Electronic structure and optical conductivity of two dimensional (2D) MoS2: Pseudopotential DFT versus full potential calculations Ashok Kumar, Jagdish Kumar, and P. K. Ahluwalia Citation: AIP Conference Proceedings 1447, 1269 (2012); doi: 10.1063/1.4710474 View online: http://dx.doi.org/10.1063/1.4710474 View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/1447?ver=pdfcov Published by the AIP Publishing
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Electronic Structure and Optical Conductivity of Two Dimensional (2D) MoS2: Pseudopotential DFT Versus Full Potential Calculations Ashok Kumar1*, Jagdish Kumar1,2 and P. K. Ahluwalia1 1
Physics Department, Himachal Pradesh University, Shimla-171005, National Physical Laboratory, K.S. Krishnan Marg, New Delhi-10012 *Email:
[email protected]
2
Abstract. We report first principle comparative study of electronic structure and optical conductivity of two dimensional (2D) MoS2 using pseudopotential based DFT and full potential calculations within generalized gradient approximation (GGA). We find direct band gap 1.83 eV and 1.79 eV respectively with pseudopotential and full potential calculations, which are in excellent agreement with recently measured direct band gap of 1.80 eV with optical spectroscopy. States around the Fermi energy are mainly derived from 4d orbitals of Mo. Calculated optical conductivity with pseudopotential finds very good agreements to full potential optical conductivity for E vector perpendicular to c axis and finds interband transitions mainly from p valance bands of S to the d conduction bands of Mo. Keywords: DFT, GGA, NAOs, Pseudopotential, PDOS, Band structure, TMDCs PACS: 71.15.-m, 78.20.Ci, 78.68.+m
INTRODUCTION Two dimensional (2D) Transition metal dichalcogenides (TMDCs) semiconductor, particularly monolayer MoS2, is emerging as a potential material for many applications including transistor technology, solar cell, photocatalysis, lubrication and optoelectronics [1-6]. The bulk 2H-MoS2 crystal is built up of weakly van der Walls bonded S-Mo-S units. Each of these stable units referred as two dimensional (2D) MoS2 monolayer (specified as 1HMoS2), consists of two hexagonal planes of S atoms and intermediate hexagonal plane of Mo atoms. Weak interlayer and strong intralayer interactions makes possible a formation of ultrathin 1H-MoS2 crystal by micro-mechanical cleavage. In the present paper we have investigated electronic structure and optical conductivity of two dimensional (2D) MoS2 using pseudopotential DFT as well as full potential calculations.
COMPUTATIONAL DETAILS Density Functional Theory (DFT) calculations have been performed by means of ab-initio pseudopotential and numerical atomic orbitals (NAOs)
based SIESTA method [7] and full potential linear augmented plane wave (FP-LAPW) based full potential Elk code [8] within generalized gradient approximation (GGA) using PBE functional. A sufficient large vacuum region is used to separate the single layer along the c axis to ensure no interaction between the layers making it effectively isolated 2D layer. Parameters a and b of our supercell used were equal to experimental bulk lattice constant i.e. 3.16 Å. In SIESTA calculations we have used relativistic Troullier Martin pseudopotential, double zeta polarization (DZP) basis sets with confinement energy of 30 meV and real space cutoff 200 Ry. A 30x30x1 and 90x90x3 Monkhorst-Pack of k points were used for electronic structure and optical conductivity calculation respectively. Calculation with Elk code has been done by using muffin tin sphere radii of 2.4a0 and 2.13a0 for Mo and S respectively. A dense grid of 14×14×2 was used to perform Brullion zone integrations. Linear optical dielectric response is calculated within the random phase approximation (RPA).
RESULTS AND DISCUSSION The electronic band structure and corresponding total and partial density of states (PDOS) with
Solid State Physics: Proceedings of the 56th DAE Solid State Physics Symposium 2011 AIP Conf. Proc. 1447, 1269-1270 (2012); doi: 10.1063/1.4710474 © 2012 American Institute of Physics 978-0-7354-1044-2/$30.00
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pseudopotential and full potential calculations are shown in figures 1 and 2 respectively. Electronic band structure has been calculated along Γ-M-K-Γ high symmetry points direction in brillouin zone. States around Fermi energy are mainly derived from 4d orbitals of Mo as can be seen in figure 1 and 2. Pseudopotential calculated band structure finds 1.83 eV band gap as compared to 1.79 eV with full potential calculations. Both the calculated direct band gap are in excellent agreement with experimental direct band gap of 1.80 eV [2].
FIGURE 1. Electronic band structure and corresponding total and partial density of states of 2D MoS2 with pseudopotential based SIESTA calculations.
FIGURE 3. Optical conductivity of 2D MoS2 within pseudopotential SIESTA and full potential Elk calculations for E vector perpendicular to c axis. Structure peaks designated by A, B, C, D, E, F are shown. TABLE 1. Structure peaks position in optical conductivity and corresponding interband transitions within pseudopotential SIESTA and full potential Elk calculations. Structure Structure Interband Energy with with Elk Transition Gap SIESTA (eV) s (eV) 2.70(A) 2.73 VB1→CB1 1.83 3.29 3.14(B) VB1→CB1 (SIESTA) VB1→CB2 3.68(C) 3.72 VB1→CB3 1.79 VB2→CB2 ( Elk) 4.35 4.20(D) VB1→CB4 VB2→CB3 VB3→CB2 5.14(E) 4.90 VB2→CB4 1.80 5.57(F) 5.75 VB5→CB2 (Exp.)[2]
ACKNOWLEDGMENTS Ashok Kumar and Jagdish Kumar are grateful to CSIR New Delhi for providing financial support in the form of Junior Research Fellowship. FIGURE 2. Electronic band structure and corresponding total and partial density of states of 2D MoS2 with full potential Elk code.
Figure 3 shows calculated optical conductivity with E vector perpendicular to c axis of 2D MoS2 within pseudopotential and full potential calculations. Corresponding structure peaks position revealing interband transitions are shown in table 1. Interband transition A is dominated by Valance band 1 (VB1) below Fermi energy to the conduction band 1 (CB1) above Fermi energy. Interband transition B is mainly due to transition from valance band 1 below Fermi energy to conduction band 1 and 2 above Fermi energy. Similarly all other interband transition are shown in table 1
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