Towards Ultra-High Resolution Mode-localised MEMS Sensors

Sensors employing mode localisation in weakly coupled resonators have been increasingly viewed as an alternative to resonant frequency shift based sensing. Much theory has been proposed highlighting the advantages of these sensors including the increased sensitivity and the promise of common mode rejection to first order environmental variations. This has led to the development of proof-of-concept sensors to sense physical quantities such as displacement, charge, mass, and acceleration. However, practical aspects of developing a sensor starting from design of a closed-loop implementation to understanding different operating regions with the aim of resolution analysis and noise optimisation have yet to be explored in depth. This work delves into these practical aspects of developing ultra-high resolution mode-localised MEMS sensors. First, the mechanical sensor is integrated with a prototype closed-loop oscillator along with the interface electronics on a printed circuit board. Key aspects of sensors such as stability, noise floor, and bandwidth are analysed using this integrated sensor system. A critical observation is made on the improvement of stability of the amplitude ratio output metric over its frequency shift counterpart at large integration times therefore, highlighting the advantage of common mode rejection to environmental factors. The common mode rejection abilities of both mechanically and electrically coupled devices are next studied at different operating regions. These are then compared to the state-of-the-art differential frequency measurements. Amplitude ratio measurements in an electrically coupled device showed an order of magnitude better rejection to temperature variations over a mechanically coupled device. Furthermore, amplitude ratio measurements in the electrically coupled device were on par with the rejection offered by the differential frequency output in the same device. This result highlights the advantage of amplitude ratio measurements that are able to achieve the same common mode rejection with the help of a single oscillator instead of the two oscillators required in differential frequency output measurements. The resolution of the mode-localised sensor is then explored with the purpose of optimising operating regions to achieve the best noise figure. A detailed theoretical analysis is first undertaken to optimise the amplitude ratio noise in different noise dominant regimes. It is predicted that the resonator-based noise (such as thermo-mechanical noise) can be optimised be operating at an amplitude ratio of $\sqrt{2}$ and the electronic sourced noises can be optimised at an amplitude ratio of $\sqrt{1.5}$ in a single ended resonator drive configuration. Additionally, both sources of noise are predicted to decrease with the decrease of the coupling stiffness. This result is then validated using experimental data to verify the claim. A further noise reduction is sought by operating the coupled resonators in the nonlinear domain with interesting observations on the variations of the amplitude ratio output metric. The phase filtering offered by the bifurcation points in the nonlinear domain is utilised to further improve the noise by 4 times. Finally, a mode-localised accelerometer design is proposed that employs a novel differential amplitude ratio output metric. Noise optimisation techniques are then used to optimise this novel output metric. A noise floor of $3$ $\mu$g/\sqrt{\mbox{Hz}} with a stability of $3$ $\mu$g is achieved thus, benchmarking the mode-localised accelerometer favourably with respect to other high-end commercial MEMS accelerometers. Additionally, their potential is demonstrated with a measurement of seismic activity. This measurement is then compared to reference data sourced from an accelerometer from the British Geological Survey. Lastly, suggestions are made to further optimise the resolution in the accelerometer to push the limits of amplitude ratio sensing thereby, putting mode-localised accelerometers at par with the best resonant accelerometers till date.Innovate UK Natural Environment Research Counci

Local characterisation of strain in silicon nanostructures

PhD ThesisStrain engineering is used in the microelectronics industry for fabricating micro- and nano-electromechanical systems (MEMS and NEMS) and state-of-the-art metal-oxide-semiconductor field-effect transistors (MOSFETs). In these devices suspended silicon beams, films and nanowires are widely used. However, the mechanical, thermal and electrical properties of silicon change significantly at the nanoscale. Therefore, an accurate knowledge of the size effect on these properties, the role of the surface and an accurate characterisation of the stress and strain distribution in these devices is needed for a complete understanding of the device operation. Likewise, state-of-the-art MOSFETs incorporate strain into the channel to improve performance due to a carrier mobility enhancement compared with unstrained silicon channel transistors. However, the mobility enhancement especially at high vertical electric fields (where commercial MOSFETs operate), is still not well understood. The SiO2/Si interface roughness exhibits, at the nanoscale, scaling behaviour with the scale of observation. However, to date, there is no experimental study of the SiO2/Si interface roughness scaling behaviour with strain. This study is needed to better understand the surface roughness scattering-limited mobility of electrons and holes in strained devices. Raman spectroscopy is a widely used technique to characterise strain. However, the conversion of Raman peak shifts to strain values requires a strain-shift coefficient. Traditionally, the reported strain-shift coefficients have been determined from experiments performed in bulk material. The applied stress has also been limited within the range 0 – 2 GPa. This range is reasonable for bulk silicon characterisation but is too narrow for silicon nanostructures and devices where higher stress values are often favourable for improving performance. Consequently, there is an outstanding need to find appropriate strain-shift coefficients for silicon nanowires and thin films under large values of stress. In this thesis strain in silicon nanostructures is experimentally and theoretically investigated for strain values ranging from 0 to 3.6%. Strain has been characterised using scanning electron microscopy (SEM), Raman spectroscopy, and theoretically with analytical calculations and finite element simulations. The combination of these techniques and the large number of samples (up to 85) has allowed the accurate determination of the ii strain-shift coefficient for the technologically important (100) silicon surface and for stress values up to 4.5 GPa. The work also enables a better understanding of the changes in silicon properties with strain when device dimensions are reduced to the nanoscale. The size dependency of the Young‟s modulus, fracture strain, thermal conductivity and the role of the surface in the size dependent physics are also investigated. It is found that some properties such as the fracture strain change with the dimensions of the sample whereas others such as the Young‟s modulus and thermal conductivity do not change. Finally, the impact of uniaxial and biaxial strain on the surface roughness of silicon nanostructures and thin films has been analysed by atomic force microscopy (AFM). It is found that the silicon surface roughness changes in different manner with uniaxial and biaxial strain. The results show that the silicon surface roughness is self-affine with strain and that this behaviour has to be considered within the models used to describe the carrier mobility in MOSFETs at high vertical electric fields.Engineering and Physical Sciences Research Council (EPSRC) HORIBA Jobin Yvon Ltd