potentially better performance than the corresponding bimaterial element.