Computational Study of Two-Dimensional Materials for Energy Applications

  • Declan Scullion

Student thesis: Doctoral ThesisDoctor of Philosophy

Abstract

Two-dimensional (2D) materials have attracted immense attention due to their novel and exceptional characteristics such as atomically thin body, large surface area to volume ratio, unique electronic properties, and high charge carrier mobilities. This makes 2D materials promising candidates for the next generation of low-power, high performance electronic devices. In this thesis, the mechanical, vibrational, thermal, and electronic properties of several 2D materials are explored and their possible application to devices is examined. The work was carried out in collaboration with experimentalists at several institutions with theoretical calculations confirming experimental measurements and improving the understanding of the observed results.

First, Professor Luhua Li’s group of Deakin University carried out Raman measurements on multilayer hBN and found that the Raman active G band in suspended hBN was not sensitive to a change in layer number; however, for substrate bound samples the change in frequency is appreciable due to a strain induced by the Si/SiO2 substrate. The trend for suspended samples is confirmed utilising density functional theory; however, an underestimation of the Γ-point frequency is observed using the van der Waals (vdWs) corrected optB88-vdW and hybrid HSE06 functionals. Increasing the amount of exact Hartree-Fock exchange used in the HSE06 functional allows for the experimental value to be reproduced exactly. Calculations on the Grüneisen parameter reveals negative values for the ZA phonon branch. A negative thermal expansion of the hBN sheet in the range ∼0-600 K is observed which increased with increasing layer number.

Experimental measurements on the thermal expansion confirmed a negative expansion in the 293-423 K range and the trend of increasing thermal expansion with layer number. Experimental measurements on the Young’s modulus of multilayer hBN and graphene show that the value for hBN is not sensitive to a change in the number of layers. This is in contrast to graphene which experiences an appreciable decrease with increasing layer number. Finite element analysis carried out by Professor Dong Qian’s group at ii the University of Texas calculated the pressure and strain on bilayer hBN and graphene close to and far away from the indenter tip during nanoindentation. Ab initio calculations on the interlayer interaction energies in bilayer graphene and hBN reveal that close to the indenter tip, the interaction energy becomes negative for graphene indicating that the equilibrium AB stacking configuration is no longer stable. Conversely, for hBN the energy increases forcing the layers to stay in their equilibrium AA’ stacking configuration.

Second, vdWs heterostructures based on C60/hBN and C60/WSe2 are examined. Professor Zhenan Bao of Stanford University used high-resolution scanning tunnelling electron microscopy and selective area electron diffraction to reveal a single crystal-like structure of C60 molecules on a hBN substrate. A comprehensive study revealed twelve orientations of C60 molecules relative to the hBN surface. Theoretical calculations on the binding energies of the twelve configurations show that the energy increases by a factor of ∼5-7 when vdWs interactions are included. Rotational energy barriers for the C60 molecule show striking similarity with experimentally measured preferential orientation of the C60 molecules.

Scanning tunnelling microscopy (STM) measurements on C60/WSe2 carried out by Professor Qing Hua Wang’s group of Arizona State University revealed a 2×2 superlattice on the orbital arrangement of C60 molecules. An additional study revealed sixteen C60 geometries relative to WSe2 surface. Calculations reveal that the binding energy increases by a factor of ∼5 when vdWs corrections are included. Calculations on the rotational energy barrier show that C60 molecules preferentially orientate with an electronrich 6:6 bond facing an electron-poor pentagonal face. Simulated STM images on all sixteen geometries generated using the local density of states from the lowest unoccupied molecular orbitals reveal 2-, 3-, and 5-fold symmetry in the orbitals of the C60 molecule. Ab initio molecular dynamics simulations reveal a coupling between neighbouring C60 molecules based on the orientation of electron-rich and electron-poor sites on neighbouring C60 molecules, confirming the calculations on the rotational energy barriers. Following the molecular dynamics calculation, the seven lowest unoccupied orbitals are plotted with each showing a unique real space configuration and being extremely diffuse in addition to exhibiting characteristics similar to that of the STM measurements.

Third, the effect of large uniaxial strain applied to the transition metal dichalcogenides (TMDCs) WS2 and WSe2 is examined through phonon calculations and Raman spec- iii troscopy. Professor Abhay Pasupathy’s group of Columbia University developed a technique to apply large uniaxial strain to 2D materials. Optical measurements on triangular flakes of TMDCs confirm large uniaxial strains of ∼6.5% have been applied to the layer. The change in the Raman active modes using unpolarised and cross-polarised light is measured with WS2 showing additional peaks compared to WSe2. Upon application of strain, a split is observed in the doubly degenerate E0 mode at the Γ-point. The application of strain causes a decrease in the frequency of the modes for both WS2 and WSe2 with the decrease being larger for in-plane modes. Under cross-polarisation the A 0 mode is suppressed; however, after the application of 2.85% strain in WS2 the mode became active again. In addition, an increase in strain in WSe2 leads to a decrease in the Raman intensity whereas in WS2 an increase is observed.

Ab initio calculations on the phonon spectra and Raman intensities of WS2 and WSe2 under strain also reveal a split in the E0 mode. All modes are found to decrease with strain, the exception being the A0 and 2LA modes in WSe2. The A0 is suppressed under cross-polarisation but becomes active again after 3% strain. Theoretical calculations allow for the assignment of the P1 and P2 peaks to the transverse optical modes of the E0 and E00 bands at the M-point of the Brillouin zone based on their frequencies. Calculations on the Grüneisen parameters in WS2 and WSe2 show excellent agreement with the experimentally measured values.

Finally, in collaboration with Professor Chih-Jen Shih’s group of ETH Zürich, the calculation of dielectric constants in 2D materials is reviewed. A high-throughput screening of 55 two-dimensional materials of disparate structure was carried out at HSE06 level including spin-orbit coupling. It is shown that increasing the length of the supercell along the non-periodic direction, L, results in a decrease of the calculated dielectric constant which is entirely unphysical. The dielectric constant is reformulated in terms of the 2D polarisability which is shown to converge within the range L=10-15 Å. Using an R2 analysis, a strong correlation is shown between the in-plane polarisability and the minimum electronic bandgap in addition to the out-of-plane polarisability and the effective thickness of the layer. A natural connection between the 2D polarisability and the screening in a 2D layer is developed. Moreover, a model to relate the 2D polarisability back to the 3D dielectric constants is found with the model reproducing the in-plane 3D dielectric constants extremely well.

Date of AwardDec 2019
Original languageEnglish
Awarding Institution
  • Queen's University Belfast
SupervisorJorge Kohanoff (Supervisor) & Elton Santos (Supervisor)

Cite this