High-resolution Electrometer with Micromechanical Variable Capacitor

We have designed, fabricated, and operated an electrometer with a noise-equivalent resolution of 535 electrons rms (86 aC). The electrometer incorporates a silicon resonator that acts as a variable capacitor and is fabricated using a new self-assembly process that demonstrates for the first time the integration of lownoise, low-leakage JFETs with SOI structures. The resolution of the measurements made with the electrometer thus far has been limited to 9500 electrons (1.5 fC) because of a large quiescent charge on the input, generated by JFET gate current. At 1.5 fC, the MEMS electrometer charge resolution is an order of magnitude better than those quoted for the best commercial instruments. Improvements that should lead to higher resolution are proposed. INTRODUCTION AND THEORY For over a century, scientists have used electrometers, instruments that measure electric charge, to study a variety of phenomena. Electrometers are used in mass spectrometers, scanning tunneling microscopes, and airborne-particle detectors, to name a few applications. In 1947, researchers built an electrometer with a resolution of 4 fC (25,000 electrons). [1] Although recent research projects have demonstrated charge sensors with subelectron resolution using cryogenics [2] or magnetically levitated rotors [3], there has been limited progress in developing practical electrometers for use in instrumentation. (The best commercial electrometer we are aware of is the Keithley 6514, which has a resolution of 10 fC) A fundamental difficulty in making a sensitive, low-frequency, solidstate electrometer is the high level of 1/f noise associated with a dc measurement. In voltage amplifiers, 1/f noise can be eliminated using the technique of chopper stabilization, typically implemented using MOS switches. MOS switching is not, however, well suited to electrometry because subthreshold leakage in the off-transistors and switch-charge injection impose a lower limit on the detectable charge value. The instrument we describe uses the principle of inputcapacitance modulation, which was also employed in the “vibrating-reed electrometer” of Palevsky et al. [1] To illustrate this technique, consider the basic electrometer circuit of Fig. 1. The charge to be measured, Q, is collected on a variable capacitor, CV and a parasitic capacitor, CP. The resulting dc voltage is P V Q V C C = + . [1] If we let CV vary sinusoidally, according to 0 ˆ cos V C C C t ω = + , [2] we expect to find a component of V at the modulation frequency ω. By performing a power-series analysis of Eqs. 1 and 2, we find the magnitude of this variation, normalized to the input charge: