The value of ��44 is more consistent and Tubacin microtubule relatively easy to measure. Moreover, at constant doping level, it is documented that ��44 is independent of temperature [36,37]. Therefore, a piezoresistive sensor with output signal proportional to the shear piezoresistive coefficient (��44) will potentially have low thermal drift. The temperature effect contributes to the output signal of piezoresistive sensors through two sources: temperature coefficient of resistance (TCR) and dependence of piezoresistive coefficients on temperature. These two sources can be addressed by controlling the microfabrication parameters. The following sections discuss the formulation of piezoresistive sensor, sensing chip design and FEA modeling.2.1.

Formulation of Sensor ResponseIn the case of semiconductors, Ohm��s Law can be expressed Inhibitors,Modulators,Libraries as:Ei=��ij Jj(1)where Ei and Ji are the Cartesian vector components of electric field and current density, respectively, ��ij is the electrical resistivity tensor [��ij = ��o(��ij + ��ijkl��kl + ��ijklmn��kl��mn + ��)], ��o is the electrical resistivity for the unstressed conductor filament, �� is Kronecker delta tensor and ��ijkl, ��ijklmn ��etc. are the components of fourth, sixth and higher order of piezoresistivity tensors, which describe the resistivity change due to the applied stress.When the semiconductor piezoresistive element is subjected to stress or strain, the resistivity components are linearly related to the stress components by:��ij=��ijo+��ijkl ��kl(2)Considering the case of biaxial state of stress, shown in Figure 1, a p-type piezoresistive element with orientation angle ? with respect to [110] direction will experience a normalized resistance change that can be described by:��RR=��11(��11+��12+��44 cos (2?)2)+��22(��11+��12?��44 cos (2?)2)+��33��12+��12 (��11?��12) sin (2?)+(��1T+��2T2+.

…)(3)where T is the difference between the operating temperature (Tw) and the reference temperature (To), and ��ij are the temperature-dependent on-axis piezoresistive coefficients. ��ij are related to T according to:��ij=��ij(o)+��ij(1)T+��ij(2)T2+….(4)where Inhibitors,Modulators,Libraries Inhibitors,Modulators,Libraries the terms (��1T + ��2T2+��3T3 + ��.) in Equation (3) account for the TCRs of the piezoresistive element. It is reported [20,22,32] that the first order TCR (��1) has a higher influence on the thermal response of piezoresistors than higher order TCRs (��2, ��3,��.).

Moreover, Inhibitors,Modulators,Libraries it was determined that ��1 is the same for Dacomitinib different crystal orientations [36,37]. In addition, in the case of heavily doped piezoresistors, (��ij(1), ��ij(2), ��) have a minor contribution to the results chemical information [20,22,30�C32].Figure 1.A piezoresistive element on (100) silicon substrate along general orientation (?) with respect to [110] while subjected to biaxial state of stress.2.2. Sensing Chip DesignThe current sensor design, shown in Figure 2, utilizes a sensing arrangement that is called sensing unit.