Patel, Trupti; (2018) Nanomechanical Resonators for SQUID readout. Doctoral thesis (Ph.D), UCL (University College London).

Abstract

Nano-electromechanical systems (NEMS) are an important new class of device, with a growing range of applications, from tests of quantum mechanics through to nanoscale metrology and a vast number of different sensors. Cryogenic operation is also possible, and at low temperatures, nanoscale resonators exhibit quantum behaviour. NEMS resonators require readout of ultra-small, atomic scale displacements. To achieve this at low temperatures we have developed an ultrasensitive nanoSQUID readout of a coupled current-carrying NEMS resonator. The NanoSQUIDs are fabricated by gallium focussed ion beam milling and are based on niobium nanobridge weak links (Dayem bridges). The nanoSQUIDs have low loop inductance and low junction capacitance resulting in high flux and energy sensitivity. This work focusses on the characterisation of the resonator and nanoSQUID after they have been incorporated onto one chip. This is done through nanoindentation to characterise resonators and electronic measurements of the SQUID using a low-temperature preamplifier. It is found that the model used based upon an Euler-Bernoilli beam is correct close the centre of the sample but does not fit data points well close to the contacts. It is found the resonators have Young’s modulus in the range of 3GPa-241GPa. Both beam and paddle-shaped resonators are investigated and the models are made based upon the two different shapes. That for the paddle is based upon the same as the beam but uses a rectangular function to describe the changing area moment of inertia along the length of the resonator. The SQUID devices are characterised and found to have a typical noise floor of 0.2μ 0/pHz. Problems which have arisen due to the orientation of the two magnetic fields and their effect on the SQUID performance are discussed. We consider the geometry and optimum coupling of rectangular and square Si3N4 resonators to matching similar shaped nanoSQUID loops. We also discuss simulations of the nanoSQUID response versus resonator position for both symmetric and asymmetric configurations. It is found that optimal coupling is achieved in the asymmetric case due to the cancelling of the change in flux in the symmetric case. The use of a normal conducting or superconducting resonator is compared. It is found that a superconducting resonator provides a much larger SQUID response when actuated towards​ the device but cannot be used in the regime due to limitations of the superconducting transition temperature of Al (the resonator) being lower than the non-hysteretic operable temperature of the SQUID. Preliminary measurements are conducted on the coupled devices. It is noted that the signal from the device in the conducting case may be read out at 2! due to the sinusoidal change in flux through the SQUID loop and position of the resonator. The possibility of measuring such a signal is first investigated using a spectrum analyser but it is found the SQUID is pushed to nonlinear regions of its transfer curve. This results in a component of the signal at 2! due to the nonlinearity of the SQUID response. Conditions under which the SQUID is still operating in small signal mode (to preserve linearity of the SQUID response) are considered and from this we conclude there is a need to use phase sensitive detection to achieve optimum sensitivity. This technique is used to conduct the final measurement of the motion of the resonator by the SQUID and a preliminary result is found.

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