Modeling of CMOS Devices and Circuits on Flexible Ultrathin Chips

The field of flexible electronics is rapidly evolving. The ultrathin chips are being used to address the high-performance requirements of many applications. However, simulation and prediction of changes in response of device/circuit due to bending induced stress remains a challenge as of lack of suitable compact models. This makes circuit designing for bendable electronics a difficult task. This paper presents advances in this direction, through compressive and tensile stress studies on transistors and simple circuits such as inverters with different channel lengths and orientations of transistors on ultrathin chips. Different designs of devices and circuits in a standard CMOS 0.18-μm technology were fabricated in two separated chips. The two fabricated chips were thinned down to 20 μm using standard dicing-before-grinding technique steps followed by post-CMOS processing to obtain sufficient bendability (20-mm bending radius, or 0.05% nominal strain). Electrical characterization was performed by packaging the thinned chip on a flexible substrate. Experimental results show change of carrier mobilities in respective transistors, and switching threshold voltage of the inverters during different bending conditions (maximum percentage change of 2% for compressive and 4% for tensile stress). To simulate these changes, a compact model, which is a combination of mathematical equations and extracted parameters from BSIM4, has been developed in Verilog-A and compiled into Cadence Virtuoso environment. The proposed model predicts the mobility variations and threshold voltage in compressive and tensile bending stress conditions and orientations, and shows an agreement with the experimental measurements (1% for compressive and 0.6% for tensile stress mismatch).