Post on 18-Jul-2015
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
OUTLINE
Goal –Understanding the band structure of
Cu.
Understanding of Cu Band structure - bulk state
Simulation
AR2PPE
Ultra-fast Laser with
OPA-SHG
OUR SOURCE: TI:SAPHIRE LASER
Red and Infrared light in the range from 650 to 1100 nm.
Power: 0.5~1.5 Watt.
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
MCPSample
q
e–
UHV
Energy
Analyzer
Pulse Counter
MCPSample
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!
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)
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
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
FROM
OSCILLATOR
TO
REGEN
FROM
REGEN
TO
OPA
GRATING
GRATING
B. EXPANDER/COMPRESSOR LAYOUT
EXPANDER
COMPRESSOR
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
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.
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
ANGLE-RESOLVED-2PPE SPECTROSCOPY
qe–
UHVPulse Counter
Energy
AnalyzerMCP
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
For stepped surfaces each state can have different reference planes.
[112]
[110]
[111]
CU(775)-STEPPED SURFACES
Cu
2cm
8.5 degree
(Side View)
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)
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
MEASUREMENT & RESULT
We can only measure Kinetic Energy and Number of output electrons!
Evac
EFermi
Evac
Ene
rgy (
eV
)
K
M
EL-GAP= 4.9 eV
Evac
EFermi
Evac
Ene
rgy (
eV
)
K
M
EL-GAP= 4.9 eV
Projection
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!
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.
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’sbook; 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
Y A
xis T
itle
X Axis Title
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
Y A
xis T
itle
X Axis Title
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
4.0Y
A
xis T
itle
X Axis Title
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
Y A
xis T
itle
X Axis Title
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
Y A
xis T
itle
X Axis Title
X L XKSD LWZ Q
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)
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.
PHOTON ENERGY DEPENDENCE
– THE BULK STATE
0
5
10
15
20
25
30
0.5
0.4
7
0.4
4
0.4
1
0.3
8
0.3
5
0.3
2
0.2
9
0.2
6
0.2
3
0.2
0.1
7
0.1
4
0.1
1
0.0
8
0.0
5
0.0
2
-0.0
1
-0.0
4
-0.0
7
-0.1
-0.1
3
-0.1
6
-0.1
9
-0.2
2
-0.2
5
-0.2
8
-0.3
1
-0.3
4
-0.3
7
-0.4
-0.4
3
-0.4
6
-0.4
9
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
0.4
7
0.4
4
0.4
1
0.3
8
0.3
5
0.3
2
0.2
9
0.2
6
0.2
3
0.2
0.1
7
0.1
4
0.1
1
0.0
8
0.0
5
0.0
2
-0.0
1
-0.0
4
-0.0
7
-0.1
-0.1
3
-0.1
6
-0.1
9
-0.2
2
-0.2
5
-0.2
8
-0.3
1
-0.3
4
-0.3
7
-0.4
-0.4
3
-0.4
6
-0.4
9
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
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
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.
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.
REFERENCES
Nonequilibrium Band Mapping of Unoccupied Bulk States Below the VaccumLevel 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)
qe–
UHV
Pulse Counter
Energy
AnalyzerMCP
Sample
Oscillator
Nd:YVO4 pump
Regen Amp
B. Expander/Compressor
D. Optical
Parametric
Amplifier
Nd:YVO4 pump
E C Out