Finite element calculations and fabrication of cantilever sensors for nanoscale detection.

Finite element analysis (FEA) is used to study the effect of geometric variations on the properties of rectangular cantilevers and U-shaped Joule-heated cantilevers. Simulations of locally thinned cantilevers as well as of cantilevers modified by the implementing of a hole or a side cut are compared with fabricated cantilevers, which are tuned by focused ion beam (FIB) milling. By locally thinning the cantilevers, the resonance frequency and the spring constant are reduced. For a hole, the internal stress is increased while for a side cut, the lateral spring constant is decreased. Good agreement between the measured and the simulated resonance frequencies is observed. Simulations of the current density and the temperature distributions attained during the passage of current through a doped silicon layer are performed to optimize the design of Joule-heated cantilevers (U-shaped) for thermal gravimetric applications. A very uniform temperature distribution over a region near the apex can be realized by slitting the U-shaped cantilever. In such a way, the heating power can be minimized by effecting only a small variation in the geometry of a U-shaped cantilever. A simple fabrication process for the fabrication of Joule-heated cantilevers is presented, which consists mainly of a uniform conductive p-doped layer.