My earlier studies on Cu(775) - a tilt cut highly crystalline copper surface using ultrafast femtosecond laser based 2-photon photoemission and its related simulation via Fortran 77.

1. MAPPING ENERGY STATES ON
CU(775) USING ANGLE-RESOLVED
TWO-PHOTON PHOTOEMISSION
Advisor: Prof. R.M. Osgood, Prof. K. Bergman
Kevin Knox, Jerry Dadap
Speaker: Po-Chun Yeh

2. OUTLINE
Goal –Understanding the band structure of
Cu.
Understanding of Cu Band
structure - bulk state
Simulatio
n
AR2PP
E
Ultra-fast
Laser
with
OPA-SHG

3. A. ANGLE RESOLVED TWO PHOTON
PHOTOEMISSION - ENVIRONMENT

4. OUR SOURCE: TI:SAPHIRE LASER
Red and Infrared light in the range from 650 to 1100 nm.
Power: 0.5~1.5 Watt.

5. 490 – 660 nm
• 2 fs pulse length
• 250 kHz repetition rate
• Bandwidth ~ 5 nm, 100 meV
• Pulse energy ~ 10 nJ
• Peak power ~ 100 kW
Ti:S Oscillator
Regen Amplifier
With CPA
Optical Parametric
Amplifier
800 nm
245 – 330 nm
(3.75 – 5 eV)
Second Harmonic
Generation
q
e–
UHV
Energy
Analyzer
Pulse Counter
MCP
Sample
q
e–
UHV
Energy
Analyzer
Pulse Counter
MCP
Sample
TECHNIQUE: 2PPE USING OPA-SHG
 Excellent tunability 3.75- 5.0 eV
 Capable of selecting transitions 
Resonances
 High pulse power, large e/pulse especially
for h ~   space charge effects
 Stability
 Reduced energy resolution for fs pulses
It ‘aint easy!

6. D. Strickland and G. Mourou, Opt. Commun. 1985
Stretcher Amplifier Compressor
Why CPA is important?
Direct amplification of ultrafast pulses
can damage Ti:S crystal and cause
self-phase modulation and gain
saturation
Amplified peak power ~ 50 MW
Peak focused intensity ~ 10 TW/cm2
CHIRPED PULSE AMPLIFICATION (CPA)

7. A. Ti:S Oscillator
Nd:YVO4 pump
C. Ti:S Regen Amp
B. Expander/Compressor
D. Optical
Parametric
Amplifier
Nd:YVO4 pump
E C Out
LAYOUT

8. CW 532 nm pump
5W from Nd:YVO4
100 fs, 100 MHz
10 nJ, 800 nm
OUTPUT TO
EXPANDER
A. SCHEMATIC OF TI:S OSCILLATOR
Ti: Sapphire
Crystal
Pumping cause population inversion -> Laser

9. FROM
OSCILLATOR
TO
REGEN
FROM
REGEN
TO
OPA
GRATING
GRATING
B. EXPANDER/COMPRESSOR LAYOUT
EXPANDER
COMPRESSOR

10. GATE
INPUT FROM EXPANDER
OUTPUT TO COMPRESSOR
10W PUMP
Nd:YVO4
C. SCHEMATIC OF TI:S REGEN AMPLIFIER
1 2 1 2
1: Inject Seed
Pulse
2: Eject
Amplified Pulse
Population
Inversion –
Gain > Loss
~25 rounds
in resonator
- AMPLIFY

11. 800 nm
800 nm
400 nm
White light
Signal 480-700 nm
Idler 930-2300 nm
D.OPA OPTICAL SCHEMATIC
Split
pulse
Halves
λ,
Double
s
Energy
Combine,
Amplify
Specific Freq.
Gives us a tunable, high
intensity/resolution, ultra-short UV
pulse as input photons.

12. B. AR2PPE
THEORY AND EXPERIMENT

13. EF
E
k||0
Evac
Observed Electron Distribution Curve
Unoccupied
State
Occupied
Surface State
Resonant
Excitation
(ii) (iii) (i)
•2PPE allows population and probing
of normally unoccupied states.
i. Excited state electron
scattered into image state.
ii. Resonantly excited from
the surface state to the
image state.
iii. Direct absorption of two
photons.
TWO-PHOTON PHOTOEMISSION

14. ANGLE-RESOLVED-2PPE SPECTROSCOPY
q
e–
UHVPulse Counter
Energy
Analyzer
MCP
Sample
Tunable femtosecond
UV source
3. Angle-Resolved
measurement &
Spherical-sector
energy analyzer
4. Electron counting
at high repetition rate
1. Sample prepared via
repeated sputtering &
annealing cycles.
2. Low Energy
Electron Diffraction
LEED Image

15. For stepped surfaces each state can have different reference planes.
[112]
[110]
[111]
CU(775)-STEPPED SURFACES
Cu
2cm
8.5 degree
(Side View)

16. COMPARISON:
2PPE FROM FLAT CU(111)
Resonant mapping of Cu(111)
surface state and n=1 state
Photoemission intensity vs. emission
angle and KE of emitted electrons.
Resonant
Peaks
Surface State
Emission
n=1 Image State
Emission
Surface state
n=1 image state
Cu (111)

17. Surface state
n=1 image state
2PPE FROM CU(775)
Resonant
Peaks
Resonant Mapping
Location of peaks – Measured KE,
2PPE Photon Energy yields map of
states

18. MEASUREMENT & RESULT
We can only measure Kinetic Energy and Number of output electrons!
Evac
EFermi
Evac
Energy(eV)
K

M
EL-GAP= 4.9 eV
Evac
EFermi
Evac
Energy(eV)
K

M
EL-GAP= 4.9 eV
Projection

19. C. BAND STRUCTURE SIMULATION

20. SIMULATION
Calculating:
 The impact of Cu(775) tilted surface.
 Possible energy states Cu(775) – Fortran 77
 Filtering the result using known Cu properties,
input conditions, and experiences.
Relation between K parallel
and Proper kinetic energy
is what we want to know
about!

21. STEP1 MODIFICATION OF TILTED SURFACE
K Parallel
K
Perpendicular
K
Tilted?
K’

22. CACULATION
 Define variable (R, n) for K parallel and K
perpendicular!
 Proof: Orthogonal Coordinates – Product
Rule
 Get tilted K(Kx, Ky, Kz)
Kx = Ky = (SQRT(3))/2 *1.74*R - 0.01*n*0.7/1.407
Kz = (SQRT(3))/2 *1.74*1.4*R + 0.01*n*1/1.407
R = Testing number from 0.100~0.900
n = +50 to -50
When R=0.5, |K| = 1.5 ± 0.5 / A (Amstrong), matching
the flat Cu(111) experimental range.

23. ENERGY STATES
 Band structure of Cu can be calculated using
tight-bonded potential model!
 Need values of K’ and characteristic parameters
of Cu, such as energy gaps, Fermi level,
effective mass, etc. (Papaconstantopoulos’s
book; papers)
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
YAxisTitle
XAxisTitle
0.0 0.1 0.2 0.3 0.4 0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
YAxisTitle
XAxisTitle
0.0 0.1 0.2 0.3 0.4 0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0YAxisTitle
XAxisTitle
0.5 0.4 0.3 0.2 0.1 0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
YAxisTitle
XAxisTitle
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
YAxisTitle
XAxisTitle
 X L  XKSD LWZ Q

24. CALCULATION OF ENERGY STATES
 Using the theory and parameters to build a
9x9 Matrix, solving the eigenvalues (≦9).
 Program on Fortran 77 (Was created by Dr.
Dimitrios and we modified it.)
Read in initial and final k values, Cu
parameters, and other settings.
Calculating the matrix on directions as
follows: Γ -> L, X -> W -> L -> K -> Γ -> K.
Call in IMSL numerical library to tri-
diagonalize and solve the matrix.
Output performance factor, eigenvectors
and eigenvalues.
Generate data for the 9 energy levels to
each set of k values. (~ 9000 data)

25. CALCULATE THE RIGHT RESULT
 If not interpreted and modified properly, the result
is useless.
Conditions:
 1. Transition happens between E7 & E6
 2. Cu work function: 4.9eV
 3. Proper energy shifting should make E7 > 0
and E6 < 0 while Zero Point Energy = Fermi
Energy
 4. Given Photon Energy hv
 5. 1st PPE: E7 – E6 = hv, error < 0.02 eV
 6. 2nd PPE: E7 + hv – Work Func. = Kinetic
Energy
In short, 2PPE happens between precise energy
states. Also, the energy of 1st PPE should lower
than work function; otherwise we will get the
wrong states.

26. PHOTON ENERGY DEPENDENCE
– THE BULK STATE
0
5
10
15
20
25
30
0.5
0.47
0.44
0.41
0.38
0.35
0.32
0.29
0.26
0.23
0.2
0.17
0.14
0.11
0.08
0.05
0.02
-0.01
-0.04
-0.07
-0.1
-0.13
-0.16
-0.19
-0.22
-0.25
-0.28
-0.31
-0.34
-0.37
-0.4
-0.43
-0.46
-0.49
ΔE(R=0.6)
ΔE(R=0.55)
ΔE(R=0.5)
ΔE(R=0.45)
ΔE(R=0.4)
ΔE(R=0.35)
ΔE(R=0.3)
ΔE(R=0.25)
ΔE(R=0.2)
ΔE(R=0.15)
0
2
4
6
8
10
12
0.5
0.47
0.44
0.41
0.38
0.35
0.32
0.29
0.26
0.23
0.2
0.17
0.14
0.11
0.08
0.05
0.02
-0.01
-0.04
-0.07
-0.1
-0.13
-0.16
-0.19
-0.22
-0.25
-0.28
-0.31
-0.34
-0.37
-0.4
-0.43
-0.46
-0.49
R=0.33
R=0.32
R=0.31
R=0.3
R=0.29
R=0.28
R=0.27
R=0.26
R=0.25
R=0.24

27. RESULT: E= 4.66EV
3.8
3.9
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
(0.3000) (0.2500) (0.2000) (0.1500) (0.1000) (0.0500) 0.0000
Ek
Ek

28. RESULT: E= 5.02EV
3.8
3.9
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
-0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0
Ek

29. DISCUSSION
2 Good 2 Bad
 Slope and shape is pretty near!
 Built up a standard procedure to do
calculation fast.
 Energy shift problem.
 n all negative/positive – need further study.

30. FUTURE PLAN
 Need more data, especially with energies
close to boundary (work func.)
 Using higher photon energy.
 Different approach on the calculation (New
model, different length, etc.)
 Re-program it on other languages with a
more user-friendly interface.

31. REFERENCES
 Nonequilibrium Band Mapping of Unoccupied Bulk States Below the Vaccum
Level by Two-Photon Photoemission, by Zhaofeng Hao, J. I. Dadap, K. Knox, M.
Yilmaz, N. Zaki, P. D. Johnson, and R. M. Osgood. (Pending on PRL)
 Electronic structure of a Co-decorated vicinal Cu(775) surface: High-resolution
photoemission spectroscopy, by S.-C. Wang, M. B. Yilmaz, K. R. Knox, N. Zaki,
J. I. Dadap, T. Valla, P. D. Johnson, and R. M. Osgood, Phys. Rev. B 77, 115448
(2008).
 Scattering of Surface States at Step Edges in Nanostripe Arrays, by F. Schiller,
M. Ruiz-Dses, J. Cordon, and J. E. Ortega, Phy. Rev. Lett. 95, 066805 (2005).
 Observation of a one-dimensional state on stepped Cu(775), by X. J. Shen, H.
Kwak, D. Mocuta, A. M. Radojevic, S. Smadici, and R. M. Osgood, Phys. Rev. B
63, 165403 (2001).
 Surface electron motion near monatomic steps: Two-photon photoemission
studies on stepped Cu(111), by X. Y. Wang, X. J. Shen, and R. M. Osgood,
Phys. Rev. B 56, 7665 (1997).
 Book: S. Hufner, Photoelectron Specstropy, 3rd ed. (Springer, Berlin, 2003)
 Book: Hai-Lung Dai, Wilson Ho, Laser Spectroscopy and Photo-Chemistry on
Metal Surfaces. (World Scientific, 1995)
 Book: Harald Ibach, Hans Luth, Solid State Physics. (Springer, 1991)

32. ~FIN~
Q&A time
Thank you for
your patience!

33. q
e–
UHV
Pulse Counter
Energy
Analyzer
MCP
Sample
Oscillator
YVO4 pump
egen Amp
B. Expander/Compressor
D. Optical
Parametric
Amplifier
YVO4 pump
E C Out