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