Elias Akiki
email: elias.akiki@univ-lille.fr

Marc Faucher

Mathias Vanwolleghem

Mattias Verstuyft

Bart Kuyken

Benjamin Walter

Jean-Francois Lampin

Guillaume Ducournau

J-F Lampin

Jean-François Lampin

High Q THz photonic crystal cavity on a low loss suspended Silicon platform

Keywords: THz waveguide, THz photonic crystal cavity, high resistivity Silicon, Quality factor, propagation losses

teaching and research institutions in France or abroad, or from public or private research centers.

I. INTRODUCTION

erahertz waves (0.3-10 THz) are the electromagnetic (EM) waves that fall between the upper edge of electronics and lower edge of photonics in the EM spectrum. These waves offer a variety of applications in different domains. Their nonionizing property, low energy and capability of penetrating different types of materials, including some opaque ones in the visible range, make them helpful for medicine, biosensors and imaging [START_REF] Siegel | Terahertz technology in biology and medicine[END_REF], [START_REF] Laman | High-Resolution Waveguide THz Spectroscopy of Biological Molecules[END_REF]. The presence of rotational resonances of many polar molecules in this frequency region allow THz waves to act as a unique spectroscopic tool [START_REF] Baxter | Terahertz Spectroscopy[END_REF], [START_REF] Hindle | Monitoring of food spoilage by high resolution THz analysis[END_REF]. For many of these applications, the availability of efficient passive and active THz components (sources, detectors, waveguides, resonators, …), is essential.

In integrated circuits low-loss waveguides are essential to transmit the EM waves between all passive and active components of a circuit and to ensure the transition from off-to on-chip. Different types of guides have been reported at THz frequencies. Metallic waveguides (MWG) with scaled dimensions similar as those used in the microwave and millimeter wave bands have been among the first reported. Despite the different fabrication techniques proposed to fabricate such integrated waveguides, they still suffer from surface roughness, high metallic losses and complicated assembly process [START_REF] Leong | WR1.5 Silicon Micromachined Waveguide Components and Active Circuit Integration Methodology[END_REF]- [START_REF] Chow | Measurements to 320 GHz of millimetre-wave waveguide components made by high precision and economic micro-machining techniques[END_REF]. While MWG are limited by size and ohmic losses, dielectric waveguides may be fabricated by waferscale foundry techniques and may be easier to integrate. Several types of dielectric waveguides have been reported, such as ridge waveguides and line defect photonic crystal (PhC) waveguides [START_REF] Ranjkesh | Silicon-on-Glass Dielectric Waveguide-Part I: For Millimeter-Wave Integrated Circuits[END_REF]- [START_REF] Tsuruda | Extremely low-loss terahertz waveguide based on silicon photoniccrystal slab[END_REF]. At THz frequencies the available material systems that combine high index, transparency and planar processing are limited. High resistivity silicon (HR-Si) is the most used material, due to its very low absorption coefficient and large non-dispersive refractive index [START_REF] Dai | Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon[END_REF], [START_REF] Grischkowsky | Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors[END_REF]. Silicon on glass waveguides presented in [START_REF] Ranjkesh | Silicon-on-Glass Dielectric Waveguide-Part I: For Millimeter-Wave Integrated Circuits[END_REF], use the refractive index contrast between Si and glass which are bonded together in order to create the guiding channel for mm-waves. The extracted propagation loss of this design correspond to 0.063, 0.028 and 0.053 dB/mm, for 55-65, 90-110 and 140-170 GHz bands. At frequencies beyond 400 GHz, the absorption of the glass substrate material increases dramatically [START_REF] Grischkowsky | Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors[END_REF], [START_REF] Naftaly | Terahertz Beam Interactions with Amorphous Materials[END_REF] and it becomes useless for guiding purposes. To avoid material losses, [START_REF] Ranjkesh | Silicon-on-Glass Dielectric Waveguide-Part II: For THz Applications[END_REF] proposes a layout where the glass is locally etched and the guiding layer is suspended by Si supporting beams (SB). A loss average of 0.054 dB/mm over 440-550 GHz frequency band is reported for this suspended waveguide. The process is laborious and the large number of SB increases the scattering losses due to roughness at the SB edges, adding to that a bonding of HR-Si/Glass followed by glass etching steps are still required. The line defect PhC with 0.4 dB/mm of average losses over 540-630 GHz, reported by [START_REF] Amarloo | Terahertz Line Defect Waveguide Based on Silicon-on-Glass Technology[END_REF], suffers likewise from increased scattering losses due to the large number of etched holes. The one reported in [START_REF] Tsuruda | Extremely low-loss terahertz waveguide based on silicon photoniccrystal slab[END_REF] covers a very short frequency band region 326-331 GHz with low losses below 0.01 dB/mm, while outside this band, losses are much higher. In this work we present the design, fabrication and characterization of a fully suspended HR-Si waveguide, that requires wafer processing with only two steps and no bonding. The advantage of this design is that it uses an air cladding without presence of any other lossy material. Only few anchors are used in order to have a mechanically stable structure and to limit the scattering losses.

> High Q THz photonic crystal cavity on a low loss suspended Silicon platform < 2

Besides analyzing the loss mechanisms in this purely index guided novel integrated THz waveguide, one-dimensional PhC wire waveguides have also been fabricated and measured. A scheme to confine the air band mode of such a PhC cavity in an air hole cavity by apodization of the PhC period is experimentally demonstrated. Such cavities have been commonly demonstrated in the visible, near and mid-infrared (midIR) [START_REF] Deotare | High quality factor photonic crystal nanobeam cavities[END_REF]- [START_REF] Kuramochi | Ultrahigh-Q onedimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings[END_REF]. At THz frequencies a similar design for 100 and 200 GHz frequencies with Q= 11900 and 2200 respectively was demonstrated by [START_REF] Hanham | LED-Switchable High-Q Packaged THz Microbeam Resonators[END_REF]. Aside from [START_REF] Hanham | LED-Switchable High-Q Packaged THz Microbeam Resonators[END_REF], 1D photonic crystal cavities were very little investigated in the THz region. Other dielectric cavities such as ring resonators and 2D PhC cavities with high quality factors up to 15000 have been reported [START_REF] Bingham | Terahertz twodimensional photonic crystal waveguide cavities[END_REF]- [START_REF] Hanham | Dielectric measurements of nanoliter liquids with a photonic crystal resonator at terahertz frequencies[END_REF]. With respect to all these achievements, this work reports a similarly high quality factor (Q≈18000) but with the resonant energy mainly confined in a PhC air hole. In this work we designed and measured a high-Q 1D PhC THz cavity, by etching a crystal of air holes in the suspended core of the membrane wire waveguide taking advantage of its low losses.

The designed cavity allows to confine THz EM waves at frequencies around 630-650 GHz in a strongly subwavelength air hole of a 1D wire PhC cavity. Achieving such a confinement in air at these frequencies, where many absorption peaks of different molecules belong, can have a huge potential for THz sensing or strong coupling applications.

In section II of this paper we present the numerical results and the design of the proposed waveguide, followed in section III by the design of the taper that ensures the low insertion losses caused by the transition from MWG of the source to the designed Si waveguide. Section IV treats the design of the PhC cavity. Finally, in V and VI, the fabrication process and the experimental measurements results of both designs are presented respectively.

II. WAVEGUIDE DESIGN

The designed THz waveguide is based on index guiding between two materials with high refractive index contrast. HR-Si is a perfect candidate for the core material of the waveguide due to its large, and frequency independent (nondispersive) refractive index (nSi= 3.42) at Terahertz (THz) frequencies [START_REF] Dai | Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon[END_REF], [START_REF] Grischkowsky | Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors[END_REF]. High resistivity float zone (HRFZ) silicon represents very low losses at THz frequencies. While such core material is considered as loss-less, cladding materials with a sufficiently lower refractive index than Si such as silica, borosilicate, crystal quartz or other Glasses have important absorption losses that moreover increase dramatically at frequencies beyond 500 GHz [START_REF] Grischkowsky | Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors[END_REF], [START_REF] Naftaly | Terahertz Beam Interactions with Amorphous Materials[END_REF]. An ideal THz guide thus consists of HRFZ-Si guiding channel surrounded by air. The high refractive index contrast between Si and air defined as

Δ = 𝑛 1 2 -𝑛 2 2 2𝑛 1 2 = 45% [32]
, allows to strongly confine modes with respect to the guiding channel dimensions. Lumerical FDTD and Lumerical mode solver [START_REF]High-Performance Photonic Simulation Software[END_REF] are used to simulate the modal analysis of the device. For an infinite width waveguide the maximal thickness allowing a single mode guiding is given by 𝑇 = 𝜆 0 2√𝑛 2 2 -𝑛 1 2 ≈ 76 µ𝑚 (at 650GHz). For finite width waveguide, mode propagation constants are numerically analyzed at several widths and thicknesses using a numerical sweep. In order to suspend this structure, anchors are designed to hold the guiding channel with two supporting silicon structures on the sides (fig. 4). The dimensions of the anchors are defined after studying their impacts on the mode perturbation and propagation losses. The higher order modes of odd symmetry (𝐸 𝑥 21 , 𝐸 𝑦 21 ) will in principle not be excited upon symmetric injection (see Section III), while the fundamental TM-like mode 𝐸 𝑦 11 will, due to its lower effective index, radiate when we will consider the Bloch modes in a PhC layout. Moreover, a TE-like excitation will not couple to this mode. Figure 5 represents the simulated losses per pair of anchors for different anchors width. All simulations are done first using the real refractive index of HR-Si, i.e. without taking material losses into account. In order to estimate anchor losses in Lumerical FDTD we launched the fundamental waveguide mode and monitored its power loss over a certain waveguide length containing 4 pairs of anchors, sufficiently spaced apart (1.5 mm) preventing any collective effect. The simulation window is closed by PML (Perfect Matched Layer) boundaries to prevent spurious numerical interface reflections. With no anchors, using these numerical conditions, losses are absent. The represented losses are therefore purely due to scattering at the anchors. The simulation results confirm that the impact of the anchors decreases with their width. In order to maintain a compromise between mechanical stability and low scattering loss the dimensions of the anchors are chosen to be 20x300x90 μm (see fig.

III. TAPER DESIGN AND INSERTION LOSSES

To characterize the designed waveguide, S-parameter measurements are done using a vectorial network analyzer (VNA) coupled to frequency extenders (VNAX) with MWG WR-1.5 ports in the frequency range 500-750 GHz. In order to achieve smooth injection and good transition from MWG ports to the silicon waveguide, adiabatic tapers are added at the inand output sides of the suspended waveguide. Wave impedance is represented by [START_REF] Ponchak | Design and analysis of transitions from rectangular waveguide to layered ridge dielectric waveguide[END_REF]

Z MWG = η 0 √ 1-( f c f ) 2 (1)
for an air filled MWG and,

𝑍 𝑆𝑖 = 𝜂 0 √ 𝜖 𝑒𝑓𝑓 (2)
for Si waveguide. With 𝜂 0 = √ 𝜇 0 𝜖 0 the free space impedance, 𝑓 𝑐 the MWG cutoff frequency which is 𝑓 𝑐 = 393 𝐺𝐻𝑧 for WR-1.5 MWG, 𝑓 working frequency and 𝜖 𝑒𝑓𝑓 = 𝑛 𝑒𝑓𝑓 2 effective permittivity of the propagating mode inside Si waveguide. To reduce the mismatch between these two impedances, the Si taper edge should be small enough, in order for the fundamental mode to still be guided but weakly confined in the Si with lowest 𝑛 𝑒𝑓𝑓 . A taper edge section of 65x90 µm, slightly confines the fundamental mode with an 𝑛 𝑒𝑓𝑓 = 1.03 at 650 GHz and therefore represent the smallest impedance mismatch with guided wave inside MWG, before 𝐸 𝑥 11 goes to cut-off (see fig. 6). A larger section leads to stronger Si confinement, resulting in a higher effective index and therefore deeper reflection dips especially at higher frequencies. Once the mode at the taper edge is excited, a gentle variation of the taper dimension is necessary to prevent that the fundamental mode couples to higher order radiative or guided modes, before reaching the Si waveguide. For that, the taper length Lt has to be much longer than the beat length Lb corresponding to the coupling length between the fundamental mode and the second symmetric mode. (3)

𝐿 𝑡 = ∆𝑊 2 tan -1 𝜃 ( 4
)
where 𝛽 1 = 𝑛 𝑒𝑓𝑓1 𝑘 0 and 𝛽 2 = 𝑛 𝑒𝑓𝑓2 𝑘 0 are the propagation constant of the two first symmetric modes, where 𝑘 0 = 2𝜋 𝜆 0

is the free space propagation constant. ∆𝑊 = 𝑊 1 -𝑊 2 =145 µm, width difference between taper edges and 𝜃 taper's variation angle. So according to the adiabaticity criterion the variation angle 𝜃 has to be smaller than

𝜃 𝑚𝑖𝑛 𝜃 ≪ 𝜃 𝑚𝑖𝑛 = ∆𝑊(𝛽 1 -𝛽 2 ) 4𝜋 (5)
.

In our design the long side of the waveguide is tapered and reduced down to 65 μm over a length of 3000 μm, while the short side corresponding to the thickness of the waveguide, remains 90 μm (fig. 4.b). This slow variation with a very small angle of 0.048 rad << 𝜃 𝑚𝑖𝑛 , allows an adiabatic transition of modes, and prevents any energy exchange with higher order guided or radiative modes. The taper designed is long enough to conserve the fundamental guided mode. Longer tapers with 4000 µm and smallest slope angle 0.036 rad, have almost the same performance.

In a MWG the electric field 𝐸 ⃗ of the fundamental mode is oriented along the short side of the waveguide, while in the dielectric one 𝐸 ⃗ is oriented along the long side. In order to have the best overlap between these two modes the MWG is rotated by 90°. The numerical aperture of such a waveguide at 500 GHz is N.A.=0.79 and 0.53 at 750 GHz so a strong diffraction occurs at the output of this MWG especially at lower frequencies (ie 500GHz). Placing the taper outside the MWG, presents high coupling losses. To estimate the insertion and return losses caused by the transition of EM wave from the MWG to the Si waveguide through the taper, a FDTD simulation has been done. The simulated structure is composed of two metallic waveguides (WR-1.5) of 191x381 µm air guiding channel, surrounded by a PEC (perfect electrical conductor) layer to form the metallic boundaries, and 2 Si (nSi=3.42) tapers in between. For several depths of insertion of the taper inside the MWG (starting at perfect butt-coupling 0mm), the simulated insertion (S21) and return (S11) loss are represented in figure 7 and 8. In figure 7 the taper is considered to be perfectly centered at the MWG ports, and the effect of its position inside the MWG along the propagation direction (Z) is presented. For different positions of taper the return losses are below -10 dB (below the red dashed line) except for perfect butt coupling, which confirms the low impedance mismatch. However, the best coupling and the lowest insertion loss is achieved for the positions where the taper is well inserted inside the MWG. For positions below 1mm, the taper cross section at the output of MWG does not exceed 100x90µm. For these dimensions the fundamental mode at low frequencies is slightly confined with low 𝑛 𝑒𝑓𝑓 = 1.1 at 500 GHz, which increases the insertion loss due to the coupling with radiative modes. Insertion losses are very low (0.15 dB at 600 GHz), for positions above 1mm.

The simulated results of insertion losses show also some oscillations that correspond to a Fabry-Pérot cavity effect, between the two MWG ports with a free spectral range ~10-15GHz, corresponding to a cavity effect of about 5mm for an effective index of ~2.5. This precisely twice the taper length (corrected with the insertions). The low ripple reconfirms the strong coupling. In figure 9 the magnitude of 𝐸 ⃗ at the transition between the MWG and the taper is represented for three different frequencies at 1mm insertion well centered inside. The large radiative field part at 500 GHz correspond to the high insertion losses represented in figure 7 at low frequencies. Experimentally, it is not easy to be perfectly aligned, so it is important to study the effect of misalignment. Figure 8 represent the insertion losses, for a X and Y off axis displacement and rotation. A Y displacement perpendicularly to 𝐸 ⃗ direction (X direction) doesn't show big effect on the insertion and return losses, while a misalignment in the direction of 𝐸 ⃗ or an angular deviation breaks the modal symmetry, and some dips appears in S21 at certain frequencies where the higher order anti-symmetric mode is excited, while S11 remains low. In conclusion, the designed taper, allows to feed the Si waveguide, from WR-1.5 MWG ports with very low losses. This novel integrated THz waveguide platform has been subsequently investigated to serve as a building block for deep subwavelength confinement of THz energy by creating a 1D PhC wire cavity. The design consists in creating a defect mode inside a photonic bandgap similar to nanocavities presented in the NIR [START_REF] Deotare | High quality factor photonic crystal nanobeam cavities[END_REF], [START_REF] Lalanne | Photon confinement in photonic crystal nanocavities[END_REF], [START_REF] Quan | Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide[END_REF], [START_REF] Kuramochi | Ultrahigh-Q onedimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings[END_REF], [START_REF] Quan | Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities[END_REF]. The bandgap and its central frequency is adjusted by choosing the proper etching period and hole radius. In this design, to simplify the fabrication process, we choose to vary the period between holes in order to create the defect mode. However, any other variation that breaks the periodicity such as changing the radius of the holes or the width of the waveguide, could also create a defect mode. Using Comsol Multiphyscis [START_REF]COMSOL: Multiphysics Software for Optimizing Designs[END_REF], the Bloch modal dispersion of two 1D photonic crystals wires with 29 µm etching radius and two different etching periods (a1=106.56 µm and a2=120.65 µm) are calculated and represented in figure 10. These particular periods, represent a large band gap (100 GHz), around 600 GHz. This frequency is chosen for the sake of the specific molecular gas sensing that we are developing this platform for [START_REF] Hindle | Monitoring of food spoilage by high resolution THz analysis[END_REF]. The design presented here can be rescaled to any reasonable THz frequency. By increasing the period, the band gap shifts toward lower frequencies, which is obviously in rough approximation to be understood by the Bragg condition 𝜆 = 2𝑛 𝐵𝑒𝑓𝑓 𝑎 with 𝜆 = 𝑐 𝑓 Bloch mode wavelength, 𝑛 𝐵𝑒𝑓𝑓 Bloch mode effective index and 𝑎 the etching period. For gas sensing purposes our design aims at achieving maximal confinement in the etched air holes (fig. 11.b). In other words, the designed cavity needs to trap an air Bloch mode (upper band in fig. 10, AM in fig. 11.a). In view of the above, this can be achieved by apodizing the crystal periodicity with an increasing step towards to the cavity center, thereby effectively pulling down the air band into the band gap. The precise apodization profile of the period from 106.56 µm to 120.65 µm will be detailed below. On the other hand, a cavity with a dielectric resonant mode could be designed in the is the dimensionless representation of losses, which is defined by the photon lifetime 𝜏 at a frequency 𝑓 0 = 𝜔 0 2𝜋 inside the cavity. It is important to design a cavity with high 𝑄 factor, corresponding to longer photon cavity lifetimes therefore increased molecular interaction time and ultimately an increased sensitivity for sensing applications. The total quality factor 𝑄 can be split into its two contributing loss mechanisms 𝑄 𝑤 for waveguide losses (in-plane losses) and 𝑄 𝑟 for radiative losses (out-of-plane losses) with

1 𝑄 = 1 𝑄 𝑟 + 1 𝑄 𝑤 (6)
The in-plane losses are governed by mirror strength (reflectivity), and material loss which depends on material conductivity. Mirror strength is governed by the number of etched holes. In our design we chose N=25 holes. This number of holes is sufficient to increase the reflectivity to 90%. Having a perfect mirror, is a way to increase 𝑄 𝑤 , but this also reduces the transmission of the defect mode (it is perfectly reflected). For a photoacoustic sensing application [START_REF] Akiki | Terahertz photoacoustic gas sensor[END_REF]- [START_REF] Verstuyft | Proposal for an integrated siliconphotonics terahertz gas detector using photoacoustics[END_REF] which this cavity is designed for, the transmission is not so important. In other applications, such as sensing by direct absorption measurements, transmission is much more important. We therefore also considered the possibility to adjust the design in order to increase the transmission, while maintaining a reasonable Q. The same cavity with a lower number of etched holes (N=21 and N=17 resp.) are also measured experimentally. The designed structure is not only adjusted to minimize the inplane, but also to minimize the out-of-plane losses in order to achieve the highest possible 𝑄 factor. One way to have low radiative losses is already achieved by having the structure fully suspended in air as described before. The absence of a substrate reduces radiative losses, by pulling up the light cone to be far away from the Brillouin-zone edge [START_REF] Joannopoulos | Photonic crystals: molding the flow of light[END_REF], [START_REF] Kuramochi | Ultrahigh-Q onedimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings[END_REF]. Similarly, in [START_REF] Akahane | High-Q photonic nanocavity in a two-dimensional photonic crystal[END_REF] the period (distance between holes) is parabolically apodized. This parabolical change, allows to obtain a Gaussian envelope of the electromagnetic field decay. The Fourier transform of such an envelope contains less k-components inside the light cone (leaky region) [START_REF] Akahane | High-Q photonic nanocavity in a two-dimensional photonic crystal[END_REF]. So finally the period variation is represented by the function below [START_REF] Chow | Measurements to 320 GHz of millimetre-wave waveguide components made by high precision and economic micro-machining techniques[END_REF].

𝑃 𝑖 = 𝑃 𝑐 + (𝑃 𝑚 -𝑃 𝑐 ) ( 𝑖 11 ) 2 (7)
With 𝑃 𝑚 the starting period (106.56) µm and 𝑃 𝑐 the central period where the air defect mode is confined (120.65µm). 𝑃 𝑖 represents the varying period between holes with i going from 0 to 11, for a total of 12 periods at both sides of the central hole (giving a total of 25 holes). After defining the parameters of our structure, we performed a 3D simulation using Lumerical FDTD, to calculate and optimize the resonance frequency and its quality factor. The Q-factor depends also on the material absorption coefficient used in the calculation. For high resistivity silicon (ρ=10 kΩ.cm) the material which we are using, absorption losses are reported in [START_REF] Dai | Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon[END_REF], [START_REF] Grischkowsky | Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors[END_REF] to be less than 0.01 cm -1 at frequencies below 1 THz. Thus in the calculations nSi=3.42 is used as material refractive index with κSi= 3 x 10 -5

for the material absorption coefficient. After making a convergence test, the numerical results present a resonance frequency at 636 GHz with a 𝑄 = 3 × 10 4 . Such a high Qfactor for air confined PhC cavities at THz frequencies has never been reported. In order to put this in perspective, rescaling this to the NIR region would (at equal photon lifetimes) imply a cavity with Q up to 10 7 , or in other words among the strongest reported. As mentioned before this design can be rescaled to other THz frequencies by judiciously varying the geometrical parameters.

V. FABRICATION PROCESS

The waveguide fabrication process consists of two etching steps. A high resistivity SOI (Silicon on insulator) wafer (ρ > 10kΩ.cm), is composed of 90µm of HR-Si, on top of 300 µm of low resistivity silicon with 2 µm of SiO2 in between. The device layer is the guiding channel, which requires one lateral etching to define the waveguide's core. The different fabrication steps are represented in figure 12. The wire guide, its anchors and the PhC crystal holes are etched in a single deep reactive ion etching step (DRIE) with the buried oxide layer as etch stop layer. We used a switched SF6/C4F8 plasma process where etching alternates with passivation, enabling to reach 90 µm depth with a 5 µm resist mask, allowing very good lateral definition for the tiny anchor beams [START_REF]US5501893A -Method of anisotropically etching silicon -Google Patents[END_REF]. Moreover, we optimized this process by using fast switching, which enables to reduce the sidewall roughness down to the range 30nm-60 nm. Similar backside processing is then performed to define the suspended structures (supported by the anchor beams). Once the guiding channel is etched from the top and the back, a final step of HF etching allows to remove the SiO2 layer. Thanks to this fabrication process, long spiral waveguide (up to 25 cm) structures with a small footprint (2x2cm), as well as different photonic crystal cavities have been fabricated and measured. The bends in these structures have a radius of 3 mm designed to present negligible radiation losses (0.02 dB/bend). Given the very high index contrast of the suspended Si guides, compact bends with radius down to 500 µm are possible (0.5 dB/bend). For space consideration the simulations of these bend losses are not shown here. In figure 13 SEM photos of the photonic crystal cavity and the suspended waveguide are shown. Note that on this scale the varying period from 106 to 120 m is not visible.

VI. EXPERIMENTAL MEASUREMENTS

The measurements of the waveguide propagation losses, and the cavities' quality factor, have been done under normal atmospheric conditions by the extraction of S parameters using a VNA (Vector Network Analyzer) with two frequency extenders and two MWG WR-1.5 ports between 500-750 GHz.

The measurements are calibrated using a waveguide TRL (Thru, Reflect, Line) method, in the plane of silicon WG injection. The calibration process is repeated twice for different frequency range and frequency step. In order to measure the propagation losses and the bandgap of the photonic crystal mirrors the setup has been calibrated over the full frequency range of the extenders in steps of 125 MHz. A fine calibration (630-650 GHz with one measured point each 8 MHz frequency step) was performed for the characterization of high-Q cavity structures. In order to extract the propagation losses in the waveguide, different lengths of spiral waveguides have been fabricated (3.8, 10.9, 19.1, 25.1 cm). These structures all share the same waveguide width and thickness and same tapered sections, and only differ in total propagation length. It is important to note that these structures all share intentionally a pecular configuration for the access tapers as can be seen in fig. 13.d. In order to suppress the perturbing effect of direct transmission between the WR1.5 VNA waveguide ports, the access tapers are 90° out of eachothers' axis.

Referring to section III optimal coupling is obtained by inserting the tapered section inside the MWG. This has been achieved by mounting the structures on dedicated 3D printed holders (see fig. Figure 14 represents the losses in dB for the four structures with different lengths. As expected from simulation the insertion losses are higher at low frequencies. The spectral loss behavior is similar for all measured structures. This indicates that it is safe to assume that nearly identical coupling conditions are achieved for all structures and that a plot of these losses as a function of length is meaningful. We believe the extra loss peaks appearing in some measurements to be the result of misalignments as observed in the simulations in fig. 8a. A linear increase with waveguide length is observed and plotted in fig. 15 for two arbitrarily chosen frequencies (600 and 700 GHz). The fitted slope α corresponds to the extracted propagation losses in dB/mm. At 600 and 700 GHz total losses of α=0.068 and α=0.058 dB/mm respectively are observed. Note that this loss coefficient includes and distributes over the entire length of the guide all loss mechanisms (bend radiation, scattering and material absorption). It should therefore be treated as an upper limit for the pure propagation loss of the proposed suspended THz platform. This is confirmed by the fact that when extrapolating in fig. 15 the linear fit to zero length in both cases would apparently lead to negative total losses. Figure 16 shows the extracted loss coefficient over the entire frequency range 500-750GHz of the extender as obtained using the above procedure.

It can be stated that this novel integrated THz waveguide platform based on suspended HR-Si dielectric wire waveguides, exhibits propagation losses that vary between 0.045 and 0.085 dB/mm with an average of 0.065 dB/mm. This average loss is equivalent to 0.032 dB/λ0. Such a value is the lowest among several other THz silicon waveguides [START_REF] Ranjkesh | Silicon-on-Glass Dielectric Waveguide-Part I: For Millimeter-Wave Integrated Circuits[END_REF]- [START_REF] Tsuruda | Extremely low-loss terahertz waveguide based on silicon photoniccrystal slab[END_REF].

For the first time over a large frequency band (250 GHz) extending up to 750 GHz, a very low propagation loss (including bend, material and scattering loss) is demonstrated. In the second part of this work we used the same measurement setup used for loss extraction to characterize the photonic crystal resonators and photonic crystal Bragg mirrors. For Bragg mirrors full band calibration is used in order to visualize the full band gap, while for the resonators a finer calibration on a limited bandwidth (630-650GHz) is used in order to resolve potential high Q resonances. Two PhC Bragg mirrors with 60 holes of 29 µm radius have been characterized: one with a period a=106.56 µm correspond to the starting period of the anodized cavity, and a second one with a=120.65 µm corresponding to its central period. Figure 17 plots the measured transmittance and reflectivity on these. In both configurations the band gap is convincingly observed, as the region of combined low S21 transmittance (-30dB down to -50dB) and high S11 reflectivity (up to -0.5dB or 90% power reflection). For the former Bragg mirror (a=106.56m) we observe a band gap from 566 to 675.4GHz, while for the latter (a=120.65m) the gap appears from 518.4 to 616.4GHz.

Referring to the band structure simulation of fig. 10, these observed band edge frequencies are in very close agreement with the numerical predictions. It is also be observed that within the allowed bands a reasonable -2dB S21 transmittance is observed, implying only 63% power transfer, while the S11 reflections back to the VNA port are still non negligible as 10-30% (-5 to -10 dB). This is to be understood as the result of the impedance mismatch at the transition between the unpatterned suspended wire guides and the etched PhC part in the suspended guide. Together with the extra small scatter losses induced by the etched holes, this also accounts for the remaining scatter losses of about 10-25%. We also observe a "gap" at higher frequencies for both structures. These gaps do not correspond to a PhC band gap but occur when the incoming waveguide mode is coupled to higher order guided and radiative Bloch modes in the region of Brillouin zone far away from the edge. Such higher order modes are not coupled back to the monomode VNA ports, leading to a "measurement gap". 0.034 = 1.88 × 10 4 is observed for the structure with N=25 holes, at 640.25 GHz. The resonant frequency is slightly blue shifted with respect to the design frequency of 636 GHz but this can be explained by a systematic fabrication shift. Indeed, SEM observation revealed a hole radius 29.4 µm, shifted by 1.3% with respect to the design radius of 29 µm. Despite the very low losses of HR-Si, their impact on the measured quality factor is not negligible. Thus, we can extract a first order upper estimation for the intrinsic material losses out of the observed Q-factor. Indeed, the observed experimental Qfactor can be considered as the result of the idealized simulated 𝑄 simulated = 5. Resimulating the cavity using these extracted values a total 𝑄 = 1.83 × 10 4 is obtained in a 3D FDTD simulation using κ 𝑆𝑖 = 𝛼𝜆 0 4𝜋 = 7 x 10 -5 as material absorption coefficient. This Q-factor of 1.83 × 10 4 is nearly equivalent to the measured one of 1.88 × 10 4 , confirming the extracted material loss α=1.9 × 10 -2 cm -1 . Moreover, the extracted value is very close to the one reported in [START_REF] Dai | Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon[END_REF], [START_REF] Grischkowsky | Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors[END_REF]. The very low transmission of this resonant mode (less than 1%) in this case is the result of two phenomena. First of all, the mirror reflection is very high (N=25), which is also a reason to have a high Q factor. A nonoptimized injection might also account for lower overall transmission. Such a demonstration of an ultra-high Q is very important for certain applications, while for others a combination of reasonable high Q and high transmission is necessary. This could be achieved by having less holes in the design. In a subsequent recalibrated fabrication run new cavities with less holes were produced with specific attention to compensate for the systematic deviation on the hole radius. As represented in figure 19 for the design with 21 and 17 holes respectively, the resonant frequency is closer to the one in simulation. As expected the Lorentzian peak of these resonant modes is wider than the previous one. The quality factor is decreasing from 1.88 × 10 4 for N=25 to 7 × 10 3 and 1.5 × 10 3 respectively for cavities with N=21 and 17. A small error still exists (less than 0.4%) on the resonance position and the resonant frequency is red shifted. However, the transmission is increasing, to reach up to 72% of transmittance (-1.4 dB) for N=17, while the mode is almost not reflected with less than 1% of reflectance (-22 dB). Similarly, for the cavity with 21 holes, S21=-3.7 dB (42%) and S11=-6.2 dB (24%).

To summarize, we demonstrate experimentally an ultra-high Q factor cavity, with a precise resonant frequency (error less than 0.5%) and a controllable transmittance by a simple adjustment of the number of mirror holes. These record Q factors at THz frequencies are among the highest ever reported.

VII. CONCLUSION

A low loss suspended Silicon platform is designed, fabricated and measured experimentally. Such an integrated platform, with a very low cost fabrication process presents very low loss.

The measured propagation loss of a long waveguide with bends on a compact surface are very low α=0.065 dB/mm at f=650 GHz. Such low loss platform is also demonstrated through the design of ultra-high Q photonic crystal cavity. A Q>18000 for air confined PhC cavities at THz frequencies is measured for the first time. Other cavity design with high Q >1500 and high transmittance power >72% is also presented experimentally in this work. This novel integrated THz waveguide platform opens up new avenues for integrated sensing but may also find interesting applications as building block for integrated THz signal processing in e.g. communication platforms.

VIII. ACKNOWLEDGEMENT

This study was undertaken as part of the Terafood project, which is financially supported by the European Regional Development Fund and the province Oost-Vlaanderen (INTERREG V FR-WA-VL 1.1.11). The authors would like to thank S. Eliet, V. Avramovic, S. Lepilliet and E. Okada the engineers of IEMN characterization center for their assistance with the experimental measurements. They would also like to thank JM Droulez, R. Peretti, C. Tannoury and T. Hannotte for their advice on numerical calculations and computer cluster use.

Fig. 1

 1 Fig. 1 Normalized propagation constant at 650 GHz as function of waveguide width (W) for a) thickness T=50 µm and b) T=90 µm.The dashed vertical orange line represents the chosen widths.

Figure 1

 1 Figure 1 represents the modes propagation constant at 650 GHz, as function of waveguide width for two particular thicknesses. As represented in figure 1.a by the orange dashed vertical line, a width (W) of 150 µm and a thickness (T) of 50 µm represents the dimensions of a single mode waveguide. This waveguide has a monomode behavior at 500-650 GHz (fig 2.a), but it disadvantages arise in the low mode confinement inside Silicon (58%) (fig 3.a). As our interest goes out to design a PhC cavity for sensing applications [34]-[36] a multimode waveguide with high confinement factor is desired. The designed channel has a width (W) and thickness (T) of 210x90 μm. With such dimensions the waveguide allows to highly confine the fundamental mode 𝐸 𝑥 11 inside the core (89%) (fig. 3.b), while the propagation of the second symmetric mode 𝐸 𝑥 31 remains prevented (fig. 1.b). This waveguide is quadrimodal, with guided, 𝐸 𝑥 11 , 𝐸 𝑦 11 , 𝐸 𝑥 21 , 𝐸 𝑦 21 -modes in the frequency band 500-650 GHz (fig. 2.b).In order to suspend this structure, anchors are designed to hold the guiding channel with two supporting silicon structures on the sides (fig.4). The dimensions of the anchors are defined after studying their impacts on the mode perturbation and propagation losses.

Fig. 2 Fig. 3 .

 23 Fig. 2 Normalized propagation constant (β/k0) of the suspednded waveguide with: a) W=150µm T=70µm and b) W=210µm T=90µm

  4.c). The lateral dimension is chosen so as to avoid any spurious leakage to the Si layer of the supporting wafer to which the anchors are attached (see fig. 4.a).

Fig. 4 .Fig. 5 .

 45 Fig. 4. a) Suspended waveguide inset: transversal cross section of the waveguide b) Taper dimensions c) supporting anchors dimensions

Fig. 6 .

 6 Fig. 6. Normalized propagation constant function of taper width variation Lb and Lt are defined by [38] 𝐿 𝑏 = 2𝜋 𝛽 1 -𝛽 2

Fig. 7 .Fig. 8 .Fig. 9 .

 789 Fig. 7. Simulated insertion losses for different position of taper inside MWG with the red dashed horizontal line indicating the 10 dB level a) S21 parameter (transmittance) b) S11 parameter (Reflectance)

Fig. 10 .

 10 Fig. 10. Band diagram of two photonic crystals with different period a) a=106.56µm and b) a=120.65 µm

  reducing the etching period instead of increasing it.Two main loss sources are present in such a cavity type. The in-plane losses, due to the mode losses in the waveguide, and the out-of-plane losses related to coupling to radiative modes. The quality factor 𝑄 = 𝜔 0 𝜏 2

Fig. 12 .

 12 Fig. 12. Fabrication process steps

Fig. 13 .

 13 Fig. 13. Images of the fabricated samples a-b) scanning electron microscope (SEM) photo of the photonic crystal cavity (a) and the suspended waveguide (b) c-d) photographic image of the photonic crystal cavity (c) and 25 cm long waveguide (d)

  13.c for an example) that are aligned using micropositioners and with the help of a camera to the MWG slit. The measured calibrated S21 and S11 parameters are power normalized in dB scale, representing respectively in logarithmic scale the normalized transmitted power from port 1 to port 2, and the normalized backreflected power to port 1 (Similarly for the two other parameters S12 and S22).𝑆 21 = 10 log 10 total losses (coupling, absorption, scattering and radiation) of the structure under test in dB scale can be obtained as 𝒍𝒐𝒔𝒔 = -𝟏𝟎 𝐥𝐨𝐠 𝟏𝟎 (

Fig. 14 .

 14 Fig. 14. Total losses for waveguides with different propagation lengths

Fig. 15 .

 15 Fig. 15. Linear fit of propagation losses at 600 and 700 GHz

Fig. 16 .

 16 Fig. 16. propagation loss in the suspended waveguide structure

Fig. 17 .

 17 Fig. 17. Measured bandgap of photonic crystal cavities with period a) a=120.65 µm and b) a=106.56 µm With the low-loss platform confirmed as well as the correct behavior of 1D PhC wire waveguides, the final characterization experiments consist in verifying the existence of high-Q apodized 1D PhC cavities. As described in the cavity design

  7 × 10 4 (where material losses have been neglected) and the contribution of the material losses. Using these values in the equation below 1/QMeasured = 1/Qsimulated+1/QMaterial (13) we can extract the material absorption losses as 1/QMaterial = 3.6x10 -5 or QMaterial= 2.8 × 10 4 . The simulated results represented in IV, shows that an α= 8 × 10 -3 cm -1 , correspond to 𝑄 Material = 6.7 × 10 4 equivalent to 𝜏 = . So by analogy the experimental extracted 𝑄 mat = 2.8 × 10 4 corresponds to 𝜏 = 1.4 × 10 -8 𝑠 and α=1.9 × 10 -2 cm -1 .

Fig. 18 .

 18 Fig. 18. Resonance frequency at 𝑓 𝑅 =640.2 GHz for cavity with N=25 hole. Inset: Zoom out of resonance plot

Fig. 19 .

 19 Fig. 19. Resonance frequencies at 𝑓 𝑅 = 634.1 and 633.63 GHz, for cavities with N=21 (dashed lines) and 17 (solid lines) hole respectively

  This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TTHZ.2020.3019928, IEEE Transactions on Terahertz Science and Technology > High Q THz photonic crystal cavity on a low loss suspended Silicon platform < 10 section III, cavities with 3 different hole numbers are measured.For Q factor calculation we used 𝑄 =

			𝑓 𝑅 𝐹𝑊𝐻𝑀 , with 𝑓 𝑅 the
	resonant frequency and 𝐹𝑊𝐻𝑀 the resonance width at 3dB. In
	fig.18 an ultra-high	𝑄 measured =	640.25

Authorized licensed use limited to: UNIVERSITE DE LILLE. Downloaded on January 05,2021 at 15:56:08 UTC from IEEE Xplore. Restrictions apply. 2156-342X (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

Authorized licensed use limited to: UNIVERSITE DE LILLE. Downloaded on January 05,2021 at 15:56:08 UTC from IEEE Xplore. Restrictions apply.

This study was undertaken as part of the Terafood project, which is financially supported by the European Regional Development Fund and the province Oost-Vlaanderen (INTERREG V FR-WA-VL 1.1.11).


Pierre Kolejak

Kamil Postava

Martin Micica

Jaromir Mathias Vanwolleghem

The Gouy phase shift in

teaching and research institutions in France or abroad, or from public or private research centers.

I. INTRODUCTION

he terahertz time-domain spectroscopy (THz-TDS) is phase sensitive technique able to determine complete complex dielectric function of a measured sample from a single transmission spectrum. THz-TDS spectrometers use sub 100-femtosecond pulsed beams. If one takes into account relatively long wavelength of the radiation, the terahertz beams are more tightly focused in contrast with longer wavelengths as the visible beams.

It is necessary to carry out reference and sample measurement in THz-TDS measurement. If optical paths of THz beams are the same for reference and sample measurement, the beams are focused in the same way on a detector for both measurements. It means also the same Gouy phases [START_REF] Feng | Physical origin of the Gouy phase shift[END_REF].

However, if the optical paths differ, especially for sample measurement including a propagation through a sample, the focusing of the THz beam on detector is changed for the sample measurement in contrast with reference measurement. Therefore, reference and sample measurements will have different complex Gouy phases, which affects measured transmission spectra.

II. COMPENSATION OF THE GOUY PHASE

The Gouy phase influence have to be compensated for obtaining the correct dielectric function of a sample. The numerical method to compensate the Gouy phase was proposed by Kužel et al. [START_REF] Kužel | Gouy shift correction for highly accurate refractive index retrieval in time-domain terahertz spectroscopy[END_REF], which uses linear approximation of the Gouy phase, where only the real part of the Gouy phase influences measurement. In a case, that the Gouy phase has a general dependence, it is more advantageous to use another technique. In our previous paper [START_REF] Koleják | Experimental Gouy phase shift compensation in Terahertz time-domain spectroscopy[END_REF], we have proposed the mechanical method for compensation of the complex Gouy phase. The method is applicable for strongly focused THz beams of general shape and included misalignments of the experimental setup.

Figure 1 shows comparison of uncompensated and compensated complex refractive index of high resistivity silicon measured in transmission setup. It is visible that uncompensated data include unphysical absorptions and dispersions.

The time domain spectrometer Teraview TPS Spectra 3000 is used for measurement in this paper. It uses 90 fs pulses at 780 nm generated by Er:doped ¿ber laser. The THz emission as well as detection are delivered by GaAs photoswitches. Measurements were carried out in the vacuum.

In this contribution, we present also technique for analyzing of errors for general data caused by the complex Gouy phase. It allows one to determine it is necessary to use the compensation methods. Also, the comparison of measured complex Gouy phase with the numerical model to simulate its detection on a finite size detector [START_REF] Koleják | Analytical model of Gouy phase influence in terahertz time-domain spectroscopy[END_REF] is provided. It allows one to minimize the Gouy phase influence in spectroscopic measurements and helps to design terahertz time-domain spectrometer setups with reduced the Gouy phase shift.

III. MODEL OF THE GOUY PHASE

The complex Gouy phase [START_REF] Feng | Physical origin of the Gouy phase shift[END_REF][START_REF] Koleják | Experimental Gouy phase shift compensation in Terahertz time-domain spectroscopy[END_REF] is the additional axial complex phase of the Gaussian beam caused by its diffraction, expressed for propagating along z-axis in form

Ƀ ෨ ሺݖሻ ൌ ቀ ௭ ௭ బ ቁ ඥݖ ଶ ݖ ଶ ǡ
where ݖ denotes the Rayleigh parameter. The real part represents the different phase velocity between Gaussian beam and plane wavefronts and affects the extraction of the real part Pierre Koleják 1,2 , Kamil Postava 1 , Martin Miþica 1,2 , Mathias Vanwolleghem 2 and Jaromír Pištora 1 of sample refractive index. Whereas, the imaginary part is associated with amplitude changes caused by the beam focusing.

The complex Gouy phase, affecting the sample measurement as is shown on Fig. 1, may be obtained from the measured data as the complex spectra ratio of the free space measurement on the standard reference z-position and the free space measured on the z-position corresponding to the focus displacement caused by a sample [START_REF] Koleják | Experimental Gouy phase shift compensation in Terahertz time-domain spectroscopy[END_REF]. It is important to note, that the standard reference position may be placed out of the beam focus. Which means the extracted complex Gouy phase by this way corresponds to the difference of complex Gouy phases on different z-position of the beam.

Moreover, the detection is carried out by a finite size detecting area. Which will also cause the detection of nonaxial components of the Gaussian beam averaged on a detection area [START_REF] Koleják | Analytical model of Gouy phase influence in terahertz time-domain spectroscopy[END_REF]. The model for describing of the averaged complex Gouy phase ۃɃ ෩ ሺȳǡ ۄሻݖ uses the integral averaging of the complex Gaussian amplitude on a finite circular area perpendicular to the beam axis which passes thought the detector center [START_REF] Koleják | Analytical model of Gouy phase influence in terahertz time-domain spectroscopy[END_REF] and gives the form

ۃɃ ෩ ሺȳǡ ۄሻݖ ൌ െ ൞ ൬ െܴ݇ ଶ ʹሾݖ ᇱ ݖ ሺȳሻሿ ൰ െ ͳ ൬ െܴ݇ ଶ ʹሾݖ ᇱ ݖ ሺȳሻሿ ൰ െ ͳ ൢ
where ȳǡ ݇ǡ ܴǡ ݖ ᇱ ǡ ݖ ᇱ mean the frequency, the wavenumber in the vacuum, the radius of a detector, the reference z-position, and the displaced z-position, respectively.

The complex Gouy phase extracted for the high resistivity silicon measurement previously shown in Fig. 1 is plotted (blue curve) in Fig. 2. The measured complex Gouy phase allows one to see whether the dependence of the real part of the Gouy phase is linear. In this case, it is possible to use the compensation method proposed by Kužel at al. [START_REF] Kužel | Gouy shift correction for highly accurate refractive index retrieval in time-domain terahertz spectroscopy[END_REF] based on the numerical compensation considering the linear dependence of the real part with zero value of the imaginary part of the Gouy phase. Figure 2 shows that the dependence is strongly nonlinear and the imaginary part of the Gouy phase also strongly affects measurement. It follows it is advantageous to use the mechanical method [START_REF] Koleják | Experimental Gouy phase shift compensation in Terahertz time-domain spectroscopy[END_REF] for measurements on this experimental setup. Generally, the nonlinear behavior may be caused also by the misalignment of the system or another effect such as non-Gaussian beam etc. Moreover, these effects are difficult to model, but the mechanical method is principally able to compensate most of them due to achieving information about how the reference is changing along z-axis. Disadvantages of the mechanical method in contrast with the numerical method is that data are compensated for the arbitrary position corresponding to the refractive index on the arbitrary position, which limits application of the method for materials with huge dispersion in broad terahertz spectral range.

The model simulating the averaged complex Gouy phase ۃɃ ෩ ሺȳǡ ۄሻݖ is shown in Fig. 2 (dashed red curve). Input parameters used in the simulation are R=1.5 mm, ݖԢ=7.95 mm, ݖ ᇱ =6.6 mm and ݖ = Ǥ ஐ (mm, Hz). The model describes the measured Gouy phase roughly due to approximations in its deriving [START_REF] Koleják | Analytical model of Gouy phase influence in terahertz time-domain spectroscopy[END_REF], but still able to demonstrate that observed phenomena may be caused by the behavior of the Gaussian beam in THz frequencies.

IV. CONCLUSION

We propose techniques for compensation of the Gouy phase, which affects transmission time-domain spectroscopy measurements. The method to analyze general influence of the Gouy phase is proposed. The model simulating the Gouy phase influence compared with measured data is also shown. These analyses lead to understand and compensate errors originated from the Gouy phase in THz-TDS systems. More detailed study of these errors will be published in our following work [START_REF] Koleják | Quanti¿cation of errors originating from Gouy phase shift in terahertz spectroscopy[END_REF].

Fig. 1

 1 Fig. 1 Real and imaginary part of complex refractive index of high resistivity silicon are shown. Uncompensated (dashed blue line) and compensated (full red line) complex refractive indices differ in the Gouy phase influence [3].

Fig. 2

 2 Fig. 2 Comparison of the measurement (blue curve) and simulation (red dashed curve) of the complex Gouy phase corresponding to the measurement of the high resistivity silicon.

VSB-Technical University of Ostrava, Nanotechnology centre and IT4Innovations, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic

Université de Lille, CNRS UMR 8520, Institut d'Electronique, de Microelectronique et de Nanotechnologie, 59652 Villeneuve d'Ascq Cedex, FranceThe Gouy phase shift in terahertz time-domain spectroscopy and its experimental estimation, modelling and compensation

ACKNOWLEDGEMENT

Partial support from the projects 18-22102S from Czech Science Foundation, SP2019/92 project, CZ 02.1.01/0.0/0.0/16 013/0001791, the Czech-French mobility project 8J19FR006, and Scholarship of the city of Ostrava are acknowledged.


Elias Akiki

Mattias Verstuyft

Guillaume Ducournau

Benjamin Walter

Estelle Mairiaux

Marc Faucher

Jean-Francois Lampin

Bart Kuyken

Mathias Vanwolleghem

Integrated high Q optical cavity on a low loss Si suspended waveguide for THz application

THz waves are used recently in many applications, and shows many interest in different domain as molecular spectroscopy, high data transmission, detection of organic molecules in space… But the integration of THz circuits for such applications is still a challenging point. In this work we demonstrate a new silicon millimetric waveguide to guide THz waves on chip, with very low propagation losses. As a complement to this achievement we show also a high Q optical cavity, formed by circular etching on the top of this waveguide.

The designed Si waveguide allows confined propagation of electromagnetic waves at THz frequencies starting from 500 GHz. A Si channel of 210μm in width and a thickness of 90μm form the core. The cladding material is absent in this design and replaced by the surrounded air in order to reduce the material losses. A highly confined fundamental optical mode represented in the insert of figure 1 is the result of this high index-contrast nhigh-Res Si/nair. The technique used here to fabricate this waveguide, consist of double face etching of an SOI (silicon-on-insulator) wafer with deep-reactive ion etching. The advantage of this technique, in contrast to previous reported ones [START_REF] Ranjkesh | Silicon-on-Glass Dielectric Waveguide-Part II: For THz Applications[END_REF], is that there is no necessity to have any other lossy material as Pyrex or glass to form the substrate. To experimentally test this waveguide, a free space S parameter measurements are done and extracted with a VNA (vector network analyzer).

In order to excite the electric fundamental mode of the Si waveguide, metallic waveguide ports of the test setup are rotated by 90 ͦ . The two ends of the designed structure are adiabatically tapered, in order to reduce impedance mismatch between metallic waveguide and silicon waveguide, for an efficient smooth coupling. An additional right angle (bending radius 3 mm) was included to the waveguide (see figure 1), helps to avoid direct coupling between transmitter and receiver ports. Modal propagation losses are extracted by, transmission measurements on 5 waveguides of increasing length (3.87, 10.9, 14.9, 19.1 and 25.1 cm). Having a linear variation of the S21 parameter as a function of length, allows to extract the slope corresponding to the attenuation constant [START_REF] Tsuruda | Extremely lowloss terahertz waveguide based on silicon photonic-crystal slab[END_REF] (see Fig. 2). An average of 0.7 dB/cm over the entire band is extracted which is at least 2 times better than the best demonstrated waveguides in this band up till now [START_REF] Leong | WR1.5 Silicon Micromachined Waveguide Components and Active Circuit Integration Methodology[END_REF].

Having demonstrated the potential of this very low loss waveguide, we benefited from this achievement to create a 1D photonic crystal cavity on the top of this waveguide (see Fig. 3), by making periodical circular etching in the core of the waveguide. Creating a defect in the etching periodicity allow us to create an optical cavity where the light is confined mostly in air at a predefined frequency.

3 different optical cavities with different etching radius size, are fabricated and measured. By increasing the etching radius of the photonic crystal, resonance frequency shifts toward highest frequencies.

Further results on this confined inline THz PhC cavities for sensing purposes will be shown. In conclusion, this demonstrated ultra-low-loss chipscale integrated THz photonic platform is a new tool integrated Thz spectroscopy with increased light-matter interation.

  Integrated high Q optical cavity on a low loss Si suspended waveguide for THz application E. Akiki 1 , M. Verstuyft 2 , G. Ducournau 1 , B. Walter 3 , E. Mairiaux 3 , M. Faucher 1 , J-F. Lampin 1 , B. Kuyken 2 , M. Vanwolleghem 1* 1 IEMN, CNRS UMR8520, Université de Lille, Villeneuve d'Ascq, France 2 Photonics Research Group, Department of Technology, Ghent University-imec, Ghent, Belgium 3 Vmicro SAS, Villeneuve d'Ascq, France *Correspondence e-mail: mathias.vanwolleghem@univ-lille.fr Abstract: A free standing silicon waveguide with very low losses at THz frequencies is presented. By dry etching of an SOI wafer, the guiding channel is formed. This process allows to have a fully suspended Si (silicon) waveguide, where the air form it cladding. The absence of material as a cladding leads to have ultra-low losses. Another achievement of this work is also presented, where this guiding channel is etched in a way to form a high Q optical cavity.

Fig. 1 Fig. 3 Fig. 2 Fig. 4

 1324 Fig. 1 Suspended Si waveguide on the VNA measurement setup; insert: fundamental electric mode confined


Lauren E Blanc

Xiaoqi Sun

Abhinandan Shyamsunder

Victor Duffort

Linda F Nazar
email: lfnazar@uwaterloo.ca

Direct Nano-synthesis Methods Notably Benefit Mg-Battery Cathode Performance

Keywords: Magnesium battery, nano-dimensional, sulfide cathode, energy storage, intercalation, conversion

Rechargeable magnesium batteries are promising candidates for next-generation electrochemical energy storage, but their development is severely hindered by sluggish solid-state diffusion and significant desolvation penalties of the divalent cation. Studies suggest that nano-sized electrode materials alleviate these issues by shortening diffusion lengths and increasing electrode/electrolyte interaction. Here, we investigate the effect of particle size and synthetic methodology on the electrochemical performance of four sulfide cathode materials in Mg batteries: layered TiS 2 , CuS, spinel Ti 2 S 4 and CuCo 2 S 4 . In these sulfide hosts, the direct preparation of nanodimensional crystallites is critical to activate or improve electrochemistry. Even promising cathode materials can appear electrochemically inert when micron-sized particles are investigated (e.g . CuCo 2 S 4 ), and mechanical milling leads to surface degradation of active material which severely limits performance. However, nano-sized CuCo 2 S 4 prepared directly reaches a capacity nearly double that of ball milled material and delivers 350 mAh g -1 at 60 °C. This work provides synthetic considerations which may be crucial in the discovery and design of novel Mg cathode materials so that promising candidates are not overlooked. By extension, in oxide materials where Mg 2+ diffusion is expected to be much more sluggish, this factor is anticipated to be even more important when screening for new hosts.

Introduction:

Overconsumption of fossil fuels has led to a plethora of environmental issues and an impending energy crisis. To reduce carbon-based emissions, energy storage technology needs to be developed to (1) facilitate a transition from gasoline powered cars to electric vehicles and (2) integrate renewable power sources into the grid. [1][2][3] Rechargeable batteries offer viable approaches to achieve these goals, but improvements are needed to progress beyond current state of the art lithium ion batteries (LIBs) which are limited by economic factors and safety concerns. [4][5][6] As an earth-abundant metal and divalent cation, magnesium-based battery technology provides large theoretical volumetric energy densities at a fraction of the cost of LIBs. [START_REF] Fichtner | Magnesium Batteries: Research and Applications[END_REF][START_REF] Ponrouch | [END_REF] Furthermore, rechargeable magnesium batteries are promising candidates for electrochemical energy storage due to limited dendritic growth and good safety of the Mg metal anode. [9][10][11][12] Despite these desirable qualities, there are major challenges hindering the development of Mg batteries due to kinetic limitations associated with the transport and electrodeposition of the divalent cation. [13,14] While much progress has been made to increase the anodic stability and improve the efficiency of advanced Mg electrolytes, [15][16][17] the paucity of known cathode materials capable of reversible Mg 2+ (de)insertion continues to plague this technology. High voltage oxides generally suffer from sluggish Mg 2+ diffusion due to strong ionic interactions between the migrating cation and the highly polarizing lattice. [18][19][20] In these oxide materials, the desolvation process at the cathode/electrolyte interphase has been shown to add an additional kinetic barrier to intercalation, [21- 23] and a strong driving force towards conversion has been widely observed. [11,[24][25][26][27][28] Although sulfide cathodes offer a lower energy density than oxides, they exhibit weaker interactions with the divalent cation and allow for more facile solid diffusion. As a result, most successful magnesium ion batteries have been prepared by balancing a sulfide cathode material with a Mg metal anode. Reversible Mg 2+ intercalation was first demonstrated by Aurbach et al. with the Chevrel phase Mo 6 S 8 as the host, [29] while we later proved that the spinel and layered phases of titanium sulfides were excellent Mg cathode candidates. [30,31] We also demonstrated that CuS cathode materials uptake Mg via a conversion reaction; however, high temperatures were required to cycle most of the capacity of micron-sized material. [32] Although these sulfide hosts provide better kinetics for Mg 2+ insertion/diffusion in comparison to oxides, their electrochemical performance requires further improvement to compete with existing technology. One potential solution is to reduce the particle size of the cathode material to allow shorter ion diffusion lengths and enhance ingress/egress of Mg 2+ ions by increasing the surface area exposed to the electrolyte. This strategy has been implemented to activate Li + insertion into olivine LiMnPO 4 [33,34] and to improve the electrochemistry of other Li-ion [35][36][37][38][39][40][41][42] as well as Mg electrode materials. [43][44][45][46][47] Nanomaterials can either be prepared (1) directly through rapid, low-temperature syntheses that limit the growth of crystallites or (2) the particle size of micron-materials can be reduced with mechanical milling processes. While a wide variety of synthetic methods have been developed to directly prepare nano-sized oxide and binary sulfide materials, most ternary sulfides are prepared with a high-temperature solid state synthesis that produces micron-sized particles. [48][49][50] In these cases, nano-sized particles must be obtained post-synthesis through a mechanical ball milling process.

Herein, we investigate the effect of crystallite size on the performance of four model Mg cathode candidates (layered TiS 2 , CuS, spinel Ti 2 S 4 and CuCo 2 S 4 ), and critically analyze the impact each method of nano-sizing has on the materials' electrochemistry. We show that the electrochemical performance of both intercalation (titanium sulfides) and conversion (CuS and CuCo 2 S 4 ) cathodes is a very strong function of particle size, but that advantages of nano-sizing are accompanied by negative consequences when micron-sized particles are subjected to mechanical milling. Even though decreasing the particle size of electrode materials enhances the risk of parasitic side-reactions and reduces their overall volumetric density due to less efficient packing, [51][52][53] this is not a major concern for the current stage of Mg battery research. The discovery of new candidates and improvement of their electrochemistry are more urgent goals to provide a platform to understand the fundamentals of multivalent cation insertion and guide further directions for research. Our study demonstrates that (1) the discovery of novel higher voltage cathodes likely requires first curtailing their crystallite sizes to nano-dimensions in order to avoid overlooking potential materials, and (2) optimal performance is obtained through direct nano-synthetic techniques.

Results and Discussion:

A wide variety of liquid-based approaches can be used to directly synthesize nano-sized binary sulfides. Two common Mg cathode materials, TiS 2 and CuS, [31,32] were prepared using wet syntheses (WS) in order to examine both intercalation and conversion electrodes, respectively (Figure 1). Nanodimensional layered TiS 2 was prepared through a liquid phase synthesis (WS) in oleylamine (at 300 °C), resulting in particle sizes around 100 nm as shown in Figure 1b. [54] CuS nano-rods (prepared by a low temperature wet synthesis) aggregated into ~300 nm spheres (Figure 1d). [55] XRD patterns of WS-TiS 2 and WS-CuS confirm that each target phase was successfully prepared, (Figure 1a,c), and the peak broadening observed is due to the small coherence length of the crystallites produced using the wet synthesis technique.

As expected, nano-sized WS-TiS 2 and WS-CuS exhibit enhanced electrochemical performance in comparison to their micron counterparts (Figure 2). As reported in our previous work, micron-sized TiS 2 is an intercalation Mg cathode material which exhibits Mg 2+ trapping after the first cycle, leading to 47% irreversible capacity at a current density of 12 mA g -1 (C/40 with 1C = 1 Mg 2+ /TiS 2 ) and 60 °C. [31] This capacity loss is reduced by using nano-sized material, which exhibits only 15% irreversible capacity after the first cycle and further decreases to 8% after the second (Figure 2a). This electrochemical performance of WS-TiS 2 displays significant improvement -yielding larger initial discharge capacities (Figure S1) and better capacity retention -in comparison to the bulk material (Figure 2a,b). At a current density of 12 mA g -1 , micron-sized TiS 2 only reaches an initial discharge capacity of 270 mAh g -1 which fades considerably to 160 mAh g -1 upon further cycling (vs. 294 and 269 mAh g -1 for WS-TiS 2 ). [31] The stepwise voltage profile of WS-TiS 2 shown in Figure 2a indicates a similar Mg 2+ insertion process as the micron-sized material, although the difference in length of each plateau reflects some change in kinetics upon decreasing the particle size. Long term cycling of WS-TiS 2 at 60 °C at a current density of 48 mA g -1 shows that the material exhibits a fairly stable capacity and retains 120 mAh g -1 at the 200 th cycle (Figure 2b). Under these conditions, the capacity of micron-sized TiS 2 fades to a comparable value after only 40 cycles. [31] Unlike micron-TiS 2 which exhibits extremely poor electrochemistry at room temperature, the nano material also shows promising electrochemical properties at 25 °C. The larger initial capacity and better capacity retention of WS-TiS 2 compared to micron-TiS 2 is a direct result of shorter Mg 2+ ion diffusion length.

We have previously demonstrated that micron-sized CuS functions as a Mg cathode by conversion chemistry; however, an elevated temperature of 150 °C was required to approach reasonable capacities. [32] Decreasing the particle size through a low-temperature liquid synthesis approach creates more accessibility of the electrode surface by the electrolyte and promotes reactivity, enhancing electrochemical performance without the requirement of elevated temperatures. Figure 2c shows the voltage profiles of the nano-sized WS-CuS cathode in a Mg cell at room temperature. On discharge at a current density of 30 mA g -1 (C/19 with 1C = 1Mg 2+ /CuS), two voltage plateaus at 1.4 V and 1.1 V are observed, each contributing to half of the 480 mAh g -1 overall capacity. The initial overpotential exhibited in the discharge profiles is likely the result of nucleation. In situ XRD demonstrates that two conversion reactions take place during the first and second plateaus of the first discharge (Figure 3): This mechanism agrees with our previous report on micron-CuS at an elevated temperature. [32] After the first charge, the XRD pattern is similar to the one obtained at the end of the first discharge plateau (corresponding to Cu 2 S and MgS) while the CuS starting phase is not observed (Figure 3). This suggests that only the lower voltage process (Equation 2) is reversible and that the irreversible nature of Equation 1 leads to the large capacity decay observed on the second cycle (Figure 2c inset).

Long term cycling of WS-CuS was carried out with a lower voltage cutoff corresponding to the end of the first charge plateau (Figure 2d). At a current density of 30 mA g -1 , the capacity drops from 193 mAh g -1 obtained on the second discharge, to 150 mAh g -1 maintained on the 50 th cycle. Although initial capacities are lower, the capacity decay is slower with higher current densities of 200 mA g -1 and 500 mA g -1 , suggestive of suppressed parasitic reactions at the faster rates. Ex situ XPS on the Mg anode at the end of charge revealed a Cu signal (Figure S2), indicating that Cu dissolution and migration to the anode takes place during cycling which is a common challenge of conversion-type chalcogenide cathodes. [56] This loss of active material contributes to the capacity decay so that a faster cycling rate allows less time for such process and results in more stable capacity retention. Thus, the electrochemical performance of nano-sized CuS can be optimized by preparing electrodes and/or designing cells in manners that minimize Cu shuttling in order to prevent this source of capacity fade. Furthermore, CuS particle morphologies with minimal agglomeration, in addition to small particle size, show exceptional promise as they exhibit reversible capacities with an impressive cycle life. [57,58] These results agree with other reports of nano-CuS prepared through a variety of methods: enhanced Mg 2+ diffusion kinetics leads to improved electrochemical performance which can be obtained by using nanoparticles to prepare Mg electrodes. [59,60] These results confirm that directly preparing nano-sized binary sulfides through a liquid synthetic route significantly improves electrochemical performance; however, this approach is not always applicable for the preparation of ternary sulfides. For example, CuTi 2 S 4 is a ternary sulfide that can be oxidized to remove Cu ions and prepare spinel Ti 2 S 4 , a well-known host for Mg 2+ intercalation. [30] This material is almost exclusively prepared via a conventional solid-state method, resulting in micronsized particles. Here, these were subjected to mechanical ball milling (BM) to reduce particle size prior to electrochemical characterization. XRD confirms that BM-Ti 2 S 4 retains its spinel structure, where the broadening of peaks is a result of the defects created during this high energy process ( Figure 4a). Figure 4b shows a decrease in particle size from the original micron-sized particles (inset) to less than 1 μm which significantly shortens the Mg 2+ diffusion length by a factor of 10. While BM-Ti 2 S 4 does show improved capacity retention in comparison to the micron-sized material, the nanomaterial actually exhibits a lower initial discharge capacity than bulk Ti 2 S 4 (Figure 4c,d). This decreased discharge capacity is a result of surface degradation of the active material during the high energy milling process. Despite its limited capacity, after initial conditioning, BM-Ti 2 S 4 shows a much lower capacity decay rate of only 0.13% per cycle, and it maintains 120 mAh g -1 capacity at the end of 70 cycles at a current density of 48 mA g -1 (C/5 with 1C = 1Mg 2+ /Ti 2 S 4 ) at 60 °C. This performance is significantly improved compared to the 0.7% capacity decay rate and 95 mAh g -1 capacity retained after the 70 th cycle for the non-ball milled material under the same conditions. These results indicate that nano-sizing materials through mechanical milling has some positive impact on electrochemical performance; however, benefits are accompanied by significant negative consequences due to (1) surface degradation inhibiting Mg 2+ ingress/egress into/from the structure and (2) the possibility of introducing impurities, thus lowering the capacity of active material (Figure S3).

The electrochemical performance of known cathodes indicates that both intercalation and conversion materials benefit significantly from a direct nano-synthesis. WS-TiS 2 and WS-CuS both exhibit increased capacities and better capacity retention as a result of the small particle size produced from their liquid synthesis. However, high energy processes to reduce particle size post-synthesis (e.g. ball milling) can have negative consequences on electrodes, as BM-Ti 2 S 4 begins with a lower initial capacity vs. bulk material. To directly assess the degree to which synthetic methodology impacts electrochemical performance, nano-sized CuCo 2 S 4 was obtained both by ball milling bulk material and through a direct nano-synthesis (Figure 5). Spinel CuCo 2 S 4 is isostructural with CuTi 2 S 4 ; however extraction of Cu ions from the former is not possible, probably owing to the lowering of the S 3p level below that of the Co 3d band. [61] We thus examined CuCo 2 S 4 itself as a cathode material. CuCo 2 S 4 prepared from a conventional solid state synthesis contains a small amount of CoS 2 impurity and particle sizes are typically >10 μm (Figure 5c,d). As prepared, micron-sized CuCo 2 S 4 requires an elevated temperature of 150 °C to exhibit any electrochemical activity. At this temperature and a current density of 10 mA g -1 (C/17 with 1C = 1Mg 2+ /CuCo 2 S 4 ), the bulk material has an initial discharge capacity of 60 mAh g -1 . Upon mechanical milling, the particle sizes decrease to hundreds of nanometers (Figure 5d) which allows the cathode to be cycled at lower temperatures. At the same current density, BM-CuCo 2 S 4 has a promising capacity of 180 mAh g -1 at only 60 °C and even exhibits some activity at room temperature (Figure 5e). Reducing the particle size of CuCo 2 S 4 has clear advantages in comparison to bulk material; however, these are not the best results that this material is capable of delivering. To achieve enhanced electrochemical performance, nano-sized CuCo 2 S 4 was directly prepared using a low temperature melt approach reported by Khan, et al. [62] Stoichiometric mixtures of Cu(I) and Co(II) ethylxanthate salts were ground and decomposed at 250 °C to produce X-CuCo 2 S 4 . This approach generates a highly porous network of nano-sized CuCo 2 S 4 particles (Figure 5a,b). When cycled at 10 mA g -1 and 60 °C, X-CuCo 2 S 4 reaches an initial discharge capacity of 350 mAh g -1 , nearly double that of BM-CuCo 2 S 4 .

The capacities observed for nano-sized materials at elevated temperature are higher than 1Mg 2+ /CuCo 2 S 4 , which renders intercalation an unlikely mechanism, and thus ex situ XRD was carried out to study the structural change of the cathode upon cycling (Figure 5f). At the end of discharge, spinel peaks disappear and MgS, Co 9 S 8 and Cu phases are formed. This suggests a conversion reaction takes place: CuCo 2 S 4 + 2.22Mg 2+ + 4.44e -→ 2.22MgS + 0.22Co 9 S 8 + Cu (3) which gives rise to the high capacity of 350 mAh g -1 , close to the theoretical value of 384 mAh g -1 . The Mg 2+ intercalation barrier in CuCo 2 S 4 might be due to Cu ions blocking the migration tunnel in the spinel structure so that the conversion reaction is more favorable. However, multiple discharge plateaus appear in the voltage profile, indicating that several individual electrochemical processes take place and the overall mechanism is more complicated than suggested by Equation 3. At the end of charge, the Cu signal disappears and spinel CuCo 2 S 4 re-forms while MgS and Co 9 S 8 remain, suggesting that a combination of reversible and irreversible transitions are occurring, as is the case for WS-CuS. This naturally limits the charge capacity to 250 mAh g -1 , although subsequent discharge recovered almost all of that capacity (Figure S4). However, continuous cycling resulted in capacity fade. In-depth electrochemical characterization of individual processes will be the subject of future studies in order to identify the transitions mentioned above and assess their reversibility. While conversion cathodes traditionally suffer from rapid capacity fade, the direct preparation of nano-composite electrodes has been previously demonstrated as a viable technique to significantly improve the performance of many materials. [63][64][65][66] Indeed, we show here that this is the case for CuCo 2 S 4 , a novel Mg cathode material.

Conclusions:

Analysis of known Mg cathodes (TiS 2 , CuS and Ti 2 S 4 ) indicates that nano-sizing electrode materials provides several advantages due to shorter Mg 2+ pathways and increased electrodeelectrolyte contact. However, the method used to prepare nano-sized electrode materials also plays a crucial role governing overall electrochemical performance. Both intercalation materials, WS-TiS 2 and BM-Ti 2 S 4 , achieve more stable capacity retention when nano-sized since the smaller grains reduce cation trapping within the lattice and buffer the volume change during cycling. However, despite its enhanced reversibility, BM-Ti 2 S 4 delivers a lower initial capacity in comparison to bulk material. Nanosizing also benefits conversion materials, as interaction with the electrolyte is promoted and additional nucleation sites are created for phase transformation, allowing cathodes to function at lower temperatures. Optimal results are achieved when nanomaterials are synthesized directly, rather than reducing particle size of bulk material since high-energy methods such as ball milling can damage the structure of the active material and negatively impact electrochemical performance.

Despite issues with nano-sized electrodes, such as decreasing volumetric capacities and enhancing side reactions, [67,38] the current stage of Mg cathode research requires the identification of more potential compounds and the improvement of the electrochemical performance of existing cathodes. This work demonstrates that nano-sizing electrode materials prior to electrochemical characterization may be crucial so that successful candidates are not overlooked. When micron-sized CuCo 2 S 4 was prepared using conventional methods, it appears electrochemically inert at most temperatures and only delivers a low (60 mAh g -1 ) capacity at 150 °C. Ball milling to reduce particle size provides a rapid and useful technique to gain insight into the material's true potential; however, negative side-effects of this method limit the capacity attained by the nanomaterial. BM-CuCo 2 S 4 shows significantly more promising results in comparison to bulk material (delivering 180 mAh g -1 at only 60 °C), but nano-sized X-CuCo 2 S 4 prepared directly from a low temperature xanthate salt melt exhibits the best performance by far (350 and 140 mAh g -1 at 60 °C and room temperature, respectively). Thus, developing synthetic techniques to directly crystallize nano-sized sulfide materials may be critical in the discovery and design of novel Mg electrodes.

Experimental Methods:

Nano-sized TiS 2 was obtained via the wet synthesis proposed by Jeong, et al. [54] In a 100 mL round bottom flask, TiCl 4 (880 μL) was added to oleylamine (12 g) and heated to 300 °C under magnetic stirring and N 2 flow. Then CS 2 (1.56 mL) was injected into the mixture, which immediately turned black upon addition. The temperature was held at 300 °C for 15 minutes to allow for the completion of the reaction. The flask was transferred to an Ar-filled glovebox after naturally cooling to room temperature, and the product was collected by filtration and washed with butanol and a mixture of 3:1 volume ratio methanol:hexane. Nano-sized CuS was synthesized by the method reported by Pradhan, et al. [55] Typically, Cu(NO-3 ) 2 •3H 2 O (2.42 g) was dissolved in ethylene glycol (EG) (200 mL), and Na 2 S 2 O 3 (1.58 g) was then added. The mixture was stirred at room temperature for 20 minutes followed by 70 °C for four hours. After cooling to room temperature, the product was collected by filtration and washed with water and ethanol.

The synthesis of micron-sized spinel Ti 2 S 4 was described in our previous publication, [30] and mechanical ball milling was then carried out to reduce the particle size. In an Ar-filled glovebox, Ti 2 S 4 (1 g) power and acetonitrile (ACN, 1.5 mL) were added to a 15 mL ZrO 2 jar containing 5 mm ZrO 2 balls (12 g), followed by a milling period of 4 hours at 30 Hz with a Pulverisette 23 mini-miller. The solid was collected after evaporation of the ACN solvent.

Micron-sized CuCo 2 S 4 was synthesized by mixing the elements in stoichiometric ratios which were then sealed in an evacuated quartz tube and heated at 450 °C for three days. The particle size was reduced by ball milling material (200 mg) in a 15 mL ZrO 2 jar containing 5 mm ZrO 2 balls (8 g) and NMP (750 mg) at 30 Hz for two hours. Nano-sized CuCo 2 S 4 was synthesized directly through a low temperature melt of ethylxanthate salts reported by Khan et al. [62] A stoichiometric mixture of copper(I) ethylxanthate and cobalt(II) ethylxanthate was heated to 250 °C under Ar flow for one hour. The X-CuCo 2 S 4 product was transferred to an Ar-filled glovebox after naturally cooling to room temperature.

X-ray diffraction (XRD) analysis was carried out on a PANalytical Empyrean diffractometer with Cu-Kα or Co-Kα radiation. Material morphologies were examined using a Zeiss field emission scanning electron microscope (SEM) equipped with an energy dispersive X-ray spectroscopy detector (EDX). Xray photoelectron spectroscopy (XPS) was carried out on a Thermo VG Scientific ESCLab 250 instrument.

The spinel Ti 2 S 4 , layered TiS 2 and CuCo 2 S 4 cathodes were prepared in an Ar-filled glovebox by mixing the as-prepared materials with Super P and polyvinyldiene fluoride (PVDF, average Mw ~534,000) in an 8:1:1 weight ratio in N-methyl-2-pyrrolidone (NMP) and casting the slurry onto Mo foil, while a weight ratio of 6:3:1 mixed in air and a carbon paper current collector was used for the CuS material. The APC electrolyte was synthesized following the reported procedure, with tetrahydrofuran (THF) or tetraglyme (G4) as the solvent. [32,68] Magnesium metal was polished with carbide paper (Mastercraft®, 180 grit SiC) and cleaned with a Kimwipe prior to use. Coin cells (2325) with Mg counter electrodes were used for cycling studies. All cell assembly and most electrode preparation was carried out in an Ar-filled glovebox, with the exception of CuS electrodes which were prepared in air. All electrochemistry was performed with a VMP3 potentiostat/galvanostat (Bio-logic).

In-situ XRD measurements for CuS were carried out by casting the cathode slurry on a glassy carbon electrode, which was then assembled in a home-made in situ cell with APC electrolyte and Mg metal anode. The cell was cycled at 30 mA g -1 and room temperature, with XRD scans recorded operando. Each scan was 30 min, corresponding to 15 mAh g -1 capacity or Δx = 0.0268 in Mg x CuS.

Associated Content:

Table of Contents:

ToC Text:

The method of preparation of nano-sized electrode materials plays a key role in their observed electrochemistry, where optimal performance is obtained through direct nano-synthesis techniques rather than mechanical milling methods. Developing such nanosynthetic routes can lead to the discovery of novel Mg cathode materials -such as CuCo 2 S 4that might otherwise be overlooked when screening for new candidates.

ToC Figure:

ToC keyword: nano-synthesis

Figure 1 :

 1 Figure 1: XRD patterns and SEM images of nano-sized (a, b) TiS 2 and (c, d) CuS prepared using wet synthesis.

Figure 2 :

 2 Figure 2: (a, b) Voltage profiles at various current densities and (c, d) capacity retention of WS-TiS 2 at 60 °C/RT and WS-CuS at 25 °C, respectively. Room temperature data were collected using APC/THF, while capacity retention data at 60 °C were obtained with APC/G4 electrolyte.

Figure 3 :

 3 Figure 3: In situ XRD of CuS cycled in APC/THF with a Mg anode at room temperature and 30 mA g -1 current density. Red patterns correspond to the first voltage plateau and blue patterns correspond to the reversible second voltage plateau. The initial and fully discharge patterns are shown in dark red and dark blue, respectively. The appearance and disappearance of the MgS (orange), Cu 2 S (green) and Cu (pink) phases demonstrates a conversion reaction.

Figure 4 :

 4 Figure 4: Comparison between micron-sized (non-BM) and ball milled (BM) spinel Ti 2 S 4 . (a) XRD, (b) SEM, (c) Voltage profiles of the first five cycles and (d) capacity retention of Ti 2 S 4 cathodes with a Mg anode and APC/G4 electrolyte cycled at a current density of 48 mA g -1 and 60 °C.

Figure 5 :

 5 Figure 5: (a) XRD pattern and (b) SEM image of X-CuCo 2 S 4 prepared using the xanthate method. (c) XRD patterns and (d) SEM images of micron-sized CuCo 2 S 4 prepared through a solid state synthesis and then ball milled (BM) to reduce particle size. (e) Voltage profiles of X-, BM-and micron-CuCo 2 S 4 cycled at 10 mA g -1 with a Mg anode at a variety of temperatures. Room temperature (RT) and 60 °C data were collected using APC/THF while 150 °C data was collected using APC/G4 electrolyte. Squares in black, blue and orange correspond to the points where XRD patterns were collected, shown in: f) Ex situ XRD of BM-CuCo 2 S 4 cycled at 10 mA g -1 and 90 °C, demonstrating a conversion mechanism.

Acknowledgments:

This work was supported by the Joint Center for Energy Storage Research (JCESR), an Energy Innovation Hub funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences. NSERC is acknowledged by L.F.N. for a Canada Research Chair and for funding through the NSERC Discovery Grants program.

Supporting Information

The Supporting Information is available free of charge on *** website at DOI: Additional information: ***

Author Information:

Corresponding Author *lfnazar@uwaterloo.ca

Notes

The authors declare no competing financial interest