These effects change the characteristics of the piezoresistors significantly. Thaysen et al. [25] showed that an increase in temperature to 110 ��C increased the fractional resistance of the piezoresistor by about 2%. This is mainly because the increase in temperature increased the TCR of the cantilever. The self-heating characteristics, however, can be exploited to useful effects. For instance, Chui et al. [26] and Binnig et al. [27] and proposed using the self-heating and self-sensing characteristics of piezoresistive microcantilevers for ultra-high density atomic force microscopy data storage. In a related work, King [28] proposed heated atomic force microscope cantilevers for nanotopography measurements.
King et al.
[29] showed thermal cantilevers have better characteristics than piezoresistive cantilevers in improving the sensitivity of and resolution of AFM topology measurements.Most of the studies on Joule heating involved experimental and numerical analyses and there are only Cilengitide few analytical models for it. Choudhury et al. [30] derived an analytical model for predicting transient self-heating in a piezoresistive cantilever under sinusoidal input voltage. They showed that for 50 Hz input a maximum temperature of about 73 ��C is generated within 2 ms. This model neglected the layered structure of the cantilever and assumed a uniform thermal conductivity for the entire cantilever.
Yang and Yin [31] included the layered structure in their steady-state analytical model for Joule heating in piezoresistive cantilever, and used thickness ratios for each layer in defining the total thermal conductivity of the cantilever.
The model is derived for piezoresistors that show temperature dependence on resistance and therefore Entinostat requires the temperature coefficient of resistance value for calculations. The present work derives both temperature-independent and -dependent models for self-heating in piezoresistive microcantilevers. To this end, the authors propose the use of volumetric ratio of each layer for defining the total thermal conductivity of the cantilever.The objective of the present work was to derive a steady-state analytical model for describing the temperature distribution in piezoresistive microcantilever by Joule heating.
The model includes the layered structure of the cantilever and uses the effective thermal conductivity calculated from the volumetric contribution of each layer. The results are compared against numerical results obtained using a commercial finite element analysis ANSYS. This work uses two different cantilever materials in the analysis. The cantilevers are made of silicon and silicon dioxide with a p-doped silicon piezoresistor encapsulated within.