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ARTICLE Designing Isoelectronic Counterparts to Layered Group V Semiconductors Zhen Zhu, Jie Guan, Dan Liu, and David Toma´Nek*

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ARTICLE Designing Isoelectronic Counterparts to Layered Group V Semiconductors Zhen Zhu, Jie Guan, Dan Liu, and David Toma´Nek* ARTICLE Designing Isoelectronic Counterparts to Layered Group V Semiconductors Zhen Zhu, Jie Guan, Dan Liu, and David Toma´nek* Physics and Astronomy Department, Michigan State University, East Lansing, Michigan 48824, United States ABSTRACT In analogy to IIIÀV compounds, which have significantly broadened the scope of group IV semiconductors, we propose a class of IVÀVI compounds as isoelectronic counterparts to layered group V semiconductors. Using ab initio density functional theory, we study yet unrealized structural phases of silicon monosulfide (SiS). We find the black-phosphorus-like R-SiS to be almost equally stable as the blue-phosphorus-like β-SiS. Both R-SiS and β- SiS monolayers display a significant, indirect band gap that depends sensitively on the in-layer strain. Unlike 2D semiconductors of group V elements with the corresponding nonplanar structure, different SiS allotropes show a strong polarization either within or normal to the layers. We find that SiS may form both lateral and vertical heterostructures with phosphorene at a very small energy penalty, offering an unprecedented tunability in structural and electronic properties of SiS-P compounds. KEYWORDS: silicon sulfide . isoelectronic . phosphorene . ab initio . electronic band structure wo-dimensional semiconductors of monosulfide (SiS). We use ab initio density Tgroup V elements, including phos- functional theory (DFT) to identify stable phorene and arsenene, have been allotropes and determine their equilibrium rapidly attracting interest due to their sig- geometry and electronic structure. We have nificant fundamental band gap, large den- identified two nearly equally stable allo- sity of states near the Fermi level, and high tropes, namely, the black-phosphorus-like and anisotropic carrier mobility.1À4 Combi- R-SiS and the blue-phosphorus-like β-SiS, nation of these properties places these and show their structure in Figure 1a and d. systems very favorably in the group of Both R-SiS and β-SiS monolayers display a contenders for 2D electronics applications significant, indirect band gap that depends beyond graphene5,6 and transition metal sensitively on the in-layer strain. Unlike 2D dichalcogenides.7 Keeping in mind that semiconductors of group V elements with the scope of group IV semiconductors such the corresponding nonplanar structure, dif- as Si has been broadened significantly by ferent SiS allotropes show a strong polariza- introducing isoelectronic IIIÀV compounds, tion either within or normal to the layers. it is intriguing to see whether the same can We find that SiS may form both lateral and be achieved in a new class of IVÀVI com- vertical heterostructures with phosphorene pounds that are isoelectronic to group V at a very small energy penalty, offering an elemental semiconductors. Even though unprecedented tunability in structural and this specific point of view has not yet re- electronic properties of SiS-P compounds. ceived attention, there has been interest in RESULTS AND DISCUSSION specificIVÀVI compounds, such as SnS, SnSe, and GeTe, for thermoelectric and pho- Since all atoms in sp3-layered structures tovoltaic applications.8À10 It appears likely of group V elements are 3-fold coordinated, that a specific search for isoelectronic coun- the different allotropes can all be topologi- * Address correspondence to [email protected]. terparts of layered semiconductors such as cally mapped onto the honeycomb lattice 11 phosphorene and arsenene may guide us to of graphene with two sites per unit cell. An Received for review May 6, 2015 yet unexplored 2D semiconducting IVÀVI easy way to generate IVÀVI compounds and accepted July 18, 2015. fl compounds that are stable and exible and that are isoelectronic to group V mono- Published online July 19, 2015 display a tunable band gap. layers is to occupy one of these sites by 10.1021/acsnano.5b02742 As a yet unexplored IVÀVI compound, a group IV and the other by a group VI we study the layered structure of silicon element. In this way, we have generated C 2015 American Chemical Society ZHU ET AL.VOL.9’ NO. 8 ’ 8284–8290 ’ 2015 8284 www.acsnano.org ARTICLE Figure 1. Atomic and electronic structure of (aÀc) R-SiS and (dÀf) β-SiS monolayers. (a and d) Ball-and-stick models of the geometry, with S and Si atoms distinguished by size and color and the WignerÀSeitz cell indicated by the shaded region. (b and e) Electronic band structure and (c and f) the electronic density of states (DOS) of the systems. The energy range between EF and 0.2 eV below the top of the valence band, indicated by the green shading, is used to identify valence frontier states. the orthorhombic R-SiS monolayer structure, shown the valencies of the silicene layers by ÀSÀS bridges. in Figure 1a, from a monolayer of black phosphorene Even though no structural information has been pro- (or R-P). The hexagonal β-SiS monolayer, shown in vided in that study, we identified a likely candidate Figure 1d, has been generated in the same way from structure and found it to be less stable than the the blue phosphorene (or β-P) structure. postulated SiS allotropes, on which we focus next. The monolayer structures have been optimized Since the electronegativity of S is higher than that using DFT with the PerdewÀBurkeÀErnzerhof (PBE)12 of Si, we expect an electron transfer from Si to S atoms. exchangeÀcorrelation functional, as discussed in the On the basis of a Mulliken population analysis, we Methods section. We found that the presence of two estimate a net transfer of 0.3 electron in R-SiS and elements with different local bonding preferences 0.2 electron in β-SiS from silicon to sulfur atoms. This increases the thickness of the SiS monolayers when charge redistribution, combined with the nonplanarity compared to the phosphorene counterparts. The 2D of the structure, causes a net polarization. We find an lattice of R-SiS is spanned by the orthogonal Bravais in-plane polarization for R-SiS and an out-of-plane lattice vectors |aB1| = 4.76 Å and |aB2| = 3.40 Å, which are polarization for β-SiS. about 3% longer than the lattice vectors of black phos- Whereas DFT generally provides an accurate de- phorene. The 2D hexagonal lattice of β-SiS is spanned scription of the total charge density and equilibrium by two Bravais lattice vectors a =|aB1|=|aB2| = 3.35 Å, geometry, interpretation of KohnÀSham energy ei- which are j1% longer than those of blue phosphor- genvalues as quasiparticle energies is more proble- ene. Unlike in the counterpart structures of the phos- matic. Still, we present our DFT-PBE results for the phorene monolayer, we find β-SiS to be more stable electronic structure of R-SiS and β-SiS monolayers in by about 12 meV/atom than R-SiS. We checked the Figure 1. Even though the fundamental band gaps are phonon spectrum of free-standing R-SiS and β-SiS typically underestimated in this approach, the predic- monolayers and found no soft modes that would cause tion that both systems are indirect-gap semiconduc- a spontaneous collapse of the structure. tors is likely correct. Our calculated band structure and An apparently different layered SiS structure had the corresponding density of states for R-SiS, pre- 13 been synthesized by exposing the layered CaSi2 sented in Figure 1b,c, suggest that the fundamental structure to S2Cl2. It appears that the S2Cl2 reagent band gap value Eg = 1.44 eV should be significantly reacted with the Ca atoms intercalated between sili- larger than in the isoelectronic black phosphorene cene layers in CaSi2 by forming CaCl2 and saturating counterpart. The band structure near the top of the ZHU ET AL.VOL.9’ NO. 8 ’ 8284–8290 ’ 2015 8285 www.acsnano.org ARTICLE valence band shows a significant anisotropy when midgap and 0.2 eV below the top of the valence band. comparing the ΓÀX and ΓÀY directions. In analogy to The valence frontier states of R-SiS in Figure 2a and phosphorene, R-SiS should exhibit a higher hole mobi- β-SiS in Figure 2b are similar in spite of the notable lity along the x-direction than along the y-direction. charge density differences caused by the larger DOS of The DFT-based fundamental band gap Eg = 2.26 eV β-SiS in this energy range. The difference between S in the monolayer of β-SiS is even larger. The band and Si atoms is also reflected in the character of the structure in the symmetric honeycomb lattice of β-SiS valence frontier states at these sites. Whereas pz states is rather isotropic, as seen in Figure 1e. The top of the contribute most at sulfur sites, silicon sites contribute a valence band is very flat, resulting in a heavy hole mass mixture of s and pz states. These frontier states differ and a large density of states (DOS) in that region, as from those of phosphorene, which are related to lone seen in Figure 1f. pair electron states. The character of frontier states not only is of interest Similar to phosphorene, the fundamental band gap for a microscopic understanding of the conduction value of SiS also depends sensitively on the in-layer channels but is also crucial for the design of optimum strain, as seen in Figure 3. Due to their nonplanarity, contacts.14 Whereas DFT-based band gaps are typically accordion-like in-layer stretching or compression of underestimated as mentioned above, the electronic SiS structures may be achieved at little energy cost, as structure of the valence and the conduction band shown in the Supporting Information. The energy cost region in DFT is believed to closely correspond to is particularly low for a deformation along the soft experimental results. In Figure 2, we show the charge x-direction, requiring j20 meV/atom to induce a density associated with frontier states near the top of (9% in-layer strain.
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