Figure 1

Surface-micromachined cantilever. Polysilicon, doped and electrically conductive, is deposited on a silicon-nitride-coated silicon wafer to form the cantilever structure. Scanning electron micrograph (top) and schematic (bottom) of the capacitive cantilever assembly. The top left image shows the overall top view of the cantilever with its lower right corner magnified and shown in the top right image, where $z=d_0=2\mu \mathrm{m}$ is the nominal gap size. The schematic in the bottom depicts the microcantilever (including its embedded holes) “suspended” from the two anchors over the substrate.Reuse & Permissions

Figure 2

The stress induced by the KF on the cantilever results in a static deflection which is sensed as a variation in the capacitance between the cantilever and the fixed substrate. The left axis displays the measured signal, while the right axis gives the corresponding Knudsen pressure yielding a total force in the range $90\mathrm{n}\mathrm{N}\le \mathrm{K}\mathrm{F}\le 0.8\mu \mathrm{N}$ for the cantilever used. The examined residual gases furnishing the thermal transpiration yield different peaks due to their respective molecular compositions. The bending due to thermal stress in the cantilever appears as the gas independent baseline below 0.5 mV in the high and low Kn regions.Reuse & Permissions

Figure 3

The experimentally observed Knudsen effect (dotted curves) and the corresponding numerical fits (solid curves) to the function $S_f(P)$. The accuracy of locations of the peak pressure $P_{\mathrm{m}\mathrm{a}\mathrm{x}}$ obtained from $S_f(P)$ is excellent (within the experimental error) for the monatomic He and Ar, good for ${\mathrm{O}}_2$, and fair for ${\mathrm{C}\mathrm{O}}_2$. The overall agreement is excellent in the respective regimes of free molecular motion for all the examined gases, but deteriorates in the lower Kn number regimes with increasing molecular degree of freedom.Reuse & Permissions

Figure 4

The KF induced bending of the cantilever in time domain (a), and as a function of laser modulation frequency (b). (a) The 500 times averaged signal (dotted curve) representing the response of the cantilever, at a pressure close to the peak pressure for the Knudsen effect in helium, to the modulated laser beam represented by the reference signal of the lock-in (solid curve). (b) The variation of the signal with the laser modulation frequency in air at the peak pressure for the Knudsen effect. The shown behavior was observed for all the examined gases. The region labeled “I” corresponds to a decreasing temperature of the cantilever with increasing frequency (decreasing exposure time) up to high enough a frequency region labeled “II” for a cross sectional temperature gradient to be built up engaging the cavities (2 and $8\mu \mathrm{m}$ “pores,” with the small pores being active in the smaller Kn region) embedded in the cantilever to participate in the thermal transpiration by exchanging momentum with the ambient molecules.Reuse & Permissions