Comprehensive Design Considerations and Noise Modeling of Preamplifier for MEMS Electrometry

The purpose of the work is to evaluate various intrinsic noise sources that limit the charge resolution of microelectromechanical systems (MEMS) vibrating-reed (VR) electrometers. We demonstrate a method of reducing total equivalent referred-to-input (RTI) noise voltage per square root hertz for an operational amplifier-based preamplifier (preamp) circuit topology. The proposed circuit's noise model accurately describes the various noise sources and total RTI noise voltage is experimentally verified. The noise analysis clarifies the path toward a preamp with a noise floor limited by thermal noise due to low-valued shunt resistance at its input. Furthermore, during the charge measurement, a variation of sensitivity occurs by changing the isolation (or dc blocking) capacitor of the preamp. This phenomenon also affects the noise performance of the circuit and the overall charge resolution for the electrometer. RTI noise voltage of 290 nV/√Hz at 5.2 kHz was measured for 50 MQ of shunt resistor and 2 pF of isolation capacitor to implement a prototype of the complete preamp, along with the MEMS device fabricated in silicon-on-glass (SOG) process. Finally, we present a charge resolution model of the proposed SOG-MEMS electrometry system. The model's underlying design principles reveal low noise preamps accessible to the circuit designers without tangible circuitries and after-the-fact noise measurement.