materials Article First-Principles Study of a MoS2-PbS van der Waals Heterostructure Inspired by Naturally Occurring Merelaniite Gemechis D. Degaga, Sumandeep Kaur, Ravindra Pandey * and John A. Jaszczak Department of Physics, Michigan Technological University, Houghton, MI 49931, USA; [email protected] (G.D.D.); [email protected] (S.K.); [email protected] (J.A.J.) * Correspondence: [email protected] Abstract: Vertically stacked, layered van der Waals (vdW) heterostructures offer the possibility to design materials, within a range of chemistries and structures, to possess tailored properties. Inspired by the naturally occurring mineral merelaniite, this paper studies a vdW heterostructure composed of a MoS2 monolayer and a PbS bilayer, using density functional theory. A commensurate 2D heterostructure film and the corresponding 3D periodic bulk structure are compared. The results find such a heterostructure to be stable and possess p-type semiconducting characteristics. Due to the heterostructure’s weak interlayer bonding, its carrier mobility is essentially governed by the constituent layers; the hole mobility is governed by the PbS bilayer, whereas the electron mobility is governed by the MoS2 monolayer. Furthermore, we estimate the hole mobility to be relatively high (~106 cm2V−1s−1), which can be useful for ultra-fast devices at the nanoscale. Keywords: merelaniite; vdW heterostructure; MoS2; PbS; carrier mobility Citation: Degaga, G.D.; Kaur, S.; Pandey, R.; Jaszczak, J.A. First- 1. Introduction Principles Study of a MoS2-PbS van Two-dimensional (2D) materials are celebrated among the scientific community, due der Waals Heterostructure Inspired to the unparalleled exquisite properties compared to their bulk counterparts, arising from by Naturally Occurring Merelaniite. the quantum confinement effects. Some of the examples of 2D materials include graphene, Materials 2021, 14, 1649. https:// h-BN, transition metal dichalcogenides (TMDs), phosphorene, MXenes, etc., which have doi.org/10.3390/ma14071649 been explored for novel device applications [1–7]. The possibility of synthesis of vertically stacked 2D structures, in which the consecutive layers interact through weak van der Waals Academic Editor: Shirley Chiang forces called van der Waals (vdW) heterostructures, can give rise to nanomaterials with desired properties [8–10]. The vdW heterostructures present unique electronic properties Received: 14 February 2021 due to the incommensurate and modulating nature of their structural configurations along Accepted: 24 March 2021 Published: 27 March 2021 the crystallographic a- and b-directions. Despite their fascinating and attractive properties, only a few groups have so far succeeded in the synthesis of such heterostructures [11–17]. Publisher’s Note: MDPI stays neutral Naturally occurring vdW structures such as cylindrite and franckeite belong to a with regard to jurisdictional claims in family of complex, misfit, layered sulfide minerals. These materials are built from the published maps and institutional affil- vertically stacked alternating layers of pseudo-quadratic (referred to as Q) and pseudo- iations. hexagonal (referred to as H) layers [18–21]. In general, the Q and H layers are a (100) slab of the rock-salt-type structure and a CdI2-type layer, respectively, and the interlayer interaction is primarily dominated by the vdW interactions. Theoretical and experimental investigations of the 2D heterostructures derived from these incommensurate layered sulfides are still at the stage of infancy. A recent theoreti- Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. cal study of MoS2-CdS heterostructure reported its enhanced photocatalytic activity [22]. This article is an open access article Heterostructures of alternating SnS2-based (H) and PbS-based (Q) layers have been synthe- distributed under the terms and sized by exfoliation of bulk natural franckeite [15,16]. Spectroscopic measurements found conditions of the Creative Commons the ultrathin franckeite nanosheet to be a p-type material with an estimated bandgap of Attribution (CC BY) license (https:// ≈0.7 eV. Note that the PbS-based Q layers in the franckeite structure are with non-isometric creativecommons.org/licenses/by/ unit-cells and thus structurally different from the ones directly derived from the PbS cubic 4.0/). bulk structure [23]. The Q layer is composed of four atomic layers of sulfide compounds Materials 2021, 14, 1649. https://doi.org/10.3390/ma14071649 https://www.mdpi.com/journal/materials Materials 2021, 14, x FOR PEER REVIEW 2 of 9 ≈0.7 eV. Note that the PbS-based Q layers in the franckeite structure are with non-isomet- ric unit-cells and thus structurally different from the ones directly derived from the PbS cubic bulk structure [23]. The Q layer is composed of four atomic layers of sulfide com- Materials 2021, 14, 1649 pounds with the formula MX, where M = Pb2+, Sn2+ or Sb3+ and X = S. The H layer2 of 9 consists of octahedrons of disulfide compounds with the formula MX2, where M = Sn4+ or Fe2+ and X = S [16]. withFollowing the formula the MX, success where of M =fabricating Pb2+, Sn2+ 2Dor Sbheterostructures3+ and X = S. The fromH layer bulk consistsfranckeite, we 4+ 2+ hereof octahedrons focus on 2D of disulfideand bulk compounds MoS2-PbS heterostructures with the formula MXthat2, a wherere inspired M = Sn by, orbut Fe simplified fromand X another = S [16]. naturally occurring member of the cylindrite group, the relatively newly discoveredFollowing mineral the success merelaniite of fabricating (Mo4Pb 2D4VSbS heterostructures15). Merelaniite from is bulkcomposed franckeite, predominantly we ofhere a stacking focus on 2Dof a and MoS bulk2-based MoS2 monolayer-PbS heterostructures (H) incommensurately that are inspired aligned by, but simplifiedwith a PbS-based bilayerfrom another (Q) [24] naturally. Both the occurring H and memberQ layers of of the merelaniite cylindrite group,are triclinic the relatively with space newly group C1. discovered mineral merelaniite (Mo Pb VSbS ). Merelaniite is composed predominantly The unit cell parameters for the H4 layer4 are:15 a = 5.547(9) Å; b = 3.156(4) Å; c = 11.91(1) Å; of a stacking of a MoS2-based monolayer (H) incommensurately aligned with a PbS-based αbilayer = 89.52(9); (Q)[24 β]. = Both 92.13(5); the H γand = 90.18(4).Q layers For of merelaniite the Q layer, are the triclinic parameters with space are: group a = 5.929(8)C1. Å; b =The 5.961(5) unit cell Å; parameters c = 12.03(1) for Å; the αH = layer91.33(9); are: aβ= = 5.547(9) 90.88(5); Å; γb == 3.156(4)91.79(4). Å; Notec = 11.91(1) that the Å; a and b directionsα = 89.52(9); areβ =parallel 92.13(5); toγ the= 90.18(4). layers, Forand the c isQ thelayer, stacking the parameters direction are: ofa the= 5.929(8) H and Å; Q layers. Inb = this 5.961(5) study, Å; thec = structure 12.03(1) Å; andα =chemistry 91.33(9); βare= simplified 90.88(5); γ =to 91.79(4).be coherently Note thataligned the aH and Q layers,and b directions composed are solely parallel of toMoS the2 layers,and PbS, and respectively,c is the stacking with direction a minimally of the H sizedand Qcommen- suratelayers. periodic In this study, supercell the structure in the a and-b plane, chemistry as displayed are simplified in Figure to be coherently1. Specifically, aligned we inves- tigateH anddQ thelayers, stability composed and electronic solely of MoS properties2 and PbS, ofrespectively, this 2D vdW with heterostructure a minimally sized employing commensurate periodic supercell in the a-b plane, as displayed in Figure1. Specifically, density functional theory. The formation of such layered PbS precipitates along the (001) we investigated the stability and electronic properties of this 2D vdW heterostructure planeemploying of molybdenite density functional (MoS theory.2) mineral The was formation recently of such reported layered, thereby PbS precipitates suggesting along the exist- ence of MoS2-PbS heterostructure [25]. We also calculate its carrier mobility to assess its the (001) plane of molybdenite (MoS2) mineral was recently reported, thereby suggesting applicabilitythe existence ofin MoSnext2--PbSgeneration heterostructure devices based [25]. We on also 2D calculatematerials. its We carrier note mobility that 2D tovdW het- erostructuresassess its applicability based on in the next-generation natural mineral devices fran basedckeite on have 2D materials. been proposed We note as that candidate materials2D vdW heterostructures for optoelectronic based devices on the natural[17,26]. mineral franckeite have been proposed as candidate materials for optoelectronic devices [17,26]. Figure 1. (a) Side view (c-axis vertical), (b) top view of the MoS -PbS heterostructure, composed of H Figure 1. (a) Side view (c-axis vertical), (b) top view of the2 MoS2-PbS heterostructure, composed of (i.e., MoS monolayer), and Q (i.e., PbS bilayer) layers. (c) The buckling parameters of the Q (PbS-like H (i.e., MoS2 2 monolayer), and Q (i.e., PbS bilayer) layers. (c) The buckling parameters of the Q (PbSbilayer)-like layer. bilayer) Color layer. code: Color Mo (grey), code: Pb Mo (orange), (grey), and Pb S(orange) (green)., and S (green). 2. Computational Model 2. Computational Model Electronic structure calculations based on density functional theory (DFT) were per- formed employing the Perdew-Burke-Ernzerhof (PBE) functional for exchange and correla- tion [27]. To account for the vdW long-range interaction between the constituent layers, a posteriori corrected semi-empirical contribution 1/r6 Grimme dispersion correction (D2) was used [28]. The valence electrons were treated explicitly, whereas the core-electrons were Materials 2021, 14, 1649 3 of 9 treated using the Projector Augmented Wave (PAW) pseudopotentials [29], as implemented in the Quantum Espresso Plane Wave package version 6.4.1 [30] The complete electronic configuration of Mo is [Kr]4d55s1, of Pb is [Xe]6s24f145d106p2 and S is [Ne]3s23p4. In the present work, the valence configurations of Mo, Pb, and S are taken to be 4s25s14p65p04d5, 6s26p25d10, and of 3s23p4, respectively.