Design and construction of a four-point bending based set-up for measurement of piezoresistance in semiconductors

Abstract

We describe an experimental set-up for measurement of piezoresistivity coefficients of crystalline semiconductors, especially p-type silicon. We have aimed at good control of doping and temperature as well as the magnitude and the direction of applied stress and electric field. This is realized by applying the stress by the well known four point bending technique to a Si beam cut from a wafer. The set-up allows for high precision mechanical loading and alignment. The mechanical loading is done by a piezoelectric actuator. This allows us to cycle the load within a closed environment. A fiber optical interferometer has been developed to measure the center deflection of the Si beams. We derive analytical expressions relating center deflection to mechanical stress. From the analytical expressions we estimate the measurement uncertainty due to imperfections in alignment and machining. We also evaluate other factors. We have good accuracy and excellent repeatability and we find that thermal effects sets the limit of uncertainty of our measurements. We measure the coefficients of piezoresistivity with an accuracy of 2%–3% when we compensate for thermal drift during the measurement.