- Email: [email protected]
Design of a hydrogen sulfide gas sensor based on a photonic crystal cavity using graphene
Journal Pre-proof Design of a hydrogen sulfide gas sensor based on a photonic crystal cavity using graphene
Afrooz Afsari, Mohammad Javadian Sarraf PII:
S0749-6036(19)31553-8
DOI:
https://doi.org/10.1016/j.spmi.2019.106362
Reference:
YSPMI 106362
To appear in:
Superlattices and Microstructures
Received Date:
02 September 2019
Accepted Date:
03 December 2019
Please cite this article as: Afrooz Afsari, Mohammad Javadian Sarraf, Design of a hydrogen sulfide gas sensor based on a photonic crystal cavity using graphene, Superlattices and Microstructures (2019), https://doi.org/10.1016/j.spmi.2019.106362
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.
Journal Pre-proof
Design of a hydrogen sulfide gas sensor based on a photonic crystal cavity using graphene aIslamic
Afrooz Afsari,a Mohammad Javadian Sarraf 1,a Azad University, Mashhad Branch, Faculty of Engineering, Dep. of Electrical Engineering, Emamieh Boulevard, Mashhad, Iran
Abstract— We report the design and simulation of a high sensitivity H2S gas sensor using a combination of graphene properties as a hydrogen sulfide-sensitive nanomaterial and features of photonic crystal cavity. The shoulder-coupled resonant cavity is introduced in the photonic crystal that consists of a triangular array of air holes on the silicon-oninsulator substrate. To adsorb H2S gas, a graphene layer is deposited on the inner wall of the two cavity air holes. Changes in the concentration of hydrogen sulfide gas alter the refractive index of graphene, thereby resulting in wavelength shift in the sensor transmittance spectrum. We achieved a sensitivity of 1.2 ×104 nm /RIU and a detection limit of 1.87×10-6 RIU. To the best of our knowledge, the sensitivity of our sensor is much higher than other sensors previously reported in the literature. Keywords: Photonic crystals, Cavity resonators, Sensors, Sensitivity, Gas detectors, Q factor. 1. Introduction: Gas sensor systems play a crucial role in industries, environmental monitoring, and safety. The use of high-precision gas sensors is required in the environments where there are hazardous gases. Such example is hydrogen sulfide gas, which is a dangerous substance commonly found in refinery environments. This gas is heavier than air, highly toxic, and explosive. In addition to toxicity, hydrogen sulfide could cause the corrosion of pipelines and storage tanks [13]. Among various gas sensors, optical sensors are suitable for gas sensing owing to their unique features, such as resistance against electromagnetic interference, rapid response, performance at room temperature, and high signalto-noise ratio [4]. Photonic crystal sensors are a type of optical sensors with periodic structures of dielectric materials. This periodicity may be present in one, two, or three dimensions. One of the prominent features of photonic crystals is their band gap. A photonic band gap is defined as the frequency range wherein the light is not able to cross the crystal. When defects in the photonic crystal structure are created, the periodicity of the structure is disrupted, and defect modes are generated [5,6]. By introducing various defects in the photonic crystal, structures such as cavities, waveguides, and photonic crystal fibers could be formed [7-10]. Up until now, numerous gas sensors have been proposed based on these structures [11-14]. Photonic crystal microcavities have strong field confinement, high-quality factors, and small mode volumes, which result in their wide applications in various fields, such as lasers [15,16], optical switches [17], and sensors [18-21]. Photonic crystal cavities are highly sensitive to environmental changes due to the light confinement of the optical mode so that a small change in the environment could cause a relatively significant frequency shift in the transmittance spectrum [5]. In gases, the changes in the refractive index as a function of the concentration are often less than 10-4 RIU [22,23]. Therefore, the sensors that only operate based on the changes in the refractive index of gases are not adequately sensitive. To increase the selectivity of the sensor, a gas-sensitive material can be incorporated into the sensor [22,24]. In the present study, graphene was employed as a sulfide hydrogen-sensitive material. Graphene is a crystalline allotrope of carbon with two-dimensional properties [25]. This two-dimensional nanomaterial has numerous applications in medicine [26], electronics [27], and sensors [28,29], owing to properties such as high thermal and electrical conductivity, high density, and large surface area. The sensitivity and detection limit of the sensor designed in the current research are 1.2 ×104 nm/RIU and 1.87×10-6 RIU respectively. 2. Material and methods In the present study, an optical gas sensor system is developed consisting of three main components: an optical source, the sensor, and an optical detector. Light sources (e.g., laser sources) and detectors (e.g., OSA) are highly Corresponding author. Email Address: [email protected] 1
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sensitive, selective, and available on the market. In the current research, the designed cavity is located in the main body of the sensor system. The photonic crystal structure presented in this paper consists of a triangular array of air holes with a radius and lattice constant of 135 and 440 nm, respectively, on the silicon-on-insulator substrate. The radius of air holes at the two adjacent columns of the cavity was chosen to be 175 nm. When we set this radius to be larger than the other ones, the confinement of light inside the cavity increased .The particle swarm optimization algorithm, which is one of the optimization algorithms in the MODE Solution software, was used to optimize the radius of the cavity air holes for improvement of the quality factor. The generation size and the maximum generations in this algorithm were taken as 20 and 50, respectively. The optimum value for the radius was obtained 205 nm using this algorithm and Quality factor was improved to 5.6 × 103. This increase in radius had no Destructive effect on the sensitivity of the sensor. As shown in Fig.1, the TE band gap of this structure extends between 0.28 to 0.4 a/. In the inner wall of the two air holes around the cavity, a graphene layer is deposited (shown in red in Fig. 2) as the material sensitive to the hydrogen sulfide gas. The deposition of the graphene layer on walls of the air holes would also be possible by using the chemical vapor deposition (CVD) method. This method varies depending on what material the graphene is to be layered on. In the past few years, various studies have been conducted on the direct growth of graphene on semiconductor substrates like silicon. [30,31]. Since the sensitivity of the sensor depends on the interaction of light and matter, and the photonic crystal cavities can create strong confinement of light, thereby enhancing the sensitivity [24]. Therefore, the cavity structure in the present study is used to design the sensor, and the sensitivity of the sensor is increased by graphene coated holes in the cavity. If multiple layers of graphene are used, the quality factor and the transmittance will be reduced. With the absorbance of the molecules of the hydrogen sulfide gas onto the graphene surface, the lattice constant of graphene changes due to Van der Waals forces, thereby leading to the alterations in the dielectric constant of graphene. These changes cause a resonant wavelength shift in the transmission spectrum of the sensor. The small changes in the gas refractive index (Δn) could be detected by measuring the shift of the cavity resonance wavelength () [32]. In the present study, the 2.5 var FDTD method and Lumerical MODE Solution software were used to calculate the transmittance spectrum of the sensor. The var FDTD, takes a 3D geometry and breaks it down into a 2D set of effective indices and then solve these indices with 2D FDTD. While requiring only the memory and simulation time of a 2D FDTD, the speed and accuracy of var FDTD is comparable to that of 3D FDTD. The time step and min mesh step were taken as 0.046 fs and 0.01 nm, respectively.
Fig. 1 Band structure of the photonic crystal of this paper.
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Fig. 2 The graphene-based cavity structure designed in this article.
3. Theory/Calculation: The sensitivity of the photonic crystal gas sensors is calculated using (1): 𝑆=
𝑛
(1)
In addition to sensitivity, the detection limit is another critical parameter in the design of photonic crystal sensors. Sensitivity and detection limit are considered as two essential parameters in the design of a photonic crystal gas sensor. The detection limit is defined as the ratio of the lowest measurable wavelength shift to sensitivity: 𝐷𝐿 =
𝑚𝑖𝑛 1 1 𝑆.𝑄 𝑆
(2)
where Q is the quality factor, which is defined as the ratio of the stored energy in the cavity to the energy loss inside the cavity: 𝑆𝑡𝑜𝑟𝑒𝑑 𝑒𝑛𝑒𝑟𝑔𝑦 𝑈(𝑡) 𝑄 = 𝜔0 = 𝜔0 𝑃𝑜𝑤𝑒𝑟 𝑙𝑜𝑠𝑠 𝑃(𝑡)
(3)
where U is the electromagnetic energy stored in the resonator, and P represents the radiated power. The quality factor also is determined as [33]:
𝑄=
𝜔0
𝜔
where ω shows the full width at half maximum. As shown in Fig. 2, the light source is located at the beginning of the input waveguide, and the detector is placed at the end of the output waveguide. The sensor transmittance spectrum is the ratio of the optical power distribution shown in the display to the optical power of the source. The absorption of the hydrogen sulfide gas onto the graphene surface leads to the change in the electrical conductivity of graphene and its refractive index. Since the photonic crystal cavity is sensitive to the changes in the refractive index of its environment, this change, as well as the change in the gas reflection factor can cause a wavelength shift in the transmitted spectrum of the sensor. Sensitivity can be calculated by measuring the amount of this shift. The electrical conductivity of graphene was is using (5), which is known as the Kubo formula [34]:
3
(4)
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𝜎(𝜔, 𝜇𝑐, Γ,T) =
je2(ω - j2)
ħ2
∂𝑓𝑑( ―𝜀) ∞ ∂𝑓𝑑(𝜀) ∫0 𝜀 ∂𝜀 ― ∂𝜀 ∞ 𝑓𝑑( ―𝜀) ― 𝑓𝑑(𝜀)
[
∫0
[
(𝜔 ― 𝑗2)2
×{(
1 𝜔 ― 𝑗2)
2
]𝑑𝜀 ―
(5)
]𝑑𝜀}
where ω is the angular frequency, e shows the electron charge, ħ represents the reduced Planck constant, and fd(ε) denotes the Dirac expression distribution function, which is: 𝑓𝑑(𝜀) =
1
(6) +1 𝑒 𝐾𝐵 𝑇 where T shows the temperature, and ħ = 5 mv and μC denotes the chemical potential of the graphene. The exposure of graphene to the hydrogen sulfide gas leads to the reduction of its electrical conductivity. The refractive index and electrical conductivity of graphene are correlated with (7), as follows [35]: 𝜎 (7) 𝑛𝑔𝑟𝑎𝑝ℎ𝑒𝑛𝑒 = 1 ― 𝑗 𝜔𝜀0𝛿𝑔 (𝜀 ― 𝜇𝐶)
where ε0 shows the vacuum dielectric constant, and δg represents the thickness of the graphene layer, which is approximately 0.34 nanometer in a single layer of graphene. The concentration variation of the hydrogen sulfide gas changes the electrical conductivity coefficient of graphene [29] (Fig. 3). The optical field of the cavity is illustrated in Fig.4.
Fig. 3 The electrical conductivity of graphene vs. hydrogen sulfide concentrations [29].
Fig. 4 Electric field distribution in the cavity.
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3. Results and discussion The structure of the designed cavity is depicted in Fig. 2. At first, the sensing performance of this structure was investigated without the use of graphene. On average, the wavelength was shifted by 0.00018 nm for every 1 ppm of hydrogen sulfide gas and the sensitivity of the sensor was obtained 905 nm/RIU. Figure 5 shows the transmittance spectrum of the sensor at concentrations of 0 and 50 ppm of the hydrogen sulfide gas. Then to increase the sensitivity, a graphene layer (thickness: 0.34 nm) is coated on the inner walls of the two air holes marked in red in Fig. 2. The sensor function and wavelength shift are investigated in the transmittance spectrum of the sensor at concentrations of 2, 5, 10, 20, 40, and 50 ppm of the hydrogen sulfide gas. The transmittance spectrum of the sensor at various concentrations of the hydrogen sulfide gas is shown in Fig. 6. Accordingly, increasing the concentration of the hydrogen sulfide gas leads to the reduction of the electrical conductivity of graphene. Since the photonic crystal cavity is sensitive to the changes in the refractive index of its environment, the changes in the electrical conductivity of graphene and the subsequent alterations in the refractive index lead to a shift in the wavelength in the transmitted spectrum of the sensor. For one ppm changes in the hydrogen sulfide gas concentration, the wavelength is approximately shifted 3.6 nanometers. As can be seen in Fig. 6, there is a relationship between the increased concentration of the hydrogen sulfide gas and the shift of the transmittance spectrum towards longer wavelengths. Fig. 7 shows the correlation of the wavelength changes with the changes in the concentration of hydrogen sulfide. Based on (1), the sensitivity of the designed sensor is 1.2×104 nm/RIU. Other important parameters in the design of cavity-based sensors are the detection limit and quality factor, which are calculated to be 1.87×10-6 RIU and 5.6×103, respectively based on (2) and (3). Finally, the performance of the sensor was examined for some problems that may arise during the manufacturing process such as deposition of graphene layer at the bottom of the holes and multilayer graphene deposition on the inner walls of the air holes. As shown in Fig. 8, graphene deposition at the bottom of the holes has no effect on the sensitivity and addition of each layer of graphene reduces the quality factor by only about 1.1%. Moreover, Fig. 9 shows that as the number of graphene layers on the inner wall of the air holes increases, the sensitivity improves, but the quality factor decreases by about 10%. Table 1 shows the sensitivity and detection limit of some of the photonic crystal cavity gas sensors, which have been reported in some recent studies.
Fig. 5 The normalized transmission spectrum of sensor as a function of wavelength for 0 and 50 ppm of H2s concentrations.
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Fig. 6 The normalized transmission spectrum of PC microcavity as a function of wavelength for different H2s concentrations.
Fig. 7 Relationships of the central wavelength, to H2s concentration.
Fig. 8 The effect of the number of graphene layers deposited at the bottom of the air holes on sensitivity and quality factor.
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Fig. 9 The effect of the number of graphene layers on sensitivity and quality factor. Table 1 Comparison of the features of the published PC refractive index sensors and our optimized PC
4. Conclusion
Ref.
RI sensitivity (nm/RIU)
Detection limit (RIU)
Our optimized cavity [36] [37] [38] [11]
1.2 × 10 4
1.87 ×10−6
1054 610 363.8 575
-
1 ×10−4 -
In the present study, we designed a high-sensitivity hydrogen sulfide gas sensor based on a photonic crystal cavity using graphene. The sensor structure was developed by the removal of the column from the air holes as a waveguide and placement of two middle holes to confine light. Besides, a graphene layer was deposited on the inner wall of the two holes in the optical path. According to the obtained results, the electrical conductivity of graphene and its refractive index change with the variation of hydrogen sulfide gas concentrations. Since the photonic crystal cavity is sensitive to the changes in the refractive index of its environment, alterations in the refractive index lead to the shift of the resonant wavelength in the transmitted spectrum of the sensor. The changes in the refractive index of a specific gas, as a function of the concentration, are often less than 10-4 RIU. Therefore, the sensors that only operate based on the changes in the refractive index of gases due to their altered concentration, do not have adequate sensitivity. Gas-sensitive materials can be used to increase the sensitivity of photonic crystal gas sensors. These materials increase the sensitivity of the cavity refractive index to the gas concentration changes. In the current research, graphene was employed as a hydrogen sulfide-sensitive material, which caused the sensitivity of this sensor to be higher than the gas sensors that only operate due to the variations in the gas refractive index. The sensitivity and detection limit of the sensor are determined to be 1.2 ×104 nm/RIU and 1.87×10-6 RIU, respectively. REFERENCES: [1] [2]
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Afrooz Afsari: Conceptualization, Methodology, Software, Data curation, Writing- Original draft preparation, Writing- Reviewing, Validation, Investigation. Mohammad Javadian Sarraf: Supervision, Editing.
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Conflict of Interest and Authorship Conformation Form Please check the following as appropriate:
All authors have participated in (a) conception and design, or analysis and interpretation of the data; (b) drafting the article or revising it critically for important intellectual content; and (c) approval of the final version.
This manuscript has not been submitted to, nor is under review at, another journal or other publishing venue.
The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript
o
The following authors have affiliations with organizations with direct or indirect financial interest in the subject matter discussed in the manuscript:
Author’s name Mohammad Javadian Sarraf Afrooz Afsari
Affiliation Islamic Azad University, Mashhad Branch Islamic Azad University, Mashhad Branch
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Highlights: The shoulder coupled Photonic crystal cavity is investigated as a gas sensor. To improve the sensitivity of the sensor, a graphene layer is deposited on the inner wall of the two-cavity air holes. Changes in the electrical conductivity of graphene leads to a shift in the wavelength in the transmitted spectrum of the sensor.
Afrooz Afsari, Mohammad Javadian Sarraf PII:
S0749-6036(19)31553-8
DOI:
https://doi.org/10.1016/j.spmi.2019.106362
Reference:
YSPMI 106362
To appear in:
Superlattices and Microstructures
Received Date:
02 September 2019
Accepted Date:
03 December 2019
Please cite this article as: Afrooz Afsari, Mohammad Javadian Sarraf, Design of a hydrogen sulfide gas sensor based on a photonic crystal cavity using graphene, Superlattices and Microstructures (2019), https://doi.org/10.1016/j.spmi.2019.106362
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.
Journal Pre-proof
Design of a hydrogen sulfide gas sensor based on a photonic crystal cavity using graphene aIslamic
Afrooz Afsari,a Mohammad Javadian Sarraf 1,a Azad University, Mashhad Branch, Faculty of Engineering, Dep. of Electrical Engineering, Emamieh Boulevard, Mashhad, Iran
Abstract— We report the design and simulation of a high sensitivity H2S gas sensor using a combination of graphene properties as a hydrogen sulfide-sensitive nanomaterial and features of photonic crystal cavity. The shoulder-coupled resonant cavity is introduced in the photonic crystal that consists of a triangular array of air holes on the silicon-oninsulator substrate. To adsorb H2S gas, a graphene layer is deposited on the inner wall of the two cavity air holes. Changes in the concentration of hydrogen sulfide gas alter the refractive index of graphene, thereby resulting in wavelength shift in the sensor transmittance spectrum. We achieved a sensitivity of 1.2 ×104 nm /RIU and a detection limit of 1.87×10-6 RIU. To the best of our knowledge, the sensitivity of our sensor is much higher than other sensors previously reported in the literature. Keywords: Photonic crystals, Cavity resonators, Sensors, Sensitivity, Gas detectors, Q factor. 1. Introduction: Gas sensor systems play a crucial role in industries, environmental monitoring, and safety. The use of high-precision gas sensors is required in the environments where there are hazardous gases. Such example is hydrogen sulfide gas, which is a dangerous substance commonly found in refinery environments. This gas is heavier than air, highly toxic, and explosive. In addition to toxicity, hydrogen sulfide could cause the corrosion of pipelines and storage tanks [13]. Among various gas sensors, optical sensors are suitable for gas sensing owing to their unique features, such as resistance against electromagnetic interference, rapid response, performance at room temperature, and high signalto-noise ratio [4]. Photonic crystal sensors are a type of optical sensors with periodic structures of dielectric materials. This periodicity may be present in one, two, or three dimensions. One of the prominent features of photonic crystals is their band gap. A photonic band gap is defined as the frequency range wherein the light is not able to cross the crystal. When defects in the photonic crystal structure are created, the periodicity of the structure is disrupted, and defect modes are generated [5,6]. By introducing various defects in the photonic crystal, structures such as cavities, waveguides, and photonic crystal fibers could be formed [7-10]. Up until now, numerous gas sensors have been proposed based on these structures [11-14]. Photonic crystal microcavities have strong field confinement, high-quality factors, and small mode volumes, which result in their wide applications in various fields, such as lasers [15,16], optical switches [17], and sensors [18-21]. Photonic crystal cavities are highly sensitive to environmental changes due to the light confinement of the optical mode so that a small change in the environment could cause a relatively significant frequency shift in the transmittance spectrum [5]. In gases, the changes in the refractive index as a function of the concentration are often less than 10-4 RIU [22,23]. Therefore, the sensors that only operate based on the changes in the refractive index of gases are not adequately sensitive. To increase the selectivity of the sensor, a gas-sensitive material can be incorporated into the sensor [22,24]. In the present study, graphene was employed as a sulfide hydrogen-sensitive material. Graphene is a crystalline allotrope of carbon with two-dimensional properties [25]. This two-dimensional nanomaterial has numerous applications in medicine [26], electronics [27], and sensors [28,29], owing to properties such as high thermal and electrical conductivity, high density, and large surface area. The sensitivity and detection limit of the sensor designed in the current research are 1.2 ×104 nm/RIU and 1.87×10-6 RIU respectively. 2. Material and methods In the present study, an optical gas sensor system is developed consisting of three main components: an optical source, the sensor, and an optical detector. Light sources (e.g., laser sources) and detectors (e.g., OSA) are highly Corresponding author. Email Address: [email protected] 1
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sensitive, selective, and available on the market. In the current research, the designed cavity is located in the main body of the sensor system. The photonic crystal structure presented in this paper consists of a triangular array of air holes with a radius and lattice constant of 135 and 440 nm, respectively, on the silicon-on-insulator substrate. The radius of air holes at the two adjacent columns of the cavity was chosen to be 175 nm. When we set this radius to be larger than the other ones, the confinement of light inside the cavity increased .The particle swarm optimization algorithm, which is one of the optimization algorithms in the MODE Solution software, was used to optimize the radius of the cavity air holes for improvement of the quality factor. The generation size and the maximum generations in this algorithm were taken as 20 and 50, respectively. The optimum value for the radius was obtained 205 nm using this algorithm and Quality factor was improved to 5.6 × 103. This increase in radius had no Destructive effect on the sensitivity of the sensor. As shown in Fig.1, the TE band gap of this structure extends between 0.28 to 0.4 a/. In the inner wall of the two air holes around the cavity, a graphene layer is deposited (shown in red in Fig. 2) as the material sensitive to the hydrogen sulfide gas. The deposition of the graphene layer on walls of the air holes would also be possible by using the chemical vapor deposition (CVD) method. This method varies depending on what material the graphene is to be layered on. In the past few years, various studies have been conducted on the direct growth of graphene on semiconductor substrates like silicon. [30,31]. Since the sensitivity of the sensor depends on the interaction of light and matter, and the photonic crystal cavities can create strong confinement of light, thereby enhancing the sensitivity [24]. Therefore, the cavity structure in the present study is used to design the sensor, and the sensitivity of the sensor is increased by graphene coated holes in the cavity. If multiple layers of graphene are used, the quality factor and the transmittance will be reduced. With the absorbance of the molecules of the hydrogen sulfide gas onto the graphene surface, the lattice constant of graphene changes due to Van der Waals forces, thereby leading to the alterations in the dielectric constant of graphene. These changes cause a resonant wavelength shift in the transmission spectrum of the sensor. The small changes in the gas refractive index (Δn) could be detected by measuring the shift of the cavity resonance wavelength () [32]. In the present study, the 2.5 var FDTD method and Lumerical MODE Solution software were used to calculate the transmittance spectrum of the sensor. The var FDTD, takes a 3D geometry and breaks it down into a 2D set of effective indices and then solve these indices with 2D FDTD. While requiring only the memory and simulation time of a 2D FDTD, the speed and accuracy of var FDTD is comparable to that of 3D FDTD. The time step and min mesh step were taken as 0.046 fs and 0.01 nm, respectively.
Fig. 1 Band structure of the photonic crystal of this paper.
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Fig. 2 The graphene-based cavity structure designed in this article.
3. Theory/Calculation: The sensitivity of the photonic crystal gas sensors is calculated using (1): 𝑆=
𝑛
(1)
In addition to sensitivity, the detection limit is another critical parameter in the design of photonic crystal sensors. Sensitivity and detection limit are considered as two essential parameters in the design of a photonic crystal gas sensor. The detection limit is defined as the ratio of the lowest measurable wavelength shift to sensitivity: 𝐷𝐿 =
𝑚𝑖𝑛 1 1 𝑆.𝑄 𝑆
(2)
where Q is the quality factor, which is defined as the ratio of the stored energy in the cavity to the energy loss inside the cavity: 𝑆𝑡𝑜𝑟𝑒𝑑 𝑒𝑛𝑒𝑟𝑔𝑦 𝑈(𝑡) 𝑄 = 𝜔0 = 𝜔0 𝑃𝑜𝑤𝑒𝑟 𝑙𝑜𝑠𝑠 𝑃(𝑡)
(3)
where U is the electromagnetic energy stored in the resonator, and P represents the radiated power. The quality factor also is determined as [33]:
𝑄=
𝜔0
𝜔
where ω shows the full width at half maximum. As shown in Fig. 2, the light source is located at the beginning of the input waveguide, and the detector is placed at the end of the output waveguide. The sensor transmittance spectrum is the ratio of the optical power distribution shown in the display to the optical power of the source. The absorption of the hydrogen sulfide gas onto the graphene surface leads to the change in the electrical conductivity of graphene and its refractive index. Since the photonic crystal cavity is sensitive to the changes in the refractive index of its environment, this change, as well as the change in the gas reflection factor can cause a wavelength shift in the transmitted spectrum of the sensor. Sensitivity can be calculated by measuring the amount of this shift. The electrical conductivity of graphene was is using (5), which is known as the Kubo formula [34]:
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(4)
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𝜎(𝜔, 𝜇𝑐, Γ,T) =
je2(ω - j2)
ħ2
∂𝑓𝑑( ―𝜀) ∞ ∂𝑓𝑑(𝜀) ∫0 𝜀 ∂𝜀 ― ∂𝜀 ∞ 𝑓𝑑( ―𝜀) ― 𝑓𝑑(𝜀)
[
∫0
[
(𝜔 ― 𝑗2)2
×{(
1 𝜔 ― 𝑗2)
2
]𝑑𝜀 ―
(5)
]𝑑𝜀}
where ω is the angular frequency, e shows the electron charge, ħ represents the reduced Planck constant, and fd(ε) denotes the Dirac expression distribution function, which is: 𝑓𝑑(𝜀) =
1
(6) +1 𝑒 𝐾𝐵 𝑇 where T shows the temperature, and ħ = 5 mv and μC denotes the chemical potential of the graphene. The exposure of graphene to the hydrogen sulfide gas leads to the reduction of its electrical conductivity. The refractive index and electrical conductivity of graphene are correlated with (7), as follows [35]: 𝜎 (7) 𝑛𝑔𝑟𝑎𝑝ℎ𝑒𝑛𝑒 = 1 ― 𝑗 𝜔𝜀0𝛿𝑔 (𝜀 ― 𝜇𝐶)
where ε0 shows the vacuum dielectric constant, and δg represents the thickness of the graphene layer, which is approximately 0.34 nanometer in a single layer of graphene. The concentration variation of the hydrogen sulfide gas changes the electrical conductivity coefficient of graphene [29] (Fig. 3). The optical field of the cavity is illustrated in Fig.4.
Fig. 3 The electrical conductivity of graphene vs. hydrogen sulfide concentrations [29].
Fig. 4 Electric field distribution in the cavity.
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3. Results and discussion The structure of the designed cavity is depicted in Fig. 2. At first, the sensing performance of this structure was investigated without the use of graphene. On average, the wavelength was shifted by 0.00018 nm for every 1 ppm of hydrogen sulfide gas and the sensitivity of the sensor was obtained 905 nm/RIU. Figure 5 shows the transmittance spectrum of the sensor at concentrations of 0 and 50 ppm of the hydrogen sulfide gas. Then to increase the sensitivity, a graphene layer (thickness: 0.34 nm) is coated on the inner walls of the two air holes marked in red in Fig. 2. The sensor function and wavelength shift are investigated in the transmittance spectrum of the sensor at concentrations of 2, 5, 10, 20, 40, and 50 ppm of the hydrogen sulfide gas. The transmittance spectrum of the sensor at various concentrations of the hydrogen sulfide gas is shown in Fig. 6. Accordingly, increasing the concentration of the hydrogen sulfide gas leads to the reduction of the electrical conductivity of graphene. Since the photonic crystal cavity is sensitive to the changes in the refractive index of its environment, the changes in the electrical conductivity of graphene and the subsequent alterations in the refractive index lead to a shift in the wavelength in the transmitted spectrum of the sensor. For one ppm changes in the hydrogen sulfide gas concentration, the wavelength is approximately shifted 3.6 nanometers. As can be seen in Fig. 6, there is a relationship between the increased concentration of the hydrogen sulfide gas and the shift of the transmittance spectrum towards longer wavelengths. Fig. 7 shows the correlation of the wavelength changes with the changes in the concentration of hydrogen sulfide. Based on (1), the sensitivity of the designed sensor is 1.2×104 nm/RIU. Other important parameters in the design of cavity-based sensors are the detection limit and quality factor, which are calculated to be 1.87×10-6 RIU and 5.6×103, respectively based on (2) and (3). Finally, the performance of the sensor was examined for some problems that may arise during the manufacturing process such as deposition of graphene layer at the bottom of the holes and multilayer graphene deposition on the inner walls of the air holes. As shown in Fig. 8, graphene deposition at the bottom of the holes has no effect on the sensitivity and addition of each layer of graphene reduces the quality factor by only about 1.1%. Moreover, Fig. 9 shows that as the number of graphene layers on the inner wall of the air holes increases, the sensitivity improves, but the quality factor decreases by about 10%. Table 1 shows the sensitivity and detection limit of some of the photonic crystal cavity gas sensors, which have been reported in some recent studies.
Fig. 5 The normalized transmission spectrum of sensor as a function of wavelength for 0 and 50 ppm of H2s concentrations.
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Fig. 6 The normalized transmission spectrum of PC microcavity as a function of wavelength for different H2s concentrations.
Fig. 7 Relationships of the central wavelength, to H2s concentration.
Fig. 8 The effect of the number of graphene layers deposited at the bottom of the air holes on sensitivity and quality factor.
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Fig. 9 The effect of the number of graphene layers on sensitivity and quality factor. Table 1 Comparison of the features of the published PC refractive index sensors and our optimized PC
4. Conclusion
Ref.
RI sensitivity (nm/RIU)
Detection limit (RIU)
Our optimized cavity [36] [37] [38] [11]
1.2 × 10 4
1.87 ×10−6
1054 610 363.8 575
-
1 ×10−4 -
In the present study, we designed a high-sensitivity hydrogen sulfide gas sensor based on a photonic crystal cavity using graphene. The sensor structure was developed by the removal of the column from the air holes as a waveguide and placement of two middle holes to confine light. Besides, a graphene layer was deposited on the inner wall of the two holes in the optical path. According to the obtained results, the electrical conductivity of graphene and its refractive index change with the variation of hydrogen sulfide gas concentrations. Since the photonic crystal cavity is sensitive to the changes in the refractive index of its environment, alterations in the refractive index lead to the shift of the resonant wavelength in the transmitted spectrum of the sensor. The changes in the refractive index of a specific gas, as a function of the concentration, are often less than 10-4 RIU. Therefore, the sensors that only operate based on the changes in the refractive index of gases due to their altered concentration, do not have adequate sensitivity. Gas-sensitive materials can be used to increase the sensitivity of photonic crystal gas sensors. These materials increase the sensitivity of the cavity refractive index to the gas concentration changes. In the current research, graphene was employed as a hydrogen sulfide-sensitive material, which caused the sensitivity of this sensor to be higher than the gas sensors that only operate due to the variations in the gas refractive index. The sensitivity and detection limit of the sensor are determined to be 1.2 ×104 nm/RIU and 1.87×10-6 RIU, respectively. REFERENCES: [1] [2]
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Afrooz Afsari: Conceptualization, Methodology, Software, Data curation, Writing- Original draft preparation, Writing- Reviewing, Validation, Investigation. Mohammad Javadian Sarraf: Supervision, Editing.
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All authors have participated in (a) conception and design, or analysis and interpretation of the data; (b) drafting the article or revising it critically for important intellectual content; and (c) approval of the final version.
This manuscript has not been submitted to, nor is under review at, another journal or other publishing venue.
The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript
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Author’s name Mohammad Javadian Sarraf Afrooz Afsari
Affiliation Islamic Azad University, Mashhad Branch Islamic Azad University, Mashhad Branch
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Highlights: The shoulder coupled Photonic crystal cavity is investigated as a gas sensor. To improve the sensitivity of the sensor, a graphene layer is deposited on the inner wall of the two-cavity air holes. Changes in the electrical conductivity of graphene leads to a shift in the wavelength in the transmitted spectrum of the sensor.