surface structure, chemisorption and...

(ii) physical properties of surfaces: surface energy, surface stress and their relevance for surface

(i) interplay between the geometric and electronic structure of solid surfaces,

Topics:

morphology(iii) adsorption and desorption energy barriers, chemical

Eckhard Pehlke, Institut für Theoretische Physik und Astrophysik,

Christian-Albrechts-Universität zu Kiel, 24098 Kiel, Germany.

Surface Structure, Chemisorption and Reactions

reactivity of surfaces, heterogeneous catalysis(iv) chemisorption dynamics and energy dissipation: electronically non-adiabatic processes

substrates for homo- or hetero-epitaxial growth of semiconductorthin films used in device technology

and steer the desired chemical reactionssurfaces can act as heterogeneous catalysts, used to induce

Solid surfaces are intriguing objects for basic research,

and they are also of high technological utility:

Technological Importance of Surfaces

The Geometric and

Sect. I:

the Electronic Structure

of Crystal Surfaces

number of space groups:number of point groups:number of Bravais lattices:

2D1710 5

3D230 32 14

o120

2D-

γa, b, 2

1

a, b

γ = 90o

b a

b a

m

2mm7

2

gonal)(tetra-

t

o

(ortho-

rhom-

(mono-m

a = bγ = 90o

4

4mm3

hexagonalh

(hexa-gonal)

a = bγ = 120o 5

3

6mm

3m6

γ

aa

aa

a

b

mp

op

oc

tp

hp

crystal systemsymbol lattice

parameters2D Bravaislattice

spacegroup

pointgroups

obliqueclin)

rectangular

square

bic)

Surface Crystallography

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(010)

fcc

y

z

x

x

z

c

a

a=c/ 2√square lattice (tp)

x

y

z z

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[110]_

a

c

rectangular lattice (op)

fcc (110)

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a

y

z

x

[110]_

[011]_

hexagonal lattice (hp)

(111) fcc

Bulk Terminated fcc Crystal Surfaces

a

2a

(2x1)

reducedinter-layerseparation

normalrelaxation

reconstruction

Surface Atomic Geometry

H/Si(111)

Examples:

Si(111) (7x7)

K. Brommer et al., Phys. Rev. Lett. 68, 1355 (1992)

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Shockley States in the Projected Band Structure

Electronic Structure of Surfaces:

cusp no surfacestate

VG 0<

VG >0��

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bridge the band gap

real energy,complex Bloch vector

e i (k + i κ )z

κ

π

ε

2 |VG|

gap

/ak

wave function matching at the surface

surface state

ψ

ψ

virtual induced gap states ~ eκ z

v

v

The Al(100) Surface State

BZ of fcc lattice

perpendicular to the surfaceAl(100) surface state in the projected band structure

19, 642 (1979).

ARUPS spectra

D. Spanjaard et al., Phys. Rev. B G.V. Hansson, S.A. Flodström, Phys. Rev. B 18, 1562 (1978).

Figures taken from: M.C. Desjonqueres, D. Spanjaard, "Concepts in Surface Physics", Springer (Berlin, 1993).

bulk band structure for wave-vectorexit angle in (011)

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molecular orbitalpicture

Electronic Structure of Semiconductor Surfaces:Dangling Bonds on Si (001)

εo

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atom after reconstructionand relaxation

sp3 +sp2

3

1

ε

ε

p

s

εo

hybrid-orbital

sp3

σ

o

εo−

*σ

empty

2 x 4 el

fullyoccupiedvalenceband

(VB)

emptyconduction

band

(CB)

occupied

db state

(CB)

(VB)

EF

band gap

db (up)(occupied)

surface dimer

Si

Si

||ε β

β||

+

emptydb (down)

+

-

pfictitious surfacewith almost

non-interacting dbs

-20 -10 0 10 20Verkippungswinkel des Si-Dimers [o]

-1.0

-0.5

0.0

0.5

Ban

dsch

wer

punk

t [eV

]

-20 -10 0 10 20Verkippungswinkel des Si-Dimers [o]

-0.2

-0.1

0.0

Ene

rgie

pro

Dim

er [e

V]

Si(001)(1x2)decoup. dimer

Si(001)

dimer buckling angle [°]

dimer buckling angle [°]

ener

gy p

er d

imer

[eV

]ba

nd c

ente

r [e

V]

p(2x2)

SiH

SiH

π∗

π

Interplay of the Atomic and Electronic Structure of Si(001)

buckled dimers surface state (HOMO)

lowest unoccupied surface state (LUMO)

symmetric dimers

highest occupied

Mechanisms for Lowering the Surface Energy

reduce density of dangling bonds

formation of bonds between dangling bonds

Jahn-Teller-like distortions: relaxation and re-hybridization

minimization of elastic strain

-> by dimerization (Si(100), ~1 eV/db)-> ad-atoms (Si(111), rebonded steps on Si(100) vicinals)

-> Pandey’s model of Si(111) (2x1)

-> dimer buckling on Si(100)

-> subsurface interstitial on Si(113)

and other mechanisms (e.g. for compound semiconductors)

π

unusual atomic configurations

Sect. II:

Material Properties of Crystal Surfaces:

Surface Energy

Surface Stress Tensor

(2) Calculation: total-energy DFTcalculations for slab geometries

(3) equilibrium crystal shape (ECS)

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n11

nn1

A1

n

A2

2

n A33

(a) (b)

2nA2A

A

side view top view

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γ (n)

(ECS)

polar plot of thesurface energy

equilibrium crystal shape

r(h)= (n)/n hγ .

nh

a surface per surface area(1) Definition: = excess free energy of γ

(ii) slab with inequivalent surfaces: derive individual surface energies from an energy density

Surface Energy and the Thermo-dynamic Stability of Facets

thermodynamic stable surface orientations

(i) slab with equivalent surfaces:

(N. Chetty, R. Martin, Phys. Rev. B 45, 6074 (1992).)

Wulff-construction

(4) Application: facet formation

Relation to surface energy: (different from liquids!)

energy with an applied strain :

Force density on a surface:

Consequence: forces acting at stress domain boundaries -> elastic relaxation -> structure formation on mesoscopic length scales.

Application:

∆ EVol

~ ε²

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σDefinition: surface stress = linear coefficient describing the change of surfaceε

( σxx xx> 0 tensile: < 0 => ∆ E

σxx

< 0 , preference for contraction,

< 0 compressive: E < 0 , preference for expansion)> 0 => xx ∆ε

ε

Surface Stress Tensor

surf

surf

J. van Heys, E.P., unpublished.

+

-

+

-

0 0,2 0,4 0,6 0,8 1Θ [ML]

0

10

20

30

σ ⊥[m

eV/Å

2 ]

hit and stickequilibrated configuration

T = 450 K

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Surface Stress Variation Induced by Surface Reactions

partially H-covered Si(001)

HOMO

LUMO

HOMO

LUMO

Sect. III:

on/from a Si(100) Surfaceof Hydrogen Molecules

and Recombinative DesorptionDissociative Adsorption

Model System:

Chemisorption on Semiconductor Surfaces

Langmuir-

mechanismHinshelwood

Surface Reactivity and Heterogeneous Catalysis

The rate of chemical reactions depends on the reaction energy-barriersalong the reaction path:

Dissociative adsorption and recombinative desorption of moleculeson a solid surface are an essential step of heterogeneous catalysis:

HSi

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pote

ntia

l ene

rgy

energy

barrier

adsorptionbarrier

desorption

chemisorption

reaction pathcoordinate

Dissociative Adsorption of a Molecule on a Solid Surface

hydrogen molecule / H-precovered Si(100)(2x2)

potential energyalong the reaction path

electronic mechanism of bond formation and breaking

locate transition state(automated search for special saddle points in the potential energy surface)

chemisorption geometries and energies(equilibrium geometries, reaction energy)

strain energy of substrate at thetransition geometry, etc.("computer experiments")

reaction path(steepest descent from transition state)

PES, vibrational frequencies

adsorption and desorptionenergy barrier

d [Å]

[Å]

dz

z

D

A

TS

PES (schematic)

analyse electronic structure(learn about bond breakingand forming mechanism)

(high-dimensional PES!)

molecular dynamics,quantum-mech. sticking calc.

A. Groß, Surf. Sci. Rep. 32, 291 (1998).

DFT for Chemisorption: Reaction Path, PES, ...

P. Kratzer, B. Hammer, J.K. Norskov,Phys. Rev. B 51, 13432 (1995).

Si9 Si15 Si21 slabClustergröße

1.80

2.30

2.80

3.30E

nerg

ie [

eV]

Edes, PW91 (Penev et al.)Edes, PW91 (Steckel et al.)Edes, B3LYP ( " )Erxn, PW91 ( " )Erxn, B3LYP ( " )

J.A. Steckel, T. Phung, K.D. Jordan, P. Nachtigall,J. Phys. Chem. B 105, 4031 (2001).

E. Penev, P. Kratzer, M. Scheffler, J. Chem. Phys. 110, 3986 (1999).

Calculation of Chemical Reactions: Things to Keep in Mind

H /Si(001)2

(1) Cluster size convergence: at least 3 surface Si-dimers should be used.

intra-dimer path

desorption barrier

reactionenergy

cluster size

ener

gy [

eV]

Calculation of Chemical Reactions:Things to Keep in Mind

H2*

H2

2.20(5) eV

2.28(9) eV

0.75 eV

0.63 eV

> 0.6 eV1.95(25) eV

=

PW91 slab 1.95 eV

PW91 cluster

0.2 eV

0.26 eV1.99 eV

0.6 eV2.5 eVQMC cluster

chemisorptionenergy energy barrier

adsorption

PW91-geometry, no ZPE:

(4) Be aware of different reaction paths!

chemisorptionenergy energy barrier

adsorption

intra-dimer

inter-dimer

(2) Quantum Monte-Carlo calculations for H /Si(100) clusters:PW91 not sufficiently accurate.

(3) Correct reaction energies and barriers for zero-point vibrations.

2

C. Filippi, S.B. Healy, P. Kratzer, E.P., M. Scheffler, Phys. Rev. Lett. 89, 166102 (2002).

(Höfer et al.)expt.

(experimental desorption energy barrier: 2.5 eV)

inter-dimer reaction path (H2),QMC-corrected, incl. approx. ZPE:

e.g., decrease reaction energy by 0.2 eV (Steckel et al.)

Different reaction paths for dissociative adsorption of hydrogen molecules on Si surfaces.Reaction barriers are influenced by electronic and geometric effects. Dramatic increase of reactivity at steps and on partially H-precovered Si(001) surfaces.

(but still useful, e.g to compare between various reaction paths!)

Sect. IV:

Molecular Dynamics of

Electronically Non-Adiabatic Processes

Time-Dependent DFT

H. Nienhaus et al., PRL 82, 446 (1999). H. Nienhaus, Surf. Sci. Rep. 45, 1 (2002).

Electron-Hole Pair Creation by Chemisorption:Experimental Evidence

chemo-luminescenceexo-electron emission

SiO

Au

Ichem

2

metal

Si-wafer

chemicurrent

Ichemmetal

H

e-

h FE

Si

H

metal

tota

l ene

rgy

unpolarized

polarized

surfaceOppenheimerBorn-

distance

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vacuum

effe

ctiv

e po

tent

ial v

z

BO

tota

l en

erg

y

reaction coordinate

Mechanism of Electron-Hole Pair Excitation

adsorbatestate ofexcited

eh-pairsexited

in thesolid

See also: J.R.Trail et al. PRL 88, 166802 (2002).

and ionsof combined motions of electronsdirect molecular dynamics simulation

loss of spin polarisation: slow tunneling process

electronic friction

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adiabatic approx. for exchange and correlation (on top of LDA, GGA):

, thus

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time-dependent electron density from self-consistent solutionfor a system of non-interacting fermions(E. Runge, E.K.U. Gross, W. Kohn):

motion of ions treated classically (Newton’s equation of motion)no entangled states

Simulation of the Combined Motion of Electrons and Ions

0 10 20 30 40time t [fs]

−0.009

0.001

0.011

0.021

velo

city

v, f

orce

f [a

tom

ic u

nits

]

H/Al(111) on top 2sqrt(3) x 2sqrt(3) SUC, Ecut = 10 Ry, 1 k−point only

v: velocity of H−atomF*0.1: (non−adiabatic) force(F−FBO)*10(E−EBO)*10: dissipation

−6 −4 −2 0 2electron energy ε wrt. EF [eV]

−10

−5

0

5

ln (

DO

S)

electronic energy spectrum after one H−oscillation(2√3 × 2√3) H/Al(111) on−top, Ecut=10Ry, 1k−point

after one oscillation (mol.−dyn.)after relaxation to BO−surface

Gaussian broadening 0.05 eV

H/Al(111) On-Top Adsorption:Electronic Friction

Dissipate of the order of 36 meV during the first H-oscillationinto electron-hole pair excitations.

improved.Simulations computationally rather demanding. Convergence has to be

surface structure, chemisorption and...

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