Ab initio study of CNT NO 2 gas sensor

Chemical Physics Letters 387 (2004) 271 276 www.elsevier.com/locate/cplett Ab initio study of CNT NO 2 gas sensor Shu Peng a, *, Kyeongjae Cho a, Pengfei Qi b, Hongjie Dai b a Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA b Department of Chemistry, Stanford University, Stanford, CA 94305, USA Received 2 September 2003; in final form 12 February 2004 Published online: 4 March 2004 Abstract NO 2 gas adsorption, diffusion, and reaction on a single walled carbon nanotube (SWNT) surface are studied using ab initio simulations. The small diffusion barriers of NO 2 on SWNT surface suggest that NO 2 molecules can produce NO and NO 3 through chemical reactions. From the estimation of diffusion barriers and binding energies of NO 2, NO, and NO 3 on a SWNT surface, we show that NO 3 is the most likely long-lived species on SWNT. This finding enables us to explain why the experimental recovery times of NO 2 gas sensors have been measured to be as long as 12 h. Ó 2004 Elsevier B.V. All rights reserved. Carbon nanotubes (CNTs) as chemical sensors [1,2] have generated strong interests in the research community since Kong et al. [3] demonstrated that single-walled carbon nanotubes (SWNT) can be used as miniature sensors to detect low concentrations of toxic gas molecules such as NO 2 and NH 3 at room temperature. Many theorists [4 6] have attempted to explain the sensing mechanism of CNTs from the perspective of NO 2 adsorption energy on the SWNT surface. However, many intriguing questions remain open. One of them is the discrepancy of recovery time between theoretical results and experimental data, whereas the recovery times from the theoretical calculations [4 6] are far shorter than those observed in experiments [3]. The NO 2 adsorption energies obtained from the theoretical calculations range from )0.34 to )0.79 ev [4 6], and the recovery time for CNTs as NO 2 gas sensors was measured to be approximately 12 h in the experiments [3]. Using transition state theory, which relates the recovery time s to the adsorption energy E B as follows: s ¼ m 1 0 e ð E B=K B T Þ ; ð1þ * Corresponding author. Fax: +16507231778. E-mail address: pengshu@stanford.edu (S. Peng). where T is temperature, K B the Boltzmann s Constant (8:62 10 5 ev K 1 ), and m 0 the attempt frequency (m 0 ¼ 10 12 s 1 for NO 2 molecules), we can obtain the recovery time of CNT sensor at room temperature, to be in the range of 0.5 ls and 16 s for the adsorption energies of )0.34 to )0.79 ev [4 6]. Conversely, the adsorption energy for a recovery time of 12 h corresponds to adsorption energy of )1.00 ev. Obviously, the recovery time and adsorption energies from the theoretical calculations [4 6] are significantly shorter and smaller than their corresponding experimental results [3]. A reexamination of the entire process of NO 2 gas molecule interacting with CNTs from a fresh angel is required. In this Letter, we first expand our calculations and analysis of NO 2 gas adsorption on SWNT to more configurations, as a complement to the existing calculations [4 6]. However, our expanding calculations still do not narrow down the gap between experimental results and theoretical calculations with respect to the SWNT recovery time. We then study the impact of NO and NO 3 on SWNTs since recent experiments indicate the existence of NO and NO 3 on SWNTs [7]. Self-consistent electronic structure calculations were performed using VASP program [8 11] based on density functional theory (DFT). Local density approximations with spin (LSDA) and without spin (LDA) were used. Since LSDA yields lower total energy than LDA for 0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.02.026

272 S. Peng et al. / Chemical Physics Letters 387 (2004) 271 276 NO 2, NO and NO 3 molecules, the calculations from LSDA will be used for comparison and those from LDA are listed as references. For SWNTs, a super cell of 16.00 16.00 L z A 3, where L z ¼ 8.52 8.70 A for nanotubes with chirality ranging from (5,0) to (11,0) is used with 6-k points along the tube axis within the Brillouin zone. The structural configurations are optimized through fully relaxing the atomic structures to minimize their total energies until the maximum force on any atom was less than 0.015 ev/ A. The binding energy E binding between a gas molecule and a SWNT is defined as, E binding ¼ Eðmolecule þswntþ EðSWNTÞ EðmoleculeÞ; ð2þ where E(molecule + SWNT) is the total energy of gas molecule adsorbed on the SWNT surface, and E(SWNT) and E(molecule) are the total energy of SWNT and gas molecule, respectively. For NO 2 adsorption on SWNT, we consider two highly symmetric categories of adsorption configurations: one in which NO 2 molecule stays parallel to a SWNT surface (Fig. 1A1 A4,), and the other in which NO 2 molecule stays perpendicular to a SWNT surface Fig. 1. Seven binding configurations for NO 2 respectively). interacting with (10,0) SWNT (upper and lower images show the side and cross-section view, Table 1 Summary of results for NO 2 interacting with (10,0) SWNT Binding configuration LSDA LDA E b (ev) a d ( A) b E b (ev) d ( A) NO 2 NO 2 //SWNT A1 BC )0.50 2.71 )0.64 2.70 A2 CT )0.50 2.70 )0.62 2.69 A3 DP )0.50 2.80 )0.63 2.80 A4 HC )0.47 2.70 )0.60 2.71 NO 2?SWNT B1 DT )0.49 2.61 )0.63 2.61 B2 BM )0.47 2.58 )0.59 2.57 B3 HM )0.49 2.61 )0.60 2.61 NO NO//SWNT A1 BC )0.38 2.64 )0.45 2.64 A2 HC1 )0.49 2.56 )0.48 2.57 A3 HC2 )0.43 2.61 )0.45 2.56 NO?SWNT B1 DT )0.33 2.65 )0.35 2.65 B2 BM )0.34 2.68 )0.34 2.72 B3 HM )0.44 2.62 )0.35 2.68 C1 DTR )0.33 2.72 )0.34 2.73 C2 BMR )0.31 2.63 )0.46 2.62 C3 HMR )0.39 2.62 )0.39 2.63 NO 3 NO 3 //SWNT A1 CT )1.17 2.87 )1.37 2.87 A2 DT )1.10 2.87 )1.34 2.87 A3 HC )1.13 2.87 )1.32 2.87 A4 HD )1.10 3.04 )1.29 3.04 All the binding configurations are shown in Figs. 1 and 2. a Binding energy. b Binding distance.

S. Peng et al. / Chemical Physics Letters 387 (2004) 271 276 273 (Fig. 1B1 B3,). The binding energies and binding distances are given in Table 1. The adsorption energy ()0.5 ev) of NO 2 molecule on SWNT is far smaller than that obtained from the experiments [3] ()1.0 ev). However, the small diffusion barrier (0.03 ev) obtained from the difference of the binding energies for different configurations show that NO 2 molecules diffuse around the SWNT surface easily and rapidly. This enhances the chance that two NO 2 molecules meet each other and form a chemical reaction. Since there are catalyst islands on SWNT, and NO 2 molecules are known to interact with catalytic surfaces to form NO and NO 3 molecules, a chemical reaction may occur as follows [12,13], NO 2 þ NO 2! NO þ NO 3 ð3þ X-ray photoemission spectroscopy measurements [7] in fact confirmed such reaction: existing molecules on the SWNT surface are NO and NO 3 with a 1:3 ratio after NO 2 molecule s adsorption. Another chemical reaction might occur 2NO ð 2 þnoþ!2no 3 þ N 2 ð4þ Since the experiments show that N 2 molecules do not stick to SWNT surface [7], we need only to investigate the possibility of NO or NO 3 adsorbed onto the SWNT surface. For NO interacting with SWNT, nine adsorption configurations are considered (Fig. 2). Binding energies ranging from )0.3 to )0.5 ev were found (Table 1). The diffusion barrier of 0.16 ev for NO molecules indicates that it is harder for them to diffuse around the SWNT surface. The small binding energy indicates that NO adsorption and desorption on the SWNT surface is not the major factor behind the long recovery time (12 h) observed in the experiments. The remaining species on the SWNT surface in the NO 2 sensing experiments are the NO 3 molecules. For NO 3 interacting with SWNT, four highly symmetric adsorption configurations (Fig. 3) are considered, with all 4 atoms having the same distance to the surface of a SWNT. The calculated binding energies, given in Fig. 3. Four local stable adsorption sites for NO 3 interacting with (10, 0) SWNT (left and right images show the side and cross-section view, respectively). Table 1, are all within the range of )1.1 to 1.2 ev. The )1 ev binding energy for NO 3 interacting with SWNT indicates that NO 3 is the most likely long-lived species on SWNT. Furthermore, charge transfer calculations show that (10,0) SWNT donates 0.14 el charge to each NO 3 molecule. Summarizing these results for three molecules (NO 2, NO and NO 3 ) interactions with SWNT, we can explain the phenomenon observed in experiments as follows: when NO 2 molecules come into contact with the SWNT surface, a reaction occurs to produce NO and NO 3 molecules. On the equilibrium, NO 2 and NO gas molecules have fast desorption time (less than 1 s at room temperature), while NO 3 molecules have longer ones (12 h). From the fact that NO 3 is the major concentration on the SWNT surface (by a 3:1 ratio), and its recovery time will accordingly determine the recovery time for the overall SWNT system, we can deduce that it is NO 3 that is responsible for the slow recovery. To further understand the conductance increases of SWNTs due to the charge transfer between NO 2, NO, NO 3 molecules and SWNTs, analysis on the density of states were performed (Fig. 4). The configuration where a molecule (NO 2, NO, or NO 3 ) is placed in the center of a C C hexagon ring is considered. When NO 2 are adsorbed on a (10,0) SWNT surface, its band gap is reduced from 0.86 to 0.80 ev. Similarly, NO and NO 3 Fig. 2. Nine binding configurations for NO interacting with (10, 0) SWNT (left and right images show the side and cross-section view, respectively).

274 S. Peng et al. / Chemical Physics Letters 387 (2004) 271 276 Fig. 4. DOS of the SWNT (10,0) and molecules (NO 2, NO, NO 3 ). molecule adsorptions change the SWNT s band gap to be 0.79, and 0.82 ev, respectively. It is clear that SWNT would donate electrons to NO 2 molecules when the adsorption occurs, because the lowest unoccupied molecular orbital (LUMO) state for NO 2 is way down the valence band structure of (10,0) SWNT. Before NO 2 molecule s adsorption, the SWNT were p-typed in the experiments, indicating that some holes have already existed inside the valence band. After NO 2 molecule s adsorption, the SWNT will generate more holes in the valence band since electron charge is transferred to the NO 2 molecules. More holes generated in the SWNTs will lead to the increase of conductivity of the SWNTs. Similar changes will occur to the NO and NO 3 molecules since LUMO states for NO and NO 3 molecules are lower than the valence band of the (10,0) SWNT. These data are consistent with the conductance changes of SWNT measured in the experiments. The binding energies for NO 2, NO and NO 3 molecules on the SWNT surface are further analyzed in terms of conductivity for direct comparison to the experimental data. Using the Langmuir Iosotherm model [14], which describes the dependence of the surface coverage of an adsorbed gas on the pressure of the gas at a fixed temperature, we obtain the following equation, p pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ASð1 hþ A 2pmK B T r hme ð E effb=k B T Þ : ð5þ Then the coverage of NO 2 (h) on the SWNT can be given by, 1 hðpþ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; ð6þ 1 þ 2pmK B T m e ð E effb =K B T Þ psr Fig. 5. Calculated DG=G 0 for p-type SWNT sensors versus NO 2 partial pressure (P) for NO 2 sticking coefficient (S) ranging from 1 to 10 8. The solid triangles represent experimental data. Comparison between calculations (see the fit line) and experimental result suggests that the sticking coefficient S ¼ 4:5 10 5.

S. Peng et al. / Chemical Physics Letters 387 (2004) 271 276 275 Table 2 Summary of results for NO 2, NO and NO 3 (molecules in the center of the carbon hexagon ring) interacting with graphite and series of SWNTs a Configuration h p E b (ev) b d ( A) c ET (el) d NO 2 SWNT(5,0) and NO 2 126.0 )0.78 2.22 0.32 SWNT(8,0) and NO 2 112.5 )0.55 2.63 0.16 SWNT(10,0) and NO 2 108.0 )0.47 2.70 0.10 SWNT(11,0) and NO 2 106.4 )0.44 2.75 0.07 Graphite and NO 2 90.0 )0.41 2.92 0.06 NO SWNT(5,0) and NO 2 126.0 )0.74 1.88 0.34 SWNT(8,0) and NO 2 112.5 )0.55 2.49 0.13 SWNT(10,0) and NO 2 108.0 )0.49 2.56 0.08 SWNT(11,0) and NO 2 106.4 )0.47 2.60 0.07 Graphite and NO 2 90.0 )0.44 2.69 0.04 NO 3 SWNT(5,0) and NO 2 126.0 )1.89 2.42 0.48 SWNT(8,0) and NO 2 112.5 )1.34 2.76 0.22 SWNT(10,0) and NO 2 108.0 )1.13 2.87 0.14 SWNT(11,0) and NO 2 106.4 )1.08 2.92 0.12 Graphite and NO 2 90.0 )1.02 3.03 0.08 a Angle between adsorption surface and molecule. b Binding energy. c Binding distance. d Electron transfer from the SWNT to molecules. where m is the molecular mass, T ¼ 300 K at room temperature, A is the surface area of SWNT, S is the sticking coefficient for the molecules on the surface, r ¼ 10 19 m 2 is the molecular cross-section, and m ¼ 10 12 /s is the molecular vibration frequency. E effb is defined as the effective binding energy (0.85 ev) since NO 2 molecules react to produce NO and NO 3 molecules with a 1:3 ratio on the SWNT surface. Assume the change of conductance DG is proportional to the NO 2 coverage h in the experiments. The calculations of DG vs. pressure (p) in the range of S ¼ 1to10 8 are given in Fig. 5. Compared to the experimental data, the estimated S ¼ 4:5 10 5 sticking coefficient is obtained. The estimated charge transfer between NO 2 and p-typed SWNT is related to the gate capacitance of the device, the diameter and length of the SWNT, as follows: DQ ¼ C g DV g ¼ dh pdl r : ð7þ For the experiments, the estimated gate capacitance can be expressed as C g 1:2 10 16 F for the nanotube with length l 4 lm, and diameter d 2 nm. d is the average charge transfer per NO 2 molecular. The charge transfer thus obtained in our calculations is on the order of d 0:1jel. The curvature effect on the Molecule SWNT interaction deserves analysis since carbon nanotube samples used in the experiments usually have some local curvature changes [15,16]. To study the curvature dependence of NO 2, NO, and NO 3 molecules adsorption on the nanotubes, DFT calculations are carried out with graphite and zigzag SWNTs ((5,0), (8,0), (10,0) and (11,0)). The adsorption configuration of a molecule staying in the center of the C C hexagon ring is considered. The binding energies (Table 2) show a trend that SWNTs larger than (10,0) would have a difference less than 0.1 ev in binding energy as compared to those on the graphite, and smaller SWNTs have significantly larger binding energies. Although SWNTs used in the experiments usually have larger diameter than (10,0) SWNTs, we can still conclude that (10,0) SWNT is a good approximation for studying the adsorption mechanism and the data should be comparable to those from experiments. The results in the table also indicate that the binding distance decreases for smaller SWNT. Furthermore, the curvature affects the charge transfer between molecules and SWNT. In summary, ab initio methods are used to analyze the process of NO 2 gas adsorption on SWNT surface. NO and NO 2 bind weakly with low diffusion barriers making it possible for the formation of NO 3 with strong binding energy and long life on SWNT surface. The high adsorption energy of 1.1 ev for NO 3 matches well with the corresponding long recovery time seen in the NO 2 sensing experiments. We also show that curvature effects significantly change the adsorption energy of gas adsorption on SWNT. These findings help us better understand SWNT as a NO 2 gas sensor. Acknowledgements S.P. wants to thank Stanford Graduate Fellowship support. The calculations are performed on origin 3800 allocated through Nanoscale Material Simulations.

276 S. Peng et al. / Chemical Physics Letters 387 (2004) 271 276 References [1] J. Fradeb, Springer-Verlag, New York Inc., 1996. [2] S. Soloman, McGraw-Hill Companies, 1999. [3] J. Kong, N. Franklin, C. Zhou, M. Chapline, S. Peng, K. Cho, H. Dai, Science 287 (2000) 622. [4] S. Peng, K. Cho, Nanotechnology 11 (2000) 57. [5] H. Chang, J.D. Lee, S.M. Lee, Y.H. Lee, Appl. Phys. Lett. 79 (2001) 3863. [6] J. Zhao, A. Buldum, J. Han, J.P. Lu, Nanotechnology 13 (2002) 195. [7] A. Goldoni, R. Larciprete, L. Petaccia, S. Lizzit, J. Am. Chem. Soc. 125 (2003) 11329. [8] G. Makov, M.C. Payne, Phys. Rev. B 51 (1995) 4014. [9] W. Kohn, L.J. Sham, Phys. Rev. B 140 (1996) 1133. [10] G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) 558. [11] G. Kresse, J. Hafner, Phys. Rev. B 49 (1994) 14251. [12] T. Jirsak, M. Kuhn, J.A. Rodriguez, Surf. Sci. 457 (2000) 254. [13] J.A. Rodriguez, T. Jirsak, S. Sambasivan, D. Fischer, A. Maiti, J. Chem. Phys. 112 (2000) 9929. [14] G.A. Somoraji, Wiley, New York, 1994. [15] M. Yu, M.J. Dyer, R.S. Ruoff, J. Appl. Phys. 89 (2001) 4554. [16] A. Rochefort, P. Avouris, J. Phys. Chem. A 104 (2000) 9807.