Download - Surfaces and Interfaces
Surfaces and Interfaces
Microscopic mechanisms and macroscopic consequences
Dr. Keith T. Butler Department of Chemistry
“God made the bulk; surfaces were invented by the devil” Wolfgang Pauli
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
At a loose end?
Early surface science
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.”
The study of surfaces • Mostly atoms are not at the surface
BULK Surface
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"
Surfaces in PV
Charge separa?on Extrac?on of carriers
Recombina?on Contact resistance
hMp://www.pveducaEon.org
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
Energy-‐band-‐diagrams
Valence Band (Occupied states)
ConducEon Band (Unoccupied states)
Vacuum level
Band-‐gap
Electron Affinity
IonisaEon potenEal
Energy-‐band-‐diagrams Type I Type II Type II
Metal/Semiconductor
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.”
Surface ClassificaEon
Surface ClassificaEon
Surface ClassificaEon
Define laKce vectors (a b c)
Surface ClassificaEon
Define the intersecEon (0 b 0)
Surface ClassificaEon
IdenEfy the fracEonal coordinates of the intercept (∞/a b/b ∞/c)
Surface ClassificaEon
IdenEfy the fracEonal coordinates of the intercept (0 1 0)
Surface ClassificaEon
(011)
Surface ClassificaEon
(111)
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
Polar/Non-‐polar surfaces
P W Tasker 1979 J. Phys. C: Solid State Phys. 12 4977
Type I Type II Type III
The Polar Catastrophe Type III
PotenE
al Ene
rgy
P W Tasker 1979 J. Phys. C: Solid State Phys. 12 4977
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 jj=1
m
∑ = −σ m+1
2(−1)m − R2 − R1
R2 + R1
#
$%
&
'(
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
Surface energy
Energy is proporEonal to the number of bonds broken.
Surface Electronic States Atom Hybrid Solid
Eg
Surface Electronic States Hybrid Surface
Eg
Atom
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
Surface recombinaEon
• Characterised by capture and release rates of carriers and energy of state
RSE
RSH
RSE
RSH
Surface passivaEon
• Chemical passivaEon
Surface PassivaEon
• Blocking layer
Surface PassivaEon
• Fixed Charge
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
Interface thermodynamics
σ12 σ1v + σ2v
Wsep Fad
Diffusion and surface segrega?on
MW Finnis 1996 J. Phys: Condens. Ma4er. 8 5811
Interface thermodynamics
• Interface energy related to weKng angle.
σ1v
σ2v
σ12
MW Finnis 1996 J. Phys: Condens. Ma4er. 8 5811
LaKce matching
• Depends on laKce parameters of the two phases
• Determines interface strain; large contribuEon to interface energy
a
b
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
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
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
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
Ohmic Contacts in PV
• Minimising losses in PV
• V ∝ I
• Ideal Ohmic contacts will not produce potenEal barriers
• Ideal contact all Fermi levels align
Metal Semiconductor Contacts
Band Bending
The SchoMky limit. SchoMky barrier – limits charge transport across the interface. Contact resistance depends exponenEally on the SchoMky barrier.
Achieving Ohmic Contacts
Ohmic n-‐type contact Ohmic p-‐type contact
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
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
Local dipoles
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
Work funcEons
“The minimum energy required to remove an electron from deep within the bulk, to a point a macroscopic distance outside the surface. ”
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
Measuring work funcEons (II)
Kelvin Probe
E
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
ContribuEons to work funcEons (Ia)
• Bulk binding energy
Bulk Polymorph WorkfuncEons
The relaEonship between crystal environment and ionisaEon potenEal. Engineer levels for improved water spliKng.
ContribuEons to work funcEons (Ib) Atom Hybrid Bond
Eg
Solid
ContribuEons to work funcEons (II)
The surface double-‐layer D
ensi
ty
Pot
entia
l
Mott-Littleton (1938) Harwell Labs, UKA. B. Lidiard, JCSFT 85, 341 (1989)
Daresbury Labs, UKA. 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
Classical region
Quantum region
Continuum region
Vacuum region
Slab region
Cappinglayer
Quantum Region
ActivePotentials
Region
FrozenPotentials
Region Vacuum Region
Slab Region
Vale
nce
Band
Maxim
um
Band Bending
CappingLayer
Vacuum Level
IP IP
IP
surf
slab
Ele
ctro
stati
cPo
tenti
al
Phys. Rev. B 89, 115320 (2014)
“Absolute” electron energies
Classical region
Quantum region
Continuum region
Vacuum region
Slab region
Cappinglayer
Quantum Region
ActivePotentials
Region
FrozenPotentials
Region Vacuum Region
Slab Region
Vale
nce
Band
Maxim
um
Band Bending
CappingLayer
Vacuum Level
IP IP
IP
surf
slab
Ele
ctro
stati
cPo
tenti
al
Phys. Rev. B 89, 115320 (2014)
Engineering electron energies
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!
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
PracEcal Session
• Building a good surface/interface
• CalculaEng a surface energy
• CalculaEng a workfuncEon from DFT
Cut the surface : METADISE
• Input unit cell and miller index
• SystemaEcally generates all cuts
• Checks for dipolar surfaces
CalculaEng a surface energy
Calculate the energy of the pure system.
Calculate the energy of a 2D slab.
SMACT-‐Interface
• Evaluate laKces with mismatch below a certain threshold.
• CuI//CdO • 110//110 • 4x4//5x5
CalculaEng Interface Energy
Calculate the separate bulk energies.
Calculate the energy of a mixed system.
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!!
Interface energy caveat
• SomeEmes interface energies calculated as above converge very slowly.
• Calculate energies for several layer thicknesses.
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)
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.
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
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
Elec
trost
atic
Pot
entia
lPro-‐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
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.