Noise in piezoresistive atomic force microscopy

The noise performance of piezoresistive atomic force microscopy (AFM) devices is investigated. The total deflection noise of a piezoresistive AFM device comprises vibrational noise from the cantilever, and Johnson and flicker noise from the piezoresistor. The vibrational deflection noise is found to have a minimum when the length of the piezoresistor is 2/3 of the cantilever length. The minimum vibrational deflection noise is (9/8 k(B)T/K)(1/2) for a free cantilever, whereas a supported cantilever has a minimum vibrational noise of (1/8 k(B)T/K)(1/2), where K is the spring constant of the device. Taking self-heating of the device into account, it is shown that an optimum power level exists at which the total equivalent displacement noise of a device is minimized. This minimum deflection noise is, for a fixed value of the spring constant, approximately proportional to the cantilever thickness, whereas it varies rather slowly with the length of the piezoresistor.