Characterisation and modelling of the mismatch of TCRs and their effects on the drift of the offset voltage of piezoresistive pressure sensors

Based on the assumption that each piezoresistor of a silicon pressure sensor has its own temperature coefficients (TCRs of the first and second order), a theoretical model has been developed in order to study the thermal behaviour of the offset voltage. We first derive the expression for the drift of the output voltage of each potentiometric circuit obtained from the whole bridge, and then that for the thermal variations of the offset voltage itself. It is shown that the existence of a small difference between the temperature coefficients of the four piezoresistors can provoke thermal variations of the output voltages whose shapes can obey to a linear or a parabolic law. On the other hand, we have used an experimental procedure, on our test pressure sensors, allowing us to extract the piezoresistors TCRs, to measure the thermal drifts of the output voltage of each half-bridge, and those of the whole bridge. The application of the theoretical model shows that there exists a good accordance with the experimental results. The parabolic shapes of the outputs of the two half-bridges, and also that of the offset voltage, are explained by the mismatch of the TCRs of the four piezoresistors. (C) 2000 Elsevier Science S.A. All rights reserved.