Fabrication-induced Variations Research Articles

Mechanical Synchronization of MEMS Electrostatically Driven Coupled Beam Filters.

Micro-electromechanical systems (MEMS) bandpass filters based on arrays of electrostatically driven coupled beams have been demonstrated at MHz frequencies. High performance follows from the high Q-factor of mechanical resonators, and electrostatic transduction allows tuning, matching and actuation. For high-order filters, there is a conflict between the transduction mechanism and the coupling arrangement needed for dynamic synchronization: it is not possible to achieve synchronization and tuning simultaneously using a single voltage. Here we propose a general solution, based on the addition of mass-loaded beams at the ends of the array. These beams deflect for direct current (DC) voltages, and therefore allow electrostatic tuning, but do not respond to in-band alternating current (AC) voltages and hence do not interfere with synchronization. Spurious modes generated by these beams may be damped, leaving a good approximation to the desired response. The approach is introduced using a lumped element model and verified using stiffness matrix and finite element models for in-plane arrays with parallel plate drives and shown to be tolerant of the exact mass value. The principle may allow compensation of fabrication-induced variations in complex filters.

High-Q 1D rod-based nanocavities.

We report an analysis of one-dimensional rod-based photonic crystal nanocavities. These cavities offer opportunities for dielectric materials which lack a matching low-refractive index substrate or are limited in under-etching possibilities to create slab-based PhC cavities. They offer high theoretical Q-values exceeding 106 for transverse magnetic polarized modes with modal volumes below 2.5(λ/n)3. For practical implementations, we propose embedding these structures in a low-refractive index polymer. An analysis of intentionally introduced variations in a rod diameter reveals which design directions should be followed in order to create cavities that are most robust for fabrication-induced variations.

Robust postfabrication trimming of ultracompact resonators on silicon on insulator with relaxed requirements on resolution and alignment.

One of the main drawbacks of the high-index-contrast silicon-on-insulator platform in integrated photonics is the high sensitivity of the resonance wavelength of resonators to dimensional variations caused by fabrication imperfection. In this work, we experimentally demonstrate an accurate postfabrication trimming technique for compensating the fabrication-induced variations in the resonance properties of nanophotonic devices. Using this technique, we reduce the variation of the resonance wavelength of 4μm diameter microdonut resonators by more than 1 order of magnitude to about 25pm, which is adequate for most interconnect, optical signal processing, and sensing applications. In addition, our proposed technique has improved misalignment toleration and throughput compared to previous reports.

Tunable Q-factor silicon microring resonators for ultra-low power parametric processes.

A compact silicon ring resonator is demonstrated that allows simple electrical tuning of the ring coupling coefficient and Q-factor and therefore the resonant enhancement of on-chip nonlinear optical processes. Fabrication-induced variation in designed coupling fraction, crucial in the resonator performance, can be overcome using this post-fabrication trimming technique. Tuning of the microring resonator across the critical coupling point is demonstrated, exhibiting a Q-factor tunable between 9000 and 96,000. Consequently, resonantly enhanced four-wave mixing shows tunable efficiency between -40 and -16.3 dB at an ultra-low on-chip pump power of 0.7 mW.

Optical Quality-Assessment of High-Order One-Dimensional Silicon Photonic Crystals With a Reflectivity Notch at $\lambda \sim 1.55\ \mu\hbox{m}$

In this paper, high-order silicon/air vertical 1-D photonic crystals (PhCs) featuring a deep reflectivity notch (Q of about 3000) within the third telecommunication transmission window are fabricated by electrochemical micromachining of silicon and optically characterized. Although, from scanning electron microscope (SEM) investigations, the microfabricated structures appear to be of high quality in terms of in-plane and out-of-plane uniformity as well as of low surface roughness, optical measurements highlight variability of the spectral position of reflectivity notches, which turns out to be affected by fine variations of structural features induced by fabrication. A nondestructive optical method is used to recover the distribution of typical fabrication features, which is not easily quantifiable with other techniques in these high aspect-ratio vertical structures, from the experimentally detected distribution of the optical features. Optical distribution is obtained by scanning the device with high spatial resolution and recording spectral reflectivity at normal incidence (in the wavelength range 1.0-1.7 μm) on different locations of the 1-D PhC surface (X-Y plane). Distribution of silicon thickness variation on the X-Y plane is then inferred by best fitting the experimental spectral reflectivity data with theoretical spectra that are calculated by taking into account nonidealities of both PhC structure and measuring setup. On-sample fabrication-induced variation of the average silicon thickness, as a function of the X-Y position, is estimated to be limited to ±80 nm (percentage error of ±1%) within a range of ±100 μm from a reference location. As a consequence of such thickness variation, a maximum shift of the reflectivity spectrum of 40 nm occurs as a function of the X-Y position in the range of ±100 μm. Sample-to-sample average silicon thickness variation among nominally equivalent structures is also tested in similar X-Y positions and found to be lower than ±1.5% (absolute variation of ±120 nm), within a range of ±15 μm, with respect to the average value on the investigated samples.

Effect of Electrical Stress on Josephson Tunneling Characteristics of ${\rm Nb/Al/AlO}_{x}/{\rm Nb}$ Junctions

Fabrication-induced variations in the critical currents of Josephson junctions significantly affect the performance and yield of complex superconducting integrated circuits. Electrical stress that may develop during plasma processing steps in the fabrication process was initially suggested as a possible cause of these variations. The effect on the Josephson and quasiparticle tunneling properties of Nb/Al/AlOx/Nb junctions with ultrathin AlOx barriers by the application of dc electrical stress was investigated. Current ramps with increasing amplitude corresponding to voltages across the barrier up to ~ 0.65 V were used to apply electrical stress. Junction conductance and current-voltage (I-V) characteristics were measured after each stress application at room temperature. As the stressing progresses, a dramatic increase in subgap conductance of the junctions, the appearance of subharmonic current steps, and a gradual increase in both the critical and the excess currents as well as a decrease in the normal-state resistance have been observed. A model is proposed wherein a progressively increasing number of defects and associated additional conduction channels (superconducting quantum point contacts (SQPCs)) are induced by the applied electric field in the tunnel barrier. The dependence of the stress effect on the polarity is also investigated and the results are presented. It is found that the magnitude of stress current needed for junction breakdown is unlikely to be supplied during plasma processing and as such, potential differences that can develop during plasma processing appear to be an unlikely cause of fabrication-induced, circuit pattern-dependent variations of Josephson junctions' critical currents in superconductor integrated circuits.

Analysis of photonic crystal waveguide discontinuities using the mode matching method and application to device performance evaluation

The application of the mode-matching (MM) method in the case of photonic crystal waveguide discontinuities is presented. The structure under consideration is divided into a number of cells, and the modes of each cell are calculated by an alternative formulation of the plane-wave expansion (PWE) method. This formulation allows the calculation of both guided and evanescent modes at a given frequency. A matrix equation is then formed relating the modal amplitudes at the beginning and the end of the structure. The accuracy of the MM method is compared to the finite-difference frequency-domain (FDFD) method and the finite-difference time-domain (FDTD) method, and good agreement is observed. The MM method requires far fewer resources than the FDFD and the FDTD methods while providing a useful physical insight to the calculation of the frequency response of waveguide discontinuities. The method is also applied to the calculation of power loss due to structural fabrication-induced variations.

Robust controlled-NOT gate in the presence of large fabrication-induced variations of the exchange interaction strength

We demonstrate how using two-qubit composite rotations a high fidelity controlled-NOT (CNOT) gate can be constructed, even when the strength of the interaction between qubits is not accurately known. We focus on the exchange interaction oscillation in silicon based solid-state architectures with a Heisenberg Hamiltonian. This method easily applies to a general two-qubit Hamiltonian. We show how the robust CNOT gate can achieve a very high fidelity when a single application of the composite rotations is combined with a modest level of Hamiltonian characterisation. Operating the robust CNOT gate in a suitably characterised system means concatenation of the composite pulse is unnecessary, hence reducing operation time, and ensuring the gate operates below the threshold required for fault-tolerant quantum computation.

Electron spin resonance features of interface defects in thermal (100)Si/SiO2

Electron spin resonance (ESR) on thermal (100)Si/SiO2 predominantly exhibiting either the Pb0 or Pb1 interface defect confirms the Pb1 point symmetry as monoclinic-I with g1=2.0058, g2=2.00 735±0.00 010, and g3=2.0022, where the g2 direction is at 3°±1° (towards the interface) with a 〈111〉 direction at 35.3° with the interface plane. Its line width is found weakly dependent on magnet angle, exhibiting a strain induced spread σg⊥∼0.00 035 in g⊥ about 2–3 times less than typical for Pb in (111)Si/SiO2. For Pb0, an axially symmetric g matrix is observed, with g∥=2.0018 and g⊥=2.0081, and σg⊥∼0.0009. From comparison of salient ESR data, it is concluded that Pb and Pb0 are chemically identical; however, systematic fabrication-induced variations in defect environment will lead to second order systematic shifts in average properties. The Pb1 defect is provisionally pictured as an unpaired Si bond on a defect Si atom at slightly subinterface plane position in the Si substrate, possibly facing an oxygen atom.