Ab-initio study of work functions of element metal surface

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Ab-initio study of work functions of element
metal surface
Xiang Ma Materals Process Design and Control
laboratory
MAE 715 final project, May 7th, 2007 Instructor
Professor Zabaras
MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Outline

• Definition of Work function
• Slab model and super cell
• Computation Methods (Density functional theory)
• Change of work function due to the orientation
  of clean surface
• Change of work function due to absorption of H
  atom
• Conclusion

MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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From Solid to Surface
A image of surface for fcc(111)

• In this course, most of the problems we deal
  with are bulk properties.
• In nature, crystals are not infinite but finite
  macroscopic three-dimensional objects terminated
  by surfaces.
• Many phenomena and processes occur at the
  interface between a condensed phase and the
  environment.
• Modeling surfaces is then of great theoretical
  and practical interest.

MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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From Solid to Surface
Atomic resolution on Pt(100)

• The key-ingredient to surface science
  experiments is ultra-high vacuum (UHV).
• To main a low pressure to assure that a surface
  stays clean for a time long enough to do some
  experiments.
• With the development of density functional
  theory, we can also explore the surface
  properties through the ab-initio study.
• A very good surface science tutorial.

MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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From Solid to Surface

• A lot of phenomenon associated with surface can
  be studied by first-principal calculation

--- surface reconstruction and surface
relaxation --- surface energy --- adsorption on
surfaces --- interface --- work function

• With the adsorption of atoms or molecules, the
  surface electronic structure is modified and the
  work function can change by several eV.
• The measurement of the work function changes can
  give valuable insight in to the condition of a
  given surface.
• Nowadays, the work function can be calculated by
  ab-initio methods in the framework of density
  functional theory.

MAE 715 Atomistic Modeling of Materials N.
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Work function definition

• Work function is defined as the minimum
  energy necessary to extract an electron from the
  metal at 0K.
• For a crystal with electrons, if is
  the initial energy of the metal and
• that of the metal with one electron removed to a
  region of electrostatic potential
• , we define

Note The removed electron is assumed to be at
rest, and therefore possesses only potential
energy.
MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Work function definition

• At 0K, the chemical potential is by
  definition

• In the limit of large systems, all polarisation
  effect can be neglected after removing the
  electron. Then chemical potential is then shown
  to coincide with the Fermi energy

• The work function, finally, is the difference
  between the Fermi level and the vacuum level.

Schematic energy diagram of a metal
MAE 715 Atomistic Modeling of Materials N.
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Work function definition

• The calculation of work function is then divided
  into two parts.
• First to perform a self-consistent calculation
  to find the Fermi energy of the slab.
• Second, we need to find the electrostatic
  potential in the vacuum level.

Macroscopic average
MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Macroscopic average

• The electronic density is the basic
  variable calculated by DFT.
• Introduce the plane-averaged electronic density

where z axis is perpendicular to the slab surface

• The macroscopic-average electronic density
  is then defined from the integration over the
  interplanar distance d of the slab

• The potential is related to the charge density
  via the Poisson equation. So we can get a similar
  relation between plane-averaged potential
  and macroscopic average

MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Macroscopic average

• By plotting the macroscopic average over the z
  axis, the vacuum level is found.
• Because the curve of the average is nearly flat
  in the vacuum provided the vacuum is large
  enough.
• Subtracting this vacuum level from the Fermi
  level get the work function for the metal surface.

MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Slab model and supercell approach

• Slab model is the most popular way to model the
  surface.
• The slab model consists of a film formed by a
  few atomic layers parallel to the crystalline
  plane of interest.
• Using plane waves needs to force a 3-D
  periodicity. The thin slabs needs to repeat in
  one direction.
• To perform a supercell calculation, one defines
  a unit cell oriented with one axis perpendicular
  to the surface of interest, containing the
  inequivalent atoms of a crystalline thin film and
  some vacuum layers.
• Ideally, the thickness of the vacuum layer and
  of the slab must be large enough for two
  successive metal surfaces not to interact
  significantly.

MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Slab model and supercell approach

• It is not trivial to construct the slab model at
  first. You need to visualize them.
• A nice web tool Surface Explorer is used for
  this purpose.

fcc(110)
fcc(100)
fcc(111)
MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Slab model and supercell approach

• XCrysDen is an application for visualizing
  crystalline and molecular structures.
• All of the slab models studied were viewed
  using XCrysDen to ensure that their
• geometries were described correctly.
• Surface primitive cell is two-dimensional, which
  is different from conventional bulk primitive
  cell.

MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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DFT calculations

• As a preliminary step towards the study of
  surface, we have to find the equilibrium lattice
  constant
• It is well known that the equilibrium atomic
  positions in a crystal surface are generally
  different from those in the ideal bulk-terminated
  surface. We need to perform a relaxation
  calculation to find the equilibrium geometry of
  the surface.
• The relaxed coordinates are put into another
  input file to perform a self-consistent
  calculation to find the Fermi energy in the slab
• Using post-process code to extract the
  electrostatic potential from the output file.
• Calculate the macroscopic average potential to
  determine the vacuum level
• Put the two values into the definition of the
  work function to determine the final solution.

MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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DFT calculations

• Basis sets --- plane wave

• Cut-off energy of 16 Ry for the plane wave
  expansion
• ultrasoft pesudopotentials
• The Fermi level is positioned using the
  Methfessel-Paxton (MP) scheme, with the smearing
  parameter set to 0.01 Ry.
• 8x8x1 special Monkhorst-Pack special k-points

• slab models

• A surface unit cell with a slab of 8 atom layers
  and 8 equivalent vacuum layers was chosen to
  model the metal surface. H atom coverage is a
  full monolayer.

• Exchange-Correlation approximation

• LDA(Perdew-Zunger form)

• Software Quantum Espresso (opEn-Source Package
  for Research in Electronic Structure, Simulation,
  and Optimization), version 3.2

MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Summarize of the computation procedure
Fit E Vs V curve to find the theoretical lattice
constant (pw.x)
self-consistent calculation to find the Fermi
energy (pw.x)
Set up the appropriate thickness of slabs and
vacuums
Extract the electrostatic potential form the
self-consistent calculation (pp.x)
Calculate the macroscopic average

(average.x)
relax the geometry of the slab (pw.x)
MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Numerical examples

• Change of work function depends on the surface
  orientation
• Change of work function due to the H atom
  adsorption

MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Lattice constant
Theoretic 7.50 bohr Experimental 7.66 bohr
LDA underestimate
MAE 715 Atomistic Modeling of Materials N.
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Al and Al(100)

• Al
• fcc structure
• a 7.50 a.u

unit cell
Al(100) side view
Al(100) top view
MAE 715 Atomistic Modeling of Materials N.
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Al(100)
Work Function
Plane-averaged electronic charge density (dashed
line) Macroscopic average (solid line)
Plane-averaged electrostatic potential (dashed
line) Macroscopic average (solid line)
MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Al(110)
Al(110) top view
Al(110) side view
unit cell
MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Al(110)
Plane-averaged electronic charge density (dashed
line) Macroscopic average (solid line)
Plane-averaged electrostatic potential (dashed
line) Macroscopic average (solid line)
MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Al(111)
B
Al(111) top view
Al(111) side view
unit cell
MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Al(111)
Plane-averaged electronic charge density (dashed
line) Macroscopic average (solid line)
Plane-averaged electrostatic potential (dashed
line) Macroscopic average (solid line)
MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Result
Calculations of Work function of Al
The results are in a good agreement with the
experimental values.
MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Result
Calculations of Work function of Copper
The results shows a little deviation from the
experimental values. It may be due to the
experiment is performed at room temperature,
while the calculation is at 0K. Overall, it shows
good accuracy using this method since the error
is within the computational range.
MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Anisotropy of the work function

• From the Cu, we see that it shows the trend
  (110), (100),(111) of increasing work function.
• This is best explained by the Smoluchowski1
  smoothing.

• This smoothing leads to a dipole moment which
  opposes the dipole created by the spreading of
  electron and thus reducing the work function
• Surface orientations of high density experience
  small smoothing, inducing a small reverse dipole,
  and thus a high work function.

1 R Smoluchowski, Phy. Rev. 60, 1941
MAE 715 Atomistic Modeling of Materials N.
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Anomaly anisotropy of Al work function

• However, from the calculation, it is seen that
  the Al doesnt obey this increasing ordering.
• In the paper 1, the author investigated this
  phenomenon and concluded that the trend of the
  work function Al can be explained by a charge
  transfer the atomic-like p orbitals of the
  surface ions perpendicular to the surface plane
  to those parallel to the surface, when compared
  to the bulk charge density.
• Thus it results from a dominant p-atomic-like
  character of the density of states near the Fermi
  energy.
• Overall, our methods recovered both the normal
  and abnormal anisotropy of then work function of
  the fcc metals.

1 C.J.Fall, N.Binggeli and A. Baldereschi, Phy.
Rev. B, 58,1998
MAE 715 Atomistic Modeling of Materials N.
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Adsorption of H on the Al(111) surface

• There are four inequivalent adsorption sites on
  an fcc (111) surface.
• We consider a monolayer of H atom adsorpted on
  one Al (111) surface.

MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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H on the Al(111) surface (top view)
bridge
ontop
fcc hollow
hcp hollow
MAE 715 Atomistic Modeling of Materials N.
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H on the Al(111) surface (side view)
hcp hollow
ontop
bridge
fcc hollow
Clean surface 4.235 eV
MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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H on the Al(111) surface
Calculations of Work function of H/Al(111) ontop
site
MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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H on the Al(111) surface

• Adsorption at the ontop and bridge site increase
  the work function while at the hollow sites
  decrease the work function.
• This is due to the dipole induced by
  H-adsorption when the H atom at the ontop and
  bridge site, it pulls away the electron from the
  surface. However, when the induced dipole opposes
  the spill-out of the electrons, it reduces the
  work function.
• The work function increases with the increase of
  the H coverage. This is because at the low
  coverage, the dipole-dipole interaction will keep
  the atoms apart , while at high coverage, the
  same interaction will cause a depolarization of
  the dipoles and increase the work function.

MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Conclusion

• The method can be used to calculate the accurate
  work function.
• The change of work function depends on the
  surface orientation, adsorption sites and the
  adsorption coverage.
• work function is the fundamental properties of
  the electronic structure of the surface. Its
  measurement can give valuable insight into the
  condition of a given surface.
• This method can also be extended to
  semiconductor.

MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)
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Acknowledgement

• Prof. Zabaras
• MPDCC cluster for the computation
• Software Quantum Espressor

Thank you!
MAE 715 Atomistic Modeling of Materials N.
Zabaras (5/7/2007)