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Fast on-wafer electrical, mechanical, and electromechanical characterization of piezoresistive cantilever force sensors
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Image of FIG. 1.
FIG. 1.

Exploded view of the piezoresistive cantilever. From the top there are: PECVD silicon nitride (tNit = 100 nm), thermal oxide (tOx = 38 nm), implanted crystalline silicon, and crystalline silicon (tSi = 325 nm). L1 = 125 μm is half of the length of the piezoresistance and also the length of the multilayer part. L2 = 250 μm is the total length of the cantilever. The implanted piezoresistance is visible on the silicon. z ti and z di are the top and the bottom z coordinates of the layers, with i = 1 for silicon nitride, i = 2 for silicon oxide, and i = 3 for silicon.

Image of FIG. 2.
FIG. 2.

(a) scanning electron microscope (SEM) image of a piezoresistive cantilever chip: two cantilevers are visible in the top part and the pads for contacting the chip are in the bottom part. (b) SEM image of two piezoresistive cantilevers. In total there are four piezoresistors per chip in a Wheatstone bridge configuration, two in the cantilevers and two in the substrate.

Image of FIG. 3.
FIG. 3.

Beam bending spring constant measurement: the AFM probe (right) is deflecting the test cantilever (left). The initial cantilever and AFM probe positions are shown in dashed lines.

Image of FIG. 4.
FIG. 4.

AFM probe deflection curves (δ P) against the total AFM probe displacement (z C). In black the AFM probe is deflected against a stiff surface. This curve is used to calibrate the AFM photodetector sensitivity. In gray the AFM probe is deflected against the cantilever under test: the difference between the two curves represent the deflection of the cantilever under test (δ C).

Image of FIG. 5.
FIG. 5.

Noise and sensitivity measurements electrical scheme. The differential voltage of the Wheatstone bridge is amplified by the low noise voltage amplifier. The noise spectrum is recorded by the signal analyzer while the sensitivity signal is recorded by the AFM electronics.

Image of FIG. 6.
FIG. 6.

Input referred noise power spectral density for the Wheatstone bridge (design B2). Integrating the noise between 1 Hz and 1 kHz, we obtain a noise average value of 5.94 μV. The bridge is 5 V DC biased and the pads are contacted by the probe card. Values of the resistances are reported in Table I.

Image of FIG. 7.
FIG. 7.

Lateral view (up) and top view (down) of the probe card design (dimensions in mm). For the probes we fixed the maximum vertical drop to 0.7 mm and the length to 16 mm to avoid any interaction with the AFM head.

Image of FIG. 8.
FIG. 8.

(a) The probe card is held by a micromanipulator onto the chuck of the AFM. (b) The probes are contacting the pads of the chip while the AFM tip performs the displacement of the cantilever for measuring the sensitivity.

Image of FIG. 9.
FIG. 9.

Electromechanical response of a piezoresistive cantilever (design B2) with no amplification. At a length of 140 μm, a stiff probe (in tapping mode) starts to deflect downwards the cantilever when the vibration decreases from around 40 nm to almost 0 nm. At the same time the output differential voltage of the Wheatstone bridge (WB) starts to increase (approach line) from 14.03 mV to 14.24 mV for a deflection of 0.91 μm. This means a displacement sensitivity of around 231 μV/um at the deflection point and a force sensitivity of 46 μV/nN at the tip. Considering the noise value of 5.94 μV, we can assure a MDF = 129 pN. In the retract curve is also visible the strong interaction between the AFM tip and the cantilever under test which is bending upwards 0.5 μm. The force curve (approach and retract) is performed over 1 s.

Image of FIG. 10.
FIG. 10.

(a) Sensitivity results for 72 chips (24 per each design). Triangles, squares, and circles refer respectively to the designs B1, B2, and B3. Averaged values and standard deviation are reported in red for each design. (b) Sensitivity wafer-map. The 24 chips of each design are positioned in 3 different rows of 8 chips each. The relative sensitivity (sensitivity divided by the averaged sensitivity,) increases as reported in the legend.


Generic image for table
Table I.

Piezoresistive cantilevers: cantilever arms (w1), total cantilever (w2), and resistance (wR) widths, spring constant k, resistance mean value, square resistance mean value, and its relative standard deviation (σ) and yield for the three different cantilever designs. Resistances and deviations are for substrate resistors and between brackets for cantilever resistors. T1 cantilevers are used for beam bending measurement.

Generic image for table
Table II.

Piezoresistive cantilever: deflection sensitivity (ΔV/δ) at 140 μm from the clamping edge, gauge factor (G), mean force sensitivity (ℜ F ) for a force applied at the tip and relative standard deviation (σ), mean voltage noise value referred to input (Vnoise) measured between 1 Hz and 1 kHz and minimum detectable force (MDF). Statistics were made on 24 chips per each design.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Fast on-wafer electrical, mechanical, and electromechanical characterization of piezoresistive cantilever force sensors