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First principles study on the spin unrestricted electronic structure properties of transition metal doped InN nanoribbons
Superlattices and Microstructures 84 (2015) 170–180
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First principles study on the spin unrestricted electronic structure properties of transition metal doped InN nanoribbons S. Caliskan ⇑, F. Hazar Physics Department, Fatih University, 34500, Buyukcekmece, Istanbul, Turkey
a r t i c l e
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Article history: Received 2 March 2015 Received in revised form 30 April 2015 Accepted 4 May 2015 Available online 14 May 2015 Keywords: InN nanoribbon First principles Energy gap Spin polarization
a b s t r a c t In the present study, first principles calculations were carried out to reveal the spin unrestricted electronic structure behavior of both pure and transition metal (TM) atom (V and Co) doped InN nanoribbons (InN-NRs). The influence of a substitutionally doped TM atom on the electronic structure nature was examined. The role of a TM dopant together with its location, governing the characteristic of spin dependent electronic property of a doped InN-NR, was addressed. The relevant properties were extracted through Hubbard correction for In-d, N-p and TM-d states. We observed that a single TM dopant diminished the spin dependent energy gap and can result in a significant induced magnetic moment in an InN-NR system. It was exposed that TM dopants can play an essential role in the spin unrestricted electronic behavior and spin polarization, which can be tuned through a V or Co atom at a certain position. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Spintronics is a field which involves the spin property of electrons [1–3]. Low dimensional systems are the fundamental structures in this field where novel and multifunctional properties can emerge. Semiconducting materials play a crucial role in spintronics [4–6]. The behavior of electron spin in ⇑ Corresponding author. Tel.: +90 2128663300; fax: +90 2128663402. E-mail address: [email protected] (S. Caliskan). http://dx.doi.org/10.1016/j.spmi.2015.05.004 0749-6036/Ó 2015 Elsevier Ltd. All rights reserved.
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these systems must be revealed to employ them in nanotechnology. Spintronic applications require spin polarization which is determined by the spin unrestricted electronic property of a system. This feature can be improved by dopants and their atomic positions in a structure [7]. Direct band gap semiconductors, such as III-nitride alloys, are preferred in optoelectronics and semiconducting industry [8]. There have been considerable works on InN structures [9,10]. These semiconducting structures have narrow band gap [9,11], low effective mass and high electron mobility [10,12]. These features make them promising semiconductors for the applications in industry and novel technology. InN structures were examined in earlier studies, both experimentally [11,13] and theoretically [14]. Theoretically, the band gap of InN was calculated to be approximately 0.7 eV [15]. This value was also observed in experimental studies [16,17]. The theoretical works employing the Density Functional Theory (DFT) revealed that the band gap (Eg ) was underestimated. As the band gap of an InN nanostructure is narrow, one may obtain zero Eg through the DFT calculations [18]. In order to overcome this matter or to correctly describe the electronic structure properties of InN materials one needs to involve Hubbard (U) correction [19,20]. This correction must be applied for In-d and N-p states [19]. U term improves the approximations used in DFT calculations [20,21]. For instance, in Ref. [21], although U term makes a correction, the bandgap of the InN was obtained as 0.34 eV. Nowadays, it is possible to produce device structures in nanoscale [22]. InN structures and other low dimensional systems in various forms (such as nanowires, sheets, nanoribbons) were widely studied [16,23]. However, in order to extract remaining issues and fully understand several properties, investigations on these systems are still going on. In low dimensional materials, due to the broken periodicity at the surface, the behavior of electrons becomes modified. It yields a distinct electronic property and interesting features, which are otherwise not exhibited in bulk form. Because of the edge effects, for instance, a nanowire or nanoribbon can exhibit a distinct electronic structure nature compared to the bulk one. Semiconducting low dimensional materials, in general, have many applications in optoelectronics or nanoelectronics [24,25]. Experimentally, semiconducting nanowires can be fabricated [26]. First principles calculations were performed to determine the electronic and structure properties of these wires [24,27]. In an earlier work InN nanowires were examined, employing both first principles and empirical tight-binding method [21]. InN materials can be fabricated in the form of nanowires [28]. InN semiconductors have a wurtzite crystal structure in bulk and nanowire forms [8]. An InN nanowire or nanoribbon (which can be employed as a fundamental structure, for instance, to fabricate field effect transistor, sensor etc.) plays a significant role in the fabrication of optoelectronic devices. Nanowires and nanoribbons, or low dimensional structures having a narrow energy band gap, are the candidate systems for the possible applications in the field of spintronics. In these systems, due to the reduced dimension, spin manipulation can be fulfilled. It is required in spintronic devices. In this work, we intended to give an extensive analysis of both pure and transition metal (TM) doped InN nanoribbon (InN-NR) structures, focusing on the spin unrestricted electronic structure behavior. In general, our purpose was to extract the influence of a substitutionally doped TM atom at a certain position on the electronic structure. We restricted ourselves to V and Co doped zigzag InN-NRs to reveal their spin unrestricted electronic structure feature. We performed first principles calculations, through DFT, employing the software package Atomistix ToolKit (ATK) [29], on the spin unrestricted electronic properties of InN-NRs in the presence of U correction. While InN nanowires were widely studied, to our knowledge, there is only one study concerning the electronic structure behavior of InN-NRs where the spin property is not involved [30]. In Ref. [30], employing first principles, for the first time electronic properties of InN-NRs were investigated. It was shown that the electronic structure of an InN-NR can be tuned by impurities and defects. Defects resulted in metallic nature in InN-NRs which otherwise showed semiconducting property. Concentrating on the spin dependent electronic structure properties, the present work gives an extensive study of both pure and TM doped InN-NRs. To this end, we obtained spin dependent band structure, density of states (DOS), partial density of states (PDOS) and spin polarization at the Fermi energy (EF ). Besides, we also exposed magnetic properties by means of magnetic moment calculations. It was found, as expected, that a TM atom played an essential role in the spin unrestricted electronic properties. We
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demonstrated that these properties or the associated spin polarization can be tuned through a certain TM atom at a certain position. It can destroy the semiconducting property of the pure InN-NR, resulting in semiconductor–metal transition. In section II, the method is presented; in section III, the numerical results and discussions are reported; concluding remarks and summary are given in section IV. 2. Method A pure zigzag InN-NR structure was constructed using a perfect InN wurtzite crystal. The supercell vector along z axis was aligned with the chiral vector (n,m) = (3,3). It forms an InN-NR with zigzag edge, having 12 atoms wide. The pure InN-NR in the supercell was composed of 12 In, 12 N and 4 H atoms which were placed to passivate the dangling bonds (H termination of the edge atoms can be required in order to get a stable InN-NR). In doped structures, where N atoms were replaced by either Co or V atoms, the TM dopants were substitutionally introduced. In order to tune the spin unrestricted electronic properties, a single TM dopant was examined at various positions. Both pure and doped InN-NR structures were then relaxed. The relaxation leads to optimized atomic distance between the atoms. During the relaxation of InN-NRs, the force tolerance was set to 0:05 eV=Å. Then, first principles calculations and analysis were carried out for the spin dependent electronic structure properties. In calculations, the exchange–correlation potential was approximated within the spin dependent generalized gradient approximation (SGGA) with Perdew–Burke–Ernzerhof (PBE) functional (SGGA.PBE) [31] for the exchange and correlation effects of the electrons (For a more detailed explanation of the calculation method employed in ATK, see Ref. [29,32]). The ATK employs the Troullier–Martins pseudopotentials [33] for the ion cores in the systems. A mesh cutoff energy of
Fig. 1. An optimized (a) pure and (b) representative TM doped InN-NR structure, passivated by H atoms, in the supercell. In, N, TM and H are denoted by brown, blue, gray and white atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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150 Ry and (1,3,99) k-point mesh within the Monkhorst–Pack scheme [34] were utilized. In order to enhance the accuracy, the double-zeta polarized basis set of local numerical orbitals was used for In, N and TM atoms. U term was involved and set to 6 eV, 1.5 eV, 3 eV and 5 eV for In-d, N-p, V-d and Co-d states, respectively [19,21]. An optimized pure and representative doped InN-NR system in the supercell are schematically depicted in Fig. 1. Upon replacing the N atom by a TM (Co or V), we relaxed the supercell and set 3
the maximum stress to 0:05 eV=Å . During the relaxation, TM doped supercell was not constrained. It resulted in an enlarged supercell as the covalent radii of these TMs (1.26 and 1.25 Å for Co and V, respectively) are greater than radius of the N atom (0.75 Å). For the pure InN-NR the volume of the 3
3
cell was 1934.52 Å . It became 2171.94 Å , for instance, for the Co doped InN-NR. The InN-NR structure was infinite along the z axis and its width was 12 atoms wide (when H atoms were excluded) along the y axis where sufficient vacuum was introduced in the supercell to prevent the interaction between repeated images. Employing such a supercell, we intended especially to exhibit how the spin unrestricted electronic structure property and spin polarization of an InN-NR at a certain energy can be altered through a specific TM dopant and its position. 3. Numerical results In this part, first principles calculation results are presented for the optimized pure (Fig. 1a) and TM doped InN-NRs where a single dopant is substitutionally added (Fig. 1b). A single N atom was replaced by either Co or V atom, yielding a dopant concentration of 3.7% in the supercell. We present the results for a single Co dopant at a certain position and V dopant at three particular positions, as shown in Fig. 2. In Fig. 2, three distinct locations in the V doped InN-NR are represented by InN-NRV1 ; InN-NRV2 and InN-NRV3 . In particular, these V doped InN-NRs were employed to observe the influence of the dopant location on the electronic structure properties. Moreover, for the sake of comparison, the spin unrestricted electronic behavior of an InN-NR containing double V dopants in the supercell (giving the V concentration of 7.7%), where two N atoms at the upper edge were replaced by the V atoms (represented by InN-NR2V ), was also examined. We mainly obtained the spin unrestricted electronic band structure, DOS in the vicinity of the EF (EF was set to zero) and spin polarization yielding an induced magnetic moment in doped systems. The pure InN-NR did not lead to spin dependent variation, implying no spin polarization. In contrast, we found that a TM dopant can result in a remarkable spin polarization or induced magnetic moment in doped InN-NR structures. In the vicinity of EF , the spin unrestricted band structure for pure InN-NR, InN-NRV1 ; InN-NRV2 ; InN-NRV3 ; InN-NR2V and a single Co doped InN-NR are illustrated in Fig. 3. The corresponding DOS spectra are presented in Fig. 4. In the spectra, for the sake of clarity, the majority (positive) and minority (negative) states are displayed separately. The DOS spectrum of the pure InN-NR has a symmetry for majority (spin-up) and minority (spin-down) variation (spin-symmetric variation). On the other hand, substitutionally doped TM atoms lead to spin-asymmetric band structure or DOS spectra. Spin asymmetry in a DOS spectrum yields spin polarization at particular energies. TM dopants result in extra states in the vicinity of the EF and break the spin-symmetric variation. For InN-NRV1 and InN-NR2V the semiconducting property was destroyed and semiconductor–metal transition was observed. This transition also occured when a single Co atom was introduced at any position and for higher (V or Co) dopant concentrations. However, for a V atom located at other positions, yielding the structures InN-NRV2 and InN-NRV3 , this property was preserved and we obtained spin unrestricted Eg . It indicates the substantial role of the position of a TM dopant in determining the electronic behavior of a doped InN-NR. The associated Eg values for the pure InN-NR, InN-NRV2 and InN-NRV3 are tabulated in Table 1. For the pure InN-NR, interestingly, the spin independent Eg was achieved as 1.20 eV which is much wider than bulk value (0.7 eV). The geometry of the structure (a perfect nanoribbon system) and adopted exchange–correlation potential together with U term may give rise to such an Eg value. It was drastically reduced for each spin direction when a single V dopant was introduced. For the system InN-NRV2 (InN-NRV3 ), majority and minority-spin Eg values became 0.42 eV and 0.33 eV (0.32 eV and
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A
B
C
Fig. 2. The supercell representing three particular dopant positions. It is composed of In (brown), N (blue) and a TM atom which can be located at A (InN-NRV1 or single Co doped InN-NR), B (InN-NRV2 ) or C (InN-NRV3 ), replacing the N atom. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
0.54 eV), respectively. It implies the crucial impact of the location of a V atom on the spin dependent Eg . The influence of a TM on Eg became more for InN-NRV3 compared to InN-NRV2 . When the system was altered from InN-NRV2 to InN-NRV3 , the majority-spin Eg was reduced while the minority one was enhanced. The change in the spin unrestricted Eg was governed by both the majority and minority states in the presence of a single V dopant as shown in Fig. 4. The main reason of spin dependent change in Eg of TM doped InN-NRs is due to the hybridization of host atoms and TM-d orbitals. For the pure InN-NR, the majority and minority spin band structures were identical (spin-symmetric), yielding a spin independent Eg . However, doping with the TM atoms affected the spin dependent energy states in the vicinity of the EF . It resulted in spin dependent Eg , giving rise to majority and minority-spin Eg . Since V doped InN-NRs were obtained to have a narrow spin dependent Eg , they may have potential spintronic applications in technology. We observed that dopant location and its concentration govern the characteristic of the electronic structure behavior which determines the spin-asymmetric band structure and associated DOS spectra. Doping the semiconducting materials with TM atoms yields diluted magnetic semiconductors (DMSs) [5,35]. The DMS plays a crucial role in the field of spintronics. It is a semiconductor, where the TM dopant concentration is low, and shows spin dependent property. In our case, when a single V atom was introduced, at specific locations, the InN-NR preserved its semiconducting property. For such a low concentration of V (3.7%), thus, a V doped InN-NR can become a DMS which can be employed as a functional and fundamental material in developing spintronic devices. In Ref. [30], the authors, employing first principles in the absence of the U term, obtained that the electronic structure of InN-NRs can be tuned by impurities and defects. Without presenting the Eg
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Energy (eV)
Energy (eV)
Energy (eV)
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Fig. 3. Majority (black) and minority-spin (red) band structure, around the EF , for pure InN-NR, single Co doped InN-NR, InN-NRV1 ; InN-NRV2 ; InN-NRV3 and InN-NR2V . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
values for the InN-NRs, they specified that defects resulted in metallic nature in InN-NRs which otherwise displayed semiconducting property. In their work, N atoms were replaced by the impurities which were not TMs. In the present work, following Ref. [30], in a similar manner, we replaced the N (anion) atoms by the TM dopants. In this way, we were able to observe the effect of the anion vacancy on the electronic structure property (InN structures have a high electron concentration which can be due to anion vacancy [36]). We carried out first principles calculations through the U term which improves the Eg . Our findings exposed the substantial role of TM dopants on the spin unrestricted electronic nature of InN-NRs. Introducing a single TM atom can crucially alter the DOS variation at certain energies. The principle spin unrestricted electronic structure property may be attributed to the induced spin orientations due to the TM dopants. Our study (through the TM atoms) and Ref. [30] (through the defects) revealed that semiconductor–metal transition can be observed, which implies the consistency of both works even if the methods used are different. In our case, the metallic property was observed in InN-NRV1 ; InN-NR2V and Co doped InN-NRs (for any Co concentration at any position). For these metallic systems, we investigated the spin polarization at the EF . It
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Fig. 4. Spin dependent DOS as a function of energy, around the EF , for pure InN-NR, InN-NRV1 ; InN-NRV2 ; InN-NRV3 ; InN-NR2V and single Co doped InN-NR. The difference in majority (positive, blue) and minority-spin (negative, red) variations yields the spin polarization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Spin dependent Eg in eV for the pure and V doped InN-NRs. System
Majority
Minority
Pure InN-NR InN-NRV2
1.20 0.42
1.20 0.33
InN-NRV3
0.32
0.54
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must be sufficiently high for the applications in the field of spintronics. InN-NRV1 ; InN-NR2V and a single Co doped InN-NR exhibited a spin polarization of 61%, 2% and 24%, respectively, at the EF . Spin polarization is defined as ðDOS" ðEF Þ DOS# ðEF ÞÞ=ðDOS" ðEF Þ þ DOS# ðEF ÞÞ, where DOS" ðEF Þ and DOS# ðEF Þ are the majority and minority-spin DOS at the EF , respectively. At a certain energy, it expresses the spin-asymmetry in the DOS spectra and stems from the interaction of nearest-neighbor host InN atoms and TM dopants (which lift the orbital degeneracy). A suppressed (enhanced) majority-spin DOS relative to the minority one implies a reduction (enhancement) in the spin polarization. It gives rise to magnetism and plays a key role in developing novel spintronic devices. Half-metals are the fundamental materials in spintronics. They exhibit metallic property for one spin direction and show semiconducting nature for the other direction. Thus, a half-metal has 100% spin polarization at the EF . Among the aforementioned metallic systems, InN-NRV revealed the highest spin polarization. However, one requires a value close to 100% to mimic the half-metallic materials. On the other hand, we observed that TM doped InN-NRs are promising systems where one can tailor the spin polarization through a particular TM atom and its position to obtain the half-metallic nature. Therefore, one can state that semiconductor–metal-(nearly) half-metallic transition is possible in InN-NRs through introducing only a single TM at certain atomic locations. In this work, we restricted our concentration to the influence of a TM atom on the spin unrestricted electronic structure properties. We chose the V and Co atoms as specific TM dopants. V-3d orbital is less than half filled and Co-3d orbital is more than half filled. Both V and Co atoms were already employed in graphene nanoribbons to expose the spin dependent properties [37]. Through these particular TM atoms, we attempted to reveal the role of a TM in InN-NR structures. As a future study, we intend to examine a detailed study concerning how the spin polarization can further be enhanced through the various dopants introduced in InN-NRs. The average magnetic moment in a TM doped system can be computed via Mulliken analysis [32]. This analysis yields the magnetic moment through the spin charge density magnetization given by majority-spin charge density minus minority-spin charge density. The majority and minority DOS of the pure InN-NR were identical, leading to a zero magnetic moment (see Fig. 4). Since the doping with TM atoms affects the spin dependent energy states, where TM-d orbitals play a major role, the DOS variation became spin-asymmetric (see Fig. 4 for the TM doped InN-NRs). It leads to spin polarization or finite magnetic moment. The average magnetic moment per atom acquired in InN-NRV1 and in single Co doped InN-NRs was calculated as 0.15 lB and 0.11 lB (lB is the Bohr magnetron), respectively. As expected, it was independent of the TM location (InN-NRV1 ; InN-NRV2 and InN-NRV3 exhibited the same average magnetic moment) but governed by strength of the hybridization between host atoms and TM-d orbitals. The main reason of spin dependent behavior of a TM doped system comes from the hybridization of host atoms and TM-d orbitals. The hybridization of host atoms and TM-d orbitals in graphene was already emphasized in earlier works [38,39]. For instance, in Ref. [38] the induced magnetism of carbon atoms in graphene due to Ni electrode was examined. It was found that the magnetic moment on a carbon atom in graphene layer was due to the strong hybridization between host and Ni-d states. A TM atom, whose d orbital is not fully filled, breaks the spin symmetry and gives rise to magnetic moment. It affects majority and minority-spin populations and induces local magnetic moment on its adjacent host atoms. For instance, in InN-NRV1 , the magnetic moments on V and adjacent In and N atoms were 3.71 lB , 0.06 lB and 0.14 lB , respectively. For a single Co doped InN-NR, those on Co, (adjacent) In and N atoms were 2.67 lB , 0.08 lB and 0.01 lB , respectively. The magnetic moment became almost zero on non adjacent host atoms, which can be attributed to the delocalization of TM-d states. It was intriguing to observe quite a larger magnetic moment on neighboring N atom compared to In atom in InN-NRV1 . It may be related to strong hybridization between N-p and V-d orbitals. Thus, the induced local magnetic moments on the host N atoms were highly sensitive to the TM type. On the other hand, replacing the V by the Co atom hardly modified the local magnetic moment on In atoms. We analyzed PDOS to elucidate the contribution of certain atoms and orbitals to the spin dependent DOS. The states near the EF underlies the electronic nature of a system. A finite value at a certain energy in PDOS spectrum means the associated states are available at this energy. We present the PDOS spectra of single Co doped InN-NR as a particular structure. It is illustrated in Fig. 5 for In, N,
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Fig. 5. Majority (blue, positive) and minority-spin (red, negative) PDOS as a function of energy around the EF . It is projected on In, N, Co-d, Co-s valence orbitals for the single Co doped InN-NR and on V-d, V-s valence orbitals for InN-NRV1 . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Co-3d and Co-4s states. In this figure, the contribution of V-3d and V-4s is also involved for the sake of comparison. Note that PDOS spectra in Fig. 5 are for TM-d, TM-s orbitals and all In and N atoms in the supercell. The PDOS variations for In and N atoms are quite similar. In the energy interval, from 0.8 eV to 0.8 eV, we see some certain well defined peaks as large as 20 eV1 and 30 eV1 , for majority (where minority become zero) and minority-spin (where majority is close to zero) PDOS of In atoms. It is clearly seen in Fig. 5 that, at all energies, the spin dependent PDOS values for N atoms are diminished compared to those for In atoms. The observed spin-asymmetry in the PDOS of In and N originates from the induced magnetic moment due to the host atoms adjacent to the TM dopant. Spin dependent PDOS spectra of host atoms imply the contribution of them to the average magnetic
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moment. In the single Co doped InN-NR, at negative energies up to 0.07 eV (0.05 eV) majority (minority) spin states of host atoms vanish. At certain energy intervals we see hardly revealed majority or minority-spin PDOS (PDOS values less than 1 eV1 ), which means that the corresponding states vanish in these energy ranges. The majority-spin PDOS of Co-d orbitals vanishes at negative energies and is almost zero, with minute peaks, at positive energies. However, minority-spin PDOS becomes absent up to 0.05 eV above which sharp peaks occur as large as 6 eV1 . On the other hand, a majority-PDOS state for Co-s is not observed up to 0.07 eV and can become as large as 20 eV1 at an energy close to 0.4 eV. Minority-spin PDOS of Co-s is nearly absent up to 0.55 eV, above which it oscillates. As for the PDOS of V-d, the minority one exhibit hardly revealed states in the whole energy interval but the majority one is finite at some energy intervals with sharp peaks at particular energies, near 0.8 eV and 0.8 eV, as large as 10 eV1 . On the other hand, in PDOS of V-s, two sharp majority-spin peaks with values close to 5 eV1 arise at 0.30 eV and 0.15 eV in the vicinity of EF . Above 0.15 eV, minority-spin PDOS of V-s dominates over the majority one with minute and considerable several peaks. It is clearly seen that both TM-3d and TM-4s orbitals have an important contribution to the PDOS spectrum. In a certain energy interval, the electronic states can be well separated as a result of these orbitals. They determine the observed spin dependent sharp peaks in PDOS and the character of majority and minority-spin spectrum around the EF . The suppressed and well defined peaks highlight the spin dependent electronic properties of the relevant systems. The associated spin dependent states can be altered mainly due to the positions of TM atoms. In general, TM dopants are responsible for the spin polarization or induced magnetic moment in any system. 4. Conclusions In this work, we particularly concentrated on the spin unrestricted behavior of InN-NRs where TM atoms were substitutionally doped. In order to expose the corresponding electronic properties, first principles calculations were carried out in the presence of U correction which improves deficiencies of DFT calculations. In general, we restricted ourselves to the effect of a TM dopant and its position on the spin dependent electronic structure of an InN-NR. Incorporating of a single TM atom revealed substantial spin polarization and induced magnetism. According to the our findings, particular H passivated InN-NRs containing a single substitutional V dopant exhibited semiconducting property if it was not positioned at the edges. We observed that the spin unrestricted Eg of an InN-NR can be controlled through locating the V atom at certain positions, which may also be accomplished via playing the shape of the geometry or the width of the InN-NR. Tailoring the spin dependent electronic structure properties and associated spin polarization, one can control and develop novel InN based spintronic devices. Tunability of the electronic structure of an InN-NR is important for the possible applications in nanoelectronics. We predict that TM dopants can enhance the functionality of InN based materials. We obtained that a TM doped InN-NR is a promising system and can be a fundamental structure in electronic devices to be applicable in spin involved nanoelectronics, due to its low electron mass and narrow band gap. We believe that the present study will be an insight and helpful for experimental works. Acknowledgement _ under Grant No 108T710. This work is supported by TÜBITAK References [1] [2] [3] [4]
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Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
First principles study on the spin unrestricted electronic structure properties of transition metal doped InN nanoribbons S. Caliskan ⇑, F. Hazar Physics Department, Fatih University, 34500, Buyukcekmece, Istanbul, Turkey
a r t i c l e
i n f o
Article history: Received 2 March 2015 Received in revised form 30 April 2015 Accepted 4 May 2015 Available online 14 May 2015 Keywords: InN nanoribbon First principles Energy gap Spin polarization
a b s t r a c t In the present study, first principles calculations were carried out to reveal the spin unrestricted electronic structure behavior of both pure and transition metal (TM) atom (V and Co) doped InN nanoribbons (InN-NRs). The influence of a substitutionally doped TM atom on the electronic structure nature was examined. The role of a TM dopant together with its location, governing the characteristic of spin dependent electronic property of a doped InN-NR, was addressed. The relevant properties were extracted through Hubbard correction for In-d, N-p and TM-d states. We observed that a single TM dopant diminished the spin dependent energy gap and can result in a significant induced magnetic moment in an InN-NR system. It was exposed that TM dopants can play an essential role in the spin unrestricted electronic behavior and spin polarization, which can be tuned through a V or Co atom at a certain position. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Spintronics is a field which involves the spin property of electrons [1–3]. Low dimensional systems are the fundamental structures in this field where novel and multifunctional properties can emerge. Semiconducting materials play a crucial role in spintronics [4–6]. The behavior of electron spin in ⇑ Corresponding author. Tel.: +90 2128663300; fax: +90 2128663402. E-mail address: [email protected] (S. Caliskan). http://dx.doi.org/10.1016/j.spmi.2015.05.004 0749-6036/Ó 2015 Elsevier Ltd. All rights reserved.
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these systems must be revealed to employ them in nanotechnology. Spintronic applications require spin polarization which is determined by the spin unrestricted electronic property of a system. This feature can be improved by dopants and their atomic positions in a structure [7]. Direct band gap semiconductors, such as III-nitride alloys, are preferred in optoelectronics and semiconducting industry [8]. There have been considerable works on InN structures [9,10]. These semiconducting structures have narrow band gap [9,11], low effective mass and high electron mobility [10,12]. These features make them promising semiconductors for the applications in industry and novel technology. InN structures were examined in earlier studies, both experimentally [11,13] and theoretically [14]. Theoretically, the band gap of InN was calculated to be approximately 0.7 eV [15]. This value was also observed in experimental studies [16,17]. The theoretical works employing the Density Functional Theory (DFT) revealed that the band gap (Eg ) was underestimated. As the band gap of an InN nanostructure is narrow, one may obtain zero Eg through the DFT calculations [18]. In order to overcome this matter or to correctly describe the electronic structure properties of InN materials one needs to involve Hubbard (U) correction [19,20]. This correction must be applied for In-d and N-p states [19]. U term improves the approximations used in DFT calculations [20,21]. For instance, in Ref. [21], although U term makes a correction, the bandgap of the InN was obtained as 0.34 eV. Nowadays, it is possible to produce device structures in nanoscale [22]. InN structures and other low dimensional systems in various forms (such as nanowires, sheets, nanoribbons) were widely studied [16,23]. However, in order to extract remaining issues and fully understand several properties, investigations on these systems are still going on. In low dimensional materials, due to the broken periodicity at the surface, the behavior of electrons becomes modified. It yields a distinct electronic property and interesting features, which are otherwise not exhibited in bulk form. Because of the edge effects, for instance, a nanowire or nanoribbon can exhibit a distinct electronic structure nature compared to the bulk one. Semiconducting low dimensional materials, in general, have many applications in optoelectronics or nanoelectronics [24,25]. Experimentally, semiconducting nanowires can be fabricated [26]. First principles calculations were performed to determine the electronic and structure properties of these wires [24,27]. In an earlier work InN nanowires were examined, employing both first principles and empirical tight-binding method [21]. InN materials can be fabricated in the form of nanowires [28]. InN semiconductors have a wurtzite crystal structure in bulk and nanowire forms [8]. An InN nanowire or nanoribbon (which can be employed as a fundamental structure, for instance, to fabricate field effect transistor, sensor etc.) plays a significant role in the fabrication of optoelectronic devices. Nanowires and nanoribbons, or low dimensional structures having a narrow energy band gap, are the candidate systems for the possible applications in the field of spintronics. In these systems, due to the reduced dimension, spin manipulation can be fulfilled. It is required in spintronic devices. In this work, we intended to give an extensive analysis of both pure and transition metal (TM) doped InN nanoribbon (InN-NR) structures, focusing on the spin unrestricted electronic structure behavior. In general, our purpose was to extract the influence of a substitutionally doped TM atom at a certain position on the electronic structure. We restricted ourselves to V and Co doped zigzag InN-NRs to reveal their spin unrestricted electronic structure feature. We performed first principles calculations, through DFT, employing the software package Atomistix ToolKit (ATK) [29], on the spin unrestricted electronic properties of InN-NRs in the presence of U correction. While InN nanowires were widely studied, to our knowledge, there is only one study concerning the electronic structure behavior of InN-NRs where the spin property is not involved [30]. In Ref. [30], employing first principles, for the first time electronic properties of InN-NRs were investigated. It was shown that the electronic structure of an InN-NR can be tuned by impurities and defects. Defects resulted in metallic nature in InN-NRs which otherwise showed semiconducting property. Concentrating on the spin dependent electronic structure properties, the present work gives an extensive study of both pure and TM doped InN-NRs. To this end, we obtained spin dependent band structure, density of states (DOS), partial density of states (PDOS) and spin polarization at the Fermi energy (EF ). Besides, we also exposed magnetic properties by means of magnetic moment calculations. It was found, as expected, that a TM atom played an essential role in the spin unrestricted electronic properties. We
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demonstrated that these properties or the associated spin polarization can be tuned through a certain TM atom at a certain position. It can destroy the semiconducting property of the pure InN-NR, resulting in semiconductor–metal transition. In section II, the method is presented; in section III, the numerical results and discussions are reported; concluding remarks and summary are given in section IV. 2. Method A pure zigzag InN-NR structure was constructed using a perfect InN wurtzite crystal. The supercell vector along z axis was aligned with the chiral vector (n,m) = (3,3). It forms an InN-NR with zigzag edge, having 12 atoms wide. The pure InN-NR in the supercell was composed of 12 In, 12 N and 4 H atoms which were placed to passivate the dangling bonds (H termination of the edge atoms can be required in order to get a stable InN-NR). In doped structures, where N atoms were replaced by either Co or V atoms, the TM dopants were substitutionally introduced. In order to tune the spin unrestricted electronic properties, a single TM dopant was examined at various positions. Both pure and doped InN-NR structures were then relaxed. The relaxation leads to optimized atomic distance between the atoms. During the relaxation of InN-NRs, the force tolerance was set to 0:05 eV=Å. Then, first principles calculations and analysis were carried out for the spin dependent electronic structure properties. In calculations, the exchange–correlation potential was approximated within the spin dependent generalized gradient approximation (SGGA) with Perdew–Burke–Ernzerhof (PBE) functional (SGGA.PBE) [31] for the exchange and correlation effects of the electrons (For a more detailed explanation of the calculation method employed in ATK, see Ref. [29,32]). The ATK employs the Troullier–Martins pseudopotentials [33] for the ion cores in the systems. A mesh cutoff energy of
Fig. 1. An optimized (a) pure and (b) representative TM doped InN-NR structure, passivated by H atoms, in the supercell. In, N, TM and H are denoted by brown, blue, gray and white atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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150 Ry and (1,3,99) k-point mesh within the Monkhorst–Pack scheme [34] were utilized. In order to enhance the accuracy, the double-zeta polarized basis set of local numerical orbitals was used for In, N and TM atoms. U term was involved and set to 6 eV, 1.5 eV, 3 eV and 5 eV for In-d, N-p, V-d and Co-d states, respectively [19,21]. An optimized pure and representative doped InN-NR system in the supercell are schematically depicted in Fig. 1. Upon replacing the N atom by a TM (Co or V), we relaxed the supercell and set 3
the maximum stress to 0:05 eV=Å . During the relaxation, TM doped supercell was not constrained. It resulted in an enlarged supercell as the covalent radii of these TMs (1.26 and 1.25 Å for Co and V, respectively) are greater than radius of the N atom (0.75 Å). For the pure InN-NR the volume of the 3
3
cell was 1934.52 Å . It became 2171.94 Å , for instance, for the Co doped InN-NR. The InN-NR structure was infinite along the z axis and its width was 12 atoms wide (when H atoms were excluded) along the y axis where sufficient vacuum was introduced in the supercell to prevent the interaction between repeated images. Employing such a supercell, we intended especially to exhibit how the spin unrestricted electronic structure property and spin polarization of an InN-NR at a certain energy can be altered through a specific TM dopant and its position. 3. Numerical results In this part, first principles calculation results are presented for the optimized pure (Fig. 1a) and TM doped InN-NRs where a single dopant is substitutionally added (Fig. 1b). A single N atom was replaced by either Co or V atom, yielding a dopant concentration of 3.7% in the supercell. We present the results for a single Co dopant at a certain position and V dopant at three particular positions, as shown in Fig. 2. In Fig. 2, three distinct locations in the V doped InN-NR are represented by InN-NRV1 ; InN-NRV2 and InN-NRV3 . In particular, these V doped InN-NRs were employed to observe the influence of the dopant location on the electronic structure properties. Moreover, for the sake of comparison, the spin unrestricted electronic behavior of an InN-NR containing double V dopants in the supercell (giving the V concentration of 7.7%), where two N atoms at the upper edge were replaced by the V atoms (represented by InN-NR2V ), was also examined. We mainly obtained the spin unrestricted electronic band structure, DOS in the vicinity of the EF (EF was set to zero) and spin polarization yielding an induced magnetic moment in doped systems. The pure InN-NR did not lead to spin dependent variation, implying no spin polarization. In contrast, we found that a TM dopant can result in a remarkable spin polarization or induced magnetic moment in doped InN-NR structures. In the vicinity of EF , the spin unrestricted band structure for pure InN-NR, InN-NRV1 ; InN-NRV2 ; InN-NRV3 ; InN-NR2V and a single Co doped InN-NR are illustrated in Fig. 3. The corresponding DOS spectra are presented in Fig. 4. In the spectra, for the sake of clarity, the majority (positive) and minority (negative) states are displayed separately. The DOS spectrum of the pure InN-NR has a symmetry for majority (spin-up) and minority (spin-down) variation (spin-symmetric variation). On the other hand, substitutionally doped TM atoms lead to spin-asymmetric band structure or DOS spectra. Spin asymmetry in a DOS spectrum yields spin polarization at particular energies. TM dopants result in extra states in the vicinity of the EF and break the spin-symmetric variation. For InN-NRV1 and InN-NR2V the semiconducting property was destroyed and semiconductor–metal transition was observed. This transition also occured when a single Co atom was introduced at any position and for higher (V or Co) dopant concentrations. However, for a V atom located at other positions, yielding the structures InN-NRV2 and InN-NRV3 , this property was preserved and we obtained spin unrestricted Eg . It indicates the substantial role of the position of a TM dopant in determining the electronic behavior of a doped InN-NR. The associated Eg values for the pure InN-NR, InN-NRV2 and InN-NRV3 are tabulated in Table 1. For the pure InN-NR, interestingly, the spin independent Eg was achieved as 1.20 eV which is much wider than bulk value (0.7 eV). The geometry of the structure (a perfect nanoribbon system) and adopted exchange–correlation potential together with U term may give rise to such an Eg value. It was drastically reduced for each spin direction when a single V dopant was introduced. For the system InN-NRV2 (InN-NRV3 ), majority and minority-spin Eg values became 0.42 eV and 0.33 eV (0.32 eV and
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A
B
C
Fig. 2. The supercell representing three particular dopant positions. It is composed of In (brown), N (blue) and a TM atom which can be located at A (InN-NRV1 or single Co doped InN-NR), B (InN-NRV2 ) or C (InN-NRV3 ), replacing the N atom. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
0.54 eV), respectively. It implies the crucial impact of the location of a V atom on the spin dependent Eg . The influence of a TM on Eg became more for InN-NRV3 compared to InN-NRV2 . When the system was altered from InN-NRV2 to InN-NRV3 , the majority-spin Eg was reduced while the minority one was enhanced. The change in the spin unrestricted Eg was governed by both the majority and minority states in the presence of a single V dopant as shown in Fig. 4. The main reason of spin dependent change in Eg of TM doped InN-NRs is due to the hybridization of host atoms and TM-d orbitals. For the pure InN-NR, the majority and minority spin band structures were identical (spin-symmetric), yielding a spin independent Eg . However, doping with the TM atoms affected the spin dependent energy states in the vicinity of the EF . It resulted in spin dependent Eg , giving rise to majority and minority-spin Eg . Since V doped InN-NRs were obtained to have a narrow spin dependent Eg , they may have potential spintronic applications in technology. We observed that dopant location and its concentration govern the characteristic of the electronic structure behavior which determines the spin-asymmetric band structure and associated DOS spectra. Doping the semiconducting materials with TM atoms yields diluted magnetic semiconductors (DMSs) [5,35]. The DMS plays a crucial role in the field of spintronics. It is a semiconductor, where the TM dopant concentration is low, and shows spin dependent property. In our case, when a single V atom was introduced, at specific locations, the InN-NR preserved its semiconducting property. For such a low concentration of V (3.7%), thus, a V doped InN-NR can become a DMS which can be employed as a functional and fundamental material in developing spintronic devices. In Ref. [30], the authors, employing first principles in the absence of the U term, obtained that the electronic structure of InN-NRs can be tuned by impurities and defects. Without presenting the Eg
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Energy (eV)
Energy (eV)
Energy (eV)
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Fig. 3. Majority (black) and minority-spin (red) band structure, around the EF , for pure InN-NR, single Co doped InN-NR, InN-NRV1 ; InN-NRV2 ; InN-NRV3 and InN-NR2V . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
values for the InN-NRs, they specified that defects resulted in metallic nature in InN-NRs which otherwise displayed semiconducting property. In their work, N atoms were replaced by the impurities which were not TMs. In the present work, following Ref. [30], in a similar manner, we replaced the N (anion) atoms by the TM dopants. In this way, we were able to observe the effect of the anion vacancy on the electronic structure property (InN structures have a high electron concentration which can be due to anion vacancy [36]). We carried out first principles calculations through the U term which improves the Eg . Our findings exposed the substantial role of TM dopants on the spin unrestricted electronic nature of InN-NRs. Introducing a single TM atom can crucially alter the DOS variation at certain energies. The principle spin unrestricted electronic structure property may be attributed to the induced spin orientations due to the TM dopants. Our study (through the TM atoms) and Ref. [30] (through the defects) revealed that semiconductor–metal transition can be observed, which implies the consistency of both works even if the methods used are different. In our case, the metallic property was observed in InN-NRV1 ; InN-NR2V and Co doped InN-NRs (for any Co concentration at any position). For these metallic systems, we investigated the spin polarization at the EF . It
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Fig. 4. Spin dependent DOS as a function of energy, around the EF , for pure InN-NR, InN-NRV1 ; InN-NRV2 ; InN-NRV3 ; InN-NR2V and single Co doped InN-NR. The difference in majority (positive, blue) and minority-spin (negative, red) variations yields the spin polarization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Spin dependent Eg in eV for the pure and V doped InN-NRs. System
Majority
Minority
Pure InN-NR InN-NRV2
1.20 0.42
1.20 0.33
InN-NRV3
0.32
0.54
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must be sufficiently high for the applications in the field of spintronics. InN-NRV1 ; InN-NR2V and a single Co doped InN-NR exhibited a spin polarization of 61%, 2% and 24%, respectively, at the EF . Spin polarization is defined as ðDOS" ðEF Þ DOS# ðEF ÞÞ=ðDOS" ðEF Þ þ DOS# ðEF ÞÞ, where DOS" ðEF Þ and DOS# ðEF Þ are the majority and minority-spin DOS at the EF , respectively. At a certain energy, it expresses the spin-asymmetry in the DOS spectra and stems from the interaction of nearest-neighbor host InN atoms and TM dopants (which lift the orbital degeneracy). A suppressed (enhanced) majority-spin DOS relative to the minority one implies a reduction (enhancement) in the spin polarization. It gives rise to magnetism and plays a key role in developing novel spintronic devices. Half-metals are the fundamental materials in spintronics. They exhibit metallic property for one spin direction and show semiconducting nature for the other direction. Thus, a half-metal has 100% spin polarization at the EF . Among the aforementioned metallic systems, InN-NRV revealed the highest spin polarization. However, one requires a value close to 100% to mimic the half-metallic materials. On the other hand, we observed that TM doped InN-NRs are promising systems where one can tailor the spin polarization through a particular TM atom and its position to obtain the half-metallic nature. Therefore, one can state that semiconductor–metal-(nearly) half-metallic transition is possible in InN-NRs through introducing only a single TM at certain atomic locations. In this work, we restricted our concentration to the influence of a TM atom on the spin unrestricted electronic structure properties. We chose the V and Co atoms as specific TM dopants. V-3d orbital is less than half filled and Co-3d orbital is more than half filled. Both V and Co atoms were already employed in graphene nanoribbons to expose the spin dependent properties [37]. Through these particular TM atoms, we attempted to reveal the role of a TM in InN-NR structures. As a future study, we intend to examine a detailed study concerning how the spin polarization can further be enhanced through the various dopants introduced in InN-NRs. The average magnetic moment in a TM doped system can be computed via Mulliken analysis [32]. This analysis yields the magnetic moment through the spin charge density magnetization given by majority-spin charge density minus minority-spin charge density. The majority and minority DOS of the pure InN-NR were identical, leading to a zero magnetic moment (see Fig. 4). Since the doping with TM atoms affects the spin dependent energy states, where TM-d orbitals play a major role, the DOS variation became spin-asymmetric (see Fig. 4 for the TM doped InN-NRs). It leads to spin polarization or finite magnetic moment. The average magnetic moment per atom acquired in InN-NRV1 and in single Co doped InN-NRs was calculated as 0.15 lB and 0.11 lB (lB is the Bohr magnetron), respectively. As expected, it was independent of the TM location (InN-NRV1 ; InN-NRV2 and InN-NRV3 exhibited the same average magnetic moment) but governed by strength of the hybridization between host atoms and TM-d orbitals. The main reason of spin dependent behavior of a TM doped system comes from the hybridization of host atoms and TM-d orbitals. The hybridization of host atoms and TM-d orbitals in graphene was already emphasized in earlier works [38,39]. For instance, in Ref. [38] the induced magnetism of carbon atoms in graphene due to Ni electrode was examined. It was found that the magnetic moment on a carbon atom in graphene layer was due to the strong hybridization between host and Ni-d states. A TM atom, whose d orbital is not fully filled, breaks the spin symmetry and gives rise to magnetic moment. It affects majority and minority-spin populations and induces local magnetic moment on its adjacent host atoms. For instance, in InN-NRV1 , the magnetic moments on V and adjacent In and N atoms were 3.71 lB , 0.06 lB and 0.14 lB , respectively. For a single Co doped InN-NR, those on Co, (adjacent) In and N atoms were 2.67 lB , 0.08 lB and 0.01 lB , respectively. The magnetic moment became almost zero on non adjacent host atoms, which can be attributed to the delocalization of TM-d states. It was intriguing to observe quite a larger magnetic moment on neighboring N atom compared to In atom in InN-NRV1 . It may be related to strong hybridization between N-p and V-d orbitals. Thus, the induced local magnetic moments on the host N atoms were highly sensitive to the TM type. On the other hand, replacing the V by the Co atom hardly modified the local magnetic moment on In atoms. We analyzed PDOS to elucidate the contribution of certain atoms and orbitals to the spin dependent DOS. The states near the EF underlies the electronic nature of a system. A finite value at a certain energy in PDOS spectrum means the associated states are available at this energy. We present the PDOS spectra of single Co doped InN-NR as a particular structure. It is illustrated in Fig. 5 for In, N,
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Fig. 5. Majority (blue, positive) and minority-spin (red, negative) PDOS as a function of energy around the EF . It is projected on In, N, Co-d, Co-s valence orbitals for the single Co doped InN-NR and on V-d, V-s valence orbitals for InN-NRV1 . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Co-3d and Co-4s states. In this figure, the contribution of V-3d and V-4s is also involved for the sake of comparison. Note that PDOS spectra in Fig. 5 are for TM-d, TM-s orbitals and all In and N atoms in the supercell. The PDOS variations for In and N atoms are quite similar. In the energy interval, from 0.8 eV to 0.8 eV, we see some certain well defined peaks as large as 20 eV1 and 30 eV1 , for majority (where minority become zero) and minority-spin (where majority is close to zero) PDOS of In atoms. It is clearly seen in Fig. 5 that, at all energies, the spin dependent PDOS values for N atoms are diminished compared to those for In atoms. The observed spin-asymmetry in the PDOS of In and N originates from the induced magnetic moment due to the host atoms adjacent to the TM dopant. Spin dependent PDOS spectra of host atoms imply the contribution of them to the average magnetic
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moment. In the single Co doped InN-NR, at negative energies up to 0.07 eV (0.05 eV) majority (minority) spin states of host atoms vanish. At certain energy intervals we see hardly revealed majority or minority-spin PDOS (PDOS values less than 1 eV1 ), which means that the corresponding states vanish in these energy ranges. The majority-spin PDOS of Co-d orbitals vanishes at negative energies and is almost zero, with minute peaks, at positive energies. However, minority-spin PDOS becomes absent up to 0.05 eV above which sharp peaks occur as large as 6 eV1 . On the other hand, a majority-PDOS state for Co-s is not observed up to 0.07 eV and can become as large as 20 eV1 at an energy close to 0.4 eV. Minority-spin PDOS of Co-s is nearly absent up to 0.55 eV, above which it oscillates. As for the PDOS of V-d, the minority one exhibit hardly revealed states in the whole energy interval but the majority one is finite at some energy intervals with sharp peaks at particular energies, near 0.8 eV and 0.8 eV, as large as 10 eV1 . On the other hand, in PDOS of V-s, two sharp majority-spin peaks with values close to 5 eV1 arise at 0.30 eV and 0.15 eV in the vicinity of EF . Above 0.15 eV, minority-spin PDOS of V-s dominates over the majority one with minute and considerable several peaks. It is clearly seen that both TM-3d and TM-4s orbitals have an important contribution to the PDOS spectrum. In a certain energy interval, the electronic states can be well separated as a result of these orbitals. They determine the observed spin dependent sharp peaks in PDOS and the character of majority and minority-spin spectrum around the EF . The suppressed and well defined peaks highlight the spin dependent electronic properties of the relevant systems. The associated spin dependent states can be altered mainly due to the positions of TM atoms. In general, TM dopants are responsible for the spin polarization or induced magnetic moment in any system. 4. Conclusions In this work, we particularly concentrated on the spin unrestricted behavior of InN-NRs where TM atoms were substitutionally doped. In order to expose the corresponding electronic properties, first principles calculations were carried out in the presence of U correction which improves deficiencies of DFT calculations. In general, we restricted ourselves to the effect of a TM dopant and its position on the spin dependent electronic structure of an InN-NR. Incorporating of a single TM atom revealed substantial spin polarization and induced magnetism. According to the our findings, particular H passivated InN-NRs containing a single substitutional V dopant exhibited semiconducting property if it was not positioned at the edges. We observed that the spin unrestricted Eg of an InN-NR can be controlled through locating the V atom at certain positions, which may also be accomplished via playing the shape of the geometry or the width of the InN-NR. Tailoring the spin dependent electronic structure properties and associated spin polarization, one can control and develop novel InN based spintronic devices. Tunability of the electronic structure of an InN-NR is important for the possible applications in nanoelectronics. We predict that TM dopants can enhance the functionality of InN based materials. We obtained that a TM doped InN-NR is a promising system and can be a fundamental structure in electronic devices to be applicable in spin involved nanoelectronics, due to its low electron mass and narrow band gap. We believe that the present study will be an insight and helpful for experimental works. Acknowledgement _ under Grant No 108T710. This work is supported by TÜBITAK References [1] [2] [3] [4]
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