Finite element analysis of differential capacitive PUF sensors

The sensors that offer unique characteristics, which cannot be duplicated fall into the category of Physical Unclonable Function (PUF) sensors. A PUF sensor for measuring mechanical parameters is reported in [1]. The reported PUF sensor uses a capacitive electrode structure (dual electrode configuration) to transform the movement of a membrane filled with conductive steel balls into change in capacitance. For each sensor, the steel balls are randomly distributed, which makes the sensor characteristics unique and unclonable. The electrical equivalent model of the dual electrode PUF sensor is presented in this paper. The dual electrode PUF sensor has a large fixed offset capacitance along with a variable capacitance. Only the variable capacitance varies with measured quantity. The offset capacitance degrades the bandwidth and resolution of sensor system. A new differential capacitive electrode structure, which nullifies the unwanted offset capacitance and provides a sensor output, which only contains variable capacitance, is proposed. The sensor design is verified using finite element analysis software COMSOL Multiphysics. To study the effect of steel balls distribution on sensor characteristics, sensors with six different steel ball distributions are simulated. The uniqueness of each of the six sensors is measured in terms of inter hamming distance - the difference between sensor outputs for the same excitation. Each sensor showed a measurebly different characteristics.