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Abstract
The design, fabrication, and transmission measurements of a photonic crystal slab edge directional coupler (PCDC) for submicron deflection sensing is presented. The dielectric modes between two structurally isolated photonic crystal edges allows for a directional coupler to be formed with low insertion loss and reduced coupling distances. The output transmission from the coupler can be related to the distance between neighbouring PC edges, thereby allowing it to be used as an intensity-based optomechanical sensor. PCDC sensors were fabricated by selectively etching the buried oxide (BOX) of surface micromachined silicon-on-insulator wafer. Based on transmission measurements, the sensitivity to horizontal separation between the edges of a fabricated PCDC of length 24.3 µm was evaluated to be 1.6 %/nm at 1495 nm. The transmission sensitivity to vertical separation between the PCDC edges of length 12.6 µm was calculated to be 0.25 %/nm, when the PCDC edges were initially displaced vertically by a distance of 300 nm. The PCDC sensors demonstrated here are compatible with broadband sources and do not depend on BOX thickness, reducing the probability of stiction.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Micro-optomechanical systems (MOMS) are relevant where precision, high speed, remote sensing, and immunity to electromagnetic (EM) interference are desirable [1]. An important class of MOMS is one which makes use of the observed changes in optical transmission associated with near-field coupling to measure the separation between a waveguide and a nearby substrate, membrane or ancillary waveguide. In such systems, the optical sensitivity to perturbations in element separation depends on the coupling strength which can be enhanced through manipulation of the evanescent field by waveguide thinning [2,3], or by the use of dispersive media such as suspended photonic crystal (PC) membrane line defects [4]. However, thin substrate-coupled membranes with high aspect ratio are prone to stiction due to the presence of undesired adhesion forces between closely separated microstructures [5]. This stiction can be mitigated by considering lateral coupling between closely spaced waveguides, instead of vertical coupling to the wafer substrate. In such a configuration the thickness of the buried oxide (BOX) is no longer an issue.
Slotted waveguide structures have been demonstrated by several groups, where the air-like modes (with even transverse electric parity) are particularly sensitive to changes in refractive index of the air gap. Enhancement of the air gap field has been demonstrated using periodic structures [6–8], or ring-assisted structures [9] for biochemical sensing applications. However, measuring changes in effective index requires expensive tunable lasers to observe changes in cavity resonances, or integrated interferometric methods that increase measurement complexity and layout footprints. In this work we instead examine the dielectric-like modes of photonic crystal edges such that both even and odd transverse electric (TE) modes overlap within the same transmission band allowing for the design of a directional coupler. By using a directional coupler as a sensor element, we reduce the measurement complexity as relative changes in the effective index between the even and odd modes are directly observable as changes in intensity at the output ports.
In a symmetrical directional coupler, power can be completely cycled between the two waveguides along the length of the coupler [10]. For directional couplers fabricated on silicon-on-insulator (SOI) with 220 nm top silicon, broadband coupler designs for 50:50 power splitting can be achieved using coupling lengths of 100–200 µm [11] while state-of-the-art designs have achieved 50:50 splitting around 20 µm (40 µm beat-length) [12]; however, this can be further reduced using a pair of PC line defects with low insertion losses [13] and beat-lengths as low as 4 µm [14]. Directional couplers assisted by periodic structures also exhibit beat-lengths that can be desensitized to variations in wavelengths [15,16]. The key advantage to using a directional coupler sensor assisted by a periodic structure is the reduced device footprint size while maintaining compatibility with inexpensive broadband light sources. The higher mechanical resonance enabled by smaller devices also results in flatter dynamic response; an important consideration for sensor array applications.
In this paper, the design, fabrication, and transmission of a directional coupler formed by silicon photonic crystal slab edges is presented. In section 2, a model for a directional coupler-based sensor is developed and numerically simulated. In section 3, the fabrication of PCDC sensors on SOI is described. In section 4, the optical transmission measurements obtained from PCDCs with different horizontal and vertical separation distances between the PC slab edges is presented followed by a conclusion in section 5. The obtained measurements validate the operating principle of the proposed sensor and its suitability as a broadband deflection sensor element.
2. Design and analysis
2.1 Analytical model for directional coupler based sensor
The directional coupler sensor geometry consists of two parallel waveguides, as shown in Fig. 1(a), separated by a horizontal separation $s$ and vertical separation $h$, as shown in Figs. 1(b) and 1(c). The coupling is considered uniform along an interaction length $L$ and negligible elsewhere. The excitation of a single waveguide creates a superposition of even and odd modes and power is completely exchanged between the waveguides along the length of the coupler [10]. The input coupling to the coupler is assumed sufficient to ignore Fabry Pérot cavity effects. In this paper we define the through port to be on the same half as the excitation and the coupled port on the opposite side as can be seen in Fig. 1(a).
Fig. 1. (a) PCDC with a fundamental TE mode excitation input, through output, and coupled output ports labelled black, red, and blue, respectively. (b) Cross-section showing PC edges with horizontal separation $s$ and vertical deflection $h$ (c) PCDC junction as viewed from top.
The strength of a directional coupler can be described by the coupling coefficient $\kappa$ which is related to the difference between the odd $k_o$ and even $k_e$ wavevectors [17] and is given by
Alternatively, the length required for power to be completely transferred from one waveguide to the other, also known as the beat-length, can be expressed as the reciprocal of the coupling coefficient given by Ignoring propagation losses, the transmission at the through output $P$ of a four-port directional coupler [18] is given by where is the accumulated phase difference between the even and odd modes and $P_0$ is the power seen at the through output in the limit of large separations. The change in optical power with respect to small changes in accumulated phase can be obtained by differentiating Eq. (3) which gives: A general conclusion of this model is that the sensitivity of $P$ with respect to $\theta$ is maximized whenever the absolute value of the sine term in Eq. (5) attains a value of 1 and power is equally shared at the outputs. This occurs at select $\theta$ values given by where $n$ is an integer.We consider the case where the two waveguides remain parallel even when one of the wave guides is perturbed by $\Delta x$ in the horizontal direction ($x$) and by $\Delta y$ the vertical direction ($y$). In this case, the change in accumulated phase difference is given by
2.2 Bulk PC band structure
The PCDC sensor was designed to operate in the C-band (1530–1565 nm) which corresponds to the minimally attenuated spectral range of silica based optical fibres. To confine light within the PC defect, the photonic band gap (PBG) must be engineered to span the desired operating wavelengths. For sufficient dielectric contrast, large PBGs are known to exist for TE modes in a triangular PC lattice of holes-in-slab [19]. The thickness of the top silicon layer was set to 220 nm by the fabrication process and the PBG was computed with plane wave expansion (PWE) using RSoft across a range of lattice pitches $a$ and hole diameters $d$. A pitch of 450 nm and hole diameter 270 nm was found to generate a suitable band structure that satisfies the PBG requirements, which is shown in Fig. 2(a).
Fig. 2. PWE simulation results for (a) TE photonic band structure for a hole-in-slab photonic crystal of thickness 220 nm, pitch 450 nm, hole diameter 270 nm, and $\textrm {n}=3.47$ [20]. (b) The projected TE band structure for PCDC with $w$=540 nm and $s$=200 nm. (c) $\textrm {E}_x$ field profile of the even and odd dielectric directional coupling modes at the band edge ($k_za/2\pi =0.5$). (d) Coupling-lengths at various separations.
2.3 PCDC band structure - edge mode determination
The projected band structure of a PCDC consisting of two edge regions of width $w$=540 nm and separated by an air gap of width $s$=200 nm is shown in Fig. 2(b). It features two pairs of defect modes within the PBG. The pair of defect modes near the upper PBG edge have their field concentrated within the air gap. Although the even air-mode is most sensitive to changes in gap geometry, the odd air-mode is strongly blue-shifted due to its TE node in the gap centre [6], and insufficient overlap exists for directional coupling to occur.
The pair of defect modes appearing near the lower PBG have a portion of their field concentrated in the dielectric region as shown in Fig. 2(c), and their properties are predominantly determined by the extended PC edge width. The width of the extended edge region was tuned to 540 nm such that the dielectric modes of the projected band structure are centred on the C-band.
The dielectric modes were sufficiently unaffected by the air gap such that directional coupling could occur across a range of frequencies wherever both modes were supported inside the light line. However, enough field energy remains in the air gap for the even mode, as shown in Fig. 2(c), resulting in optomechanical coupling that pulls down the dispersion for decreasing separation while the dispersion of the odd mode remains stable. For the dielectric-like directional coupling modes, the even mode with the nonzero air gap field has the higher effective index than the odd mode. This seems counter intuitive but is consistent as the gap separation goes to zero. Here, the even mode transitions to the fundamental TE mode while the odd mode transitions to the second order TE mode. In this case, the fundamental TE mode should have the higher refractive index than the second order mode, as is typical for conventional waveguides.
The post-processed coupling-lengths were computed using Eq. (1) and are shown in Fig. 2(d) for various horizontal separations $s$. The curves in Fig. 2(d) are only defined where the even and odd modes are both supported simultaneously. A nonlinear relationship between $L_b$ and wavelength can be observed, however the curves are reasonably flat near wavelength of 1550 nm allowing $\kappa$ to be insensitive to the change in excitation wavelength around that region. The beat-length of the PCDC is less than 15 µm. For comparison, the TE beat-length for a pair of silicon waveguides measuring 220 nm by 500 nm that are horizontally separated by 200 nm is 87 $\mu$m computed using Lumerical MODE solver. This shows that at least 5 to 6 fold reduction in coupler length can be obtained in PCDC’s.
2.4 3D FDTD transmission and coupling strength of PCDC
Three-dimensional finite-difference time-domain (3D FDTD) calculations with Lumerical was used to simulate the transmission from a PCDC of finite length. The PCDC is interfaced asymmetrically with rib and strip waveguides as shown in Fig. 1(c). On the through side of the directional coupler, a 150 nm partial silicon etch defines the cladding of a rib waveguide intended to protect the BOX during selective etching to release the membrane. The coupled side, which forms the edge of the released PC membrane, was interfaced with strip waveguides that support the membrane after selective etching. The fundamental TE mode of the interfacing rib waveguide was used as the FDTD excitation source.
The through transmission from coplanar ($h$=0) PC edges of length $54a$ is shown in Fig. 3(a) for varying air gap separations. A broadband regime can be identified centred around 1540 nm, where the $\kappa$ dependence on wavelength is minimized. The fringes seen are due to Fabry Pérot effects arising from reflections at the input and output junctions. At 1540 nm, the through transmission increases from zero to its maximum value as the horizontal separation $s$ increases from 130 nm to 200 nm and the directional coupler transitions from $L=3L_b$ to $2L_b$. Figure 3(b) shows the exchange of power between the output ports of the coupler as the PC edges are separated. As the coupler and waveguide losses have been subtracted from the transmission loss, the observed 2.2 dB loss is due to the conversion of the fundamental TE mode of the rib waveguide to the even and odd DC modes, indicating a loss of 1.1 dB per junction. In the flat band below 1515 nm, the even mode becomes radiative and only the odd mode of the directional coupler is supported. This is consistent with the PWE simulation. Therefore, the phase difference between the even and odd mode is no longer observable in the transmission.
Fig. 3. FDTD simulation results for coplanar PC edges ($h=0$) of length $54a$, (a) the through transmission spectra at varying air gap separations. (b) At 1540 nm, power is exchanged between the through and coupled outputs as the PC edges are separated. (c) The coupling coefficient $\kappa$ computed using Eq. (2) and the beat-lengths determined by the mode profiles.
The change in the coupling coefficient $\kappa$ with air gap separation s is plotted in Fig. 3(c) and was evaluated using Eq. (2). The beat-lengths $L_b$ required in Eq. (2) were determined from the simulated field profiles along the propagation length of the directional coupler. The field profiles for two separations, $s$=150 nm and 200 nm respectively are shown in Figs. 4(a) and 4(b) from which the beat-lengths of 20$a$ and 27$a$, respectively are obtained (i.e. the distance where the first complete exchange of power occurs). The oscillation of the field profiles is due to the periodicity of the PC which arises as per the Bloch theorem. Similarly, the through transmission from PC edges separated by 200 nm, 350 nm, and 510 nm for varying vertical displacements is shown in Fig. 5.
Fig. 4. FDTD simulation results for the $|\textrm {E}_x|^2$ field profile along the propagation length of a PCDC with (a) $s$=150 nm and (b) $s$ =200 nm.
Fig. 5. FDTD simulation results for PC edges separated by 200 nm and length $54a$, (a) the through transmission spectra at varying vertical displacements. (b) At 1540 nm, power is exchanged between the through and coupled outputs as the PC edges are separated. (c) The coupling coefficient $\kappa$ was computed using Eq. (2) and the beat-lengths determined by the mode profiles.
2.5 PCDC sensitivity
The change in optical power due to small changes in horizontal (x-direction) and vertical spacing (y-direction) is measured by the horizontal and vertical sensitivities which can be computed using Eqs. (9a) and (9b) respectively. Both the sensitivities are dependent on the product of respective $\alpha$ and $\theta$ values. To evaluate the sensitivity parameter of the PCDC, the logarithmic derivative of $\kappa$ in each direction namely $\alpha _x$ and $\alpha _y$ were computed using Eq. (8). The computed values of $\alpha _x$ and $\alpha _y$ for different $s$ and $h$ values are shown in Figs. 6(a) and 6(b) respectively.
Fig. 6. The sensitivity parameter for (a) horizontal and (b) vertical deflections obtained by curve-fitting the logarithm of $\kappa$ obtained from FDTD simulations.
For the coplanar case ($h$=0), from Fig. 6(a) we notice that a smaller $s$ value results in a larger $\alpha _x$ value and likewise from Fig. 3(c) a smaller value of $s$ ensures a larger $\kappa$ and thereby also of $\theta$ via their relationship expressed in Eq. (4). This ensures that a smaller $s$ value results in a larger value of $\alpha _x\theta$, thereby achieving larger horizontal sensitivity in the coplanar case. In addition, due to the symmetry that exists about the mid-slab plane, $\alpha _y$ remains zero regardless of the value of horizontal separation $s$ as seen in Fig. 6(b). Therefore, to capture vertical deflections using the PCDC one requires an initial vertical displacement of the PC edges, i.e, non-zero value for $h$ at any value of $s$.
For the non-coplanar case ($h$>0), we notice from Fig. 5(c) that at any given fixed value of $h$, $\kappa$ and thereby $\theta$ via Eq. (4) decreases with increasing $s$, and likewise from Fig. 6(b) we notice a similar trend for $\alpha _y$. Hence the vertical sensitivity also decreases with increasing $s$. In contrast, at a given value of $s$, increasing $h$ decreases the value of $\kappa$ and thereby $\theta$ with values approaching zero at larger values of $h$ (see Fig. 5(c)), while increasing $h$ increases the value of $\alpha _y$ (see Fig. 6(b)) with the rate of increase reducing to zero at larger values. This ensures that their product reaches an optimum value at some intermediate value of $h$, which was computed to occur around $h$=300 nm.
3. Fabrication
The PCDC structures were surface micromachined using IMEC ePIXfab silicon photonic process supported through CMC Microsystems. Selective etching of the BOX was done at the University of Western Ontario Nanofabrication Facility. PCDCs of varying lengths were fabricated to measure the power output behaviour corresponding to various multiples of the beat-length.
The fabricated structure, as shown in Fig. 7(a), consists of a central PC membrane whose two parallel edges form the inside half of two separate PCDCs. The strip waveguides of the PCDC also act as mechanical supports to the membrane. Both output ports of one of the two PCDCs were accessed and used to validate the directional coupling of the PCDC. The PC edge that forms the outer half of a PCDC is interfaced with rib waveguides that remain rigidly connected to the substrate after BOX etching whereas the PC edge of the inner half located on the membrane is free to move.
Fig. 7. SEM micrograph of PC membrane before BOX etching showing (a) overall view, and PCDC with air gap separations (b)191 nm and (c) 278 nm
Scanning electron microscopy (SEM) images were taken before releasing the PCDC membranes and they are shown in Figs. 7(b) and 7(c). The PC pitch, hole diameter, and edge width shown in the images have values of 450 nm, 275 nm and 545 nm respectively. To evaluate the horizontal sensitivity, structures with air gap widths of 190 nm and 280 nm were fabricated. Selective etching of the BOX was done using a buffered hydrofluoric acid wet-etch at room temperature followed by critical point CO$_2$ drying.
The wet-etch was done using either a "partial" or a "full" photoresist mask. Compressive strain known to exist in flip-bonded SOI can lead to buckling of the membrane. The extent of the buckling depends on the support structure length, geometry, and imperfections [21,22]. By using a partial mask on one set of devices to reduce the length of the support structures, buckling was avoided, and coplanar PC edges were obtained (corresponding to $h$=0). Additionally, using a full photoresist mask, the PC membrane was fully released from a second set of devices and the subsequent buckling introduced a vertical displacement of 300 nm between the PC edges. The vertical sensitivity was obtained by comparing the transmission between the partially etched and fully etched structures, as shown in Figs. 8(a) and 8(b) respectively.
4. Measurement results and discussion
The devices were excited with a polarization-maintaining fibre optic array positioned near the chip surface and aligned to grating couplers (GC). A tunable laser source providing 1 mW excitation was swept across a spectrum range from 1460–1610 nm while a power meter recorded the transmission at each optical frequency. Transmission was normalized using the spectrum acquired from a blank device included on the chip that allowed for the removal of the GC artefacts.
4.1 Dependence on horizontal separation s
For devices with the partial BOX etch corresponding to $h$=0, the through transmission from PCDCs of varying lengths was measured. The results from the measurements are shown in Fig. 9 for two different horizontal separations of 190 nm and 280 nm respectively. The measured transmission spectra when compared with FDTD simulations (Fig. 3) show an overall 40 nm shift which can be attributed to deviations from design geometry in the fabricated devices.
Fig. 9. The measured through PCDC transmission spectra with partially etched BOX and fixed PC edge width 545 nm and air gap width measured to be (a) 190 nm and (b) 280 nm, respectively.
In Figs. 9(a) and 9(b), a 30 nm wide band in the transmission centred at 1495 nm can be observed with a peak value which changes with the length of the PCDC. From these measured results, the beat-length at each air gap separation $s$ was extracted by fitting a curve using Eq. (3) for the through transmission values of PCDCs with different fabricated lengths $L$ at a wavelength of 1495 nm. This is illustrated in Figs. 10(a) and 10(b) for air gap separations $s$ of 190 nm and 280 nm respectively. Here, the $P_0$ required was determined from the transmission measured through an isolated PC edge. The beat-lengths were computed to be 22$a$ and 33$a$ for PCDC separations 190 nm and 280 nm respectively. The coupling coefficients $\kappa$=0.16 rad/µm and $\kappa$=0.11 rad/µm respectively were computed using Eq. (2).
Fig. 10. The through PCDC transmission at 1495 nm (blue dots) for PCDCs fabricated with different lengths fit to Eq. (3) (dashed line) for a separation of (a) $s$=190 nm and (b) $s$=280 nm.
The horizontal sensitivity parameter $\alpha _x$ was computed using Eq. (8a). Since measurements were obtained for only two values of the horizontal separation, the derivative was replaced with a two-point finite-difference approximation. The coupling coefficient $\kappa$ used in Eq. (8a) was determined by taking the geometric mean ($\kappa =\sqrt {\kappa _1\kappa _2}$, where $\kappa _1$ and $\kappa _2$ are the coupling coefficients at horizontal separations 190 nm and 280 nm respectively). This resulted in an $\alpha _x$ of 4.2 µm$^{-1}$.
For the specific device with a PCDC length of $54a$, horizontal separation of $s$=190 nm, and vertical separation $h$=0 nm, $\theta$ was computed to be 1.23$\pi$ using Eq. (4) and the horizontal sensitivity of this specific device was computed to be 1.6% of $P_0$ per nanometer (%/nm), using Eq. (9a).
4.2 Dependence on vertical separation h
The transmission from both the through and coupled output ports of a PCDC of length $28a$ and horizontal separation $s$=190 nm with partial and full BOX etch are shown in Figs. 11(a) and 11(b) respectively. An exchange of power can be seen between the coupler outputs, thereby validating the operating principle of the sensor. We observed that in the buckled position the fully released PC membrane had a displacement of 300 nm (corresponding to $h$=300 nm). This value was obtained with an optical microscope using a focus variation method.
Fig. 11. The measured through and coupled transmission spectra for a PCDC with air gap width $s$=190 nm and length $28a$ (a) with partial BOX etch ($h$=0) and (b) with full BOX etch ($h$=300 nm).
A similar broadband change in transmission was observed at both outputs centred at 1495 nm where the beat-length is maximized, as shown in Figs. 11(a) and 11(b). For both vertical positions, both directional coupling modes are supported between 1485–1534 nm. At wavelengths longer than 1534 nm only the even mode exists and the outputs become equal. Additionally, as can be seen in Figs. 11(a) and 11(b), the cut-off frequency of the even mode changes from 1550 nm at $h$=0 nm to 1540 nm at $h$=300 nm which can be attributed to the increase in PC edge separation.
The vertical sensitivity is computed similarly to the horizontal case. The vertical sensitivity parameter $\alpha _y$ was computed using Eq. (8b). Since measurements were obtained for only two values of the vertical separation, the derivative was replaced with a two-point finite-difference approximation. The coupling coefficient $\kappa$ used in Eq. (8b) was determined by taking the geometric mean ($\kappa =\sqrt {\kappa _1\kappa _2}$, where $\kappa _1$ and $\kappa _2$ are the coupling coefficients at vertical separations 0 nm and 300 nm respectively). However, in this case we compute the coupling coefficient at $h$=300 nm to be 0.054 rad/µm using Eq. (3) where $P_0$ was taken to be the sum of the coupled and through transmission outputs. This resulted in an $\alpha _y$ of 3.8 µm$^{-1}$.
For the specific device with a PCDC length of $28a$, horizontal separation of $s$=190 nm, and vertical separation $h$=300 nm, $\theta$ was computed to be 0.22$\pi$ using Eq. (4) and the vertical sensitivity of this specific device was computed to be 0.25 %/nm, using Eq. (9b).
4.3 Discussion
The values of coupling coefficient $\kappa$ computed from measurements show good agreement to the ones computed from FDTD simulations and this comparison is shown in Table 1. We observed a reasonable agreement between the measured and simulated values with $\alpha _{x,\textrm {meas}}$=4.2 µm$^{-1}$ and $\alpha _{x, \textrm {FDTD}}$=5.0 µm$^{-1}$ taken at the midpoint $s$=235 nm and with $\alpha _{y, \textrm {meas}}$=3.8 µm$^{-1}$ and $\alpha _{y, \textrm {FDTD}}$=1.4 µm$^{-1}$ taken at the midpoint $h$=150 nm. Since only two-point derivatives were used to evaluate $\alpha _x$ and $\alpha _y$, there is some uncertainty in how these sensitivity parameters evolve between the different separations, particularly in the vertical direction near $h$=0.
Table 1. Simulated and measured coupling coefficients
We attribute the 40 nm blue-shift observed between the simulated and measured transmission spectrum to variations in the dimensions of the finer geometric features in the fabricated membrane which can include larger PC hole diameters, smaller edge widths and larger air gap separations, or possibly a thinner device layer, compared to the computational model. Uncertainties in the SEM measurement due to charging effects, which can be significant in these membrane structures, also contribute to the differences. The shift can be accounted for within the tolerance uncertainties in fabrication and SEM measurements. However, the response of the device is as expected and the working principle of the PCDC design has been validated.
5. Conclusion
A photonic crystal directional coupler utilizing two adjacent parallel PC edge modes was designed, fabricated, and demonstrated for use in optomechanical sensing applications. The devices were fabricated using industry standard silicon photonic fabrication processes followed by selective wet-etching of the BOX. The vertical sensitivity in this work is comparable to our previous work on vertical substrate-coupled PC sensors that had reported a peak sensitivity of 0.5 %/nm for a PC line-defect of length 24$a$ when suspended 160 nm from the substrate [4]. Crucially, the new designs presented in this paper do not depend on the membrane-substrate distance and therefore reduce the probability of stiction. The designs presented here also have the added capability of measuring horizontal deflections.
Directional coupler-based sensors integrate an interferometric measurement platform into a single sensor element since the phase difference between even and odd DC modes is directly observed at the coupler outputs. Having demonstrated this sensing mechanism, future work will include testing the displacement sensor under a range of dynamic conditions - driven by acoustic or by thermo-mechanical means. The small size and compatibility with broadband sources offer a potential solution to chip-scale submicron deflection measurement and the future development of dense sensor arrays with potential uses in industrial control systems, automotive sensors, avionics, and environmental monitoring.
Funding
Natural Sciences and Engineering Research Council of Canada; Canada Foundation for Innovation; CMC Microsystems; Government of Ontario.
Acknowledgments
The authors would like to acknowledge CMC Microsystems for funding and technical support including access to design software, foundries, and select measurement equipment. Funding for this research was also provided by the Natural Sciences and Engineering Research Council of Canada (NSERC), Canadian Foundation for Innovation (CFI) and Ontario Graduate Scholarship (OGS). The devices were fabricated through IMEC ePIXfab foundry and post processed at the University of Western Ontario Nanofabrication Facility.
Disclosures
The authors declare no conflicts of interest.
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