Three-point bending setup for piezoresistive gauge factor measurement of thin-film samples at high temperatures

We present a new method for measuring the piezoresistive gauge factor of a thin-film resistor based on three-point bending. A ceramic fixture has been designed and manufactured to fit a state-of-the-art mechanical testing apparatus (TA Instruments Q800). The method has been developed to test thin-film samples deposited on silicon substrates with an insulating layer of SiO₂. The electrical connections to the resistor are achieved through contacts in the support points. This insures that the influence of the electrical contacts is reduced to a minimum and eliminates wire-bonding or connectors attached to the sample. During measurement, both force and deflection of the sample are recorded simultaneously with the electrical data. The data analysis extracts a precise measurement of the sample thickness (<1% error) in addition to the gauge factor and the temperature coefficient of resistivity. The sample thickness is a critical parameter for an accurate calculation of the strain in the thin-film resistor. This method provides a faster sample evaluation by eliminating an additional sample thickness measurement or alternatively an option for cross checking data. Furthermore, the method implements a full compensation of thermoelectrical effects, which could otherwise lead to significant errors at high temperature. We also discuss the magnitude of the error sources in the setup. The performance of the setup is demonstrated using a titanium nitride thin-film, which is tested up to 400 °C revealing the gauge factor behavior in this temperature span and the temperature coefficient of resistivity.