We demonstrate charge detection with single-electron resolution at high readout frequency using a silicon field-effect transistor (FET) integrated with double resonant circuits. A FET, whose channel of 10-nm width enables a single electron to be detected at room temperature, is connected to resonant circuits composed of coupled inductors and capacitors, and these double resonant circuits provide two resonance frequencies. When the FET is driven by a carrier signal at the lower resonance frequency, a small signal applied to the FET's gate modulates the resonance condition, resulting in a reflected signal appearing near the higher resonance frequency. Such operation utilizing the double resonant circuits enables charge detection with a single-electron resolution of 3 × 10-3 e/Hz0.5 and a readout frequency of 200 MHz at room temperature. In addition, a variable capacitor used in the double resonant circuits allows charge-sensing characteristics to be controlled in situ.

A micro-electromechanical systems (MEMS) Duffing resonator is driven by two adjacent frequency tones into the nonlinear regime. We show that if the two-tone drive is applied at a frequency where a bistable response of the nonlinear oscillator exists, then the system output will be modulated by a relaxation cycle caused by periodically jumping between the two solution branches of the bistable response. Although the jumps are caused by the beating of the drives, the existence and period of this relaxation or hysteresis cycle is not solely dictated by the beat frequency between the two driving tones, but also by their amplitude and detuning with respect to the device resonance frequency. We equally demonstrate how the period of the cycles can be tuned via added tension in the device and how these oscillations can be used as a means of sensitive pulse-width modulated readout of MEMS sensors.

The aim of this work is to theoretically investigate the possibility of Kerr frequency combs in mechanical systems. In particular, whether microelectromechanical devices (MEMS) can be used to generate frequency combs in a manner that is analogous to the optical frequency combs generated in optical microresonators with Kerr-type nonlinearity. The analysis assumes a beam-like micromechanical structure, and starting from the Euler-Bernoulli beam equation derives the necessary conditions in parameter space for the comb generation. The chapter equally presents potential means for the physical implementation of mechanical Kerr combs.