Monoatomic aluminum nitride nanochains and

Vacuum 136 (2017) 40e45

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Monoatomic aluminum nitride nanochains and nanorings: DFT studies Saeid Onsori a, *, Leila Fatahiyan b a b

Department of Chemistry, Central Tehran Branch, Islamic Azad University, Tehran, Iran Young Researchers and Elite Club, Yadegar-e-Imam Khomeini (RAH) Shahr-e- Rey-Branch, Islamic Azad University, Tehran, Iran

a r t i c l e i n f o

a b s t r a c t

Article history: Received 4 November 2016 Received in revised form 13 November 2016 Accepted 14 November 2016 Available online 15 November 2016

Employing density functional theory calculations, we have studied a series of AlN nanochains and nanorings. We chiefly found that the chains have linear construction with triplet spin state that tend to be converted to the stable rings. By increasing the length of chains they show more metallic character. The Al-N bonds of chains are alternatively changed but those of the ring is equivalent. The HOMO-LUMO energy gap of chains was predicted to be very narrow in comparison to that of the rings. Unlike the chains, the ring buildings show resonance behavior. Depending the number of AlN units (being odd or even), the rings show different electronic properties. The HOMO and LUMO of chains are destabilized and stabilized, respectively, by increasing the length. We compared our results with those of the corresponding BN nanostructures. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Nanostructures Ab initio calculations Electronic properties Aluminum nitride

1. Introduction Numerous nanostructures have been synthesized and attracted a large attention for their different properties and brilliant applications [1e14]. Graphene with unique electronic properties was proposed to be the base of next generation circuits, thus the monoatomic carbon chains are predicted to display a key role in circuit manufacturing [15e18]. It seems that there is a similarity between carbon and AlN structures which can be documented by comparing graphene with hexagonal AlN, diamond with cubic AlN, carbon nanotubes with AlN nanotubes, and fullerenes with AlN nanocages [19e24]. The AlN is a wide band gap compound which shows high hardness, stability, thermal conductivity, and low coefficient of thermal expansion. It is often used in thin film devices as a substrate [25]. During the last decade numerous efforts have been dedicated to synthesis, characterization, and potential applications of AlN nanostructures [26e39]. In this work, we inspect the electronic, energetic, and structural properties of AlN nanochains and also their corresponding nanorings by means of density functional theory (DFT) calculations. Previously, DFT calculations have been employed to investigate similar carbonaceous and BN structures, indicating valuable results

* Corresponding author. E-mail address: [email protected] (S. Onsori). http://dx.doi.org/10.1016/j.vacuum.2016.11.023 0042-207X/© 2016 Elsevier Ltd. All rights reserved.

[40e42]. Our main purpose is investigating the property dependence on the structural configuration, spin state, and size of these systems. We will compare our results with those of BN nanochain [42] and will investigate the possible existence of these nanostructures. It is anticipated to extract some physical rules that illuminate the property alterations from small to the big scales. The results of electronic properties give insight into the potential applications in the electron field emitters, electronic devices, and sensor industries. For example, controlling the electronic properties of the studied structures can be achieved by the change of shape and size based on the calculations which is important in circuit industry. The AlN nanostructures have drawn an extensive attention for their possible applications in the filed emitters [38]. An important parameter that controls the performance of a field emitter is work function [43,44] and it depends on the Fermi level, thereby on the HOMO and LUMO. The dependency of these parameters on the shape and size of the AlN nanostructures has been investigated herein [45]. 2. Computational details Frontier molecular orbitals and natural bond orbital (NBO) analyses, and all the other calculations were performed using B3LYP density functional which was executed in the GAMESS program [46]. The B3LYP is a commonly used approach, and has been revealed to be a reliable and commonly used method in the

S. Onsori, L. Fatahiyan / Vacuum 136 (2017) 40e45

exploration of different nanostructures [47e56]. The 6311 þ G* basis set was used for all calculations by analogy with calculations on BN nanochains and nanorings [42]. Different chains of AlN and also analogous ring conformers were inspected. In open shell AlN compounds, for HOMO-LUMO gap (Eg) calculations, the HOMO will be exchanged by the SOMO (singly occupied molecular orbital) which is the highest orbital with an unpaired electron. To scrutinize the relative stability of the AlN different configurations, the binding energy is defined as follows:

Ebin ¼ E ðAlNÞn nEðAlNÞ n

(1)

where E((AlN)n) is the electronic energy of (AlN)n chain or ring, and E(AlN) is the electronic energy of the smallest unit of AlN molecule. Based on Eq. (1), for AlN molecule (n ¼ 1) Ebin is zero. Physically it means that the AlN molecule is the unit cell with no interaction with the other species.

3. Results and discussion 3.1. AlN molecule First, we calculated the potential energy curves for the hypothetical AlN diatomic molecule with both singlet and triplet spin states at B3LYP level of theory with 6311 þ G* basis set. The results (Fig. 1 and Table 1) demonstrate that the triplet spin state geometry with two unpaired electrons is energetically more stable than the singlet one by about 26.6 kcal/mol. The comparison of this finding with experimental results [57] and spectroscopic constants [58] supports the assignment of the AlN molecule ground state to a 3 П state, similar to the BN molecule [42]. The NBO charge analysis (Table 1) shows that the singlet state corresponds to a more ionic description of the AlN molecule than the triplet state and is more instable. In Fig. 1, the repulsive part of the potential energy curve is described well for both the singlet and triplet state but the attractive part is strongly in error for singlet spin state. Similar to the case of triplet state, it is expected that in the large enough distances the binding energy between Al and N atoms becomes zero but B3LYP overestimates this energy. This phenomenon is a challenging problem for DFT calculations especially when there exist degenerate levels which is known as static correlation error [59]. The electronic configuration of N atom is 1s22s22p3 which gives the spin multiplicity of 4 with a three-fold degenerate state. At large distance the spin multiplicity of completely separated N and Al system is one during the scan process which fails to calculate accurate results.

Fig. 1. Potential energy curves for singlet and triplet spin state AlN molecule dissociation at B3LYP level of theory with 6311 þ G* basis set.

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Table 1 Relative energy (E, kcal/mol), Al-N distance (d), and the NBO charge is transferred from Al to N atom, the HOMO, LUMO and Eg energies (eV) for AlN molecule at B3LYP level. The energy of the most stable state is assumed to be zero. Basis set

AlN

E

d(Å)

Frequency

Q(e)

HOMO

LUMO

Eg

6311 þ G*

Singlet Triplet Singlet Triplet

26.6 0 26.4 0

1.68 1.80 1.67 1.79

926 730 940 749

1.247 0.902 1.143 0.876

6.58 6.29 6.56 6.32

5.02 3.88 4.95 3.80

1.56 2.41 1.60 2.52

cc-pVQZ

Spin density plot (Fig. 2) displays that the unpaired electrons are located on the both Al and N atoms. Furthermore, the coupledcluster singles/doubles (CCSD) approach with 6311 þ G* basis set indicates a stability by about 21.22 kcal/mol for triplet state. The calculated Al-N bondlength is about 1.80 and 1.68 Å for triplet and singlet states, respectively and vibrational frequency is about 730 and 926 cm1. Experimental value of vibrational frequency is 748 cm1 [33], which is in agreement with the value of triplet state. The HOMO, LUMO, and Eg values (Table 1) show that both structures have narrow gap which is a kinetic stability index. Smaller gap refers to the lower kinetic stability. Experimental value of band gap of bulk AlN is about 6.2 eV [60] and the computed Eg for (5, 0) zigzag AlN nanotube and AlN nanosheet at B3LYP level of theory is about 4.20 and 4.68 eV [21,61], respectively, which are much larger than the Eg of AlN molecule. Compared to the electronic properties of a BN molecule at the same theoretical level, the HOMO and LUMO of AlN is somewhat more instable and the Eg is smaller. The Eg of BN molecule is about 1.92 and 2.77 eV for singlet and triplet states, respectively [42]. This indicates the lower kinetic stability of AlN molecule compared to the BN one. The HOMO of singlet state is two-fold degenerate level (Fig. 2) and located on the N atoms but the LUMO is not degenerate and is largely localized on the Al atom. The SOMO and LUMO in the triplet state are not degenerate and both of them are located on both Al and N atoms. All of the calculations were repeated with a larger basis set (cc-pVQZ) at the same B3LYP level of theory and the results are collected in Table 1. The results indicate that this larger basis set does not importantly affects the energetic, electronic or geometric parameters. Therefore, we select 6311 þ G* basis set for our study, preventing expensive and time-consuming computations and also for comparison with the pervious study on the BN nanochains [42]. 3.2. The system of (AlN)2 For (AlN)2, two geometries were expected including square ring and linear chain. A linear chain may be singlet or triplet. Our calculations indicate that the triplet state is energetically more stable. Vibrational frequencies are calculated to be in the range of 49e1176 cm1, presenting a true local minimum. The largest frequency indicates a stretching mode of whole chain. The spin density plan (Fig. 3) specifies that the probability of finding of the unpaired electrons is much more on the end atoms. The energy of SOMO and LUMO levels is about 5.83 and 4.64 eV which are more localized (Fig. 3) at the N and Al head of the chain, respectively. Thus, the Eg is about 1.19 eV (Table 2). The SOMO and LUMO of (AlN)2 are higher than those of (BN)2 [42] and its Eg is smaller. This indicates more metallic character and lower kinetic stability of the AlN structures compared to the BN ones. The MEP plot (Fig. 3) also demonstrates that N atoms are electron rich and Al atoms are electron deficient places, especially at the ends. For the (AlN)2 square ring an unstable saddle point with a high negative vibrational frequency (151 cm1) is predicted which is not reported here.

42


Fig. 2. (a) Spin density; (b) the LUMO; and (c) the two-fold degenerate SOMO profiles of AlN molecule. In the molecular orbitals, the different colors reflect positive or negative orbital phases.

3.3. The system of (AlN)3 The (AlN)3 linear stable structure is triplet and the Al-N bonds are alternatively decreased and increased. Spin density plot (Fig. 4) supports that the unpaired electrons more confined on the end N and Al atoms. Starting from N head the first Al-N bond is the largest one with the length of 1.86 Å, the second Al-N bond is 1.67 Å, and so on. This suggests that there exists an unoccupied orbital on the each end N and Al atom and a lone pair on the each N ones. The SOMO and LUMO of the linear (AlN)3 lie at 5.18 and 4.87 eV, generating an Eg of 0.31 eV which is smaller than that of (AlN)2. The (AlN)3 ring structure (Fig. 4) is more stable than the linear one by about 53.2 kcal/mol. The calculated vibrational frequencies are in the range of 196e924 cm1, confirming a local minimum. The Al-NAl, N-Al-N angles, and Al-N bonds are about 94.6 , 145.3 , and 1.76 Å, respectively, and the structure has D3h symmetry. Unlike the linear structure, all bonds are equivalent in the ring which displays a resonance. The HOMO and LUMO lie at 6.65 and 3.39 eV. The HOMO is a two-fold degenerate antisymmetric orbital and the LUMO is a non-degenerate symmetric one, as shown in Fig. 4. The Eg is about 2.73 eV which is much more than that of linear structure. 3.4. The system of (AlN)4 We have predicted two (AlN)4 isomers entailing a chain and a ring with triplet and singlet states, respectively. The ring conformer is more stable than the linear one by about 73.0 kcal/mol (Table 2). Like the linear (AlN)3, the (AlN)4 chain is formed alternatively from a long and a short Al-N bonds. The end bonds are larger compared to the central ones and are about 1.81 Å. The electronic properties of (AlN)4 such as SOMO, LUMO location, and spin density are also similar to those of (AlN)3. The SOMO and LUMO energies of the

linear isomer are about 5.30 and 5.03 eV, respectively, producing an Eg of 0.27 eV. The SOMO antisymmetric and the LUMO is symmetric (Fig. 5). The SOMO mainly is localized on the nitrogen atoms but the LUMO mainly is located on the central Al atom and somewhat on the other Al ones. The ring geometry is nearly like a square in which N atoms are placed at four apexes. Each side of the square includes an N-Al-N atom groups which is a little deviated from straight line and the NAl-N angle is about 163.6 . In comparison with the (AlN)4 ring this angle is smaller than the N-B-N one by about 2.5 [42]. Furthermore, the Al-N-Al angle is about 106.4 (it is103.9 for B-N-B [42]) and all the Al-N bonds are equal being about 1.74 Å. The point group for ring structure is D4h. Similar to the case of linear structure, here the he HOMO is antisymmetric and mainly located on the N atoms with energy of 6.66 eV. The LUMO also is a symmetric level which mainly located on the center and Al atoms with energy of 3.39 eV (Fig. 5). The ring structure has a large Eg about 3.26 eV in comparison to the linear one, demonstrating that it is an insulator unlike the linear structures that are semimetal or semiconductor. 3.5. The system of (AlN)5 Linear and ring structures for (AlN)5 with triplet and single states, are predicted, respectively. Similar to the smaller chains, the (AlN)5 chain is constructed alternatively from long and short Al-N bonds. The SOMO and LUMO energies are about 6.01 and 5.73 eV, respectively, producing an Eg of 0.28 eV for the linear construction. The ring arrangement is like a pentagon with D5h symmetry in which the N atoms are located at apexes and all Al-N bonds are equal with length of about 1.33 Å. The Al-N-Al angels are about 115.8 and the N-Al-N angels are about 172.2 in which Al atom is somewhat projected out of the ring. The ring structure is more stable than the linear one by about 129.8 kcal/mol. The HOMO


43

behavior.

3.6. The larger (AlN)n systems Different properties of (AlN)n, n ¼ 6, 7, 8, 9, 10 are collected in Table 2 for both linear and ring conformations. It can be concluded that a certain trend obtained for the electronic properties of the chains by length increasing. The SOMO level is especially destabilized and the Eg is decreased. This trend shows that by increasing the length a chain converts from semiconductor to a semimetal material. This can be interpreted using the particle in a onedimensional (1D) box model of quantum mechanics. In this model, a “particle” with mass m is limited to a 1D “box” along the xaxis between x ¼ 0 and x ¼ L. Resolving the Schrodinger equation for the this model, the energy level for each electron is given

En ¼

n2 h2 8mL2

(2)

where h is Planck's constant, L is the box length, and m is the particle mass. The permissible energies are quantized levels (n). We take up that the AlN chain is the 1D box with the length L and the electrons are confined to the conjugated Al-N bonds and cannot transfer beyond the boundaries. As the electron wavefunction extends beyond the terminal Al and N atoms, we add approximately one-half bond length at each end. It gives a length equal to the number of atoms times the average Al-N bond length (b). Each energy level (n) label a molecular orbital capable of accepting up to 2 electrons. The Eg for the AlN chain can be considered from Eq. (2) as Fig. 3. (a) Spin density; (b) LUMO; and (c) SOMO of linear (AlN)2. (d) Molecular electrostatic potential surface whichis defined by the 0.0004 electrons/b3 contour of the electronic density. Color ranges for in a.u.: blue, more positive than 0.010; green, between 0.010 and 0; yellow, between 0 and -0.010; red, more negative than 0.010. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).

Table 2 Relative energy (E, kcal/mol), binding energy (Ebin, kcal/mol) Al-N distance (Å), the HOMO, LUMO and Eg energies (eV) for (AlN)n chains and rings. The energy of the most stable state is assumed to be zero. The numbers in the first column are designated to the number of AlN units in the structures. n

Isomer

E

Ebin

Al-N-Al

Al-N

EHOMO

ELUMO

Eg

2 3

Chain Chain Ring Chain Ring Chain Ring Chain Ring Chain Ring Chain Ring Chain Ring Chain Ring

e 53.2 0.0 73.0 0.0 89.9 0.0 96.3 0.0 100.3 0.0 113.5 0.0 115.2 0.0 116.1 0.0

49.6 61.2 79.0 75.8 94.1 79.8 99.6 85.8 101.9 88.7 103.1 90.3 104.5 92.1 104.9 93.4 105.6

e e 94.6 e 106.4 e 115.3 e 122.9 e 129.7 e 135.6 e 140.0 e 144.0

e e 1.76 e 1.74 e 1.72 e 1.71 e 1.71 e 1.70 e 1.70 e 1.67

5.83 5.18 6.65 5.30 6.66 5.23 6.91 5.22 6.78 5.20 6.82 5.02 6.70 5.01 6.70 5.01 6.60

4.64 4.87 3.92 5.03 3.39 5.00 3.30 5.06 3.24 5.06 3.12 4.90 3.02 4.91 2.93 4.92 2.85

1.19 0.31 2.73 0.27 3.26 0.23 3.61 0.16 3.54 0.13 3.69 0.12 3.68 0.10 3.77 0.09 3.75

4 5 6 7 8 9 10

and LUMO of the ring structure lie at 8.19 and 1.23 eV, creating an Eg of 6.96 eV. The HOMO and LUMO of pentagon (Table 2) are stabilized and destabilized in comparison to those of the tetragon, thereby generating larger Eg and indicating higher insulator

Eg ¼ ELUMO EHOMO ¼

h2 8mL

2

nLUMO 2 nHUMO 2

(3)

For N electron AlN system, we can write

nHOMO ¼

N 2

(4)

nLUMO ¼

N þ1 2

(5)

L¼

2N b 12

(6)

where 12 is sum of electrons of an Al and a N atom. Replacing nHOMO; nLUMO; and L in the right hand of Eq. (3) gives

Eg ¼

. . ð2N þ 1Þ N2 9h2 2ma2

(7)

Based on Eqs. (6) and (7), increasing the length of the AlN chain the Eg will decrease which is in agreement with our findings. From Table 2, it can be found that all the ring structures are more stable than the corresponding chains due to more negative binding energies but by increasing the number of AlN unit the energy difference is slightly decreased. By increasing the AlN blocks of rings, the Al-N bonds become shorter and the stability of chains and rings significantly starts increasing, then the increment became very slow. The LUMO level of large rings with odd number of AlN is more stable than that of the rings with even number. The Eg of rings alternatively somewhat increases and decreases for odd and even number of AlN unit, respectively. It has been indicated that bulk AlN materials are wide-band gap (~6.2 eV) semiconductor while its low dimensional graphene-like h-AlN is not wide-band gap semiconductor [60]. Our results may help understanding growth and

44


Fig. 4. (a) Linear structure (b) spin density (c) ring structure, (d) HOMO and (e) LUMO for (AlN)3. Distance is in Å.

Fig. 5. The optimized structures of chain and ring (AlN)4 and their frontier molecular orbitals. Distance in Å.

synthesis of AlN nanostructures and explaining the effect of the size on the electronic properties especially on the Eg Refs. [62,63]. 4. Conclusions We investigated the energetic, electronic, and structural properties of AlN nanochains and nanorings by means of DFT calculations. We show that AlN nanochains are biracial compounds that intensively tend to be closed and formed a ring. They have alternatively single and double bonds through the chain. The Al atoms

are not saturated and are strong Lewis acids. By increasing the length of the chain it tends to be converted from an insulator to a semimetal material. The ring constructions are steadier than the corresponding chains and show more insulator character. The rings with odd or even AlN units display different electronic properties. By increasing the AlN units from 2 to 10, the Eg is gradually decreased from 1.19 to 0.09 eV in AlN chains and increased from 2.73 to 3.75 eV in AlN rings. The binding energies for (AlN)10 chain and ring are about 93.4 and 105.6 kcal/mol, respectively, indicating higher stability of the rings.


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