Stress, Strain, Piezoresistivity, and Piezoelectricity

Abstract

In contrast to the fixed strain incorporated in logic devices for a fixed or constant improvement in device performance, piezoresistive strain sensors respond to variable strain through a modulation in the device resistance. The underlying physics of performance improvement in logic devices and strain transduction in piezoresistive strain sensors is the same: symmetry-breaking strain of the semiconductor crystal lattice warps the energy bands, splits the energy levels, and changes the carrier scattering rates, which changes the carrier mobility and the device resistance. While improvement of logic device performance requires an increase in mobility, which dictates the “sign” of the fixed strain, strain sensors respond to both negative (compressive) and positive (tensile) strains. Since the strain is fixed in logic devices, the linearity of mobility increase with strain is not an issue since the strain is theoretically frozen into the device by stressors incorporated into the device structure during the manufacturing process. In contrast, piezoresistive strain sensors are designed to transduce or detect varying strains by producing a proportional change in resistance. Hence, linear resistance change with strain is important to sense/transduce strains of varying amplitudes into an electrical signal without introducing distortion. For a transducer, the measured resistance vs. strain curve can be used to calculate the input strain from the strain sensitivity or calibration slope of the sensor. For a piezoresistive strain sensor, the upper limit of the measurable strain is usually defined as the maximum strain abovewhich nonlinear deformation occurs. In contrast, there is no maximum allowable stress in strain-enhanced logic devices as long as there is performance enhancement, provided that the stress is manufacturable and the device is reliable.