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(a) Diagram showing the electric field and charges present at the gold-silicon Schottky barrier fabricated on the surface of a cantilever. The forces on the charges produced by the electric field result in a net compression of the depletion layer. As a result of Poisson’s ratio of the silicon, this compression in the direction produces extension in the direction parallel to the surface of the cantilever and bending of the cantilever as shown in the figure. (b) Scanning electron micrograph of cantilevers 1 and 2. On the right hand side of the image, the edge of the epoxy contact can be seen.
Current-voltage characteristics of the diodes deposited on the cantilevers measured in this study. Note that cantilevers 1 and 2 were on the same substrate and, therefore, the same continuous diode was used to drive them. The inset shows the detail of the measurement range used in this study, as well as the turn on.
Frequency response of the cantilevers measured in this study at a dc reverse bias of and an ac amplitude of .
Response of the devices as the ac signal is changed at a fixed dc reverse bias of . The solid lines show a fit to the data based on the model given in Eq. (1) by using the parameters given in Table I.
Response of the devices as the dc signal is changed at a fixed ac signal of amplitude. The thin solid lines show a fit to the data based on the model given in Eq. (1) by using the parameters given in Table I.
Properties of the cantilevers measured in this study. Cantilevers 1 and 2 were located on the same substrate; cantilever 3 was on a different substrate. is the width of the cantilever, is its length, and is its thickness—these parameters were measured in a scanning electron microscope (SEM), with the exception of the thickness of cantilever 3—which is estimated from the resonant frequency. Note that the cantilever thickness was found to significantly vary along its length. is its estimated dopant density (obtained by fitting to the observed data and within the manufacturer’s specified range of ), is its quality factor (obtained from the response curves in Fig. 2), is its measured resonant frequency, and is the predicted resonant frequency accounting for both the mass of the deposited gold (Ref. 14) (the gold was thick with a density of ) and the mass of the tip (Ref. 15) (dimensions obtained from SEM). All three cantilevers were fabricated from (001) silicon wafers with edges along the ⟨110⟩ directions so the silicon has a Young’s modulus, and a  to  Poisson’s ratio of . The dielectric constant of carrier depleted silicon is and its density is .
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