The piezoresistive response of n- and p-type hydrogenated nanocrystalline silicon thin films, deposited by hot-wire (HW) and plasma-enhanced chemical vapor deposition (PECVD) on thermally oxidized silicon wafers, has been studied using four-point bending tests. The piezoresistive gauge factor (GF) was measured on patterned thin-film micro-resistors rotated by an angle θ with respect to the principal strain axis. Both longitudinal (GFL) and transverse (GFT) GFs, corresponding to θ = 0° and 90°, respectively, are negative for n-type and positive for p-type films. For other values of θ (30°, 45°, 120°, and 135°) GFs have the same signal as GFL and GFT and their value is proportional to the normal strain associated with planes rotated by θ relative to the principal strain axis. It is concluded that the films are isotropic in the growth plane since the GF values follow a Mohr’s circle with the principal axes coinciding with those of the strain tensor. The strongest p-type pirezoresistive response (GFL = 41.0, GFT = 2.84) was found in a film deposited by PECVD at a substrate temperature of 250 °C and working pressure of 0.250 Torr, with dark conductivity 1.6 Ω−1cm−1. The strongest n-type response (GFL =− 28.1, GFT =− 5.60) was found in a film deposited by PECVD at 150 °C and working pressure of 3 Torr, with dark conductivity 9.7 Ω−1cm−1. A model for the piezoresistivity of nc-Si is proposed, based on a mean-field approximation for the conductivity of an ensemble of randomly oriented crystallites and neglecting grain boundary effects. The model is able to reproduce the measured GFL values for both n- and p-type films. It fails, however, to explain the transversal GFT data. Both experimental and theoretical data show that nanocrystalline silicon can have an isotropic piezoresistive effect of the order of 40% of the maximum response of crystalline silicon.
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