Micro and Nano Machined Electrometers

This chapter introduces ultrasensitive charge measurement by frequency modulation on micromachined resonators and oscillators at room temperature. The frequency modulation type resonant electrometers have merits of high resolution and large dynamic range. Fundamentals of vibration system is firstly introduced, including resonance of a beam resonator. Oscillations of the resonator with closed loop methods are introduced to obtain and track resonant frequency. Designs, principles and models of several capacitive resonant electrometers are presented. The axial strain modulation and lateral stiffness perturbation charge measurement schemes are studied respectively. Finally, we introduce a prototype of resonant electrometer employing single anchored circular beam resonator with parallel-plate capacitors as transducers based on lateral stiffness perturbation scheme. The prototype of resonant electrometer has sub-electron resolution and high charge sensitivity. The micromachined resonant electrometers may be key components to develop advanced instruments, such as voltmeters, ammeters and multimeters.

Resonant micro-electrometers have been the research interest to many groups around the world. Conventionally, the resonant electrometers rely on a frequency-shift based readout. In this chapter, a new type of resonant micro-electrometer based on mode-localization effect is introduced and discussed. This new electrometer implementation is one subset of a broader family of sensors termed as “mode-localized sensors”. The readout metric of this category of sensors is essentially based on amplitude modulation, which is a key identifier of this approach. In addition to the sensing paradigm shift, the mode-localized sensors have a distinguishable topology to the convention based on a single resonator: that is, typically more than one resonators are intentionally coupled to each other through a coupling element, to allow spatial energy extension. Due the advantages that accompany the unique configurations, such as higher sensitivity and common mode rejection capabilities, the new sensing scheme has quickly attracted researchers’ attention. And naturally it has been adapted for electrometer applications. Currently, the resolution that can be achieved by an electrometer utilizing this approach can be less than 10 e/Hz\(^{1/2}\). Future directions to further enhance the sensor performance are also discussed.

We present a comprehensible introduction to capacitive gate-based sensing, a technique for charge state readout of gate-defined semiconductor quantum dots. The objective of this chapter is to introduce the reader to the fundamental concepts necessary to understand the technique from a theoretical perspective and to be able to apply the method experimentally. We aimed to maintain a pedagogical tone with necessary rigour to keep it accessible and self-contained. We start by introducing the fundamentals of single-electron effects in single and double quantum dots i.e. Coulomb blockade. We use the constant interaction model and the effect of quantum confinement with a focus on explaining the electrical impedance of these systems under direct current excitation. We then explain how these properties are modified under the effect of an electrical excitation at high-frequency. More particularly, we focus on the appearance of a new component to the impedance, the so-called parametric capacitance when single-electrons tunnels back and forth between stable charge states because of the effect of the drive. We show how the parametric capacitance is composed by two physically distinct terms, the quantum capacitance and the tunneling capacitance, associated to adiabatic and non-adiabatic tunneling processes, respectively. In the second part of this chapter, we introduce the experimental technique. We show how embedding the devices in a high-Q lumped-element LC resonator can be used to probe the parametric capacitance of the system. We first present the fabrication technique of superconducting niobium nitride (NbN) spiral inductors and how these can be used in conjunction with the devices to construct high-Q resonators at radio-frequencies (rf). We show how the resonator can be characterized and optimized for optimum sensitivity of the charge state of the quantum dot system. Finally, we present an experimental demonstration of rf capacitive gate-based sensing utilizing a NbN inductor coupled to the gate of a silicon nanowire field effect transistor. Coulomb blockade manifest in these devices at milikelvin temperatures allowing probing their parametric capacitance when driven by an external high-frequency excitation. Based on the theoretical concepts in combination with the experiential demonstration presented, this chapter provides a pedagogical introduction to rf gated-based charge sensing.

This chapter describes the concept of a micro electrometer based on a time-modulated variable capacitor. The roots of the device concept trace back to a period prior to the availability of microfabrication technology and techniques. This chapter shows how microfabrication technology, when aptly applied to older concepts that were previously realized using conventional machining techniques, can provide significant advancements in performance. This is particularly the case where the parasitic elements at the interface between parts of the system have an impact on the sensor performance. Through tighter integration of constituent parts, significant improvements in performance can be realized through further miniaturization.

Designing charge sensors for electrometry is deemed significant because of the sensitivity and resolution issues in the range of micro-scales. This chapter presents the design of microelectromechanical systems (MEMS) vibrating-reed (VR) electrometer developed based on micromechanical variable capacitors in silicon-on-glass (SOG) process. By using vibrating-reed technique, the resonator is driven at the frequency above the corner frequency of Flicker noise and the charge measurement is performed at the second harmonic of the resonator’s frequency. This chapter also describes the noise characterization and the referred-to-input (RTI) noise reduction methods for operational amplifier (opamp) based preamplifier. The design of an improved noninverting topology overcame the issues of leakage current and charge resetting during measurement. A comprehensive noise model has been proposed considering all electronic noise contributors including the preamp in conjunction with capacitive MEMS sensor in silicon-on glass (SOG) process and ancillary components. The research findings proved that the blocking capacitor and shunt resistor have significant impact on the RTI noise of the preamp and the charge resolution of the electrometer. The noise analysis and measurement results provide a practical guideline for low noise electrometer interface circuit design. Trade-offs among opamp selection, blocking capacitor value, shunt resistor value etc. have been discussed to provide an original and in-depth analysis for noise and resolution performance optimization in the design of MEMS electrometers.

An electrometer is a sensor to measure electric charge. Electrometers are needed in various applications, ranging from the detection of ionization charges in nuclear physics, counting ions in mass spectroscopy, and space exploration, among others. Most electrometers measure the charge indirectly. For instance, solid-state electrometers measure the electric potential that is generated by an induced charge across the electrodes of a known capacitance. Devices such as gold-leaf electrometer, on the other hand, measure the columbic force between charges. Yet some other electrometers utilize a continuously varying capacitor to convert input charge to an AC current which is often easier to measure. Solid-state and vacuum-tube based electrometers have been developed as miniaturized, low-cost alternatives to traditional systems. These devices, however, suffer from drift, low-frequency noise, and leakage. Micromachined electrometers have been developed to address such short comings. Resonant sensing is often employed due to the need for resolving rather small forces from input charges. In this chapter, we will look at two main approaches for the design of micromachined electrometers, where the input charge affects the response of either a single micro-resonator or the combined response of coupled micro-resonators. We also discuss some micromachined devices for the measurement of electric field, as such devices in many applications can be utilized as electrometers.

Micromachined mechanical variable capacitor is a key component of many microelectromechanical systems (MEMS) devices, such as pressure sensor, accelerometer, gyroscope, electrometer, etc. Optimization of these devices require a systematic consideration of parameter design in both mechanical and electrical domains. This chapter introduces the system-level modelling of a variable capacitor-based MEMS electrometry system. To simultaneously simulate the mechanical and electrical components, Matlab Simulink was adopted as the simulation environment to build the system model. Four main modelling blocks were developed to model the entire system, including electrostatic force generator, equivalent circuit representation of spring-mass-damper mechanical system, time-dependent variable capacitor controlled by in-line equation, and integration of variable capacitor into the actual detection circuitry. The whole electrometry system was successfully simulated in Simulink, and the detailed simulation results are shown in this chapter, such as the waveforms of driving force, shuttle displacement, time-varying capacitance and charge induced output voltage. The simulated results agreed well with the experimental results, for example, the simulated charge sensitivity is 7.2 × 10⁷ V/C, which is close to the experimental results of 9.5 × 10⁷ V/C with the same design parameters. Using this technique, any variable capacitor-based MEMS sensors can be modelled in Simulink by simply changing the mathematical calculation blocks to implement the in-line equation for the time-dependent capacitance. Therefore, this technique provides a useful tool that allows a fully combined simulation of both mechanical and electronic systems.