Quantum Capacitance of Silicene-Based Electrodes from First

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Quantum Capacitance of Silicene-Based Electrodes from First-Principles Calculations Guangmin Yang, Qiang Xu, Xiaofeng Fan, and Weitao Zheng J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b08955 • Publication Date (Web): 17 Jan 2018 Downloaded from http://pubs.acs.org on January 17, 2018

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The Journal of Physical Chemistry

Quantum Capacitance of Silicene-Based Electrodes from First-Principles Calculations

G. M. Yanga,b, Q. Xub,c, Xiaofeng Fanb,*, W. T. Zhengb, †

a

College of Physics, Changchun Normal University, Changchun 130032, China

b

Key Laboratory of Automobile Materials (Jilin University), Ministry of Education, and

College of Materials Science and Engineering, Jilin University, Changchun, 130012, China c

College of Prospecting and Surveying Engineering, Changchun Institute of Technology,

Changchun 130032, China

*,†Correspondence and requests for materials should be addressed, [email protected] (X. Fan); [email protected] (W. T. Zheng)

ABSTRACT Silicene with a buckled atomic layer has double surfaces with high surface/volume ratio similar to nanocarbon materials and is expected to have potential applications for supercapacitors. With first-principles calculations, it is found that the introduction of vacancy defects with the doping in silicene can enhance the quantum capacitance of silicene-based electrodes. The enhancement of quantum capacitance is attributed to the presence of localized states around Fermi level. Furthermore, the quantum capacitance is observed to increase with the increase of defect's concentration. It is also observed that the localized states around Fermi level lead to the spin-polarization in the cases of B-doping and S-doping near the vacancies.

1. INTRODUCTION The decreasing availability of fossil fuels with worsening climate change propel us toward the use of renewable and sustainable resources, such as solar energy and wind energy1, and the development of new technologies, such as electric vehicles or hybrid 1

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electric vehicles. One of the important global calls is to develop advanced electrical energy storage systems, such as rechargeable batteries and electrochemical capacitors with high performance. At present, electrochemical double-layer capacitors (EDLCs) are the most common devices among several types of electrochemical capacitors. EDLCs2-9 are a kind of supercapacitors with a simple charging circuit and long lifetime, and have relatively low energy density but high power delivery, compared to batteries. In EDLCs, the charges are stored electrostatically with a reversible adsorption of ions from the electrolyte into active materials. Charge separation with polarization at the electrode-electrolyte interface leads to the creation of capacitance. In order to achieve high capacitance, an electrochemically stable electrode-electrolyte interface is required with high specific surface area. Traditionally, carbon-based active materials are used in EDLCs. Graphene, a free-standing monolayer of carbon atoms with high surface area, has been regarded as one of the ideal electrodes for EDLCs10-13. In the process of practical implementation, graphene-based materials have been limited by poor accessibility to the electrolyte. To obtain high capacitance for supercapacitors, the choice on electrode materials is a key factor. The doping or functionalization of graphene was reported to enhance the capacitance considerably. Inspired by graphene, silicene which is made of two-dimensional layered nanosheets has been developed14-18. Through experiments, silicene sheets with different super-structures have been successfully synthesized on various substrates19 via epitaxial growth on the Ag(111)20, ZrB2(0001)21, and MoS222 surfaces. Silicene with a buckled layer structure has high surface area23. With sufficient space for the adsorption of Li ions and by preventing the fracture of structures owing to the intercalation of Li ions, it has been proposed to be used as an anode material for Li ion batteries24-26. Similar to graphene, it is also expected to be one of the ideal electrodes for EDLCs. Recently, the experimental and theoretical results of low-dimensional electrodes, such as carbon nanotubes and graphene, have indicated that the total interfacial capacitance is mainly from the contribution of quantum capacitance and differential electrochemical double layer27-29. For instance, under a low applied potential, quantum capacitance of graphene was observed to limit the performance. It is evident that understanding quantum capacitance is

important

for

improving

the

total

interfacial

capacitance

of 2


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supercapacitors30-32. To the best of our knowledge, quantum capacitance of silicene has not been studied for supercapacitor. It is known that quantum capacitance is related with the density of states. It has been proposed that the dopants, defects, and adsorption of functional groups induced by chemical treatment and/or in the processing of growth can modify the quantum capacitance. As one of the most important structural defects, vacancies have been observed to impact the electronic structures of silicene33. It is expected that vacancies with dopants can strongly modulate the quantum capacitance. In this work, we are focused on these important issues for silicene-based electrode materials in nanoelectronic and supercapacitor applications. With first-principles methods, we explore the effect of vacancy concentration and dopants including N, P, B, and S on quantum capacitance and electronic structure of silicene, in order to enhance the quantum capacitance via the way of doping. On the basis of these results, we analyze the possibility of the way about defects with doping which is adopted to enhance the performance of silicene-based electrodes. We observe that the quantum capacitance is significantly improved by introducing single vacancy.

2. COMPUTATIONAL METHODS The present calculations are performed on the basis of on DFT with the projector augmented wave potentials method34 as implemented in the VASP35. For the exchange-correlation energy of interacting electrons, the generalized gradient approximation with the parameterization of Perdew-Burke-Ernzerhofis (PBE) 36 is used. To ensure that the total energy is converged at 1 meV/atom level, the appropriate plane-wave basis and k-space integral are chosen. For the plane wave expansion, the kinetic energy cutoff of 450 eV is determined to be enough. To sample the k-points, the Monkhorst-Pack method is used. About the partial occupancies for each orbital, Methfessel-Paxton method is used for the smearing parameter with the width of 0.1 eV. The convergence criteria of structural optimization were chosen as maximum force on each atom less than 0.02 eV/Å with energy change less than 1×10−4 eV. In order to consider the possible magnetism of defective silicene, the spin-polarized calculation is also taken. The calculated lattice constant of silicene is 3.84 Å, which is consistent with the other 3



theoretical results15,

17

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and similar to the experimental report21. On basis of the lattice

parameters of primitive cell, we construct different supercells as the ideal structural models such as 2×2, 3×3, 4×4, 5×5, 6×6, 7×7, and 8×8 with hexagonal structures, in order to simulate the effect of doping including the dopants-B, N, P, and S, and defects in the electronic structure. In the supercells, a vacuum space of 18 Å along the z direction is constructed to decoupling the artificial interaction of layers. The Brillouin zones of 2×2, 3×3, 4×4, 5×5, 6×6, 7×7, and 8×8 supercells are sampled with Γ-centered k-point grid of 24×24, 16×16, 12×12, 10×10, 8×8, 7×7, and 6×6, respectively. These proposed structural models are fully relaxed. The formation energies of four types of defects including single vacancy, double vacancy, and two types of N-doping can be calculated using the formulas ∆E SV ( DV ) ( x) = E df − Sil ( x) − nµ Si ,

(1)

∆E P − N ( x) = E df − Sil ( x) − ( n − 1) µ Si − µ N ,

(2)

and ∆E3− N ( P , B , S ) ( x) = E df − Sil ( x) − (n − 3) µ Si − 3µ N ( P , B , S ) ,

(3)

where ∆ESV(DV)(x), ∆Ep-N(x), and ∆E3-N(P,B,S)(x) represent the formation energies of single vacancy (double vacancy), pyridine-N doping with single vacancy, and triple-N(P, B, and S) doping with single vacancy, respectively; Edf-Sil(x) represents the total energy of defected silicene with four-type defects; µSi and µN(P, B, S) represent the total energies per atom of pristine silicene, and N2 molecule in the gas phase (P4, B12, and S8), respectively. The different defect concentrations are obtained via different sizes of the silicene model in Figure 1. The concentrations of these defects are considered by using the formulas, CSV= 1/(n+1), CDV= 1/(n+2), Cp-N= 1/(n+1), and C3-N= 3/(n+1). In order to explore the structural stability after the doping, temperature-dependent dynamics processes are analyzed using first-principles molecular dynamics (MD) simulations from VASP code37-39. We test the MD time for the structural relaxation from initial state to equilibrium state at the proposed temperature from 2 ps to 15 ps. It is found that the MD time 3ps is reasonable for the initial relaxation process about the defective silicene system. The MD simulations were performed at the temperatures of 300, 700, 1200, and 1500 K for a duration of 3ps, after a structural relaxation with 3ps. In the processes, 4


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each time step of MD was 1 fs. After the system is in thermal equilibrium, the average length oscillations for both Si−Si and Si−N (B) bonds are analyzed for each temperature. In order to check the reliability of MD simulations in proper small supercell, the effect of cell size is considered by analyzing the simulations in different supercells from 6×6 to 12×9. It is well known that perfect screening can lead to the confinement of excess charge in the surface of an ideal metal. Therefore, the capacitance of a metal contact, which is usually a part of the electrode, is not considered40. We can observe that silicene-based 2D materials don't have the characteristic of good screening. As the electrode materials are used, their intrinsic capacitance (quantum capacitance) is expected to have a prominent influence on the performance of devices, such as supercapacitors and field-effect transistors41,

42

. The

quantum capacitance can be defined by the formula, CQ=dσ/dΦ, where dσ and dΦ represent the differentials of charge density and local potential, respectively. By the local potential Φ, the electrochemical potential µF can be shifted rigidly. Therefore, the excess electronic charge density owing to the local potential can be expressed as43 +∞

∆Q = −e∫ D( E )[ f ( E ) − f ( E − eΦG )]dE

(4)

−∞

where f(E), D(E) and E represent the Fermi-Dirac distribution function, density of states, and energy of Fermi level EF, respectively. For pristine silicene, without considering the temperature effect, the quantum capacitance can be presented as

CQ = e2

g s gυ eΦ , 2π (hvF ) 2

(5)

where gs(=2) and gv (=2) represent the spin and valley degeneracies of silicene, respectively, ħ and VF is Planck’s constant and carriers' Fermi velocity near Dirac point. With the analytical expression of ∆Q, the quantum capacitance of other 2D materials is obtained by the differential d∆Q/dΦ, and expressed by the formula41, 43, +∞

CQ = e2 ∫ D( E ) FT ( E − eΦG )dE , −∞

(6)

where FT(E) represents the thermal broadening function and is expressed as

FT ( E ) = (4k BT )−1 Sech 2 ( E / 2k BT ) ,

(7)

5



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where kB is the Boltzmann constant. In the calculations, the temperature T is set to room temperature (300 K). The density of states D(E) is reformed with high precision using a linear interpolation method for the integral calculation.

3.RESULTS AND DISCUSSION 3.1 Modification induced by vacancy concentration and defect The Si–Si bond length of pristine silicene is 2.268 Å. This is slightly smaller than bulk Si (2.368 Å) owing to sp3/sp2-like hybridization44. Silicene has a buckled honeycomb atomic arrangement (Figure 1a). Figure 2a shows the band structure of pristine silicene. As demonstrated by the experiments, it has a zero band gap with a Dirac point appeared at K point where the valence and conduction bands touch with each other45. We calculated the quantum capacitance and surface charge versus the potential drop of pristine silicene as shown in Figures 2b and c. The simulation results of CQ for pristine silicene are consistent with the theoretical calculation using equation (5) without considering the temperature effect. CQ is almost zero at the local potential Φ = 0 V and increases linearly with the increase in |Φ|. The Fermi velocity obtained from the results of angle-resolved photoemission spectroscopy is approximately 0.3×106 ms-1, and less than that reported for graphene46. Therefore, the quantum capacitance of silicene should be higher than that of graphene. From our calculations, CQ of silicene is approximately two times larger than that of graphene for small |Φ|. For the local potential less than −0.5 V, CQ of silicene is observed to increase rapidly and is different from that of graphene. In Figure 3A, the formation energies of different models about defected silicene including single vacancy, double vacancy, and two kinds of N-doping are calculated as the functions of defect's concentration. Owing to the breaking of Si–Si bonds, the formation energy (∆ESV) of single vacancy is found to be high. There is an increase in ∆ESV with the increase in vacancy concentration33. A decrease in ∆ESV is also observed for the vacancy concentration of more than 12.5%. This suggests that there may be a new structure or coupling between vacancies owing to the weakening of local strain. The formation energy of double vacancy (∆EDV) is observed to be high and increases with the increase in concentration. However, it can be observed that the formation of double vacancy will become easier if there is a single 6


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vacancy in silicene. For the formation energies of two kinds of N-doping defects, there is an increasing trend with the increase of defects' concentration. This may be from the contribution of localized strain energy near the defects. For each concentration of defects or vacancies, the formation energy of triple-N doping with single vacancy (∆E3-N) is smaller than that of pyridine-N doping (∆Ep-N), and ∆ESV is larger than ∆Ep-N and ∆E3-N. The reason may be that the N atoms near the vacancy with an isolated electron pair can decrease the dangle-bond's energy, compared to the single vacancy. Figure 3B shows the formation energies of the models of the doping of triple atoms with single vacancy—N, P, B, and S—by fixing the dopant concentration at 9.4%. Among them, S-doped silicene has the lowest formation energy. Here, the N2 molecule, P4, B12, and S8 are used as the reference states in the calculations with formula (3). It is noticed that the P-, B-, and S-doping with the dopants P4, B12, and S8 are easier than the N-doping with N2 molecule due to the negative formation energy. In order to further investigate the thermal stability of doped silicene, we conducted MD simulations at 300, 700, 1200, and 1500 K for 3000 fs after a structural relaxation process of 3000fs. Figure 4a and 4b show the average length variation of Si−Si and Si−N bonds at 300, 700, 1200, and 1500 K about the model in Figure 1d with the N concentration of 5.6% (simulated in a supercell of 3√3×3√3 with 51 atoms) and 1.4% (simulated in a supercell of 6×6 with 71 atoms). It is observed that the doping systems are thermally stable at 300 and 700 K. At 1200 K, we observe an increase and slight fluctuation of Si−Si bond lengths by following the change of simulation time. After the temperature rises to 1500 K, a drastic increase in both the Si−Si and Si−N bond lengths is observed. It is evident that the doped silicene systems begin to break down at temperatures near 1500 K via the destruction of both Si−Si and Si-N bonds. Comparing the doping concentration of 5.6% (Figure 4a) with 1.4% (Figure 4b), it can be observed that the increase of doping concentration does not apparently change the thermal stability. We also simulate the thermal stability of single pyridine-B doping and triple-N doping, and the results (Figure S6 of SI) are similar to that of single pyridine-N doping discussed above. In addition, we consider the size effect of supercell and simulation time, since small supercell in MD simulation is possible to have 7



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artificial super-stability. Different supercell from 6×6 with 68 atoms to 12×9 with 204 atoms for the model in Figure 1d with the high N concentration of 16.7% are analyzed. Interestingly, with the increase of supercell size, the thermal deviation (or thermal noise) from the average value for bond length has a trend of decrease in Figure S7 of SI. This is agreed with the better statistical averaging for supercell with large number of atoms in MD simulation. Therefore, doped silicene is thermally stable in the temperature range used by supercapacitors. In order to explore the defect influence on CQ, single-vacancy silicene models (in Figure 1b) with different vacancy concentrations are analyzed. The total DOS is shown in Figure 5A. The total DOS and local density of states (LDOS) of dangle-bond Si (also named as defect Si) with the single-vacancy concentrations of 2% are shown in Figures 5B(a)-(c). Figure 5C shows the calculated quantum capacitance of single-vacancy silicene with different concentrations, as a function of Φ. For different vacancy's concentrations, the surface charge versus potential drop with Φ at the range from −0.6 eV to 0.6 eV is shown in Figure 5D. Following the increase of defect's concentration from 1.4% to 12.5%, the maximum of CQ increases from 1.91 µF/cm2 at −0.38V to 102.65 µF/cm2 at −0.19V. This can be attributed to the defect Si demonstrated by the LDOS. From the calculated charge accumulations in Figure 5D, an enormous enhancement occurs, irrespective of negative or positive bias. This phenomenon is due to an increase in the number of available states around the Fermi energy. Furthermore, it is observed that the performance of surface charge versus potential drop is the best under low bias as the concentration increases to 5.6%. From DOS, the local minimum of the states attributed to the Dirac point is shifted upward owing to the down-shift of Fermi level. This indicates the p-type doping of single vacancy. Moreover, owing to the anchoring of local defect states from vacancy, the down-shift of Fermi level is slow with the increase in vacancy concentration. Compared with pristine silicene, the defects with low concentration don't modulate obviously the band structure, as demonstrated by the band structure of single-vacancy silicene with the concentration of 1.4% (Figure S1 of SI). With the increase in vacancy concentration, e.g., at the concentration of 3.1% (Figure S1 of SI), additional energy bands can be observed and they are introduced by single vacancy. Compared with 8


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pristine silicene, the Fermi level of single-vacancy silicene with the concentration of 3.1% is shifted downward by approximately 0.49 eV with an energy gap of 0.31 eV. We also explore the double vacancy effect (Figure 1c) on CQ with the change in defect concentration. As shown in Figures 6A and B, the double vacancy introduces a defect state near Fermi level. From the band structure, at the double-vacancy concentration of 3.1% (Figure S2 of SI), it can be observed that the band gap is opened owing to the double vacancy. With the increase of concentration to 5.6%, the states near Fermi level exhibit an apparent increase. Furthermore, the band gap is closed. From Figures 6C and D, CQ increases irrespective of negative or positive bias and the charge accumulations are enhanced. It can be observed that the localized states near Fermi level introduced by double vacancy are not high at low concentration owing to the disappearance of dangling bonds around the vacancy. Interestingly, at the concentration of 5.6%, CQ is apparently enhanced for small electrode potential |Φ|.

3.2 Modification induced by N-doping concentration Based on the N-doping configuration in Figure 1d, the band structure of silicene has been distinctly modified owing to the introduction of N impurities. The total DOS is shown in Figure 7A. The total DOS and LDOS of dangle-bond Si and doping-N with the N concentration of 2% are shown in Figures 7B(a)-(d). It can be observed that the DOS of N-doped silicene is similar to that of pristine silicene, besides a small down-shift of Fermi level and the local defect states near Fermi level. Compared with pristine silicene, the Fermi level of pyridine-N doping with the concentration of 3.1% is shifted downward by approximately 0.28 eV with an energy gap of 0.15 eV (Figure S3 of SI). Therefore, it is modified to become a p-type semiconductor. In Figure 7C, the relation between the pyridine-N doping and CQ is shown. Following the increase of N concentrations from 1.4% to 5.6%, the maximum of CQ increases from 20.16 to 73.28 µF/cm2 around 0 V. For the N concentration of 1.4%, 2%, 3.1%, and 5.6%, the maxima of CQ for pyridine-N doping silicene in the range of −0.6 V to 0.6 V are 22.55 µF/cm2 at 0.048 V, 20.16 µF/cm2 at 0 V, 40.92 µF/cm2 at 0.12 V, 73.28 µF/cm2 at −0.07 V, respectively. This significant improvement of CQ is due to the increase of DOS near Fermi 9



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level from the contribution of the shift of Dirac point and impurity states. From the LDOS, the doping N doesn't apparently contribute to the local defect states near Fermi level, which are mostly from the defect Si around the vacancy. The defect Si with two covalent bonds formed with the nearby Si atoms has two residual electrons to form an isolated pair of electrons. The isolated pair results in the localized states near Fermi level and also leads to electron deficiency for the occupation of π states near Fermi level. This results in the p-type doping. Figure 7D presents the surface charge density versus potential for pyridine-N doping with different concentrations. The N-doping near the vacancy can enhance the charge accumulations. The performance is the best at the N concentration of 5.6%. This is attributed to the formation of a peak in DOS, when the N concentration is increased to 5.6%. We also consider the concentration effect of the triple-N doping with single vacancy shown in Figure 1f. The DOS and band structure of silicene have been modified obviously owing to the contribution of N impurities, shown in Figure 8A. From the LDOS in the case with the N concentration of 6% in Figures 8B(a)-(c), the Si near the vacancy and the doped N don't introduce the localized states near Fermi level. However, the N-modified vacancy results in the renormalization of energy bands near Fermi level with the down-shift of Fermi level and the formation of band gap. At the N-doping concentration of 9.4% (Figure S4 of SI), the Fermi level is shifted downward to approximately 0.44eV below the valance band maximum and the energy gap is approximately 0.47 eV. It is a typical p-type semiconductor without an impurity state in the band gap. With the increase in the N concentration, the shift of Fermi level doesn't change apparently and the band gap increases. Therefore, in the curve of CQ in Figure 8C, the position of local minimum is shifted to approximately 0.3 V–0.5 V with the doping of N. Following the increase of N concentration from 4.2% to 37.5%, the maximum of CQ increases from 15.94 to 58.68 µF/cm2 at approximately 0 V. It is evident that the renormalization of energy bands near Fermi level and the down-shift of Fermi level result in the increase of CQ for a small voltage. Figure 8D shows the surface charge versus potential drop for different N-doping concentrations in the range of −0.6 to 0.6 V. The charge accumulation undergoes an enormous enhancement at positive bias.

3.3 Modification induced by different atoms (P, B, N and S) 10


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In order to study the effect of different dopants on electronic properties of single-vacancy silicene, we have selected B, N, S, and P as the dopants. The structural models are shown in Figures 1e-h and the concentration of the dopant is 9.4%. Figure 9A shows the DOS and LDOS of these doped single-vacancy silicenes. Except for the N-doping discussed above, all these dopants—B, S, and P—introduce localized states near Fermi level with a small band gap at the Dirac point. The B-doping and S-doping result in spin polarization, as shown in Figure S5 of SI. For B-doping, the band gap is almost closed owing to the separation between the spin-up and spin-down bands near Fermi level. For S-doping, the band gap is apparently opened with the up-shift of Fermi level, although the spin-up band is separated from the spin-down near Fermi level. The P-doping results in the down-shift of Fermi level (0.38 eV) with a band gap of 0.43 eV. The quantum capacitances of single-vacancy silicene with these doped atoms are analyzed in Figure 9B. For the N-, B-, P-, and S-doping, the local maxima of CQ near 0 V are 42.29 µF/cm2, 55.9 µF/cm2, 43.33 µF/cm2, and 43.27 µF/cm2, respectively. Evidently, the high quantum capacitance is attributed to the localized states near Fermi level. This indicates that the doping with single vacancy can significantly improve the CQ of pristine silicene. Figure 9C shows the surface charge versus potential drop Φ between −0.6 eV and 0.6 eV for different dopants. It is observed that the charge accumulation is more dominant at negative bias for B and positive bias for N. Among these dopants, B-doping with vacancy exhibits the best performance for charge accumulation. This may be attributed to the spin-polarized localized states near Fermi level and the closing of band gap.

4．．CONCLUSION We explored the electronic structure and quantum capacitance of defected silicene with the doping and vacancies by first-principles methods. The thermal stability of doped silicene was demonstrated using molecular dynamics simulations. The quantum capacitance of silicene is larger than that of graphene owing to the relatively lower Fermi velocity derived from the bands near Dirac point. With the doping and vacancy defects, the quantum capacitance of silicene can be enhanced apparently. It was observed that these modulating methods modified obviously the band structures of silicene. The localized states are 11



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introduced near the Dirac point with the shift of Fermi level. The enhancement of quantum capacitance was found to be from the contribution of localized state near Fermi level. The quantum capacitance was observed to increase by following the increase of defect's concentration, such as the N-doping with single vacancy. Compared to the N- and P-doping single-vacancy silicene, B and S could strongly bond with Si atoms with very low formation energy. Moreover, B-doping and S-doping resulted in spin polarization near Fermi level. It was observed that the vacancy and doping atoms played an important role in modulating quantum capacitance. We expect these results stimulate the further experimental works on the doped silicene and shed some light on silicene-based electrodes for the applications of supercapacitors.

Supporting Information Available: The electronic structures of silicene with different types of defects are shown in Figure S1-S5. Average Si−Si bond length and Si−B bond length plotted at different temperatures is shown in Figure S6. The cell size effect in MD simulation is considered in Figure S7.

ACKNOWLEDGEMENTS X. Fan acknowledges the financial support from the National Key R&D Development Program of China (Grant No. 2016YFA0200400) and the National Natural Science Foundation of China (Grant No. 11504123 and No.51627805). G. M. Yang would like to acknowledge the support by the Natural Science Foundation (51641202), thirteenth Five-year Planning Project of Jilin Provincial Education Department Foundation (Grant No.JJKH20170651KJ), Natural Science Foundation of Changchun Normal University (Grant No. 2015-010) and Natural Science Foundation of Jilin Province (Grant No. 20170101099JC).

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Figure 1

Figure 1. Atomic structures of proposed silicene models including (a) pristine silicene, defected silicene with (b) single-vacancy, (c) double-vacancy, and single-vacancy silicene with the doping of (d) single pyridine-N, (e) triple-B, (f) triple-N, (g) triple-P and (h) triple-S.

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Figure 2

Figure 2. (a) Band structure of pristine silicene, and (b) calculated quantum capacitance (CQ) and (c) curves of surface charge vs. potential drop of pristine silicene and graphene, respectively.

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Figure 3

Figure 3. (A) The formation energies of different defects including (a) single-vacancy, (b) double-vacancy (c) pyridine-N doping with single-vacancy, (d) triple-N with single-vacancy, as a function of defect concentration, and (B) triple-N, triple-P, triple-B, and triple-S with single-vacancy by fixing the dopant’s concentration of 9.4%.

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Figure 4

Figure 4. Average Si−Si bond length and Si−N bond length plotted over 3000 fs duration at different temperatures for the model in Figure 1d with the N concentration of (a) 5.6% and (b)1.4%.

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Figure 5

Figure 5. (A) Density of states (DOS) of single-vacancy silicene with different concentrations including (a) 1.4%, (b)2%, (c)3.1%, (d)5.6%, and (e)12.5%, (B) density of states (DOS) and local density of states (LDOS) of defect Si atoms (DSi1, DSi2 and DSi3) with the single-vacancy concentrations of 2%, (C)calculated quantum capacitance (CQ) of single-vacancy silicene with different concentrations corresponding to Figure 5A, as a function of local electrode potential(Φ), and (D) surface charge vs. potential drop for different vacancy concentrations and Φ between -0.6 eV and 0.6 eV. The results are obtained with the supercells including (a) P(6ൈ6), (b) P(5ൈ5), (c) P(4ൈ4), (d) P(3ൈ3), and (e) P(2ൈ2).

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Figure 6

Figure 6. (A) Density of states (DOS) of double-vacancy silicene with different concentrations including (a) 5.6%, (b) 3.1%, (c) 2%and (d) 1.4%,(B) density of states (DOS) and local density of states (LDOS) of defect Si with the double-vacancy concentrations of 1.4%, (C) calculated quantum capacitance (CQ) of double-vacancy silicene with different concentrations corresponding to Figure 6A, as a function of local electrode potential(Φ), and (D) surface charge vs. potential drop for different vacancy concentrations and Φ between -0.6 eV and 0.6 eV.

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Figure 7

Figure 7. (A) Density of states (DOS) of defected silicene model in Figure 1(d) with different N-doping concentration including (a) 1.4%,(b) 2%, (c) 3.1%, (d) 5.6%, (B) density of states (DOS) and local density of states (LDOS) of N and defect Si ((DSi1 and DSi2 ) with N-doping concentration including 2%, (C) calculated quantum capacitance (CQ) of single-vacancy silicene with different N-doping concentrations corresponding to Figure 7A, as a function of local electrode potential(Φ), and (D) surface charge vs. potential drop for different N-doping concentrations and Φ between -0.6 eV and 0.6 eV.

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Figure 8

Figure 8. (A) Density of states (DOS) of defected silicene model in Figure 1(f) with different triple N-doping concentrations including (a)4.2%, (b) 6%, (c) 9.4%, (d) 16.7% and (e) 37.5%, (B) density of states (DOS) and local density of states (LDOS) of N with N-doping concentrations 6%, (C) calculated quantum capacitance (CQ) of different triple N-doping concentration corresponding to Figure 8A, as a function of local electrode potential(Φ), and (D) surface charge vs. potential drop for different triple N-doping concentrations and Φ between -0.6 eV and 0.6 eV.

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Figure 9

Figure 9. (A) Density of states (DOS) and local density of states (LDOS) of N, B, P and S of defected silicene model in Figure 1(e)-(h) with doping concentrations of 9.4%, (B) calculated quantum capacitance (CQ) corresponding to Figure 9A, as a function of the local electrode potential(Φ), and (C) surface charge vs. potential drop and Φ between -0.6 eV and 0.6 eV. Note that the total DOS and LDOS are the sum of spin-up and spin-down bands for the cases of the S-doping and B-doing.

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TOC Graphic

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Quantum Capacitance of Silicene-Based Electrodes from First

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