Design of low loss suspended Silicon waveguide and high Q photonic crystal cavity for use as a photoacoustic gas sensor

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Absorption spectroscopy is an old well-known technique, that studies the interaction between electromagnetic waves and matter. This interaction allows discovering the optical, electronic, and chemical properties of a material, such as refractive index, conductivity, and energy levels. While microwave, infrared, UV, and visible spectroscopy are commercially used for a long time, THz spectroscopy is only starting to emerge as a result of recent improvements in the availability of power sources and better detection techniques. The THz low energy (0.41-41.5 meV) is able to probe the rotational energy levels of polar molecules or low energy vibrational levels of flexible molecules (figure I.3.1). These molecular excitations are represented by a specific resonance frequency which is unique to each molecule and called its “fingerprint”. This technique is used to measure the transmitted signal intensity of a broadband or a tunable monochromatic source through a test sample.


Before being used in spectroscopic techniques, the photoacoustic (PA) effect was discovered in 1880 by Bell when he demonstrates the first optical telecommunication system the photophone [57]. The schematic of Bell’s photophone experiment is illustrated in figure I.4.1. He uses a thin glass metalized disk to reflect the sunlight toward a selenium cell connected to a telephone receiver. The thin disk would bend and vibrate under the effect of the speaker’s sound wave. The sunlight reflected on the disk surface is then modulated in response to the vibrations of the disk. A telephone receiver allows finally to hear the voice from the modulated light collected by the selenium cell.
It took almost 90 more years for this discovery to find its true potential as a spectroscopic tool. Thanks to the demonstration of laser sources in 1960 [58], that photoacoustic was applied for the detection of water vapor and CO2 gas molecules in 1968 [59]. As described previously in section I.3 an atomic or molecular system is excited, by going from the ground ( ) to a higher energy state ( ) following the interaction with an electromagnetic wave of ℎ photon energy. This excitation phenomenon is followed by two principal relaxation processes, radiative and non-radiative relaxation. The radiative relaxation is related to stimulated or spontaneous emission, while the non-radiative one is mainly manifesting itself as heat generation caused by molecular collisions. THz energy corresponds to the excitation of rotational and vibrational energy levels. At these energy levels, the non-radiative relaxation process is dominant. When the light interacting with molecules is modulated, a pressure acoustic wave is generated resulting from the periodic heat dissipation of the relaxation process. Therefore, in contrast to the direct absorption spectroscopy, which measures the intensity of light absorbed by the excited molecules, this technique with zero background measures the pressure wave created by the molecules’ response. In absorption spectroscopy, the attenuation of the transmitted light isn’t only limited by the molecular absorbance, but it is also the result of the experimental setup absorption and reflection losses, such as the one caused by the cell windows. In addition to this, a direct measurement of the transmitted light is sometimes accompanied by the detection of black body radiations. Therefore, to eliminate all these undesired effects a background correction is necessary, by measuring the transmitted signal in absence of gas molecules. However, the detection of the acoustical signal in the PAS technique is only attributed to the molecular absorption resulting in a zero background measurement.
The THz photoacoustic spectroscopy is illustrated in figure I.4.2. A modulated THz light is absorbed by the gas molecules, followed by a nonradiative relaxation process leading to the generation of periodic heat waves. The produced heat is then detected as an acoustic wave using a microphone.

Dielectric THz waveguide

As opposed to metallic waveguides, dielectric ones do not depend on metallic reflectivity, but rather on the total internal reflection between two dielectric materials with different refractive indices = √ . Dielectric waveguides were first used in the optical domain, then extended for the first time to mmW in 1958 [80]. The investigations of dielectric waveguides in the mmW region continue in the 1970s and 1980s [81]–[83], until the 1990s when the THz region was reached for the first time [84]. The main advantage of dielectric waveguide over metallic ones is obviously the absence of conduction losses. The propagation losses in such structures are governed by material absorption loss and radiative loss. For high modal confinement and low loss propagation THz waveguide, materials with large refractive index contrast and low losses are necessary to form the core and cladding of the waveguide. At THz frequencies, the available material systems that combine high index, transparency, and planar processing are limited. In recent years the use of HR-Si for THz applications has attracted considerable interest, due to its very low absorption coefficient and large non-dispersive refractive index [85], [86]. The Silicon-on-glass waveguides shown in figure I.5.2 (a), presented by Ranjkesh et al. [87], 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 was found to be 0.63, 0.28, and 0.53 dB/cm, for 55-65, 90-110, and 140-170 GHz bands. At frequencies beyond 400 GHz, the absorption of the glass substrate material increases dramatically [86], [88] and it becomes useless for guiding purposes. To avoid material losses, [89] proposes a layout where the glass is locally etched and the guiding layer is suspended by Silicon supporting beams (SB). A schematic of this suspended Si waveguide on a glass substrate is presented in figure I.5.2(b). An average loss of 0.54 dB/cm 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 is still required. Other types of dielectric waveguides known as line defect PhC or slab waveguides were also reported. The guiding principle of a line defect PhC waveguide is quite similar to the previously presented ridge waveguide. However, instead of only using the refractive index contrast between two different materials such as air/HR-Si or glass/HR-Si, it also uses the bandgap properties of a PhC for guiding purposes. Periodic holes are etched in the HR-Si on both sides of the guiding channel to create a cladding with an effective index lower than the refractive index of the HR-Si representing the core of the waveguide. The PhC and PhC cavities will be the main topics of the discussion in the following section. Figure I.5.2 (c) shows the schematic of a line defect PhC waveguide design proposed by [90].


Photonic crystal THz cavities

One of the greatest advantages of a PhC is its ability to behave like an optical cavity and traps photon at a precise energy for very long times. A PhC cavity is the result of a point defect introduced into the geometry of a perfect periodic PhC. The defect can be created in several ways as removing a hole from the periodic structure, shifting the position of the holes, changing the filling material of the holes… By breaking the periodicity of the structure, a resonant cavity mode appears inside the photonic bandgap. Such characteristics make the PhC useful for many applications: lasing, light-matter strong coupling, sensing … In this work we are interested in designing a PhC cavity on top of a HR-Si waveguide to confine the THz energy at the absorption peak of a gas molecule for very long time. This allows to increase the light-molecule effective length interaction and thus increase the sensitivity of the designed gas sensor. The trapped photon lifetime is described by the cavity quality factor expressed by: = 0 (I.5.3) with 0 = 2 0 the angular frequency of the resonant trapped mode. For a long photon lifetime, it is then necessary to design cavities with a high Q factor. 2D slab (etched membrane) and 1D wire (etched waveguide) photonic crystal cavities are highly studied in the visible, near, and mid-infrared [97]–[109]. Because of the fabrication simplicity at the millimetric wavelength scale, 2D and 3D PhC cavities were reported in the 10-110 GHz frequency range [110]–[114]. At THz frequencies, high Q PhC cavities are less explored and this is due to the limited availability of low loss material in this frequency range. 2D metal-coated dielectric slab photonic crystal cavities were reported in [115], [116]. These structures suffer from high metal ohmic losses and present low quality factors less than 140. Thanks to the low loss of high resistivity silicon several 2D slab PhC cavities with highest quality factors up to Q≈10800 were presented in [117]–[120]. Aside from [121], 1D wire photonic crystal cavities were very little investigated in the THz region. In [121] a Q of 11900 was measured for a resonant defect mode at a frequency of 100 GHz. A review of some available THz photonic crystal cavities and their performances is presented in table I.5.2. In this work, we present a 1D-wire PhC cavity with ultra-high Q factors for a resonant defect mode trapped in an air hole of the PhC. The frequency of the confined mode is adjusted to overlap with an absorption peak of a gas molecule. Therefore, the interaction between the gas molecules and the THz light is enhanced to finally increase the sensitivity of the proposed gas sensor.

Table of contents :

Résumé et contenu de la thèse
Summary and thesis content
List of abbreviations
List of Figures
List of tables
Chapter I: Introduction
I.1. Introduction on Terahertz (THz) waves:
I.2. THz for food
I.3. THz absorption spectroscopy
I.3.1. Molecular absorption
I.4. THz photoacoustic spectroscopy
I.4.1. Molecular relaxation and heat production
I.4.2. Local heat production into acoustic wave generation
I.4.3. Acoustical signal amplitude and PA sensitivity
I.4.4. Cylindrical acoustical resonators
I.4.5. Pressure wave detection: microphones, cantilevers, and quartz tuning forks
I.5. THz components
I.5.1. THz waveguides
I.5.1.1 Metallic THz waveguide
I.5.1.1 Dielectric THz waveguide
I.5.2. Photonic crystal
I.5.2.1 Photonic crystal THz cavities
I.6. Conclusion of this chapter
I.7. References
Chapter II: Design of low loss suspended Silicon waveguide and high Q photonic crystal cavity for use as a photoacoustic gas sensor
II.1. Triple resonator photoacoustic gas sensor
II.2. Waveguide design
II.2.1 Modal analysis
II.2.2 Anchors and bends losses
II.2.2.1 Anchors losses
II.2.2.2 90° bend loss
II.2.3 Coupling and Insertion losses
II.3. 2 Photonic crystal cavity design
II.3.1 Solid/photonic crystal approach and photonic band gap
II.3.2 Photonic band gap design
II.3.2 Photonic crystal cavity: Quality factor and modal volume
II.3.3 Photonic crystal cavity design using FEM
II.3.3 Photonic crystal cavity design and quality factor calculation using FDTD
II.4. Conclusion of this chapter
II.5. References
Chapter III: Experimental setups and methods
III.1. Fabrication process
III.2. THz electromagnetic characterization
III.2.1. S parameters extraction using Vector Network Analyzer (VNA)
III.2.2. THz Time-Domain Spectroscopy (THz-TDS)
III.2.3. Setups used for THz transmission measurements and mode imaging using AMC VDI source
III.3. Mechanical characterization
III.3.1. Laser Doppler Vibrometer (LDV)
III.3.2. Modulated blue laser for membrane’s mechanical modes optical excitation
III.3.3. Focused Ion Beam (FIB) and Scanning Electron Beam (SEM)
III.4. Conclusion of this chapter
III.5. References
Chapter IV: Experimental characterization results
IV.1. Waveguide propagation loss
IV.1.1 Cut-back method for total propagation losses extraction
IV.1.2 Anchors, bends, and material loss
IV.1.4 Insertion losses: Metallic waveguide/Si taper transition
IV.2. Waveguide multimodal analysis (TDS measurements)
IV.3. Photonic crystals
IV.3.1 Bragg reflectors and bandgaps
IV.3.2 High-Quality factor cavities
IV.3.3 High transmittance cavities
IV.3.4 650 GHz cavities
IV.4. Pt layer deposition on Poly-Si membranes
IV.5. Poly-Si membrane resonance frequency at atmospheric pressure
IV.6. Poly-Si membrane resonance frequency at low pressures
IV.7. Conclusion of this chapter
IV.8. References
Chapter V: H2S photoacoustic detection with a poly-Si membrane
V.1. Gas cell design
V.2. Experimental setup
V.3. Poly-Si membrane dynamics
V.4. Detection of pure H2S with two different THz alignments
V.5. The H2S absorption spectrum in the range 620-690 GHz
V.6. Detection limit
V.7. SNR of three different THz alignments
V.8. Conclusion of this chapter
V.9. References
Conclusion and perspectives
List of publications


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