+ All Categories
Home > Documents > Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii)...

Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii)...

Date post: 28-Jul-2019
Category:
Upload: phungliem
View: 223 times
Download: 0 times
Share this document with a friend
24
Eckhard Pehlke, Institut für Laser- und Plasmaphysik, Universität Essen, 45117 Essen, Germany. Surface Structure and Chemisorption (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 reactivity of surfaces -> heterogeneous catalysis (iii) adsorption and desorption energy barriers, chemical
Transcript
Page 1: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

Eckhard Pehlke, Institut für Laser- und Plasmaphysik, Universität Essen,45117 Essen, Germany.

Surface Structure and Chemisorption

(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

reactivity of surfaces -> heterogeneous catalysis(iii) adsorption and desorption energy barriers, chemical

Page 2: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

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

Page 3: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

The Geometric and

Sect. I:

the Electronic Structure

of Crystal Surfaces

Page 4: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

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

Page 5: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

������������������������������������������������������

������������������������������������������������������

������������������������������������

������������������������������������

(010)

fcc

y

z

x

x

z

c

a

a=c/ 2√square lattice (tp)

x

y

z z

���������������������������������

���������������������������������

����������������������������������������

����������������������������������������

[110]_

a

c

rectangular lattice (op)

fcc (110)

��������������������������������������������������������

��������������������������������������������������������

a

y

z

x

[110]_

[011]_

hexagonal lattice (hp)

(111) fcc

Bulk Terminated fcc Crystal Surfaces

Page 6: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

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)

Page 7: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

����������������������������������������������������������������������������������������������������������������������������

����������������������������������������������������������������������������������������������������������������������������

������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

������������������������

Shockley States in the Projected Band Structure

Electronic Structure of Surfaces:

cusp no surfacestate

VG 0<

VG >0���������������

���������������

��������

��������

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

z

z

surface state

ψ

ψ

virtual induced gap states ~ eκ z

v

v

Page 8: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

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)

_

Page 9: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

���������

���������

���������

���������

��������

��������

���������������������������������������������������������������

���������������������������������������������������������������������������������������

������������������������

molecular orbitalpicture

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

εo

���������

���������

������

������

��������

��������

���������������������������������������������������������������

���������������������������������������������������������������

��������������������������

��������������������������������������������������������

��������������������������������������������������������

��������������������������������������������������������

��������������������������������������������������������

������������

������������

������������

���������������������������� ��������

����������������

������������������������

atom after reconstructionand relaxation

sp3 +sp2

3

1

ε

ε

p

s

εo

hybrid-orbital

sp3

σ

o

εo−

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

Page 10: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

-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)

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

highest occupiedsurface state (HOMO)

lowest unoccupied surface state (LUMO)

symmetric dimers

Page 11: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

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

Page 12: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

Sect. II:

Material Properties of Crystal Surfaces:

Surface Energy

Surface Stress Tensor

Page 13: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

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

(3) equilibrium crystal shape (ECS)

� �

���

������ �����

���� ������� �

�� ���n1

1

nn1

A1

n

A2

2

n A33

(a) (b)

2nA2A

A

side view top view

���� � ����

����

� � �

���

���������

��

������

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

Page 14: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

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

��� � ��� �

������

� ��� � ��� ����

������ �

��

��������

������ ���

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

Page 15: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

������������������������������������������������������������

������������������������������������������������������������

SB

f

SAl l1 2

SA ������ �

��

��������

������ ���

2469 (1988). O.L. Alerhand, D. Vanderbilt, R.D. Meade, J.D. Joannopoulos, Phys. Rev. Lett. 61, 1973 (1988).

Measurement of surface stress anisotropy: strain surface (by bendingthe wafer) and determine the relative area of (1x2) and (2x1) dimerizedterraces.

SA SASB

F.K. Men, W.E. Packard, M.B. Webb, Phys. Rev. Lett. 61,

Surface Stress Anisotropy: Si(100)

single atomic-height stepstunneling microscope image,

miscut angle Θ = 0.3°A

(S step separation ~ 500 Å)From Swartzentruber et al., Phys. Rev. Lett. 65, 1913 (1990).

Page 16: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

������������� �

�� � �

�� �

�� � �

�� �

�� � �

�� �

�� � �

��

� � ��� ����� �� ���� �� ������� � � �

������� � ��� ! ������� ! ������� "! ������� � �������

������� #����� ! ������� ������� "! ������� � �������

��#�� ���$$ �� ���� � %! & '! ������� � �

������ �

��

��������

������ ���

Si(001) p(2x2)

Influence of the Reconstruction on Surface Stress Anisotropy

Stress anisotropy calculated from total energy differences:

J. Dabrowski, E. P., M. Scheffler, Phys. Rev. B 49, 4790 (1994).T.W. Poon, S. Yip, P.S. Ho, F.F. Abraham, Phys. Rev. B 45, 3521 (1992).M.B. Webb, F.K. Men, B.S. Swartzentruber, R. Kariotis, M.G. Lagally, Surf. Sci. 242, 23 (1991).

Page 17: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

slab geometry with up to 12 Si layers, H-termination on both sidesPW91 GGA for the XC functionalHamann pseudopotentials for Si, 1/r Coulomb potential for Hkinetic-energy cut-off for plane-wave basis-set: 50 Ry9 special k-points in the irreducible part of the Brillouin zone

DFT total-energy calculations with fhi96md

5.24 5.34 5.44 5.54 5.64c|| [Angstroem]

−31.436

−31.416

−31.396

2E(N

)−E

(2N

) [

eV] σ = − 0.01 eV/Angstroem

2

5.43 5.44 5.45 5.46 5.47 5.48c|| [Angstroem]

−0.05

−0.03

−0.01

0.01

0.03

0.05

dE/d

A [

eV/A

ngst

roem

2 ]

−0.007 eV/Angstroem2

zus.

relaxiert

The "Reference Surface" Si(111) (1x1) - H

Method

withadditionalrelaxation

Calculation of Surface Stress from Total-Energy Differences:

Page 18: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

Sect. III:

on/from a Si(100) Surfaceof Hydrogen Molecules

and Recombinative DesorptionDissociative Adsorption

Model System:

Chemisorption on Semiconductor Surfaces

Page 19: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

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:

Page 20: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

HSi

�������������������������

�������������������������

��������������������

��������������������

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

Page 21: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

-0.4-0.2

00.2

0.40.6

0.81-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.5

0

0.5

z [Å]d [Å]

V

The (most intensely studied) intra-dimer reaction path:

small sticking coefficient -> large adsorptionenergy barrier

desorbing hydrogen molecules do not havelarge (> thermal) kinetic energies

Apparently contradictory experimentalobservations:

of freedom in the adsorption/desorption dynamics.It is essential to include the "mechanical" surface degree

separation of hydrogenz molecule from surface

d surface degree offreedom

K.W. Kolasinski et al., Phys. Rev. Lett. 72, 1356 (1994).

Microreversibility?

2

SiSi

What makes H /Si a fascinating system?

HH

W. Brenig, A. Groß, R. Russ (see e.g. Phys. Rev. B 54, 5978 (1996)).

(model-potential)

Page 22: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

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).

Page 23: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

2.0 1.5 1.0 0.5 0.0Abstand zur Monohydridkonfiguration [Å]

0

1

2

3E

nerg

ie r

elat

iv M

onoh

ydrid

konf

. [e

V]

Hydrogen Molecules on Partially H-Precovered Si(001)

Existence of small adsorption energy barriers for H3 and H2 sites (inter-dimer paths).Comparative study of adsorption sites with fewer pre-adsobed H atoms:

Reaction path without adsorption energy-barrier for H4 site.

2.41 eV

2.06 eV

2.49 eVen

ergy

rel

ativ

e m

ono-

hydr

ide

[eV

]

separation from mono-hydride conf. [A]

H

Si

HOMO

LUMO

+

+

[Å]dHH

xz

Si

H

MH

H20.53

0.03.850.53

3.5 eV

0.0 eV

z [Å]

Highly Reactive Sites for the Dissociative Adsorption of

Page 24: Surface Structure and Chemisorption - Theory Department · Surface Structure and Chemisorption (ii) ... A1 n A2 2 nA3 3 (a) (b) n2 A A2 A ... (model-potential) locate transition state

Si9 Si15 Si21 slabcluster size

1.80

2.30

2.80

3.30

ener

gy [e

V]

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

Things to Keep in Mind ...

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

(1) Cluster size convergence:

(2) Semi-local approximation to XC functional (PW91) is not sufficiently

for the inter-dimer TS (with PW91 geometries):

PW91: E(rxn) = 1.95 eV, E(TS) = 2.15 eV, E(ads) = 0.2 eV

QMC: E(rxn) ~ 2.4 eV, E(TS) ~ 3.0 eV, E(ads) ~ 0.6 eV

Current QMC calculations by S. Healy, C. Filippi

Si clusters with >= 3 surface dimers should beused.

accurate for H /Si reaction barriers.2

PW91 calculations are nevertheless usefull tocompare between various reaction paths!

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

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

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

J.A. Steckel, T. Phung, K.D. Jordan, P. Nachtigall, J. Phys. Chem. B 105, 4031 (2001).H /Si(001)intra-dimer path

2

reactionenergy

barrierdesorption


Recommended