Microscopy and Spectroscopy:DFT-based Analysis of Surface Science Techniques

Karsten Reuter

Fritz-Haber-Institut der Max-Planck-Gesellschaft

Berlin (Germany)

Surface physics

Heterogeneous CatalysisMicroelectronics / Nanotechnology

…to applied

Carbon nanotubes

Scanning probes and surface states

from fundamental…

- Variety of quite well established experimental techniques:scanning probe STM/S, AFM, …diffraction LEED, RHEED, SXRD, …ion scattering LEIS, SIMS, …desorption TPD, …vibrational HREELS, IRAS, …electron spectroscopies XPS, UPS, AES, …

(100)

(111) (110)

Surface Science ansatz and its experimental techniques

- Obtain atomic-scale understanding by studyingwell-defined single-crystal surfaces in UHV

- Common target quantities forsurface characterization:

geometric & vibrational structurechemical compositionelectronic structure

I. Scanning Tunneling Microscopy

General concept of scanning probe microscopies

Courtesy of Ch. Wöll

Scanning tunneling microscopy

�T �S

EF EF

Evac

Tip Sample

EF

EF

Vext

Negative tip bias:Probe empty

substrate states

Positive tip bias:Probe filled

substrate states

EF

EF

Vext

+

(1986 Nobel Prize Binning/Rohrer)

Tunneling is a convolution of tipand sample states, dominated by

electrons at EF, which see the lowest barrier

Scanning tunneling microscopy(1986 Nobel Prize Binning/Rohrer)

Tunneling highly sensitive to barrier width:- high vertical resolution

- high lateral resolution (pinnacle atom)

Characteristic experimental setups:W/Pt/Ir tips, 0-3 V bias, 1 pA – 10 nA� with „typical“ gap resistance of 107 – 1010 �

this leads to „typical“ tip heights of 3-6 Å

Vt

Constant height (CH) Constant current (CC) Spectroscopy (STS)

STM theory I

J. Bardeen, Phys. Rev. Lett. 6, 57 (1961)

Bardeen approach (Fermi‘s golden rule):

����

�� jiijMwij ��� 2 2

�

Probability to tunnel fromoccupied state i (with energy �i)into unoccupied state j (with energy �j)

� �

����

��

empty

occ

2empty

occ 4 2 t

j

iji

j

iij ij

ewe MI ��� �

)()( )2('

)2( 4

Fsample'F

tip2

'2

2

2

2

0

0 eVEEdkdkde

kkkk

eVKT M �� ����

����

� �

Tunneling current is given by a combination of the local densities ofstates of the sample and the tip, weighted by the tunneling matrix element M

STM theory II

J. Tersoff and D.R. Hamann, Phys. Rev. Lett. 50, 1998 (1985);Phys. Rev. B 31, 805 (1985)

Tersoff-Hamann approximation:

Low bias limit, spherical tip model(M, �tip ~ constant)

),( ~ F

0sample

oeV

rEdtI ��� ��sample

ro

Tunneling current is simply proportional to the local density ofstates of the sample at the position of the center of the tip

STM theory III

Beyond Tersoff-Hamann:

Never forget: STM image is a convolution of tip and surface electronic structure;NOT a topographic image!

- Realistic tip structure

Modified Bardeen approach

� ���

�� )()( )()( 22

'*

''* rrrrdSmkk kkkkM �����

- Tip-surface coupling beyond perturbation theory

Scattering formalism (Landauer-Büttiker)Keldysh Green‘s functions

)(G)(G ~ ˆ �� �� �� ijjiijjI

W. Hofer et al., Rev. Mod. Phys. 75, 1287 (2003)

- Mesoscopic surface structure (domains, terraces, steps)- Atomic-resolution images (reconstructions,

adsorbate geometries)- Alloy surface composition (chemical contrast)- Magnetic domains (magnetic tip)- Electronic structure (STS)- Manipulation (tip-induced diffusion, chemistry)

Applications…

Pt(111), (1�m x 1�m)

Fe on Cu(111), “quantum corral”

20 Å

Si(111)-(7x7) DAS-modelG. Binning et al., Phys. Rev. Lett. 50, 120 (1983)

M.F. Crommie, C.P. Lutz, and D.M. Eigler, Science 262, 218 (1993)

Blobs are just blobs…

Ag6-triangularreconstruction

J. Schnadt et al., Phys. Rev. Lett. 96, 146101 (2006)

p(4x4)O / Ag(111)

C.I. Carlisle et al., Phys. Rev. Lett. 84, 3899 (2000)

Ag2O(111)-like overlayers

A. Michaelides, K. Reuter, and M. Scheffler,

JVST A 23, 1487 (2005)

II. X-ray Photoelectron Spectroscopy(XPS or ESCA)

Experimental setup

- Excitation with photons of energy h�(best: monochromatized X-ray beam, synchrotron)

- Measure kinetic energy Ekin of emitted photoelectrons

Ekin = hv – EB - �

Primary structure of XPS spectra

Spectra characterized by- inelastic background (staircase structure)- Auger peaks (do not shift with h�!)- XPS peaks and satellites

(secondary structure within 30-60 eVfrom main line)

� Compositional analysis (ESCA,Nobel Prize, Siegbahn 1981)

XPS may be envisaged as a three-step-process:

i) absorption and ionization(initial-state effects)

ii) response of atom and creation of photoelectron (final-state effects)

iii) transport of electron to surface and escape (extrinsic losses)

Surface core level shifts (SCLS)

- XPS as probe of the local chemical/electronicenvironment

- Focus on better defined relative shifts withrespect to main (bulk) line

- For extraction of peak positions need:(i) proper background subtraction(ii) theory of lineshapes

Ideal �-function broadened by:- finite core-hole lifetime (Lorentzian)- excitations (phonons, holes, plasmons)

- In practice: do a multi-parameter fit for- chosen number of peak components- for each adjust

peak intensitypeak position (core-level position)line width (� core-hole lifetime)

� pos. shifts 0 neg. shifts �

Screening

+

-

+

-

--- --

time

- Partial screening / full many-body problem: XPS satellites…- Perfect screening limit: �SCLS = Isurf - Ibulk

SCLS theory I

�SCLS = [ Esurf(nc – 1) – Esurf(nc) ] – [ Ebulk(nc – 1) – Ebulk(nc) ]

� �SCLS � - [ �csurf(nc) – �c

bulk(nc) ]initial

Initial-state approximation:

D. Spanjaard et al., Surf. Sci. Rep. 5, 1 (1985)

� �

� � � � �

�

�

�

�

�

2c

c

cccc

2c2

c

c2

cc

cccc

)(2

1

)(2

1)()()(

nnnnn

nnnEn

nnEnEnnE

����

���Taylor expansion:

SCLS theory II

�SCLS = [ Esurf(nc – 1) – Esurf(nc) ] – [ Ebulk(nc – 1) – Ebulk(nc) ]

B. Johansson and N. Martensson, Phys. Rev. B 21, 4427 (1980);J.F. Janak, Phys. Rev. B 18, 7165 (1978).

� �21)()()1( cc

1c

ccc �

�

ndnnnEnEnE

n

n�

� �SCLS � - [ �csurf(nc - ½) – �c

bulk(nc - ½) ]

Final-state calculation:

Impurity calculations: - Equivalent-core (Z+1) approximation

- �SCF approachSlater-Janak transition state approach

S1S2 b

Ru(0001)

sp-band

d-band

M. Methfessel, D. Henning, and M. Scheffler,Surf. Sci. 287/288, 785 (1993)

Application: SCLS of close-packed TM surfaces

Application: Quantitative calculation of adsorbate-induced SCLSs

p(2x1)p(2x2)

(2x2)-3O (1x1)-O

O @ Ru(0001)

S. Lizzit et al., Phys. Rev. B 63, 205419 (2001)

Application: Complex structure determination

(�5 x �5)R27° surface oxide on Pd(100)

M. Todorova et al., Surf. Sci. 541, 101 (2003)

Tutorial: The Si(001) dimer reconstruction

bulk truncated geometry

alternating dimers?asymmetric dimers?symmetric dimers?

DFT-based analysis of Surface Science experiments

- Very powerful approach. New standards in particular through multimethod approaches

- Scrutinize experimental „numbers“. Read experimental sections!

- Many experimental quantities can be computed with DFT, BUT:

Caution with xc accuracy! Exploit differences etc.

- Never forget: Our analysis helps understanding the experiment, but equallytheir data provides crucial feedback on our accuracy