Computational Predictions for Single Chain Chalcogenide ... - MDPI

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Computational Predictions for Single Chain Chalcogenide-Based One-Dimensional Materials Blair Tuttle 1,2, *, Saeed Alhassan 3 and Sokrates Pantelides 1,4 1 2 3 4

*

Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, USA; [email protected] Department of Physics, Penn State Behrend, Erie, PA 16563, USA Department of Chemical Engineering, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, UAE; [email protected] Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN 37235, USA Correspondence: [email protected]; Tel.: +1-814-898-6311

Academic Editor: Ho Won Jang Received: 9 March 2017; Accepted: 2 May 2017; Published: 17 May 2017

Abstract: Exfoliation of multilayered materials has led to an abundance of new two-dimensional (2D) materials and to their fabrication by other means. These materials have shown exceptional promise for many applications. In a similar fashion, we can envision starting with crystalline polymeric (multichain) materials and exfoliate single-chain, one-dimensional (1D) materials that may also prove useful. We use electronic structure methods to elucidate the properties of such 1D materials: individual chains of chalcogens, of silicon dichalcogenides and of sulfur nitrides. The results indicate reasonable exfoliation energies in the case of polymeric three-dimensional (3D) materials. Quantum confinement effects lead to large band gaps and large exciton binding energies. The effects of strain are quantified and heterojunction band offsets are determined. Possible applications would entail 1D materials on 3D or 2D substrates. Keywords: nanowires; chalcogenides; ab initio calculations

1. Introduction Thin films, including few atomic layers and monolayers, grown on substrates have been studied for decades using methods such as molecular beam epitaxy, pulsed laser deposition, or even simple oxidation. A breakthrough idea by Novoselov and Geim [1] in 2004 to exfoliate and study a monolayer from a layered material, namely graphite, led to the explosive growth of new research into two-dimensional (2D) materials, which now includes free-standing monolayers, bilayers, etc., fabricated in a variety of ways, but also monolayers and bilayers on substrates. The number of 2D materials with unique and unusual properties has grown rapidly and has generated enormous interest from both a basic [2–5] and applied [3,6,7] research perspective. Two-dimensional materials are promising for electronic [8], optical [9], catalytic [10] and other applications. Given the maturity of techniques to grow and examine 2D materials and devices [11–14], we turn our attention to analogous one-dimensional (1D) systems. Since at least the discovery of carbon nanotubes, there has been great interest in material systems in which electrons mainly propagate in only one dimension. For carbon nanotubes, semiconducting or metallic tubes are possible depending on a tube’s bonding topology. Boron-nitride nanotubes [15] and other nanotubes have been fabricated and studied. Moreover, wires with nanometer scale diameters have also been grown using Si [16], Se [17] and GaAsSb [18], to name a few. One-dimensional materials have been used in a variety of two- and three-terminal electrical devices [11,13]. Recently,

Nanomaterials 2017, 7, 115; doi:10.3390/nano7050115

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sub-nanometer scale wires were sculpted from 2D monolayer transition-metal dichalcogenides [8]. As scaling proceeds, materials and devices made from single chain 1D systems are becoming realizable. In chemistry of course, there exist many molecular monomers, which can be combined to form single chain oligomers or polymers. Indeed, there has been a long history of theoretical studies of molecular chains, including both finite and infinite systems [19–22]. There is continued interest in polymer chains and crystalline polymers. For instance, recent studies of crystalline polymers examined dielectric properties for a large number of carbon-based polymers [23]. Many infinite chains are known to be stable. Early studies of S and Se chains explored the electronic and structural properties and provided a fundamental understanding of these 1D systems [21]. Also, early theoretical studies of polyacene and sulfur nitride infinite chains elucidated the nature of their superconducting properties [19,24]. Motivated by the emerging possibility of 1D materials for a wide variety of applications, we present new state-of-the-art theoretical results for chalcogenide-based 1D materials. In this paper, we apply modern electronic structure methods to calculate a range of properties of selected 1D materials. Given the recent interest in chalcogenide-based 2D materials [2,25,26], here we consider chalcogenide-based 1D systems. Specifically, we examine individual chains of chalcogens (S, Se, Te) and of silicon dichalcogenides (SiS2 and SiSe2 ), all of which are insulating. In addition, we consider a single strand of SNH, which is insulating, and a strand of S–N, which is metallic. Finally, for comparison, we include infinite carbon-based chains of polyphenylene (C6 H4 ) [27] and polyacene (C4 H2 ) [19,20], which can be viewed as a single strand cut from monolayer graphene. Carbon systems are included since these systems are well understood experimentally and theoretically and so provide a good benchmark. We find that chalcogenide-based1D materials can in principle be exfoliated from three-dimensional (3D) polymeric crystals with relative ease (i.e., exfoliation energies are relatively small). While growth mechanisms are not explicitly calculated, as new 1D materials are grown, experimentalists can use the present results to understand the fundamental versus the growth-dependent electrical/mechanical properties. Quantum confinement effects lead to increased band gaps and larger exciton binding energies when compared to their bulk counterparts. We also calculate strain moduli and the deformation potentials for electrons and holes of these 1D materials. Electronic band offsets are reported for select heterojunctions. The properties considered are critical for applications and the prospects for applications are discussed in the context of the new results. Finally, these results should help in the selection of materials to be synthesized based on 1D applications of interest. 2. Results To examine the properties of 1D materials, we begin with unit cells of the corresponding bulk orthorhombic crystals. The equilibrium lattice constant of an isolated 1D chain is found by allowing the chain length and atomic positions to relax until a minimum energy structure is found. In Table 1, the 1D lattice constants (ao ) are reported. The values are close to previously reported values and/or to the c-axis of the corresponding orthorhombic 3D crystal. The mechanical strain modulus in one dimension is defined as Esm =

1 d2 U L de2

(1)

where L is the periodic length of the one-dimensional material, U is the total energy of the material, and de = dx/L is the differential strain factor. The strain modulus (Esm ) is a measure of the energy needed to vary the lattice constant of the material. We have calculated the strain moduli for our selected 1D materials and report the results in Table 1. The strain modulus results show a clear trend for materials that contain chalcogens: going down the periodic column, from S to Se to Te, the strain modulus becomes smaller, indicating weaker covalent bonding as expected. A similar but less pronounced effect is found comparing SiS2 to SiSe2 results. As expected, the sp3 orbitals of Si enhance covalent bonding with chalcogenides. The carbon chains considered (C6 H4 , C6 H4 ) have notably higher strain moduli due to their strongly covalent C–C bonds. It is notable that hydrogenation

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of S–N results in a lower strain modulus, suggesting that the inclusion of hydrogen weakens the S–N bonding. Figure 1 reports the iso-surfaces of the electronic charge density for S–N and SNH. Indicative of a weakening S–N bond, the charge moves from around the S atoms in S–N to between the N and H 7, 115 3 of 11 atoms in Nanomaterials SNH. To 2017, be more quantitative, the charge at the mid-point of a S–N bond is 16% larger in 1D S–N than in 1D SNH. Finally, tellurium is the most ductile material considered here and would be quantitative, the charge at the mid-point of a S–N bond is 16% larger in 1D S–N than in 1D SNH. attractiveFinally, for device applications where strain is inherently part of would fabrication and operation. tellurium is the most ductile material considered ahere and be attractive for device applications where strain is inherently a part of fabrication and operation.

Table 1. Results from our calculations for extended one-dimensional (1D) materials. The 1D lattice Table 1. Results from our calculations one-dimensional materials. The constant (a strain modulus (Esm ) and for theextended exfoliation energy (Eexf.(1D) ) are reported in1D thelattice first three o ), the (ao), the strain modulusenergy (Esm) andisthe exfoliationusing: energyE(Eexf.= ) are reported in the first three columns.constant Specifically, the exfoliation calculated exf. EBulk /NBulk − E1D /N 1D where the exfoliation energy is calculated using: Eexf. = EBulk/NBulk − E1D/N1D where NBulk NBulk andcolumns. N1D areSpecifically, the number of atoms in the bulk and 1D calculations, respectively. All the G0 W0 and N1D are the number of atoms in the bulk and 1D calculations, respectively. All the G0W0 band gap band gap results (Egap ) are reported below. Indirect gaps are reported in parentheses in the two cases results (Egap) are reported below. Indirect gaps are reported in parentheses in the two cases where the where theindirect indirect gap is lower the direct Thecolumn last column the deviation of the gap is lower thanthan the direct gap. gap. The last includesincludes the deviation of the direct gap direct gap versus strain. versus strain. Material S S Se Se Te Te SiS SiS2 2 SiSe SiSe 22 CC 6H 6H 44 SNH SNH SN SN C4 H2 C4H2

Material

ao (Å) Esm (eV/Å) Eexf. (eV/at.) Eexf. (eV/at.) Esm (eV/Å) 4.404 6.78 0.08 4.404 6.78 0.08 4.966 4.32 0.20 4.966 4.32 0.20 5.682 2.78 0.27 5.682 2.78 0.27 5.588 10.56 5.588 10.56 0.07 0.07 5.939 5.939 8.19 8.19 0.09 0.09 4.364 31.0731.07 0.12 0.12 4.364 4.700 3.10 3.10 0.14 0.14 4.700 4.556 5.06 5.06 0.05 0.05 4.556 2.468 50.9 0.18 2.468 50.9 0.18

ao (Å)

Egap (eV) Dgap (eV/%) Dgap (eV/%) 4.73 (4.60) −0.13 4.73 (4.60) −0.13 3.05 (3.00) −0.06 3.05 (3.00) −0.06 2.41 −0.05 2.41 −0.05 6.91 (6.34) −0.02 6.91 (6.34) −0.02 (4.92) −0.11 5.255.25 (4.92) −0.11 2.602.60 +0.11 +0.11 5.145.14 −0.07 −0.07 N/AN/A N/A N/A N/A N/A N/A N/A Egap (eV)

Figure 1. Atomic and electronic structure for S–N and SNH2 one-dimensional (1D) systems. Figurerepresent 1. Atomic and electronic structure for S–N and SNH2 The one-dimensional (1D) systems. Grey is for Grey regions surfaces of constant charge density. charge density isosurface regions represent surfaces of constant charge density. The charge density isosurface is for 2.3 × 10−4 − 4 3 2.3 × 10 electrons per Å . Large yellow, small grey and small white spheres represent S, N and electrons per Å 3. Large yellow, small grey and small white spheres represent S, N and H, respectively. H, respectively. In principle, some of the 1D materials considered here can be isolated using the corresponding 3D materials and exfoliation techniques. Theconsidered exfoliation energy is anbe important In principle, some of the 1D materials here can isolatedquantity using for theunderstanding corresponding 3D the physics of a layered material [28]. The exfoliation energies has been calculated by comparing the materials and exfoliation techniques. The exfoliation energy is an important quantity for understanding energy per atom for the single chain to the bulk material. While van der Waals interactions are difficult the physics of a layered material [28]. The exfoliation energies has been calculated by comparing the to capture theoretically, the results reported in Table 1 help us understand the trends and electronic energy per atom for the single chain bulk material. While der areTe difficult structure of these materials (hereto wethe consider a hypothetical bulkvan form of SWaals similarinteractions to that of Se and to capture the results in Table 1 form helpofus3Dunderstand the trends electronic fortheoretically, comparison purposes since reported the room-temperature S comprises sulfur rings).and The pure systems display the expected trends, with theSlowest andtoTethat the of Se structurechalcogenide of these materials (here we considerexfoliation a hypothetical bulkS having form of similar highest exfoliation energy. This trend is expected since covalency decreases from S to Se to Te, and and Te for comparison purposes since the room-temperature form of 3D S comprises sulfur rings). electrons are free to participate in inter-chain bonding. To explore the nature of the interThe puretherefore chalcogenide systems display the expected exfoliation trends, with S having the lowest and chain bonding in the pure chalcogenides, we fix the 1D and 3D coordinates found with van de Waals Te the highest exfoliation energy. This trend is expected since covalency decreases from S to Se to interactions and then turn off the van de Waals interaction. The exfoliation energies dramatically Te, and therefore to participate in isinter-chain explore the decrease, electrons suggesting are the free inter-chain interaction mainly vanbonding. de Waals To in character. Thenature silicon of the inter-chain bonding in the pure chalcogenides, wetrend, fix the 1Dvalues and 3D coordinates found with dichalcogenides exhibit a similar but moderate with similar to S. Hydrogenated S–Nvan de Waals interactions and then turn off the van de Waals interaction. The exfoliation energies dramatically decrease, suggesting the inter-chain interaction is mainly van de Waals in character. The silicon

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dichalcogenides exhibit a similar but moderate trend, with values similar to S. Hydrogenated S–N has a larger exfoliation energy than pure S–N, which has the lowest exfoliation energy of the systems considered here.2017, Apparently, the dipole of the N–H bond produces a larger van der Waals effect Nanomaterials 2017, 7, 115 of than 11 Nanomaterials 7, 115 4 of411 the metallic electrons of the pure S–N. The carbon chains considered (C6 H4 , C6 H4 ) have exfoliation in aoflarger exfoliation energy than pure S–N, which has the lowest exfoliation energy of the systems hashas a larger energy than pure S–N, which has theexfoliation lowest exfoliation energy of the the middle theexfoliation range found in the present materials. The energies reported insystems Table 1 are considered here. Apparently, the dipole of the N–H bond produces a larger van der Waals effect than considered here. Apparently, the dipole of the N–H bond produces a larger van der Waals effect than only slightly larger than the value for graphene. electrons of the pure S–N. The carbon chains considered C64H 4) have exfoliation thethe metallic electrons of the pure S–N. The carbon chains considered (C6(C H64H , C4,6H ) have exfoliation in in The Gmetallic 0 W0 band structures have been calculated for our selected 1D chains. We have checked the middle of the range found in the present materials. The exfoliation energies reported in Table the middle the range found thechain present materials. The exfoliation energies reported in Table 1 1are that the bands of perpendicular to in the direction are flat indicating that the supercell used are only slightly larger than the value for graphene. are only slightly larger than the value for graphene. sufficiently large to eliminate interactions between neighboring chain. The 1D band structures for The G00W 0 band structures have been calculated selected chains. have checked that The G0W band structures have been calculated forfor ourour selected 1D1D chains. WeWe have checked that pure chalcogenides and the other insulating systems are reported in Figures 2used andare 3, sufficiently respectively. the bands perpendicular to the chain direction are flat indicating that the supercell the bands perpendicular to the chain direction are flat indicating that the supercell used are sufficiently The band gaps are reported inbetween Table 1.neighboring For the pure chalcogens, the valence band gap is very flat. large to eliminate interactions between neighboring chain. The band structures pure chalcogenides large to eliminate interactions chain. The 1D1D band structures forfor pure chalcogenides Sulfurand and selenium 1D chains both have valence band maxima at G which is only 0.13 eV and 0.05 eV, and the other insulating systems are reported in Figures 2 and 3, respectively. The band gaps are reported the other insulating systems are reported in Figures 2 and 3, respectively. The band gaps are reported respectively, higher than at X. For all pure chalcogenides, the conduction band minimum is at the X in Table 1. For pure chalcogens, valence band gap is very flat. Sulfur and selenium chains in Table 1. For thethe pure chalcogens, thethe valence band gap is very flat. Sulfur and selenium 1D1D chains both have valence band maxima atwhich G which is only 0.13 and 0.05 respectively, higher than at For X. For at have valence band maxima at G is only 0.13 eVeV and 0.05 eV,eV, respectively, higher than at X. point.both For the silicon dichalcogenides, the minimum gap is indirect with the valence band maximum all pure chalcogenides, the conduction band is the at the Xdirect point. For silicon dichalcogenides, pure chalcogenides, conduction band at X point. For thethe silicon dichalcogenides, Γ andall the conduction bandthe minimum near X. minimum Inminimum Table 1,isboth the and indirect minimum gaps are gap isthe indirect with valence band maximum atand  and conduction band minimum thethe minimum gap is indirect with thethe valence band maximum at  thethe conduction band minimum reported inminimum cases where minimum gap is indirect. The hydrogenated chains, polyphenylene and near X. Table In Table 1, both the direct and indirect minimum gaps are reported in cases where the minimum near X. In 1, both the direct and indirect minimum gaps are reported in cases where the minimum sulfur nitride, have direct minimum gaps at Γ. The pure chalcogenides are semiconducting with wide gap is indirect. The hydrogenated chains, polyphenylene and sulfur nitride, have direct minimum gaps gap is indirect. The hydrogenated chains, polyphenylene and sulfur nitride, have direct minimum gaps band gaps of 4.73, 3.05 and 2.41 eV for S, Se and Te, respectively. The band gap for the chalcogenides at The . The pure chalcogenides semiconducting with wide band gaps of 4.73, 3.05 and 2.41 at . pure chalcogenides areare semiconducting with wide band gaps of 4.73, 3.05 and 2.41 eVeV forfor S, S, are lower as the materials covalency increases. Polyphenylene has lower a gap slightly larger covalency than sulfur. and respectively. The band gap chalcogenides materials Se Se and Te,Te, respectively. The band gap forfor thethe chalcogenides areare lower as as thethe materials covalency The dichalcogenides (SiS2 and and SNHlarger are significantly more insulating materials. Generally, increases. Polyphenylene has a2 )gap slightly larger than sulfur. The dichalcogenides (SiS 2 and SiSe increases. Polyphenylene hasSiSe a gap slightly than sulfur. The dichalcogenides (SiS 2 and SiSe 2) 2) 1D chains have larger band gaps and lower dielectric constants than their bulk counterparts. The effect and SNH are significantly more insulating materials. Generally, chains have larger band gaps and and SNH are significantly more insulating materials. Generally, 1D1D chains have larger band gaps and lower dielectric constants than their bulk counterparts. The effect is less dramatic, however, is lesslower dramatic, however, forthan the more insulating materials. dielectric constants their bulk counterparts. The effect is less dramatic, however, forfor thethe more insulating materials. more insulating materials.

Figure 2. Near gap bands are reported for several 1D insulating systems, including S, Se, and Te. Figure 2. Near bands reported several insulating systems, including S, Se, Figure 2. Near gapgap bands areare reported forfor several 1D1D insulating systems, including S, Se, andand Te.Te.

Figure 3. Near bands areare reported forforseveral 1D insulating systems, including SiSe ,C Figure 3.gap Near gap bands are reported for several insulating systems, including SiS C Figure 3. Near gap bands reported several 1D1D insulating systems, including SiSSiS 2, SiSe 2, C2,62H 46H 22,, SiSe 6 4H4 and SNH andand SNH 2. 2. 2 . SNH

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To understand the electronic structure of the materials, we examine the charge densities in To understand the 4, electronic structure the materials, we examine charge densities in a a couple cases. In Figure the charge density of isosurfaces are reported for thethe valence band maximum couple cases. In band Figureminimum 4, the charge density isosurfaces are charge reported for the valence band for maximum and conduction states of Se and SiSe2 . The isosurfaces are similar Se and and conduction band minimum states of Se and SiSe 2. The charge isosurfaces are similar for Se and SiSe2 , and these plots are representative of the isosurfaces of the other 1D systems studied here. SiSe2charge , and these plots are representative of theband isosurfaces of the other 1D systems studieddistributes here. The The density isosurface for the valence maximum state indicates that charge charge densityto isosurface valencebonding. band maximum state indicates thatstate charge distributes perpendicular the plane offor thethe Se zig-zag The valence band maximum is characterized perpendicular to the plane of the Se zig-zag bonding. The valence band maximum state is characterized by a non-bonding p-orbital localized on the chalcogen atom. This behavior is natural for chalcogen by a non-bonding p-orbital localized the chalcogen atom. This is natural for chalcogen atoms with two strong covalent bonds.onFigure 4 also shows that thebehavior conduction band minimum state atoms withlocalization two strong on covalent bonds. Figure 4 also shows along that the conduction band state has charge the chalcogen atom with p-orbital x-direction where theminimum bond is along has charge localization on the chalcogen atom with p-orbital along x-direction where the bond is along the x–y direction (see Figure 4). In the silicon dicalchogenides, there is also some p-orbital charge the x–y direction Figure 4). The In the silicon dicalchogenides, also some p-orbital charge localization on the(see silicon atom. charge localization reportedthere hereisare consistent with previous localization on the silicon atom. The charge localization reported here are consistent with previous analysis for S and Se chains [21]. analysis for S and Se chains [21].

Figure 4. 4. Atomic Atomic and and electronic electronic structures structures are are reported reported for for Se Se (SiSe (SiSe22)) valence valence band band maximum maximum (VBM) (VBM) Figure and conduction conduction band band minimum minimum (CBM). and (CBM). Grey Grey regions regions represent represent surfaces surfaces of of constant constant charge charge density. density. Large dark dark (blue) (blue) and and small small light light (green) (green) spheres spheresrepresent representSi Siand andSe, Se,respectively. respectively. Large

Applying these chains in opto-electronic devices would require a consideration of the effects of Applying these chains in opto-electronic devices would require a consideration of the effects of strain on the electronic properties. The band gap versus lattice strain is reported in Figure 5 for strain on the electronic properties. The band gap versus lattice strain is reported in Figure 5 for selected selected chalcogenide-based 1D materials. Here, we focus on direct gap variations, which are more chalcogenide-based 1D materials. Here, we focus on direct gap variations, which are more important important for optical applications. We find the variation of gap to strain is linear. Table 1 reports the for optical applications. We find the variation of gap to strain is linear. Table 1 reports the slope of the slope of the gap variation with strain. The relative % strain is defined as 100 × Δa/ao where Δa gap variation with strain. The relative % strain is defined as 100 × ∆a/ao where ∆a difference between difference between the strained lattice value and ao, the minimum lattice. The band gaps vary by the strained lattice value and ao , the minimum lattice. The band gaps vary by about 0.1 eV for each 1% about 0.1 eV for each 1% of lattice strain. For the chalcogens, compressive strain (although difficult of lattice strain. For the chalcogens, compressive strain (although difficult to realize) would increase to realize) would increase the band gaps whereas tensile strain would lower the band gaps. We find the band gaps whereas tensile strain would lower the band gaps. We find most of the band gap change most of the band gap change is due to the variation in the conduction band minimum. This is is due to the variation in the conduction band minimum. This is reasonable since the valence band reasonable since the valence band edge wavefunctions are non-bonding p-orbitals (see Figure 4), edge wavefunctions are non-bonding p-orbitals (see Figure 4), which are insensitive to variations in the which are insensitive to variations in the bond lengths. The polyphenylene (C6H4) chains (dashed line) bond lengths. The polyphenylene (C6 H4 ) chains (dashed line) displays the opposite band gap trend displays the opposite band gap trend with strain because of its different chemical bonding. with strain because of its different chemical bonding. Specifically, we find that, for polyphenylene, Specifically, we find that, for polyphenylene, most of the lattice strain is accommodated by the single most of the lattice strain is accommodated by the single linkage C–C bond whereas in the other cases linkage C–C bond whereas in the other cases strain is accommodated symmetrically throughout the strain is accommodated symmetrically throughout the system. The variation in band edges with strain system. The variation in band edges with strain would be important when considering heterojunction would be important when considering heterojunction device applications where significant strain device applications where significant strain can be expected. Combining the strain moduli results can be expected. Combining the strain moduli results above and these deformation results, one can above and these deformation results, one can determine the strain necessary to modify the band determine the strain necessary to modify the band edges by a desired amount. edges by a desired amount.

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Figure 5. Direct band energy (eV)versus versusrelative relative % % strain, in in text. TheThe chalcogen-based Figure 5. Direct band gapgap energy (eV) strain,asasdefined defined text. chalcogen-based systems have positive slopes and are represented by solid lines whereas C6H4 has a negative slope and systems have positive slopes and are represented by solid lines whereas C6 H4 has a negative slope and is represented by a dashed line. is represented by a dashed line.

Recently, 2D graphene nanoribbon heterojunctions have been grown and examined experimentally

Recently, 2D graphene heterojunctions grown and examined [16] while 2D metal dichalcogenide heterojunctions have been examined theoretically [25]. In Table 2, Figure 5. Direct band gapnanoribbon energy (eV) versus relative % strain, ashave defined been in text. The chalcogen-based experimentally [16] 2D metal dichalcogenide heterojunctions been examined systems havewhile positive slopes andoffset are represented solid lines whereas C6H4 has negative slope and we report predictions for the band of Te–Se,by SiSe 2–SiS 2, and SN–SNH 1Da have heterojunctions. The represented by averaged a dashed structureisand the local potential ΔV) arefor reported in Figure 6 for of theTe–Se, Se–Te heterojunction theoretically [25]. Inplanar Table 2, we line. report predictions the band offset SiSe2 –SiS2 , and while in Figure 7 we report the interfacial band diagram for the Se–Te heterojunctions. Se–Te and SN–SNH 1D heterojunctions. The structure and the planar averaged local potential The (∆V) are reported Recently, 2D graphene nanoribbon heterojunctions have been grown and examined experimentally SiS 2–SiSe2 heterojunctions are non-polar. The SN–SNH junction has a polar interface. The local potential in Figure[16] 6 for the2D Se–Te heterojunction while in Figure 7 we report the theoretically interfacial band diagram for metalslope dichalcogenide have been examinedinterfacial [25]. effect, In Table thereforewhile has a linear away fromheterojunctions the interface dipole. Subtracting dipole we2, the Se–Teweheterojunctions. The Se–Te and SiS –SiSe heterojunctions are non-polar. The SN–SNH report predictionsband for the band offset of2Table Te–Se,2.2 SiSe 2, and SN–SNH 1D heterojunctions. The determine the SN–SNH offset reported in The2–SiS conduction band offset for SN–SNH is 3.21 junction structure has a polar Thelocal local potential therefore has a linear away from the and theinterface. planar averaged potential ΔV) are reported in Figure 6 for theslope Se–Te heterojunction eV, which is also the Schottky barrier for this metal–insulator system. While lattice mismatch is a while in Figure 7 we report the interfacial band diagram for the Se–Te heterojunctions. The Se–Tereported and interface dipole. interfacial dipole effect, we determine thedoSN–SNH band concern for Subtracting even 2D heterojunctions [2], single-chain 1D materials not suffer thisoffset limitation SiS 2 –SiSe 2 heterojunctions are non-polar. The SN–SNH junction has a polar interface. The local potential in Table 2. Thejunction conduction forinSN–SNH is 3.21two eV,chains whichwhich is also thediffering Schottky barrier for although atoms band maybeoffset needed order to connect have bonding therefore has a linear slope away from the interface dipole. Subtracting interfacial dipole effect, we this metal–insulator system. While lattice mismatch is a concern for even 2D heterojunctions topologies. For instance, phosphorous can be used to connect 1D Se and SiSe2 chains as illustrated in [2], determine the SN–SNH band offset reported in Table 2. The conduction band offset for SN–SNH is 3.21 single-chain materials do not suffer this limitation although atoms maybe needed in Figure 8.1D One can use these heterojunction band offset results tojunction assess the potential of extended 1Dorder eV, which is also the Schottky barrier for this metal–insulator system. While lattice mismatch is a junctions for a variety of have applications. We find thetopologies. Se–Te would notinstance, be suitable for semiconductorto connect two chains which differing bonding For phosphorous can be concern for even 2D heterojunctions [2], single-chain 1D materials do not suffer this limitationused insulator because the are tooinsmall but 8. theOne interface of Se–P–SiSe 2 may be useful to connect 1Dapplications Se junction and SiSe asoffsets illustrated Figure can use these 2 chains although atoms maybe needed in order to connect two chains which haveheterojunction differing bondingband for electron quantum wells. Overall, given the lack of lattice mismatch and their range band gaps, offset results to assess potential of extended junctions for1D a Se variety of 2applications. We find topologies. For the instance, phosphorous can be1D used to connect and SiSe chains asofillustrated in the 1D chalcogenide-based heterojunctions are promising for a variety of applications. Figure 8. be Onesuitable can use for these heterojunction band offset applications results to assess the potential of extended Se–Te would not semiconductor-insulator because the offsets are too1Dsmall junctions of forSe–P–SiSe a variety of applications. We for findelectron the Se–Tequantum would notwells. be suitable for semiconductorbut the interface may be useful Overall, given the lack of Table 2. For four 2heterojunctions, we report the valence and conduction band offsets. insulator applications because the offsets are too small but the interface of Se–P–SiSe2 may be useful lattice mismatch and their range of band gaps, 1D chalcogenide-based heterojunctions are promising for electron quantum wells. Overall, given the lack of lattice and their range of band gaps, Material VBO (eV) CBOmismatch (eV) for a variety of applications. 1D chalcogenide-based heterojunctions are promising for a variety of applications. Te–Se 0.44 0.20 SiSe 2–SiS2 1.00 0.42 Table 2.Table For four heterojunctions, we report the valence and conduction band offsets. 2. For four heterojunctions, we report the valence and conduction band offsets. SN–SNH2 1.93 3.21 Se–P–SiSe 2 0.13 1.72 Material VBO (eV) CBO CBO (eV) Material VBO (eV) (eV) Te–Se 0.44 0.20 Te–Se 0.44 0.20 SiSe 2–SiS2 1.00 0.42 SiSe 1.00 0.42 2 –SiS2 SN–SNH 2 1.93 3.21 SN–SNH2 1.93 3.21 Se–P–SiSe 0.13 1.72 Se–P–SiSe 0.13 1.72 2 2

Figure 6. Atomic positions and change in local potential (eV) as a function of z-distance, in Å, for Se–Te.

˚ for Se–Te. Figure 6. Atomic positions and change in local potential (eV) as a function of z-distance, in A Figure 6. Atomic positions and change in local potential (eV) as a function of z-distance, in Å, for Se–Te.

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Figure 7. Heterojunction band band diagram for the system. Figure 7. Heterojunction diagram forSe–Te the Se–Te system. Figure 7. Heterojunction band diagram for the Se–Te system.

˚ for the Figure 8. Atomic positions and change in local potential (eV) as a function of z-distance, in A Figure 8. Atomic positions and change in local potential (eV) as a function of z-distance, in Å, for the Se–P–SiSe2 junction. Figure 8. Atomic positions and change in local potential (eV) as a function of z-distance, in Å, for the Se–P–SiSe 2 junction. Se–P–SiSe2 junction.

3. Discussion 3. Discussion 3. Exfoliation Discussiontechniques may be used to isolate these chalcogenide-based 1D materials. A procedure Exfoliation techniques may be used to isolate these chalcogenide-based 1D materials. A procedure may may start fromfrom the techniques adhesive exfoliation originally used to isolate graphene [29].1D This method been Exfoliation may be used tooriginally isolate these chalcogenide-based materials. Ahas procedure start the adhesive exfoliation used to isolate graphene [29]. This method has been optimized and applied to other 2D systems [30]. Once 2D materials have been isolated, one may be able may start from the adhesive exfoliation originally used to graphene [29].isolated, This method has been optimized and applied to other 2D systems [30]. Once 2Disolate materials have been one may be able to use a transmission electron microscope (TEM) to isolate an arbitrary-length single strand, creating optimized and applied to other 2D systems [30]. Once materials have been isolated, maycreating be able a to use a transmission electron microscope (TEM) to 2D isolate an arbitrary-length singleone strand, a 1D system. ThisThis TEM technique has has longlong has(TEM) been used to create single-strand chains ofstrand, carbon atomsatoms to 1D usesystem. a transmission electron microscope to isolate ancreate arbitrary-length single creating a TEM technique has been used to single-strand chains of carbon from graphene [31]. Another possibility may be toto grow chains on using molecular 1Dfrom system. This TEM technique has long has been used tosingle create single-strand chains of molecular carbon atoms graphene [31]. Another possibility may be growsingle chains on surfaces surfaces using beam beam epitaxy, other growth techniques, asbe has implemented tosurfaces construct 1D molecular structures of [32]. from graphene [31]. Another possibility may to been grow single chains on beam epitaxy, oror other growth techniques, as has been implemented to construct 1D using structures of GaAs GaAs [32]. epitaxy,Quantum or other growth techniques, been implemented to construct 1D structures of 1D GaAs [32]. confinement effects as arehas important for predicting the electronic structure of materials. Quantum confinement effects are important for predicting the electronic structure of 1D materials. Quantum confinement effects are important for predicting the electronic structure of 1D materials. Selenium is a case in point. In bulk crystalline Se, we calculate the minimum direct band gap to be 1.62 Selenium is aiscase point. crystalline calculate the minimum minimum direct band gaptotobebe Selenium a case in point.InInbulk bulk crystalline Se, we calculate the direct gap 1.62 eV, close to theinexperimental estimate of 1.8Se, eVwe [33]. The diagonal components ofband the dielectric tensor 1.62 eV, close to the experimental estimate of 1.8 eV [33]. The diagonal components of the dielectric eV,are close theand experimental of 1.8 eV [33].constants The diagonal components of the dielectric tensor ~ εperpto~12 εpara ~ 20. estimate These large dielectric result in a small exciton binding energy tensor are ε~12 ~12 and ~20. In These large ingap a exciton small exciton binding perp para are0.02 εperp εpara ~εmaterial. 20. These large dielectric result a small binding energy ~ eV forand the bulk contrast, adielectric 1D constants chainconstants of Se has result ainband of 3.05 eV, almost double energy ~0.02 eV the bulk confined material. In contrast, a in 1Dlarge Se has aofband gapalmost of For 3.05double eV, 0.02 for value. the for bulk material. In contrast, a 1D result chain of Sechain hasexcitonic aofband gap 3.05systems. eV, theeV bulk Quantum electrons in the 1D instance, almost double the bulkexciton value.confined Quantum confined electrons result in the 1D systems. the1D bulk value. Quantum electrons result large excitonic 1D systems. For Se has a large binding energy, ~1.7 eV.inFor 1D Se, in thelarge G0in Wexcitonic 0the direct gap is 3.05 eVinstance, but when For1D instance, 1D Se has a large exciton binding energy, ~1.7 eV. For 1D Se, the G W direct gap 0 0 Se has a effects large exciton binding energy, eV. For 1D Se, the 0W0 direct 1D gapSeiswould 3.05 eVmake but when excitonic are included the direct ~1.7 gap reduces to 1.34 eV.GTherefore, aisgood 3.05 eV but when excitonic effects are included the direct gap reduces to 1.34 eV. Therefore, 1D Se excitonic effects included theBy direct gap reduces to we 1.34find eV. that Therefore, 1DTe Se would would be make a good absorber in theare visible range. a similar analysis, pure 1D useful as an would make a good absorber in the visible range. By a similar analysis, we find that pure 1D Te would absorber in the visible range. By a similar analysis, we find that pure 1D Te would be useful as an infra-red (IR) absorber with an optical gap of 0.9 eV. Excitonic effects are smaller for the more be infra-red useful as an infra-red (IR) absorber with an optical gap of 0.9 eV. Excitonic effects are smaller for the (IR)1Dabsorber insulating chains. with an optical gap of 0.9 eV. Excitonic effects are smaller for the more more insulating 1D chains. 1D single-chain materials for applications, we should take a new look at old insulating 1Dconsidering chains. When When considering 1D1D single-chain materials for we should take newlook look When considering single-chain materials forapplications, applications, we should take aanew atatold materials. For instance, selenium has had a long history in semiconductor device applications. Selenium oldmaterials. materials. For instance, selenium has had a long history in semiconductor device applications. selenium has had a long history in semiconductor device applications. Selenium rectifiersFor areinstance, ubiquitous in antique radios. More recently, there has been interest in the electrical and Selenium rectifiers areof ubiquitous inselenium antiqueMore radios. More recently, there has been interest in the rectifiers are ubiquitous in antique radios. recently, there interest in the electrical and optical properties amorphous (a-Se) thin films forhas usebeen in photoconductor devices [34,35]. electrical and opticalof properties of amorphous selenium (a-Se) films for could use inalso photoconductor optical properties amorphous selenium (a-Se) thin films forthin use in photoconductor devices One-dimensional selenium chains combined with plasmonic materials serve as[34,35]. efficient devices [34,35]. One-dimensional selenium chains combined with plasmonic materials also serve [9]. One-dimensional chains combined plasmonic materials could also2could serveplasmonics as efficient photoconductorsselenium in nano-opto-electric deviceswith similar to the current use of 2D MoS with

photoconductors in nano-opto-electric devices similar to the current use of 2D MoS2 with plasmonics [9].

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as efficient photoconductors in nano-opto-electric devices similar to the current use of 2D MoS2 with plasmonics [9]. Lasers may also be a promising application of 1D chalcogenide-based materials. The large exciton binding energies (mentioned above) make these materials good candidates for optically pumped lasers. Decades ago, one-dimensional GaAs quantum wires were used for laser applications [36]. Over the years, advances in growth techniques have reduced the diameter of such quantum wire systems [32,37]. The use of carbon nanotubes for lasing systems has also been achieved [38]. Based on the band-offsets reported here, chalcogenide-based 1D heterojunction systems are promising for optically pumped single-chain lasers. 4. Methods We employ density functional theory (DFT) [39,40] and examine the properties of these materials using the VASP computer code [41,42]. A plane-wave basis with a cutoff energy of ~300 eV was used based on the standard projected augmented wave (PAW) potentials to treat core electrons [43,44]. Calculations were performed with the generalized-gradient corrected functional of Perdew, Becke and Ernzerhof (PBE) [45] to treat exchange and correlation. In addition, for bulk calculations, van der Waals (vdW) interactions were treated in a semi-empirical fashion using the method of Grimme [46]. All atomic coordinates and lattice parameters were relaxed to their equilibrium values at T = 0 K using a force tolerance of 0.01 eV/Å. Single strands are isolated using supercells including a vacuum of ~1.0 nm. Tests with a larger vacuum at ~2 nm found no significant changes to the quantities reported here. We have calculated the mechanical properties at the PBE level of theory. For electronic structure, we use the non-self-consistent G0 W0 approximation [47,48] which accounts for the many-body electron interactions but retains the input PBE wavefunctions. The G0 W0 quasi-particle electronic bands are calculated for a 75 × 1 × 1 k-point mesh. From the G0 W0 quasi-particle bands, we calculate excitonic effects with the Bethe–Salpeter equation (BSE) which accounts for the interaction of a quasi-electron and a quasi-hole. The present calculations employ the Tamm–Dancoff approximation as implemented in the Vienna Ab initio Simulation Package (VASP) [26]. The four highest valence bands and the four lowest conduction bands were used as a basis for excitonic eigenstates. Employing the BSE, we calculate direct excitation energies and intensities, which can be compared with optical absorption experimental data. Heterojunction offsets are calculated in the standard band alignment method [49,50] using PBE for the interface potential alignment and, consistent with recent advances [51], we employ the G0 W0 results for the bulk band edges. 5. Conclusions Innovation in the growth and design of 2D materials motivated the present exploration of extended 1D materials. Specifically, there is interest in chalcogenide-based thin films including 2D materials (e.g., SiSe). Techniques for creating molecular-scale transistors from single nanotubes [38] and other similar advances also motivates the search for single chain 1D materials that may also be useful in such applications. In this study, we calculate the properties of chalcogenide-based 1D materials including S, Se and Te along with silicon-dichalcogenides (SiS2 and SiSe2 ) and sulfur nitrides (S–N and SNH). The main results of our study are presented in Table 1 where we report the strain moduli, the exfoliation energies, band gaps, and gap deformation potentials. Strain moduli and band gaps decrease whereas the exfoliation energies increase, as we consider chalcogenides going down the periodic column, i.e., S to Se to Te. Trends found in Table 1 are explained qualitatively in terms of the covalency of bonding. The covalent bond density is examined specifically in the case of S–N and SNH showing a weakening S–N covalent bond with the addition of H. The band gaps and excitonic binding energies for the insulating 1D materials considered here are found to be larger than their respective bulk counterparts.

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All chalcogenides have negative band deformation potentials. Finally, we consider heterojunction band offsets for several 1D systems. We propose that 1D chalcogenide-based materials may be isolated from the corresponding bulk materials, which are readily available, following the procedure used to successfully isolate graphene and single chains of carbon from graphene. Nano-opto-electronics is one promising application area for these materials. Specifically, Se and Te may be good visible and IR absorbers, respectively. Also, the use of 1D heterojunctions may allow the realization of optically pumped atomic-scale lasers. Overall, the present calculations provide a view of the properties of several chalcogenide-based single molecular chain systems, which are promising for electronic, opto-electronic and other applications. Acknowledgments: This work was supported in part by the Gas Subcommittee Research and Development under the Abu Dhabi National Oil Company (ADNOC) and by the McMinn Endowment at Va nderbilt University. Calculations were performed in part on the Penn State Lion X supercomputers. Author Contributions: All authors conceived and designed the calculations; B.T. performed the main calculations; all authors contributed to analyzing the results and wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

References 1.

2. 3. 4. 5.

6. 7. 8.

9. 10. 11. 12.

13.

14.

Novoselov, K.S.; Novoselov, K.S.; Geim, A.K.; Morozov, S.V.; Jiang, D.; Zhang, Y.; Dubonos, S.V.; Grigorieva, I.V.; Firsov, A.A. Electric Field Effect in Atomically Thin Carbon Films. Science 2004, 306, 666–669. [CrossRef] [PubMed] Singh, A.K.; Hennig, R.G. Computational prediction of two-dimensional group-IV mono-chalcogenides. Appl. Phys. Lett. 2014, 105, 042103. [CrossRef] Liu, H.; Neal, A.T.; Zhu, Z.; Luo, Z.; Xu, X.; Tománek, D.; Ye, P.D. Phosphorene: An Unexplored 2D Semiconductor with a High Hole Mobility. ACS Nano 2014, 8, 4033–4041. [CrossRef] [PubMed] Tran, V.; Soklaski, R.; Liang, Y.; Yang, L. Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus. Phys. Rev. B 2014, 89, 235319. [CrossRef] Chernikov, A.; Berkelbach, T.C.; Hill, H.M.; Rigosi, A.; Li, Y.; Aslan, O.B.; Reichman, D.R.; Hybertsen, M.S.; Heinz, T.F. Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer. Phys. Rev. Lett. 2014, 113, 076802. [CrossRef] [PubMed] Conley, H.J.; Wang, B.; Ziegler, J.I.; Haglund, R.F.; Pantelides, S.T.; Bolotin, K.I. Bandgap Engineering of Strained Monolayer and Bilayer MoS2 . Nano Lett. 2013, 13, 3626–3630. [CrossRef] [PubMed] Singh, A.K.; Mathew, K.; Zhuang, H.L.; Hennig, R.G. Computational Screening of 2D Materials for Photocatalysis. J. Phys. Chem. Lett. 2015, 6, 1087–1098. [CrossRef] [PubMed] Lin, J.; Cretu, O.; Zhou, W.; Suenaga, K.; Prasai, D.; Bolotin, K.I.; Cuong, N.T.; Otani, M.; Okada, S.; Lupini, A.R.; et al. Flexible metallic nanowires with self-adaptive contacts to semiconducting transition-metal dichalcogenide monolayers. Nat. Nano Lett. 2014, 9, 436–442. [CrossRef] [PubMed] Butun, S.; Tongay, S.; Aydin, K. Enhanced Light Emission from Large-Area Monolayer MoS2 Using Plasmonic Nanodisc Arrays. Nano Lett. 2015, 15, 2700–2704. [CrossRef] [PubMed] Zhuang, H.L.; Hennig, R.G. Theoretical perspective of photocatalytic properties of single-layer SnS2 . Phys. Rev. B 2013, 88, 115314. [CrossRef] Leonard, F.; Talin, A.A. Electrical contacts to one- and two-dimensional nanomaterials. Nat. Nano 2011, 6, 773–783. [CrossRef] [PubMed] Bom, N.M.; Soares, G.V.; de Oliveira Junior, M.H.; Lopes, J.M.J.; Riechert, H.; Radtke, C. Water Incorporation in Graphene Transferred onto SiO2 /Si Investigated by Isotopic Labeling. J. Phys. Chem. C 2016, 120, 201–206. [CrossRef] Van’t Erve, O.M.J.; Friedman, A.L.; Li, C.H.; Robinson, J.T.; Connell, J.; Lauhon, L.J.; Jonker, B.T. Spin transport and Hanle effect in silicon nanowires using graphene tunnel barriers. Nat. Commun. 2015, 6, 7541. [CrossRef] [PubMed] Tuttle, B.R.; Alhassan, S.M.; Pantelides, S.T. Large excitonic effects in group-IV sulfide monolayers. Phys. Rev. B 2015, 92, 235405. [CrossRef]

Nanomaterials 2017, 7, 115

15. 16. 17. 18. 19. 20. 21. 22. 23.

24. 25. 26. 27. 28. 29.

30.

31. 32. 33. 34.

35. 36. 37.

10 of 11

Yin, J.; Li, J.; Hang, Y.; Yu, J.; Tai, G.; Li, X.; Zhang, Z.; Guo, W. Boron Nitride Nanostructures: Fabrication, Functionalization and Applications. Small 2016, 12, 2942–2968. [CrossRef] [PubMed] Cai, J.; Pignedoli, C.A.; Talirz, L.; Ruffieux, P.; Söde, H.; Liang, L.; Meunier, V.; Berger, R.; Li, R.; Feng, X.; et al. Graphene nanoribbon heterojunctions. Nat. Nano Lett. 2014, 9, 896–900. [CrossRef] [PubMed] Bäppler, S.A.; Plasser, F.; Wormit, M.; Dreuw, A. Exciton analysis of many-body wave functions: Bridging the gap between the quasiparticle and molecular orbital pictures. Phys. Rev. A 2014, 90, 052521. [CrossRef] Tellurium (Te) Effective Masses. Non-Tetrahedrally Bonded Elements and Binary Compounds I; Madelung, O., Rössler, U., Schulz, M., Eds.; Springer: Berlin/Heidelberg, Germany, 1998; pp. 1–6. Kivelson, S.; Chapman, O.L. Polyacene and a new class of quasi-one-dimensional conductors. Phys. Rev. B 1983, 28, 7236–7243. [CrossRef] Mishima, A.; Kimura, M. Superconductivity of the quasi-one-dimensional semiconductor—Polyacene. Synth. Metals 1985, 11, 75–84. [CrossRef] Springborg, M.; Jones, R.O. Sulfur and selenium helices: Structure and electronic properties. J. Chem. Phys. 1988, 88, 2652–2658. [CrossRef] Lovinger, A.J.; Padden, F.J., Jr.; Davis, D.D. Structure of poly(p-phenylene sulphide). Polymer 1988, 29, 229–232. [CrossRef] Sharma, V.; Wang, C.; Lorenzini, R.G.; Ma, R.; Zhu, Q.; Sinkovits, D.W.; Pilania, G.; Oganov, A.R.; Kumar, S.; Sotzing, G.A.; et al. Rational design of all organic polymer dielectrics. Nat. Commun. 2014, 5, 4845. [CrossRef] [PubMed] Seel, M.; Collins, T.C.; Martino, F.; Rai, D.K.; Ladik, J. SNx with hydrogen impurities in the coherent-potential approximation. Phys. Rev. B 1978, 18, 6460–6464. [CrossRef] Amin, B.; Singh, N.; Schwingenschlögl, U. Heterostructures of transition metal dichalcogenides. Phys. Rev. B 2015, 92, 075439. [CrossRef] Ramasubramaniam, A. Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides. Phys. Rev. B 2012, 86, 115409. [CrossRef] Viljas, J.K.; Pauly, F.; Cuevas, J.C. Modeling elastic and photoassisted transport in organic molecular wires: Length dependence and current-voltage characteristics. Phys. Rev. B 2008, 77, 155119. [CrossRef] Chen, X.; Tian, F.; Persson, C.; Duan, W.; Chen, N.-X. Interlayer interactions in graphites. Sci. Rep. 2013, 3, 3046. [CrossRef] [PubMed] Novoselov, K.S.; Geim, A.K.; Morozov, S.V.; Jiang, D.; Katsnelson, M.I.; Grigorieva, I.V.; Dubonos, S.V.; Firsov, A.A. Two-dimensional gas of massless Dirac fermions in graphene. Nature 2005, 438, 197–200. [CrossRef] [PubMed] Huang, Y.; Sutter, E.; Shi, N.N.; Zheng, J.; Yang, T.; Englund, D.; Gao, H.-J.; Sutter, P. Reliable Exfoliation of Large-Area High-Quality Flakes of Graphene and Other Two-Dimensional Materials. ACS Nano 2015, 9, 10612–10620. [CrossRef] [PubMed] Jin, C.; Lan, H.; Peng, L.; Suenaga, K.; Iijima, S. Deriving Carbon Atomic Chains from Graphene. Phys. Rev. Lett. 2009, 102, 205501. [CrossRef] [PubMed] Arbiol, J.; de la Mata, M.; Eickhoff, M.; Morral, A.F.I. Bandgap engineering in a nanowire: Self-assembled 0, 1 and 2D quantum structures. Mater. Today 2013, 16, 213–219. [CrossRef] Stuke, J. Review of optical and electrical properties of amorphous semiconductors. J. Non-Cryst. Solids 1970, 4, 1–26. [CrossRef] Tanioka, K.; Yamazaki, J.; Shidara, K.; Taketoshi, K.; Kawamura, T.; Ishioka, S.; Takasaki, Y. An avalanche-mode amorphous Selenium photoconductive layer for use as a camera tube target. IEEE Electron. Device Lett. 1987, 8, 392–394. [CrossRef] Frey, J.B.; Belev, G.; Tousignant, O.; Mani, H.; Laperriere, L.; Kasap, S.O. Dark current in multilayer stabilized amorphous selenium based photoconductive X-ray detectors. J. Appl. Phys. 2012, 112, 014502. [CrossRef] Wegscheider, W.; Pfeiffer, L.N.; Dignam, M.M.; Pinczuk, A.; West, K.W.; McCall, S.L.; Hull, R. Lasing from excitons in quantum wires. Phys. Rev. Lett. 1993, 71, 4071–4074. [CrossRef] [PubMed] Yoshita, M.; Hayamizu, Y.; Akiyama, H.; Pfeiffer, L.N.; West, K.W. Fabrication and microscopic characterization of a single quantum-wire laser with high uniformity. Phys. E Low-Dimens. Syst. Nanostruct. 2004, 21, 230–235. [CrossRef]

Nanomaterials 2017, 7, 115

38.

39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51.

11 of 11

Ostojic, G.N.; Zaric, S.; Kono, J.; Moore, V.C.; Hauge, R.H.; Smalley, R.E. Stability of High-Density One-Dimensional Excitons in Carbon Nanotubes under High Laser Excitation. Phys. Rev. Lett. 2005, 94, 097401. [CrossRef] [PubMed] Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Phys. Rev. 1964, 136, B864–B871. [CrossRef] Kohn, W.; Sham, L.J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133–A1138. [CrossRef] Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169–11186. [CrossRef] Kresse, G.; Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 1996, 6, 15–50. [CrossRef] Blöchl, P.E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953–17979. [CrossRef] Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 1999, 59, 1758–1775. [CrossRef] Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865–3868. [CrossRef] [PubMed] Grimme, S. Semiempirical gga-type density functional constructed with a long-range dispersion correction. J. Comp. Chem. 2006, 27, 1787. [CrossRef] Shishkin, M.; Kresse, G. Implementation and performance of the frequency-dependent GW method within the PAW framework. Phys. Rev. B 2006, 74, 035101. [CrossRef] Fuchs, F.; Furthmüller, J.; Bechstedt, F.; Shishkin, M.; Kresse, G. Quasiparticle band structure based on a generalized Kohn-Sham scheme. Phys. Rev. B 2007, 76, 115109. [CrossRef] Van de Walle, C.G.; Martin, R.M. Theoretical calculations of heterojunction discontinuities in the Si/Ge system. Phys. Rev. B 1986, 34, 5621–5634. [CrossRef] Tuttle, B.R. Theoretical investigation of the valence-band offset between Si(001) and SiO2 . Phys. Rev. B 2004, 70, 125322. [CrossRef] Shaltaf, R.; Rignanese, G.M.; Gonze, X.; Giustino, F.; Pasquarello, A. Band Offsets at the SiSiO2 Interface from Many-Body Perturbation Theory. Phys. Rev. Lett. 2008, 100, 186401. [CrossRef] [PubMed] © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).