Optoelectronic and charge carrier hopping properties of ultra-thin boron nitride nanotubes

Accepted Manuscript Optoelectronic and charge carrier hopping properties of ultra-thin boron nitride nanotubes Stevan Armaković, Sanja J. Armaković, Svetlana S. Pelemiš, Jovan P. Šetrajčić PII: DOI: Reference:

S0749-6036(14)00478-9 http://dx.doi.org/10.1016/j.spmi.2014.12.010 YSPMI 3527

To appear in:

Superlattices and Microstructures

Received Date: Accepted Date:

11 December 2014 15 December 2014

Please cite this article as: S. Armaković, S.J. Armaković, S.S. Pelemiš, J.P. Šetrajčić, Optoelectronic and charge carrier hopping properties of ultra-thin boron nitride nanotubes, Superlattices and Microstructures (2014), doi: http://dx.doi.org/10.1016/j.spmi.2014.12.010

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Optoelectronic and charge carrier hopping properties of ultra-thin boron nitride nanotubes 1,*

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University of Novi Sad, Faculty of Sciences, Department of Physics, Trg Dositeja Obradovića 4, 21000, Novi Sad, Serbia, 2

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Stevan Armaković, 2Sanja J. Armaković, 3Svetlana S. Pelemiš, 1Jovan P. Šetrajčić

University of Novi Sad, Faculty of Sciences, Department of Chemistry, Biochemistry and Environmental Protection, Trg Dositeja Obradovića 3, 21000, Novi Sad, Serbia,

University of East Sarajevo, Faculty of Technology, Zvornik, Karakaj bb, 75400 Zvornik, Republic of Srpska, Bosnia and Herzegovina

Corresponding Author: Stevan Armaković, Telephone: +381 21 485 2816 E-mail: [email protected]

Abstract: Optoelectronic properties of ultra-thin boron nitride nanotubes and charge carrier hopping properties between them were investigated within density functional theory. The study encompassed calculations of optoelectronic quantities, such as reorganization energies, oxidation and reduction potentials and charge carrier hopping rates between mentioned nanotubes. Charge coupling was calculated applying full quantum mechanical treatment, while Marcus theory was used for calculations of charge carrier hopping rates. Results indicate differences between investigated types of boron nitride nanotubes. With the increase in dimensions of boron nitride nanotubes optoelectronic properties are improving, while charge carrier hopping rates are the highest for (6,0) boron nitride nanotube. Keywords: boron nitride nanotubes, dft, optoelectronics, charge hopping

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1. Introduction Ever since they have been firstly predicted in 1994 by Rubio et al [1] and successfully synthesized in 1996 by Chopra et al [2], boron nitride nanotubes (BNNTs) are considered as one of the most intriguing non-carbon nanotubes [3]. They are seen as adequate candidate structures for substitution of conventional carbon nanotubes (CNTs) [4]. Their structural similarity with CNTs is related with hexagonal structure in which boron and nitrogen atoms are placed instead of carbon atoms [2, 5]. Regarding conductive properties, contrary to of CNTs, which can be semiconducting or metallic, BNNTs are always electrical insulators with relatively large band gap of around 5.8 to 6.0 eV and this property is nearly independent to both tube diameter and chirality [3, 6, 7]. The popularity of nanotube like structures based on non-carbon elements, such as BNNTs and boron-phosphide nanotubes (BPNTs), is constantly increasing and numerous theoretical and experimental studies have been performed so far [8]. With regard to carbon, boron and nitrogen atoms, their property related with small covalent radius (namely the generation of considerable strain energy) makes for them possible to form very stable low-dimensional structures with smaller coordination. Contrary to carbon, boron and nitrogen structures, low coordination structures based on Si atoms, are predicted to be unstable [8-11]. Beside conductive properties, reactivity properties are what mainly distinguish BNNTs over CNTs. Namely, exterior surfaces of BNNTs are more reactive, thanks to which functionalization through sidewall decoration, chemisorption and adsorption is more effective [12, 13]. This is especially important for the practical applications of BNNTs, as this increased reactivity can be used for the production of efficient sensors for the detection of common atmospheric pollutants, otherwise hardly detected by CNTs [13-15]. In this study we decided to theoretically investigate the optoelectronic properties of (3,0), (4,0), (5,0) and (6,0) BNNTs within the DFT, for the first time. The aim of this work was the analysis of the effects of BNNTs dimensions to some of the crucial optoelectronic properties, important for practical application. We were encouraged with the fact that characterization experimental studies of optoelectronic properties of BNNTs have been performed [16, 17] and also with the fact that biosensor for glucose [18] and light emitting device [7] based on BNNTs have been successfully manufactured. Efficiency of electronic materials is related with high charge mobilities and efficient charge injection [19]. When it comes to the charge transport, at room temperatures the most important mechanism is hopping mechanism, which is used for study of charge mobilities in systems investigated in this work. Within this mechanism, charge hopping rate, k ET , is the main quantity that regulates the charge carrier mobility and represents the rate constant or the hopping rate for charge transport between adjacent molecules. k ET turned out to be useful quantity and in the framework of Marcus theory can be expressed as [20, 21]: 2

K ET =

4π 2 h

⎡ −λ ⎤ t 2 exp⎢ ⎥. 4π λ k B T ⎣4 kB T ⎦ 1

(1)

The last equation is principally dictated by two key quantities, the reorganization energy, λ , and charge transfer integral (or charge coupling), t . It should be noted that we shall regard to the results of Marcus theory as a first approximation and the obtained values of charge mobilities shall be treated only as qualitative trends, due to the simplicity of used models [22, 23].

2. Computational details All DFT calculations were performed with Schrödinger Jaguar 8.4. program and its corresponding optoelectronics and electron coupling modules [24]. Optoelectronic properties, namely oxidation and reduction potential (OP and RP respectively), electron and hole reorganization energies (ERE and HRE respectively) were obtained using the screening calculation method which is intended to produce high quality results using small basis set [25]. Charge transfer integrals and hopping rates of electrons and holes were obtained employing full quantum mechanical treatment. Hopping rates were calculated according to the Marcus theory. In this study we used the following computation procedure. Firstly, geometries of monomer systems of BNNTs were optimized with extensively checked B3LYP [26, 27] functional with 6-31G+d,p basis set in order to obtain initial information on structures. Then, optoelectronic properties (OP, RP, HRE and ERE) were obtained within screening calculation method at B3LYP/MIDI! level of theory. The usage of this level of theory is explained later, in chapter 3.2. Then, dimer BNNT structures were obtained at M06-2X/6-31G+d,p level of theory, as M06-2X functional is recommended in situations when non-covalent interactions take place [28-30], Finally, charge transfer rates were calculated at recommended B3LYP/LACV3P** level of theory.

3. Results and discussion

3.1.

Structural considerations

Typical quantum molecular descriptors, energies of frontier molecular orbitals (HOMO and LUMO) and chemical hardness (η), obtained after geometrical optimizations of structures investigated in this study are summarized in Table 1, while their geometries are provided in Figure 1. 3

Table 1. Energies of HOMO and LUMO orbitals with HOMO-LUMO gap and distance, l, between monomers. Results for monomer systems of BNNTs are obtained at B3LYP/631+G(d,p) while dimmer systems of BNNTs were obtained at M06-2X/6-31+G(d,p) level of theory l Structure HOMO LUMO HOMO-LUMO gap η [eV] [eV] [eV] [eV] [Å] BNNT(3,0) -6.98 -3.76 3.22 1.61 BNNT(3,0) Dimer -8.30 -2.30 6.00 3.00 1.56 BNNT(4,0) -6.82 -3.72 3.10 1.55 BNNT(4,0) Dimer -8.07 -2.38 5.69 2.84 1.59 BNNT(5,0) -6.78 -2.80 3.98 1.99 BNNT(5,0) Dimer -7.96 -1.67 6.29 3.14 1.62 BNNT(6,0) -6.95 -2.12 4.83 2.41 BNNT(6,0) Dimer -6.07 -1.67 4.40 2.20 2.06

Figure 1. Structures obtained after geometrical optimizations: a) (3,0), b) (4,0), c) (5,0) and d) (6,0) BNNTs. It can be seen in Table 1 that the most stable monomer system in this study was the (6,0) BNNT, with the value of 2.41 eV for η. All other investigated monomer systems have significantly high values of this quantity describing global stability, while the lowest value is calculated for the (4,0) BNNT. In this case the value of η was 1.55 eV. Concerning the stability of dimer systems, the most stable system was (3,0) BNNT with η of 3.00 eV, while the lowest η was calculated for the dimer system of (6,0) BNNT. It was interesting to note that all but one dimer system have significantly higher η than its monomer system. That difference is higher than 1 eV. Only (6,0) BNNT dimmer system has lower value of η than its monomer system, namely in this case the η of dimmer system is lower for 0.21 eV than η of monomer system. However, all investigated systems are having significantly high value of η. 4

As for distance between monomer units of dimer structure, l , the situation is very similar in all cases except, again, in the case of (6,0) BNNT. In the first three cases the distance is having values ca. 1.60 Å, while in the case of (6,0) BNNT this quantity has significantly higher value, 2.24 Å. This quantity is very important for the charge carriers mobility, as diffusion coefficient is depending on the second power of l .

3.2.

Oxidation and reduction potentials and reorganization energies

As mentioned in Computational details chapter, optoelectronic properties are calculated within screening method [25]. Within this method MIDI! basis set (which is in Jaguar program denoted as MIDIX) is used, which produces results similar in quality as 6-31Gd, but on the other side much improved over 3-21Gd. However, since MIDI! doesn’t have coverage for many elements in the periodic table, by default for any element for which MIDI! is not defined, 6-31Gd is used. If however 6-31Gd is not defined for certain element, LACV3P is used [25]. Concerning the oxidation and reduction potentials, OP and RP respectively, they are calculated within Koopmans approximation using the following equation: OP (or RP) = S × OE + I

(2)

where S, OE and I denotes slope, orbital energy and intercept, respectively. The values of slope and intercept were obtained by linear regression against experimental OP and RP over wide range of organic light emitting diode (OLED) materials, including hole and electron transporting materials, emitting materials, organics and organometallic complexes [25]. The value of orbital energy is HOMO energy from the neutral molecule for the OP, and the LUMO energy for the RP. These values were developed using B3LYP with the default basis set, which is MIDI! in this case. This means that these values are not suitable for other functionals and basis sets, other than B3LYP and MIDI!. Precisely, the value of slopes for OP and RP were -17.50 and -22.50 V, respectively, while the values of intercept for OP and RP were –2.17 and –0.35 V, respectively [25]. Results concerning the OP and RP are provided in Figure 2. The measure of the strength of the local electron-phonon coupling is reorganization energy [19-21]. This parameter consists of two contributions; the inner and the outer one. The inner contribution, λi is determined by fast changes in molecular geometry and the outer contribution, λ 0 , is determined by slow variations in polarization of surrounding medium. Thus, the following relation can be formed λ = λ0 + λi , while the outer contribution is commonly neglected [19-21]. The importance of the reorganization energies lies in the fact that this parameter can be used for assessment of the impact of charge (hole and electron) injection [31]. Reorganization energies can be calculated according to following formulas: 5

( )

where E 0 G 0

λ1 = E 0 (G * )− E 0 (G 0 ),

(3)

λ2 = E * (G 0 )− E * (G * ),

(4)

λi = λ1 + λ2

(5)

( )

and E * G * are the ground state energies of the neutral and ionic states,

( )

respectivelly. E 0 G * is the energy of the neutral molecule at the optimal ionic geometry,

( )

while E * G 0

is the energy of the charged state at the optimal geometry of the neutral

molecule. According to equation (3), the reorganization energy should be minimized in order to obtain high charge transfer rates. The lower the value of λ is in equation (3), the higher will be the charge transfer rates. With the increase of dimensions of studied BNNTs in this study, HRE and ERE decreased significantly, Figure 2, indicating better charge injection properties.

Figure 2. OP and RP together with HRE and ERE. Precise values of mentioned parameters are given above and below columns RP/OP can be interpreted as the tendency of structure to gain/loose electrons and thus to become oxidized/reduced. According to results presented in Figure 2, OP remains almost unchanged as the tube type changes, while the RP significantly increase. This result shows that with the increase of tube diameter, electron affinity increases significantly. This also 6

indicates that electron charge transfer between BNNT should increase substantially with the increase of tube diameter, which will be confirmed latter through charge transfer rates. HRE also decrease significantly with the increase of tube diameter. Namely, HRE decreases subsequently from 1.26 to 0.38 eV from (3,0) to (5,0) tubes, while for (6,0) tube HRE is somewhat larger, 0.50 eV, than for (5,0) tube, but still it is much lower than initial value of 1.26 eV. Concerning the ERE, it decreases subsequently with the increase of tube diameter, from 0.42 to 0.21 eV. Reorganization energies clearly decrease, which indicates that charge transfer rates should be improved with the increase of tube diameter, according to equation (1).

3.3.

Charge transfer integrals and hopping rates

The probability for electron tunneling between two adjacent molecules is described by the charge transfer integral, t . This parameter reflects the strength of the electronic interaction between two adjacent molecules. t is clearly spatially dependent; it is determined by relative arrangement of the molecules between which the charge transfer is observed. The electronic coupling between two molecules is defined by the matrix element t = ψ a H ψ b , H being the electronic Hamiltonian of the system, while ψ a and ψ b are the wave functions of two charge localized states [19, 21]. In certain situations, for example for the case of cofacially stacked molecules, this parameter can be computed/approximated as one half the splitting of the frontier orbitals of the complex [19]. However, it is better to apply the full quantum mechanical treatment, calculating the wave functions before and after electron transfer. According to equation (1), t should be maximized in order to obtain higher charge transfer rates. In other words, the higher the t is between two molecules, the higher will be the charge transfer rate between them. Results of charge transfer integrals, t , and charge transfer rates, k ET , are provided in Table 3.

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Table 3. Electron coupling between BNNTs and corresponding charge hopping rates Structure BNNT(3,0) Dimer

BNNT(4,0) Dimer

BNNT(5,0) Dimer

BNNT(6,0) Dimer

Transfer direction Forward Hole Backward Hole Forward Electron Backward Electron Forward Hole Backward Hole Forward Electron Backward Electron Forward Hole Backward Hole Forward Electron Backward Electron Forward Hole Backward Hole Forward Electron Backward Electron

t

k ET

[eV] 0.064825 0.064827 0.477668 0.477636 0.385763 0.385769 0.016590 0.016589 0.054827 0.054840 0.032987 0.032943 3.173604 3.173610 4.570192 4.570258

[s-1] 8.08×106 6.90×109 4.38×1015 2.92×1010 2.27×1010 8.26×1011 6.41×1011 1.89×1010 1.91×1012 2.15×1012 6.62×1012 7.86×1011 1.86×1015 1.83×1015 1.02×1017 9.68×1016

Full quantum mechanical treatment of electron coupling enables one to obtain both forward and backward charge couplings and charge carrier hopping rates. As provided in Table 3, it can be seen that charge coupling for both forward and backward transfer is practically the same. The first difference is at the fourth decimal. However, as expected, the differences in hopping rates are quite different, ranging to several orders of magnitude. The highest both hole and electron hooping rates have been calculated for (6,0) BNNT and this results can be attributed to several reasons. This type of BNNT has the largest surface which consequences in the largest orbital overlap. Both HRE and ERE are the lowest of all calculated in this study, while t is the highest. Although the distance between (6,0) BNNTs is the highest of all investigated in this work, electron affinity according to RP is the highest, thus enabling the more efficient electron hopping. The lowest hole kET was calculated for the (3,0) BNNT, but it was more interesting that for this case electron kET was the highest after the (6,0) BNNT. This can be attributed to the fact that in this case t has significantly high value because BNNTs are close to each other, enabling the significant orbital overlap. Both (4,0) and (5,0) BNNTs had significantly high values of kET, with (5,0) having higher values. However, it was interesting to observe that t has much higher value for the case of hole transfer between (4,0) BNNTs than t for the case of electron transfer between (4,0) BNNTs and both holes and electrons transfer between (5,0) BNNTs. Nevertheless, relatively low t between (5,0) BNNTs didn’t affect the kET since in this case reorganization energies are 8

significantly reduced. Furthermore, according to RP, electron affinity is much improved, thus enabling better charge transfer.

4. Conclussion In summary, DFT computations have been applied in order to determine optoelectronic properties of ultra-thin BNNTs (m,0), where m goes from 3 to 6. Charge coupling was calculated applying full quantum mechanical treatment while charge carrier hopping rates have been calculated within the framework of Marcus theory. Chemical hardness indicates that investigated structures are stable. Average distance between monomer units was similar for (3,0), (4,0) and (5,0) BNNT, namely the distance was around 1.6 Å. In the case of (6,0) BNNT, the distance was higher and has a value of around 2.06 Å. Obtained results indicate that with the increase of tube dimensions reorganization energies of both holes and electrons are decreasing, except for the case of (6,0) BNNT where HRE is somewhat higher than for (5,0) BNNT, but still significantly lower than the HRE of the (3,0) BNNT. This is positive effect, since for better charge mobility reorganization energies should be minimized. The highest electron coupling and the best charge carrier hopping rates are calculated for the largest BNNT investigated in this work, namely the (6,0) BNNT. It can be concluded that charge carrier hopping properties increase with the increase of BNNT dimensions.

5. Acknowledgment This work is done within the project of the Ministry of Education and Science of Republic of Serbia grant no. OI 171039. Many thanks to our dear friend and collague Vladimir Jokić, University of Novi Sad, Faculty of Sciences, Department of Physics, for the technical support we received.

6. Dedication This work is dedicated to our late dear friend and colleague Igor Vragović who worked at Departmento de Fisica Aplicada, Universidad de Alicante. Thanks to his kind support and very useful guides we were able to obtain results of this and several other papers, through which we contribute to scientific community.

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Graphical abstract

Highlights

• • • •

optoelectronic properties of ultra-thin BNNTs are investigated charge coupling and charge carrier hopping rates between BNNTs are calculated full quantum mechanical treatment is used for the calculations of charge couplings charge carrier hopping rates are calculated within Marcus semi-empirical theory

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