www.tyndall.ie What theory can tell us about ALD mechanism simon.elliott@tyndall.ie 17th International Conference on Atomic Layer Deposition Denver, Colorado, USA 2017 Simon D. Elliott & co-workers www.tyndall.ie atomic The length scales of ALD nanomicrometre www.tyndall.ie atomic The length scales of ALD modelling nanomicrometre Density functional theory Computationa l fluid dynamics Atomistic simulations Coarse grained models www.tyndall.ie atomic Atomic scale modelling for ALD Density functional theory www.tyndall.ie + Precursor molecules S. D. Elliott, Semicond. Sci. Technol. 27, 074008 (2012); S. D. Elliott et al., Adv. Mater. 28, 5367 (2016). PRECURSOR PROPERTIES www.tyndall.ie Adsorption onto simple surfaces S. D. Elliott, Semicond. Sci. Technol. 27, 074008 (2012); S. D. Elliott et al., Adv. Mater. 28, 5367 (2016). SUBSTRATE MODELS www.tyndall.ie Adsorbates on 3D-structured surfaces S. D. Elliott, Semicond. Sci. Technol. 27, 074008 (2012); S. D. Elliott et al., Adv. Mater. 28, 5367 (2016). MULTIPLE ADSORBATES www.tyndall.ie Gas flow and film morphology S. D. Elliott, Semicond. Sci. Technol. 27, 074008 (2012); S. D. Elliott et al., Adv. Mater. 28, 5367 (2016). https://www.youtube.com/watch?v=tR1AQicsLRY KINETIC MONTE CARLO SIMULATIONS www.tyndall.ie Atomic-scale simulations System is stationary in time System undergoing transition, e.g. due to light Solve the time-independent non-relativistic Schrödinger equation H=E Nuclei & electrons in external field or electrons nuclei +++ ++ ++ + + - - - - -- -- - - - www.tyndall.ie Atomic-scale simulations System is stationary in time Solve motion of nuclei on potential energy (PE) hypersurface, E Quantum mechanics for electrons Quantum or classical mechanics for nuclei Solve the manyelectron Schrödinger equation H=E System undergoing transition, e.g. due to light Solve the time-independent non-relativistic Schrödinger equation H=E Nuclei & electrons in external field + or or electrons nuclei +++ ++ ++ + + - - - - -- -- - - - Coupled electron-nuclear dynamics www.tyndall.ie Atomic-scale simulations Solve motion of nuclei on potential energy (PE) hypersurface, E Quantum mechanics for electrons Quantum or classical mechanics for nuclei Solve the manyelectron Schrödinger equation H=E + electrons nuclei +++ ++ ++ + + - - - - -- -- - - - www.tyndall.ie Atomic-scale simulations Solve motion of nuclei on potential energy (PE) hypersurface, E Quantum mechanics for electrons Solve the manyelectron Schrödinger equation H=E + post-HF methods (e.g. CAS, CCSD) single determinant; h= (HF or DFT) semi-empirical methods (e.g. Hückel, TB) analytical potential E fitted to expt/theory <103 atoms <102 atoms<105 atoms<106 atoms Quantum or classical mechanics for nuclei as exact as neededapproximate electrons nuclei +++ ++ ++ + + - - - - -- -- - - - www.tyndall.ie Atomic-scale simulations post-HF methods (e.g. CAS, CCSD) single determinant; h= (HF or DFT) semi-empirical methods (e.g. Hückel, TB) analytical potential E fitted to expt/theory Fixed potential energy function, varying only with interatomic geometry. Analogy: always bring an umbrella, just in case it will rain. www.tyndall.ie Atomic-scale simulations post-HF methods (e.g. CAS, CCSD) single determinant; h= (HF or DFT) semi-empirical methods (e.g. Hückel, TB) analytical potential E fitted to expt/theory Wavefunction-based description of electrons, but solutions fitted to known data. Analogy: bring umbrella if weather statistics for this day averaged over many years indicate high likelihood of rain. yr.no www.tyndall.ie Atomic-scale simulations post-HF methods (e.g. CAS, CCSD) single determinant; h= (HF or DFT) semi-empirical methods (e.g. Hückel, TB) analytical potential E fitted to expt/theory Many-electron wavefunction is anti-symmetric product of many one-electron wavefunctions (“orbitals”). HARTREE-FOCK THEORY: Solve one-electron problem in mean field due to other electrons  Missing dynamical correlation Insist that each orbital is empty or doubly-occupied  Missing static correlation (e.g. when HOMO=LUMO) Analogy: bring umbrella if rain is forecast for today. yr.no www.tyndall.ie Atomic-scale simulations post-HF methods (e.g. CAS, CCSD) single determinant; h= (HF or DFT) semi-empirical methods (e.g. Hückel, TB) analytical potential E fitted to expt/theory Many-electron wavefunction is anti-symmetric product of many one-electron wavefunctions (“orbitals”). DENSITY FUNCTIONAL THEORY: Solve one-particle problem in mean field that mimics electron correlation  Some dynamical correlation included Insist that each orbital is empty or doubly-occupied  Missing static correlation (e.g. when HOMO=LUMO) Analogy: bring umbrella if hour-by-hour weather forecast indicates high likelihood of rain now. yr.no www.tyndall.ie Atomic-scale simulations post-HF methods (e.g. CAS, CCSD) single determinant; h= (HF or DFT) semi-empirical methods (e.g. Hückel, TB) analytical potential E fitted to expt/theory Many-electron wavefunction by mixing configurations and/or reference states from single-electron solutions. Analogy: bring umbrella if radar shows that rain is approaching. yr.no www.tyndall.ie Lejaeghere et al. compared the calculated values for the equation of states  for 71 elemental crystals from 15 different widely used DFT codes  employing 40 different potentials. Although there were variations in the  calculated values, most recent codes and methods converged toward a  single value, with errors comparable to those of experiment. www.tyndall.ie 103 atoms per cell Length scale 10-9 m Time scale 10-12 s Surface represented by infinitely-repeating 4 layer slab of (111)oriented fcc-Cu separated by vacuum; • VASP program; • Functional due to Perdew, Burke & Ernzerhof with vdW-optB88 correction; • Plane waves to 450 eV cutoff; • PAW treatment of cores; • k-point at  is adequate for large p(66) cell with 18 Å vacuum; • Self consistent steps to 10-4 eV; • Geometry optimised by conjugate-gradient; • Activation energies Ea by nudged elastic band. VASP: Kresse, G.; Hafner, J. J. Phys.: Condens. Matter 1994, 6, 8245. PBE: Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865–3868. Slab: Payne, M. C.; Teter, M. P.; Allan, D. C.; Arias, T. A.; Joannopoulos, J. D. Rev. Mod. Phys.1992, 64, 1045–1097. Density functional theory for slabs www.tyndall.ie • Isolated cluster of atoms in gas phase; • TURBOMOLE program; • Functional due to Becke & Perdew (1986) or Perdew, Burke & Ernzerhof (1996); • Basis set of localised atomic orbitals: def2- TZVPP; • Effective core potentials on heavy atoms; TURBOMOLE: Ahlrichs, R.; Bär, M.; Häser, M.; Horn, H.; Kölmel, C. Chem. Phys. Lett. 1989, 162, 165. Becke, A. D. Phys. Rev. A 1988, 38, 3098; Perdew, J. P. Phys. Rev. B 1986, 33, 8822. Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865–3868. Eichkorn, K.; Weigend, F.; Treutler, O.; Ahlrichs, R. Theor. Chem. Acc. 1997, 97, 119. + Density functional theory for molecules 103 atoms in vacuum Length scale 10-9 m Time scale 10-12 s www.tyndall.ie + H. Ablat Hybrid ALD - MLD TMA + acrylate + ethanolamine www.tyndall.ie Bonding in hybrid MLD/ALD films H C O N Al O‐Al‐N stretch  computed at  511 cm‐1 …measured  with FTIR at  514 cm‐1 www.tyndall.ie Bonding in hybrid MLD/ALD films H C O N Al O‐Al‐N stretch  computed at  610 cm‐1 … measured at  610 cm‐1 with  FTIR www.tyndall.ie Bonding in hybrid MLD/ALD films H C O N Al O‐Al‐N stretch  computed at  610 cm‐1 … measured at  610 cm‐1 with  FTIR www.tyndall.ie Bonding in hybrid MLD/ALD films H C O N Al O‐Al‐N stretch  computed at  610 cm‐1 … measured at  610 cm‐1 with  FTIR Little known about structure of exposed ‘surface’ during polymer MLD. DFT can reveal how oligomers form. www.tyndall.ie + Combinatorial approach to precursor design ALD of Si3N4 www.tyndall.ie www.tyndall.ie Precursors screened: Si(Cl)R2 with R=H, Cl or CH3 Si2(Cl)R5 with R=H or Cl Enthalpy and kinetic barrier evaluated for model reactions: NH3 (g) + Si(Cl)(H)R2 (g)  H2N‐Si(H)R2 (g) + HCl (g) NH3 (g) + Si(Cl)(H)R2 (g)  H2N‐Si(Cl)R2 (g) + H2 (g) optimum www.tyndall.ie Knowledge about ALD mechanism allows metrics for precursor design to be defined. Large numbers of precursors can be automatically generated and screened. optimum www.tyndall.ie Improved models of substrates and growing surfaces ALD of Al2O3 www.tyndall.ie pink=Al,red=O,white=H www.tyndall.ie How adsorption energy affects exposure required for saturation ALD of Si3N4 C. Murray www.tyndall.ie “Growth rate” in ALD? Individual reaction steps  activation energies  kinetics of individual steps  kinetics of overall growth process. Rate at which growth process takes place  exposure needed  dependence of growth on process time  throughput. Self-limiting surface chemistry  saturation  maximum thickness increment per cycle (GPC). www.tyndall.ie Reactivity of ALD SiO2 versus Si3N4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.01 0.1 1 10 100 1000 DepositionRate(A/cycle) Exposure (Torr sec) Deposition rate vs Exposure at 450°C Si 1 + O2 Si1 + NH3 Si 3 + NH3 Si 2 + NH3 SiO2SiO2 Si3N4Si3N4 What Si precursor can solve this problem? Require 100x greater exposure of Si precursor to achieve saturation for Si3N4 relative to SiO2 www.tyndall.ie Reactivity of ALD SiO2 versus Si3N4 X H Si H H L L H L X Si LH H SiX SiX Silicon precursor SiL2H2 with ligands L Substrate is growing film of SiO2 (X=O) or Si3N4 (X=NH) By-product is protonated ligand Chemisorbed precursor fragment www.tyndall.ie Reactivity of ALD SiO2 versus Si3N4 Unbound precursor X H Si H H L L Desorption of by-product H L X Si LH H SiX SiX Si H H L L X H Bound precursor SiX X HSi LL H H Bound by-product SiX X HSi LL H H Transition State SiX www.tyndall.ie -90 -70 -50 -30 -10 10 30 50 70 90 ΔE(kJ/mol) SiH2dma2 SiH2dma2 NH2 Surface OH Surface Reactivity of ALD SiO2 versus Si3N4 BP86/SV(P) at T = 0 K Ea = 80.0 kJ/mol Ea = 51.7 kJ/mol Major difference is in strength of initial molecular adsorption, not in choice of precursorOH surface model for SiO2 NH2 surface model for Si3N4 transition state desorption of by-productunbound precursor bound precursor bound by- product SiH2(NMe2)2 precursor C. M. Murray et al., ACS Appl. Mater. Interf. 6, 10534 (2014). www.tyndall.ie Reactivity of ALD SiO2 versus Si3N4 NH2 surface model for Si3N4 SiH2(NMe2)2 precursor In some cases, simple model of isolated adsorbate on surface is adequate to explain growth behaviour. www.tyndall.ie Accuracy of DFT results Importance of van der Waals interactions during precursor adsorption ALD of CuY. Maimaiti www.tyndall.ie vdW interactions during adsorption Cu(dmap)2 dmap=dimethyl-amino-propoxide Cu-O break? Cu-N break?  form Cu-Cu Cu-O break? Cu-N break? …and vdW interactions? Cu=pink,O=red,N=blue,C=grey,H=white How do Cu precursors adsorb onto the growing Cu surface? www.tyndall.ie vdW interactions during adsorption Y. Maimaiti et al., J. Phys. Chem. C 119, 9375–9385 (2015). Chemisorption onto edge or kink for all functionals, regardless of vdW treatment: www.tyndall.ie vdW interactions during adsorption Adsorption onto flat Cu(111) is sensitive to van der Waals forces, alignment of Cu-O and cleavage of Cu-N: Y. Maimaiti et al., J. Phys. Chem. C 119, 9375–9385 (2015). E(physisorbed) E(chemisorbed) PBE -0.4 eV (3 sites) -1.5 eV (1 site) vdW-DF2 -1.0 eV (3 sites) -2.0 eV (1 site) optB88-vdW -1.6 eV (1 site) -3.2 eV (3 sites) PBE-D3 no sites -3.5 eV (4 sites) www.tyndall.ie vdW interactions during adsorption Adsorption onto flat Cu(111) is sensitive to van der Waals forces, alignment of Cu-O and cleavage of Cu-N: Y. Maimaiti et al., J. Phys. Chem. C 119, 9375–9385 (2015). No consensus yet on how best to incorporate vdW contribution to adsorption. www.tyndall.ie Accuracy of DFT results Isolated ligands can persist on surface for entire cycle ALD of Al2O3 M. Shirazi www.tyndall.ie Cooperative effect in surface kinetics CH3 Al Ea=0.28 eV from 3-coordinate OH OH CH3 Al Ea=0.74 eV from 2-coordinate OH OH TMA pulse: Computed activation energies for transfer of H+ from surface-OH to adsorbate-CH3, resulting in desorption of CH4: www.tyndall.ie Cooperative effect in surface kinetics Ea=0.26 eV from 3-coordinate OH no reaction from 2-coordinate OH CH3 CH3 OH OH TMA pulse: Computed activation energies for transfer of H+ from surface-OH to adsorbate-CH3, resulting in desorption of CH4: www.tyndall.ie Cooperative effect in surface kinetics Ea=0.26 eV from 3-coordinate OH Ea=0.74 eV from 2-coordinate OH when neighbouring AlCH3 is missing CH3 OH TMA pulse: Computed activation energies for transfer of H+ from surface-OH to adsorbate-CH3, resulting in desorption of CH4: Cooperative effect: neighbouring adsorbate increases coordination number of O and thus increases Brønsted acidity of OH. CH3 OH www.tyndall.ie Cooperative effect in surface kinetics large grey=Al, red=O, white=H, small grey=C No chemisorption of single H2O to single Al(CH3) OH2 single Al(CH3) H2O pulse www.tyndall.ie Cooperative effect in surface kinetics large grey=Al, red=O, white=H, small grey=C Al H2O Ea=0.52 eV No chemisorption of single H2O to single Al(CH3) OH2 single Al(CH3) 3.Al(CH3) cluster H2O pulse www.tyndall.ie Cooperative effect in surface kinetics large grey=Al, red=O, white=H, small grey=C Al H2O Ea=0.52 eV No chemisorption of single H2O to single Al(CH3) OH2 single Al(CH3) 2H2O 3.Al(CH3) cluster Ea=0 H2O pulse www.tyndall.ie Cooperative effect in surface kinetics large grey=Al, red=O, white=H, small grey=C 2H2O 3.Al(CH3) cluster Ea=0 Kinetics of surface reactions strongly affected by local environment. Effect of local film morphology on kinetics is not yet known. Reactions are accelerated by high local concentration of ligands. www.tyndall.ie Cooperative effect in surface kinetics Persistent H – VV literature TU/e logo www.tyndall.ie + What theory can tell us about ALD mechanism SUCCESSES: Screening based on intrinsic chemistry; Oligomer formation during MLD CHALLENGES: Volatility? Thermal stability? Simon Elliott simon.elliott@tyndall.ie www.tyndall.ie What theory can tell us about ALD mechanism SUCCESSES: Sketch out reaction mechanism; Account for many experimental anomalies CHALLENGES: Accuracy of weak interactions; Need more realistic surface geometries for kinetics Simon Elliott simon.elliott@tyndall.ie www.tyndall.ie What theory can tell us about ALD mechanism SUCCESSES: More accurate activation energies; Indications of how morphology evolves CHALLENGES: Automatic search? Simon Elliott simon.elliott@tyndall.ie