technology presented here is expected to lead to a more accurate and practical way to calibrate AFMs, and improved force-displacement probes. Force-displacement sensors and actuators that can be integrated into a system-on-a-chip typically come in three types: transducers that convert a change in mechanical strain to a change in resistance [11] or change in voltage [12], or transducers that convert a change in mechanical displacement to a change in capacitance [13,14]. Of these, capacitive sensors offer the greatest sensitivity. For example, on-chip capacitance meters have detected changes comb drive capacitance on the order of zeptofarads, which corresponds to a deflection of MEMS flexures on the order of 100 femtometers [15]. Indeed, the MEMS electrical precision is available. What has been lacking is a corresponding precision for MEMS mechanical properties, which we present here. In addition, we also show that the accuracy of force and displacement by our method is independent of the accuracy of capacitance, which is often subject to variations in parasitic capacitance between electrical probed measurements. Our mechanical measurements are functions of changes in capacitance and the precision of capacitance. Following this introduction, a statement of the problems is discussed in Section 2. A brief overview of electrical probe method is discussed in Section 3. A description of our device and how we calibrate its force and displacement are discussed in Section 4. Descriptions of sensitivity and uncertainty of our method are presented in Section 5. Last, we summarize our finding and subsequent research directions in. 2 PROPERTY VARIATION It is well known to researchers in the area of micro and nano electro mechanical systems (M/NEMS) that mechanical performance strongly depends on geometric and material properties. These fabricated properties are difficult to predict and difficult to measure. The problem with prediction is that, given any fabrication recipe, the geometric and material properties vary between fabrication facilities, between fabrication runs, and across the wafer itself. A problem with many measurement methods is that they often yield uncertainties that on the order of property variation. Even with standard commercial fabrication foundries, there are significant variations in geometric and material properties. For example, in Figure 1 we show an optical image of our MEMS that was fabricated using the standard MEMCAP PolyMUMPs process [16]. Two scanning electron microscopy (SEM) insets in Figure 1 show magnified views the tip of a comb drive finger and gap. The insets show significant geometric variations such as fillets instead of sharp 90° corners; coarse sidewalls instead of smooth surfaces; flexure widths which have recessed ~20%; and gaps which have increased ~20%. For clarity, the original layout geometry of the device is superimposed on the SEM insets as dashed lines. Compared to layout geometry, the enlarged gaps decrease capacitance; the narrowed and Figure 1: Layout versus fabrication. An optical image shows a MEMS comprising a comb drive supported with a pair of fixed-guided flexures. Two scanning electron microscopy images show magnified views of the fabricated geometry, where layout geometry is depicted as dashed lines. Due to process variation, flexure stiffness have been reduced, capacitance has been reduced, sharp corners have been replaced with fillets and chamfers. 68
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