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Surfaces and Interfaces
- 1. Surfaces and Interfaces Microscopic mechanisms and macroscopic consequences Dr. Keith T. Butler Department of Chemistry k.t.butler@bath.ac.uk “God made the bulk; surfaces were invented by the devil” Wolfgang Pauli
- 2. Content • Background and history of surfaces – History – Importance • Important concepts for surface definiEons – Energy-‐band-‐alignment diagram – Miller indices – Tasker notaEon – Polar surfaces • Surface energeEcs and electronic structure – Bond breaking approximaEon – Surface Tamm states • Surfaces in PV – Trapping – PassivaEon • Interface classificaEons and formaEon • Strain and supercells • WeKng angle and cohesion • Coherent/Semi-‐coherent/Incoherent • Interfaces in PV • SchoMky barrier / Ohmic contacts • Charge neutrality level • Band Alignment in PV • Work funcEons and electron energies • Measuring work funcEons • CalculaEng work funcEons • Bulk/surface contribuEons • Work funcEon engineering • PracEcal examples • CalculaEon of surface/interface energy in DFT • Band alignment from DFT SURFACES INTERFACES
- 3. At a loose end?
- 5. Benjamin Franklin and the old wives tale “[T]he oil, though not more than a teaspoonful, produced an instant calm over a space several yards square which spread amazingly and extended itself gradually till it reached the lee side, making all that quarter of the pond, perhaps half an acre, as smooth as a looking glass.”
- 6. The study of surfaces • Mostly atoms are not at the surface BULK Surface
- 7. The study of surfaces & interfaces “The interface is the device” Herbert Kroemer Nobel prize in Physics 2000 “For developing semiconductor heterostructures used in high-‐speed-‐ and opto-‐electronics"
- 8. Surfaces in PV Charge separa?on Extrac?on of carriers Recombina?on Contact resistance hMp://www.pveducaEon.org
- 9. Content • Background and history of surfaces – History – Importance • Important concepts for surface definiEons – Energy-‐band-‐alignment diagram – Miller indices – Tasker notaEon – Polar surfaces • Surface energeEcs and electronic structure – Bond breaking approximaEon – Surface Tamm states • Surfaces in PV – Trapping – PassivaEon • Interface classificaEons and formaEon • Strain and supercells • WeKng angle and cohesion • Coherent/Semi-‐coherent/Incoherent • Interfaces in PV • SchoMky barrier / Ohmic contacts • Charge neutrality level • Band Alignment in PV • Work funcEons and electron energies • Measuring work funcEons • CalculaEng work funcEons • Bulk/surface contribuEons • Work funcEon engineering • PracEcal examples • CalculaEon of surface/interface energy in DFT • Band alignment from DFT SURFACES INTERFACES
- 10. Energy-‐band-‐diagrams Valence Band (Occupied states) ConducEon Band (Unoccupied states) Vacuum level Band-‐gap Electron Affinity IonisaEon potenEal
- 11. Energy-‐band-‐diagrams Type I Type II Type II Metal/ Semiconductor
- 12. Energy-‐band-‐diagrams “If, in discussing a semiconductor problem, you cannot draw an Energy-Band-Diagram, this shows that you don’t know what you are talking about” “If you can draw one, but don’t, then your audience won’t know what you are talking about.”
- 15. Surface ClassificaEon Define laKce vectors (a b c)
- 16. Surface ClassificaEon Define the intersecEon (0 b 0)
- 17. Surface ClassificaEon IdenEfy the fracEonal coordinates of the intercept (∞/a b/b ∞/c)
- 18. Surface ClassificaEon IdenEfy the fracEonal coordinates of the intercept (0 1 0)
- 21. ClassificaEon IdenEfy intercepts FracEonal coordinates of intercepts If fracEons result in step (ii) then round up all indices by mulEplicaEon; e.g. (1/3,0,1) -‐> (1,0,3) NegaEve numbers are indicated by an over-‐bar
- 22. Polar/Non-‐polar surfaces P W Tasker 1979 J. Phys. C: Solid State Phys. 12 4977 Type I Type II Type III
- 23. The Polar Catastrophe Type III PotenEal Energy P W Tasker 1979 J. Phys. C: Solid State Phys. 12 4977
- 24. Examples of Polar Surfaces • A polar surface can exist – with modificaEons. • Zincblende (100) • Mechanisms for stabilisaEon: – Change in stoiciometry in surface layers – AdsorpEon of ions on the surfaces – Electron redistribuEon 2D electron gas C. Noguera , J. Phys.: Condens. MaMer 12 R367 σ j j=1 m ∑ = − σm+1 2 (−1)m − R2 − R1 R2 + R1 # $ % & ' (
- 25. Content • Background and history of surfaces – History – Importance • Important concepts for surface definiEons – Energy-‐band-‐alignment diagram – Miller indices – Tasker notaEon – Polar surfaces • Surface energeEcs and electronic structure – Bond breaking approximaEon – Surface Tamm states • Surfaces in PV – Trapping – PassivaEon • Interface classificaEons and formaEon • Strain and supercells • WeKng angle and cohesion • Coherent/Semi-‐coherent/Incoherent • Interfaces in PV • SchoMky barrier / Ohmic contacts • Charge neutrality level • Band Alignment in PV • Work funcEons and electron energies • Measuring work funcEons • CalculaEng work funcEons • Bulk/surface contribuEons • Work funcEon engineering • PracEcal examples • CalculaEon of surface/interface energy in DFT • Band alignment from DFT SURFACES INTERFACES
- 26. Surface energy Energy is proporEonal to the number of bonds broken.
- 27. Surface Electronic States Atom Hybrid Solid Eg
- 28. Surface Electronic States Hybrid Surface Eg Atom
- 29. Content • Background and history of surfaces – History – Importance • Important concepts for surface definiEons – Energy-‐band-‐alignment diagram – Miller indices – Tasker notaEon – Polar surfaces • Surface energeEcs and electronic structure – Bond breaking approximaEon – Surface Tamm states • Surfaces in PV – Trapping – PassivaEon • Interface classificaEons and formaEon • Strain and supercells • WeKng angle and cohesion • Coherent/Semi-‐coherent/Incoherent • Interfaces in PV • SchoMky barrier / Ohmic contacts • Charge neutrality level • Band Alignment in PV • Work funcEons and electron energies • Measuring work funcEons • CalculaEng work funcEons • Bulk/surface contribuEons • Work funcEon engineering • PracEcal examples • CalculaEon of surface/interface energy in DFT • Band alignment from DFT SURFACES INTERFACES
- 30. Surface recombinaEon • Characterised by capture and release rates of carriers and energy of state RSE RSH RSE RSH
- 31. Surface passivaEon • Chemical passivaEon
- 32. Surface PassivaEon • Blocking layer
- 33. Surface PassivaEon • Fixed Charge
- 34. Content • Background and history of surfaces – History – Importance • Important concepts for surface definiEons – Energy-‐band-‐alignment diagram – Miller indices – Tasker notaEon – Polar surfaces • Surface energeEcs and electronic structure – Bond breaking approximaEon – Surface Tamm states • Surfaces in PV – Trapping – PassivaEon • Interface classificaEons and formaEon • Strain and supercells • WeKng angle and cohesion • Coherent/Semi-‐coherent/Incoherent • Interfaces in PV • SchoMky barrier / Ohmic contacts • Charge neutrality level • Band Alignment in PV • Work funcEons and electron energies • Measuring work funcEons • CalculaEng work funcEons • Bulk/surface contribuEons • Work funcEon engineering • PracEcal examples • CalculaEon of surface/interface energy in DFT • Band alignment from DFT SURFACES INTERFACES
- 35. Interface thermodynamics σ12 σ1v + σ2v Wsep Fad Diffusion and surface segrega?on MW Finnis 1996 J. Phys: Condens. Ma4er. 8 5811
- 36. Interface thermodynamics • Interface energy related to weKng angle. σ1v σ2v σ12 MW Finnis 1996 J. Phys: Condens. Ma4er. 8 5811
- 37. LaKce matching • Depends on laKce parameters of the two phases • Determines interface strain; large contribuEon to interface energy a b
- 38. Coherent Interface Interface laKce planes must match. The same atomic configuraEon across the interface. Examples: CuSi alloys GaAs/AlAs InAs/GaAs Ge/Si PbTe/CdTe The energy of coherent interfaces: Mismatching bond energy Strain energy is negligible Energy 0 – 200 mJ/m^2
- 39. Semi-‐coherent Interface When strains are sufficiently large. EnergeEcally favorable to to form misfit dislocaEons at interfaces. Examples: InAs/GaAs The energy of semi-‐coherent interfaces: Strain plus chemical bonding Energy 200 – 500 mJ/m^2
- 40. Incoherent interface Very different configuraEons on either side of the interface. OR laKce constants > 25% difference. Examples: High angle grain boundaries Inclusions in alloys The energy of incoherent interfaces: Very large structural contribuEon. Energy 500 -‐1000 mJ/m^2
- 41. Content • Background and history of surfaces – History – Importance • Important concepts for surface definiEons – Energy-‐band-‐alignment diagram – Miller indices – Tasker notaEon – Polar surfaces • Surface energeEcs and electronic structure – Bond breaking approximaEon – Surface Tamm states • Surfaces in PV – Trapping – PassivaEon • Interface classificaEons and formaEon • Strain and supercells • WeKng angle and cohesion • Coherent/Semi-‐coherent/Incoherent • Interfaces in PV • SchoMky barrier / Ohmic contacts • Charge neutrality level • Band Alignment in PV • Work funcEons and electron energies • Measuring work funcEons • CalculaEng work funcEons • Bulk/surface contribuEons • Work funcEon engineering • PracEcal examples • CalculaEon of surface/interface energy in DFT • Band alignment from DFT SURFACES INTERFACES
- 42. Ohmic Contacts in PV • Minimising losses in PV • V ∝ I • Ideal Ohmic contacts will not produce potenEal barriers • Ideal contact all Fermi levels align
- 44. Band Bending The SchoMky limit. SchoMky barrier – limits charge transport across the interface. Contact resistance depends exponenEally on the SchoMky barrier.
- 45. Achieving Ohmic Contacts Ohmic n-‐type contact Ohmic p-‐type contact
- 46. ConsideraEons for devices n-‐type p-‐type Space charge PosiEve NegaEve Metal work funcEon Small / shallow Large / deep Examples Li, Na, Ca, K, Au, Ag, Fe
- 47. Charge Neutrality Level/Surface States States in the gap of the semiconductor. Can result in addiEonal charge transfer. New local charge region. Region ~ 0.2 – 0.3 nm
- 48. Local dipoles
- 49. Content • Background and history of surfaces – History – Importance • Important concepts for surface definiEons – Energy-‐band-‐alignment diagram – Miller indices – Tasker notaEon – Polar surfaces • Surface energeEcs and electronic structure – Bond breaking approximaEon – Surface Tamm states • Surfaces in PV – Trapping – PassivaEon • Interface classificaEons and formaEon • Strain and supercells • WeKng angle and cohesion • Coherent/Semi-‐coherent/Incoherent • Interfaces in PV • SchoMky barrier / Ohmic contacts • Charge neutrality level • Band Alignment in PV • Work funcEons and electron energies • Measuring work funcEons • CalculaEng work funcEons • Bulk/surface contribuEons • Work funcEon engineering • PracEcal examples • CalculaEon of surface/interface energy in DFT • Band alignment from DFT SURFACES INTERFACES
- 50. Work funcEons “The minimum energy required to remove an electron from deep within the bulk, to a point a macroscopic distance outside the surface. ”
- 51. Measuring work funcEons (I) Ultraviolet Photoemission Spectroscopy (UPS/PES) hMps://www.tu-‐chemnitz.de/physik/HLPH/elec_spec.htmlhMps://www.tu-‐chemnitz.de/physik/HLPH/elec_spec.html
- 52. Measuring work funcEons (II) Kelvin Probe E
- 53. Measuring Work funcEons Just look it up…right? § “A single group often obtains different values on different crystals, different cleaves, or different days” Surface Science of Metal Oxides: Henrich & Cox
- 54. ContribuEons to work funcEons (Ia) • Bulk binding energy
- 55. Bulk Polymorph WorkfuncEons The relaEonship between crystal environment and ionisaEon potenEal. Engineer levels for improved water spliKng.
- 56. ContribuEons to work funcEons (Ib) Atom Hybrid Bond Eg Solid
- 57. ContribuEons to work funcEons (II)
- 58. The surface double-‐layer DensityPotential
- 59. Mott-Littleton (1938) Harwell Labs, UK A. B. Lidiard, JCSFT 85, 341 (1989) Daresbury Labs, UK A. A. Sokol et al, IJCQ 99, 695 (2004) Limitation: Convergence in region sizes and accurate analytical MM potentials Current Implementation: ChemShell (QM/MM driver) Bulk Values: An Embedded Crystal
- 60. Classical region Quantum region Continuum region Vacuum region Slab region Capping layer Quantum Region Active Potentials Region Frozen Potentials Region Vacuum Region Slab Region ValenceBand Maximum Band Bending Capping Layer Vacuum Level IP IP IP surf slab Electrostatic Potential Phys. Rev. B 89, 115320 (2014) “Absolute” electron energies
- 61. Classical region Quantum region Continuum region Vacuum region Slab region Capping layer Quantum Region Active Potentials Region Frozen Potentials Region Vacuum Region Slab Region ValenceBand Maximum Band Bending Capping Layer Vacuum Level IP IP IP surf slab Electrostatic Potential Phys. Rev. B 89, 115320 (2014) Engineering electron energies
- 62. Real capping layers PbO2 SiO2 TiO2 Capping layer IP Φ ΔΦ (wrt ITO) SiO2 11.07 6.87 +0.77 TiO2 10.19 5.99 -‐0.11 PbO2 10.25 6.05 -‐0.05 Phys. Rev. B 89, 115320 (2014) ITO replacement CIGS, Si High Φ OPV!
- 63. Content • Background and history of surfaces – History – Importance • Important concepts for surface definiEons – Energy-‐band-‐alignment diagram – Miller indices – Tasker notaEon – Polar surfaces • Surface energeEcs and electronic structure – Bond breaking approximaEon – Surface Tamm states • Surfaces in PV – Trapping – PassivaEon • Interface classificaEons and formaEon • Strain and supercells • WeKng angle and cohesion • Coherent/Semi-‐coherent/Incoherent • Interfaces in PV • SchoMky barrier / Ohmic contacts • Charge neutrality level • Band Alignment in PV • Work funcEons and electron energies • Measuring work funcEons • CalculaEng work funcEons • Bulk/surface contribuEons • Work funcEon engineering • PracEcal examples • CalculaEon of surface/interface energy in DFT • Band alignment from DFT SURFACES INTERFACES
- 64. PracEcal Session • Building a good surface/interface • CalculaEng a surface energy • CalculaEng a workfuncEon from DFT
- 65. Cut the surface : METADISE • Input unit cell and miller index • SystemaEcally generates all cuts • Checks for dipolar surfaces
- 66. CalculaEng a surface energy Calculate the energy of the pure system. Calculate the energy of a 2D slab.
- 67. SMACT-‐Interface • Evaluate laKces with mismatch below a certain threshold. • CuI//CdO • 110//110 • 4x4//5x5
- 68. CalculaEng Interface Energy Calculate the separate bulk energies. Calculate the energy of a mixed system.
- 69. Pro-‐Eps for surfaces in VASP • k-‐point sampling in the surface normal direcEon can be drasEcally reduced. • Vacuums of ~ 15 Angstrom are usually large enough…check this for convergence though. • Slab thickness required varies – depends on the system type. Generally – more broken bonds @ surface means more surface states requires a thicker slab … eg layered systems are easy!!
- 70. Interface energy caveat • SomeEmes interface energies calculated as above converge very slowly. • Calculate energies for several layer thicknesses.
- 71. Pro-‐Eps: CalculaEng a band alignment diagram from DFT ICORELEVEL = 1 NEDOS = 1000 NBANDS = 468 1: Get the energy levels of the bulk structure DFT band structure (usually with a hybrid funcEonal) Get energy difference between core state and VBM hMps://github.com/keeeto/VASPBands Core level, serves as a reference state Increase NEDOS – nicer DOS plots Increase # bands quicker convergence -‐ NBANDS = # electrons (spin unpolarised) -‐ NBAMDS = 2x #electrons (spin polarised)
- 72. Pro-‐Eps: CalculaEng a band alignment diagram from DFT ICORELEVEL = 1 LVHAR = .TRUE. 2: Calculate the electrostaEc potenEal of the slab structure Core level, serves as a reference state Hartree potenEal – converges more quickly than total potenEal. Get the VBM from core level plus energy difference from the bulk calculaEon. Avoids surface state influence.
- 73. Pro-‐Eps: CalculaEng a band alignment diagram from DFT 2: Calculate the electrostaEc potenEal of the slab structure ExtracEng the electrostaEc potenEal from LOCPOT file. Our code MacroDensity does this for a range of systems and electronic structure codes. hMps://github.com/WMD-‐Bath/MacroDensity input_file = 'LOCPOT.slab' lattice_vector = 4.75 output_file = 'planar.dat' # No need to alter anything after here #------------------------------------------------------ PlanarAvergae.py > python PlanarAverage.py
- 74. Pro-‐Eps: CalculaEng a band alignment diagram from DFT 2: Calculate the electrostaEc potenEal of the slab structure ExtracEng the electrostaEc potenEal from LOCPOT file. Our code MacroDensity does this for a range of systems and electronic structure codes. hMps://github.com/WMD-‐Bath/MacroDensity input_file = 'LOCPOT.slab' lattice_vector = 4.75 output_file = 'planar.dat' # No need to alter anything after here #------------------------------------------------------ PlanarAvergae.py > python PlanarAverage.py
- 75. ElectrostaticPotentialPro-‐Eps: CalculaEng a band alignment diagram from DFT Bulk calculaEon the core state eigenenergies are 1- 1s -87.8177 2s -87.9364 2p -87.9364 2- 1s -87.9771 2s -88.1009 2p -88.1009
- 76. Important Points • Surfaces consEtute a small part of a system, but have a huge influence on properEes. • Energy-‐band-‐diagrams are criEcal for designing devices. • Single material calculaEons can be used to predict offsets in hetero-‐juncEon systems…but cauEon is always advised. • Both experimental and theoreEcal characterisaEon of surfaces are difficult and should be used to compliment one another wherever possible.