Surfaces and Interfaces

transcript

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

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

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

Define laKce vectors (a b c)

Define the intersecEon (0 b 0)

IdenEfy the fracEonal coordinates of the intercept (∞/a b/b ∞/c)

IdenEfy the fracEonal coordinates of the intercept (0 1 0)

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

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

∑ = −σ m+1

2(−1)m − R2 − R1

R2 + R1

Content

SURFACES INTERFACES

Surface energy

Energy is proporEonal to the number of bonds broken.

Surface Electronic States Atom Hybrid Solid

Surface Electronic States Hybrid Surface

Content

SURFACES INTERFACES

Surface recombinaEon

•  Characterised by capture and release rates of carriers and energy of state

Surface passivaEon

•  Chemical passivaEon

Surface PassivaEon

•  Blocking layer

Surface PassivaEon

•  Fixed Charge

Content

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.

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

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

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

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

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

ContribuEons to work funcEons (II)

The surface double-‐layer D

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

Band Bending

CappingLayer

Vacuum Level

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

Band Bending

CappingLayer

Vacuum Level

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

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)

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.

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

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

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.