Atomistic mechanism for graphene based gaseous sensor working

Applied Surface Science 470 (2019) 448–453

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Atomistic mechanism for graphene based gaseous sensor working a

b

Hui-Fen Zhang , Dong-Ping Wu , Xi-Jing Ning a b

a,⁎

T

Applied Ion Beam Physics Laboratory, Institute of Modern Physics, Fudan University, Shanghai 200433, China State Key Laboratory of ASIC & System, Fudan University, Shanghai 200433, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Graphene gaseous sensor Mechanism Diffusion model

Graphene based gaseous sensor has been shown experimentally to have high potential for detecting gas molecules by measuring the conductance change as induced by the adsorbed molecules on graphene. Currently, there is no atomistic based theoretical model that is able to adequately explain the working of the sensor. Based on a single-atom statistical model, the kinetics of adsorption and desorption of gas molecules on graphene was investigated in the present work, and an atomistic mechanism for the functioning of the sensor is proposed which relies on the change of the conductance when the adsorbed molecules diffuse into the defective sites. This mechanism is in agreement with previous experimental measurements and indicates some possible ways to increase the sensitivity and response speed of the sensor.

1. Introduction Graphene based gaseous sensor (GBGS) paves the way for detecting gas molecules with higher sensitivity and faster response because of the high carrier mobility and single atomic thickness of graphene, which accounts for sensitive change of the conductance induced by adsorbed molecules on graphene sheet [1]. Actually, a large number of experiments have showed that GBGS is sensitive to a small amount of various molecules, such as H2O, CO, NO, NO2, NH3 and so on [1,2]. It is worthy to note that the detection limit in different experiments ranges from partial-per-million (ppm) up to partial-per-trillion (ppt) [3–5] and the response time disperses between tens of seconds and thousands of minutes [6,7]. Yang et al. reported that the response rate for detecting acetone molecules can be significantly sped up by ten times with ultraviolet irradiating the graphene sheet [8] and recently, Ricciardella et al. showed that the response rate to NO2 with the graphene sample prepared by mechanical exfoliation is five times faster than the one by chemical vapor deposition, which indicates that graphene sample with fewer defects works better than the ones of more defects [9]. However, some experiments suggest that preparing more defects in the graphene sheet will enhance the response rate and sensitivity [5,10]. In addition, it was observed that the response rate increases with the temperature of graphene sheet [6,11]. Obviously, for achieving higher sensitivity and faster response it is highly desired to develop a theoretical model on atomic level for understanding how these factors affect the conductance change of graphene. To our best knowledge, very limited theoretical work concerns the

⁎

above issue except the one that considers the conductance change of graphene is proportional to the fractional coverage of the sheet covered by the target molecules [12,13]. The authors employed Langmuir model of adsorption and desorption to derive the equation on the fractional coverage as the function of time, but found the derived results do not coincide with the experiments [12,13]. Clearly, this theoretical work cannot also explain why the sensitivity of GBGS can be enhanced by the defects of graphene. For understanding the mechanism for GBGS working extensively, we have to calculate exactly the rate of adsorption and desorption of gas molecules on graphene sheet, to which transition state theory (TST) can be applied in principle. However, there exist some artificial parameters in TST leading to the calculated results deviating in a very large range [14]. Compared to TST, a single-atom statistical model [14] works without any artificial factors and its accuracy has been proved by many examples [14–18]. So in the present work, the single-atom statistical model was employed to calculate the rate for the adsorption and desorption of gas molecules on graphene surface and the results show that the coverage of the sheet would reach saturation within tens of microseconds under common experimental conditions. Obviously, this result denies the assumption that the conductance change of graphene is proportional to the fractional coverage of gas molecules on graphene surface. Based on this fact, a model for GBGS working is suggested as that the gaseous molecules initially landing on the graphene sheet diffuse into defective sites where they form clusters and contribute to the conductance change. This model can explain nearly all the experimental phenomena and coincides with previous calculations on the

Corresponding author. E-mail addresses: [email protected] (H.-F. Zhang), [email protected] (D.-P. Wu), [email protected] (X.-J. Ning).

https://doi.org/10.1016/j.apsusc.2018.11.149 Received 10 October 2018; Received in revised form 12 November 2018; Accepted 19 November 2018 Available online 20 November 2018 0169-4332/ © 2018 Elsevier B.V. All rights reserved.

Applied Surface Science 470 (2019) 448–453

H.-F. Zhang et al.

where

δt =

m

∫x

x0 +d

dx / 2(ε − V (x ))

(5)

0

with V (x ) being the potential felt by the molecule. As the result, the desorption rate for an adsorbed molecule is

t rd = = Δt

1 Zd

(∫

∞ Ed

εe

− ε

kB Td dε

)

2

ε

∞ ∫Ed (δt ) ε e− kB Td dε

(6)

For an unit area of the surface, the number of the adsorbed moleθ cules is N = S , so the total desorption rate for all the adsorbed molecules reads

Fig. 1. The adsorption and desorption potential energy of a gas molecule on graphene surface.

Rd = rd · conductance of graphene affected by adsorbed molecules [19].

θ S

According to obtained as

(7) dN dt

= Ra − Rd , the rate of fractional coverage (RFC) is

2. Kinetics of the adsorption and desorption

kB Tg 1 dθ · =n dt 2πm Za

Understanding the kinetics of adsorption and desorption of gas molecules on graphene surface is the key to understand the mechanism for GBGS working. Although the TST can be applied in principle to calculate the rate of adsorption and desorption of gas molecules on graphene surface, the calculated results depend too much on some artificial parameters in TST [14]. Usually, Arrhenius law ν0 e−E / kB T is applied instead of TST. However, the attempting frequency ν0 cannot be determined accurately. In previous literatures, ν0 is frequently set in a range of 1011–1013/s, which obviously results in very different desorption rate. According to the single-atom statistical model [14], the Maxwell velocity distribution for ideal gas molecules, or the kinetic energy distribution ε1/2e−ε / kB T , holds still exactly for molecules in condensed gas, liquid or solid, so the adsorption rate for realistic gaseous molecules with mass m and number density n at temperature Tg overcoming the barrier Ea [Fig. 1] and landing on an unit area of a surface is

Rc = n

kB Tg

1 2πm Za ·

∫E

∞

εe

−

ε kB Tg dε

ε e kB Tg dε and kB is the Boltzmann constant. On the where Za = ∫ adsorption, a single molecule would occupy an area of S on the surface, resulting in an effective adsorption area (1 − θ ), where θ is the fractional coverage of the surface, and the total adsorption rate per unit area reads kB Tg

1 2πm Za

Ra = (1 − θ)·n

·

∫E

Eb

a

εe

−

ε kB Tg dε

εe

ε kB Tg dε ·S·(1

− θ) −

1 Zd

(∫

∞ Ed

εe

− ε

kB Td dε ε

2

) ·θ

∞ ∫Ed (δt ) ε e− kB Td dε

This equation shows that RFC is a complicated function of time depending on n, m, Ea, Eb, Ed, d, Tg, Td and S. Specifically, RFC is nearly proportional to n, S and m−1/2, while S and m change in a small range, about 10 Å2 and 100 atomic unit, respectively, and therefore have little effects on RFC. Under common experimental conditions, Tg = 300 K, so we need only examine the influence of n, Ea, Eb, Ed, d, and Td on RFC. Previous study has indicated that for most molecules approaching to graphene surface, the Ea is nearly to zero [20] and the value of d for various molecules should be in a small range of 1–4 Å, which leads to small difference in RFC according to Eq. (5). Consequently, RFC and therefore the time for the balance of the adsorption and desorption (TBAD) as well as the saturated area θS covered by the target molecules are mainly dependent on n, Eb, Ed and Td. To examine the dependence of TBAD and θS upon Ed and Td, the calculations using Eq. (8) were performed with Ea = 0 eV, Eb = 0.01 eV, m = 5 × 10−23 g (a molar mass of 30), d = 3 Å, S = 10 Å2 and n = 2.5 × 1015 atoms/cm3, corresponding to a gas concentration of 100 ppm. As shown in Fig. 2, the θS increases exponentially with increasing of Ed in a range of 0.2–0.8 eV. As an example, for Td = 300 K, the θS increases from 4.71 × 10−8 up to 9.37 × 10−2 as Ed increases from 0.2 to 0.6 eV and gradually approaches to 1 with further increasing of Ed. Previous theoretical results show that for smaller gas

(1)

a

a

−

(8)

− ε

∞ 0

∫E

Eb

(2)

where Eb is introduced for considering the fact that the molecules with kinetic energy larger than Eb will immediately escape from the surface just after its colliding with the surface. On the desorption of a molecule on graphene surface at temperature Td, according to the single-atom statistical model [14], the total period for the molecule with kinetic energy ε larger than Ed within a time unit is

t=

1 Zd

∫E

∞

εe

− ε kB Td dε

d

∞

(3)

− ε ε e kB Td dε

with Td the temperature of the surface inwhere Zd = ∫0 stead of the one of the gas. The averaged time for a molecule located at x0 with ε > Ed moving along the x direction by a distance d to escape from the potential valley [Fig. 1] is ε

Δt =

∞ ∫Ed (δt ) ε e− kB Td dε ∞ Ed

∫

εe

Fig. 2. Function of TBAD (inset is the saturated fractional coverage θS ) on the desorption energy Ed with desorption temperature Td = 300 K, 400 K and 500 K for given gas concentration of 100 ppm.

− ε

kB Td dε

(4) 449

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3. The mechanism for GBGS working

molecules, such as NO2, NH3, H2O, CO and NO, the adsorption in the perfect region of graphene is physical and the corresponding adsorption energy or desorption barrier Ed is in a range of 0.1–0.5 eV [10,19–22], so the corresponding θS diverses by about six magnitudes of orders. Clearly, the Ed has strong effects on θS , while the influence of Td is much weaker than that of Ed. Fig. 2 shows that the θS for Ed < 0.6 eV decreases about 1–2 magnitudes of orders when Td increases every 100 K. Intuitively, the behavior of θS upon Ed and Td can be easily understood because larger Ed impedes more molecules to escape from the surface, while larger Td promotes the escaping. Nevertheless, the dependence of TBAD on Ed and Td is not so direct. It seems reasonable that the larger the Ed and the lower Td, the smaller the desorption rate should be and therefore the shorter TBAD would be. However, Fig. 2 indicates that the TBAD increases exponentially with increasing of Ed in a range of 0.2–0.6 eV and decreases obviously with increasing of the Td. As examples, the TBAD increases from 6.79 × 10−9 to 7.61 × 10−3 s with Ed increasing from 0.2 to 0.6 eV for Td = 300 K and decreases about 1–3 orders of magnitudes when Td increases from 300 K to 500 K. In the above calculations, Eb is set as 0.01 eV, corresponding to about 15% of the molecules colliding with the surface can be adsorbed. When Eb rises to 0.1 eV, about 95% of the incident molecules would be adsorbed on the surface, while the TBAD kept nearly unchanged for the Ed in a range of 0.2–0.6 eV although θS increases about ten times. For Ed larger than 0.8 eV, the TBAD increases from 0.01 s with Eb = 0.1 eV to 0.09 s with Eb = 0.01 eV and the corresponding θS approaches to 1. Obviously, the influence of Eb on TBAD and θS is much weaker than Ed and Td. In the above calculations, the concentration of target molecules is set as 100 ppm, while in common experiments the gas concentration may be smaller. Our calculations using Eq. (8) with the same parameters as those for Fig. 2 (Td = 300 K) show that the TBAD for the Ed of 0.2–0.6 eV changes little when gas concentration decreases from 100 ppm to 10 ppb [Fig. 3] while the θS decreases by about four orders. For Ed larger than 0.6 eV, the TBAD for lower gas concentrations gets significantly longer than the ones for higher concentration and the θS approaches to 1. From the above calculations we can see that the key factor affecting TBAD and θS is Ed, which is in a range of 0.1–0.5 eV for many target molecules (H2O, CO, CO2, NO, NO2, NH3) [10,19–22]. It is worthy to note that for GBGS working at room temperature to detect these molecules with concentration smaller than 100 ppm, the TBAD and θS are only several microseconds (or smaller) and 10−3 (or smaller), respectively.

For a realistic graphene sheet there must exist some defects, but most of the areas should be perfect six-ring structure, so it is more probable for gas molecules to land at the perfect sites rather than the defective ones. If the molecules landing at the perfect sites affect the conductance of graphene, then the change of the conductance should be proportional to the fractional coverage θ [12,23], which is named as adsorption model (AM) for GBGS working in the followed text. On the other hand, it is also possible that the molecules landing at the perfect sites have little effects on the conductance of graphene and diffuse to the defects, such as single vacancy, double vacancy, edge defect or topological defect, where they are strongly adsorbed (trapped) and contribute to the conductance change. This mechanism is named as diffusion model (DM) for GBGS working. If AM is valid, then the response time experimentally defined as the period for GBGS exposed to the target gas reaching 90% of the maximum of the conductance change should be shorter than the TBAD defined in last section. However, the response time observed in previous experiments for CO2, NH3, NO, NO2, SO2 is in a range from tens of seconds to thousands of minutes [3–5,7,10,11,23–25], which is too much longer than the corresponding TBAD calculated in the last section [Figs. 2 and 3]. For NH3 gas with a concentration of 200 ppm, an experiment due to Yavari et al. showed that the response time at room temperature is longer than 120 min [7]. Under the same experimental conditions implemented by the same group for detecting NO2, the response time is about 20 min. In another experiment for detecting NO2 with concentration between 2.5 and 50 ppm, no saturation of conductance change was observed within two hours [6]. According to theoretical results [10,19,20,26], the desorption barrier Ed of NH3 (or NO2) on perfect graphene surface ranges from 0.031 to 0.11 eV (or 0.067–0.48 eV). Based on Eq. (8), the response time of NH3 (or NO2) with concentration of 200 ppm should be less than 1.2 × 10−10 s (or 1.5 × 10−4 s), and from Fig. 3, we can see that TBAD for the NO2 gas with concentration ranging from 1 ppm to 100 ppm is less than three hundreds of microseconds. In an experiment for detecting SO2 gas of 50 ppm, there was no saturation of the conductance change within 30 min when the GBGS worked at room temperature, and when the temperature was increased up to 100 °C, the conductance increased by 76% in the first two minutes and gradually approached to saturation within 30 min [27]. The theoretical Ed of SO2 ranges from 0.012 to 0.314 eV [28–32] and the TBAD from Eq. (8) is less than 0.5 μs for the GBGS at room temperature with gas concentration of 50 ppm. When Td increases to 100 °C, the TBAD is only 2.4 × 10−8 s. The shortest response time, 8 s, was observed in an experiment for detecting CO2 gas of 100 ppm, and kept nearly unchanged when the temperature of GBGS changes from 22 °C to 60 °C [33]. The main difference between this experiment and the others mentioned above is that this graphene sheet is obtained by mechanical cleavage from graphite other than by vapor deposition in the other experiments. The Ed for CO2 via DFT calculations is less than 0.2 eV [22,29,30], with which the calculated TBAD is just about eight nanoseconds. Considering the possible deviation of the ab initio calculations, we set the Ed as 0.4 eV, and the TBAD is just eight microseconds, which is still much shorter than the experimental results. Obviously, the above results strongly deny the validness of AM. Actually, previous first principles calculations have showed that the molecules, such as NO2 and NH3 adsorbed on perfect graphene do not change the conductance at all, while larger changes of the conductance occur when the molecules are adsorbed on the defective sites of graphene [19]. Some other theoretical results also indicated that many molecules, such as H2O, CO2, NO, CO, NO2, NH3 and SO2 adsorbed on pristine graphene result in little charge transfer [10,21,26,31,34]. According to the DM, just when the target molecules landing at the perfect areas diffuse into the defective sites they result in the conductance change of graphene. So the response time should depend on

Fig. 3. Function of TBAD (inset is the saturated fractional coverage θS ) on the desorption energy Ed with gas concentration of 100 ppm, 1 ppm and 10 ppb under the desorption temperature of 300 K. 450

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the diffusion rate of the target molecules on the graphene surface instead of the TBAD and the sensitivity of GBGS should be increased with the density of defects within certain contents. Salehi-Khojin et al. found that pristine graphene has no response to some organic molecules while defective graphene shows higher sensitivity (more than 50 times) to these molecules [30]. An experiment due to Chung et al. [5] for detecting NO2 showed that after the graphene was irradiated by ultraviolet lamp for 70 s the sensitivity and response rate of GBGS were raised by two folds and eight times, respectively. It is well known that ultraviolet not only generates highly reactive ozone molecules that can produce defects on graphene surface but also clean the surface of graphene resulting in faster diffusion of NO2 molecules on the surface. Ricciardella et al. detected NO2 vapors with three different graphene sheets fabricated by mechanical exfoliation (ME-GR), liquid phase exfoliation (LPE-GR) and chemical vapor deposition (CVD-GR) and found that the response rate of ME-GR is faster than LPE-GR and CVD-GR by 1.5 and 5 times, respectively [9]. This phenomenon is in agreement with the fact that the surface of ME-GR is cleaner than the other two and on it the NO2 molecules diffuse much faster. According to the DM, the response rate of GBGS can be sped up by increasing the temperature of graphene because the diffusion of gas molecules on graphene surface increases with the temperature. Indeed, in an experiment for NO2 detection, the response rate for GBGS at room temperature (21 °C) got clearly faster when the temperature increased up to 149 °C [11]. In another experiment for detecting SO2, the response rate was also significantly speeded by heating the graphene sheet up to 100 °C [27]. Obviously, these phenomena cannot be understood by the AM. In addition, the conductance of GBGS as the function of time in some experiments displays a rapid change firstly and then a slow change, which cannot be fitted by a single exponential function derived from AM [10,12,13,33]. Lee et al. [10] regarded the rapid and slow processes as the adsorption of target molecules at the perfect and defective sites, respectively. Similar mechanism for GBGS working was also suggested by S. Novikov [4] except that they considered the defective sites instead of the perfect sites are occupied firstly. However, the measured response time for NO2 with concentration of 200 ppm in the rapid process is more than 80 s [10], which is much longer than the calculated TBAD, 7 ns, from Eq. (8) with the theoretical Ed = 0.2 eV [10]. According to the DM, the gas molecules landing on the graphene diffuse into the defective sites where they result in the conductance change, corresponding to the rapid response process. When all the defects are filled, the gas molecules might form a cluster around a defect, which is based on the fact that the bind energy in clusters is much larger than the adsorption energy of the clusters on graphene sheet, such as the situation for H2O clusters [35]. As the cluster grows gradually with further coming of the gas molecules, which should correspond to the slow response process, since the gas molecules clustering lately do not directly contact with the defect and the charge transfer between the gas molecules and graphene is smaller. It should be noted that the target molecules may also land directly at the defective sites of the graphene sheet. According to Figs. 2 and 3, for the adsorption of the target molecules with concentration of tens ppm, the TBAD is about 1 s with the desorption barrier larger than 1 eV and is yet much shorter than the experimental results. So we guess that there may exists a large adsorption barrier Ea that hinders the target molecules to land directly on the defective sites. As an example, we calculated the Ea for a NO2 molecule approaching a single vacancy of a graphene sheet by density of functional theory (DFT) within Vienna ab initio simulation package (VASP). Projected augmented-wave (PAW) potential was used to describe the electron-ion interaction and PerdewBurke-Ernzerhof (PBE) of generalized gradient approximation (GGA) was employed to consider the exchange-correlation functional. Considering the Van der Waals force between NO2 and the graphene surface, vDW-DF2 was adopted. We used a rectangular supercell for graphene sheet containing 60 carbon atoms with (or without) a vacancy at

Fig. 4. The most stable structure of NO2 on perfect graphene (a) and defective graphene with a single vacancy (b).

Fig. 5. Dependence of the total energy of a NO2 molecule on the graphene with a single vacancy on their distance along the direction vertical to the graphene surface.

Fig. 6. Dependence of the total energy of a NO2 molecule on perfect graphene on their distance along the direction perpendicular to the graphene surface.

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sensors. Acknowledgement This work was supported by the National Natural Science Foundation of China (Nos. 61474028, 61774042); the Shanghai Municipal Natural Science Foundation (No. 17ZR1446500); and the National S&T Project 02 (No. 2013ZX02303-004) and “First-Class Construction” project of Fudan University. References [1] J. Kong, N.R. Franklin, C. Zhou, M.G. Chapline, S. Peng, K. Cho, Nanotube molecular wires as chemical sensors, Science 287 (2000) 622–625, https://doi.org/10. 1126/science.287.5453.622. [2] F. Schedin, A.K. Geim, S.V. Morozov, E.W. Hill, P. Blake, M.I. Katsnelson, Detection of individual gas molecules adsorbed on graphene, Nat. Mater. 6 (2007) 652–655, https://doi.org/10.1038/nmat1967. [3] G. Chen, T.M. Paronyan, A.R. Harutyunyan, Sub-ppt gas detection with pristine graphene, Appl. Phys. Lett. 101 (2012) 053119, , https://doi.org/10.1063/1. 4742327. [4] S. Novikov, N. Lebedeva, A. Satrapinski, Ultrasensitive NO2 gas sensor based on epitaxial graphene, J. 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Fig. 7. Dependence of the total energy of a NO2 molecule on graphene with a single vacancy on the distance of NO2 molecule and the vacancy along the direction parallel to the graphene surface.

the center region. The vacuum thickness, distance between two adjacent graphene layers, is 18 Å for the perfect graphene, while 12 Å is sufficient for graphene with a single vacancy. Vacuum thickness is frozen but the other two vectors are fully relaxed during the geometry optimization. The kinetic energy cut-off is 400 eV and the k-mesh in Brillouin zone is 5 × 5 × 1. The electronic self-consistency will stop when the difference of the energy is smaller than 1 × 10−5 eV and the force acted on each atom is less than 0.04 eV/Å. Firstly, we optimized the system of a NO2 molecule on the graphene sheet and obtained the stable structures of the molecule at a perfect site and a single vacancy, as shown in Fig. 4(a) and (b), respectively, then moved the NO2 molecule departing from the sheet step by step to obtain the total energy as the function of the distance. The mimicking of the NO2 molecule departing from the vacancy shows that the carbon atoms around the vacancy were “dragged” towards the molecule, resulting in local bend of the graphene sheet, and when the distance between the molecule and the sheet is larger than 1.905 Å the graphene sheet turned into a plane, accompanied by sudden dropping of the total energy [Fig. 5], which forms a barrier of 1.06 eV (Ea = 1.06 eV) for a NO2 molecule directly landing at the vacancy. However, no barrier (Ea = 0 eV) exists for a NO2 molecule landing on the perfect region of the graphene sheet [Fig. 6]. Applying Eq. (8) with the date drawn from Figs. 5 and 6, the calculations for the gas molecule concentration of 100 ppm show that the fractional coverage θS of the perfect region (Ea = 0 eV, Ed = 0.306 eV) and the vacancy region (Ea = 1.06 eV, Ed = 2.96 eV) of the graphene sheet at room temperature is 1.76 × 10−6 and 0, respectively, indicating that the NO2 molecules can hardly directly land at the vacancy. The molecules landing on the perfect area of the graphene sheet can diffuse into the vacancy because no barrier exists for the diffusion as shown in Fig. 7. 4. Conclusions Based on the kinetics study of the adsorption and desorption of gas molecules on graphene sheet, the mechanism at atomistic level for GBGS working was suggested to be that just when the target gas molecules landing on the perfect areas of graphene diffuse into the defective sites they induce the sensitive changes of conductance, which is in qualitative agreement with the previous experiments. Based on this mechanism, a possible way to enhance the sensitivity of GBGS is to introduce some defects onto the graphene sheet, and for speeding the response rate we can clean the contamination on the surface of graphene, or heat the graphene up to higher temperature. The kinetic model for adsorption and desorption on surface developed in this work would find its vast application in the investigation of various gas 452

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