UST
PHYSICAL BIOLOGY Center for
ULTRAFAST SCIENCE & TECHNOLOGY
Plasmon Charge Density
Probed By
Ultrafast Electron Microscopy
Sang Tae Park and Ahmed H. Zewail
California Institute of Technology
2013.12.09. Femtosecond Electron Imaging and Spectroscopy Workshop
Outline
• Structural dynamics
• ultrafast electron microscopy
• design
• capability
• Visualization of plasmons
• photon-induced near field electron microscopy
• interaction of electron and (plasmon) field
• induced charge density
Motivation
• Structural dynamics
• direct visualization of microscopic/macroscopic
manifestation of bonding interaction
• microscopic, atomic motions
• macroscopic beyond lattice unit cell
• complimentary to spectroscopy
• full picture of dynamics and interplay between electronic and
nuclear interactions
light ~500 nm
x-ray
~1 Å
electron ~2 pm
Electron probe
• advantages
• vs. optical microscopy
• very high spatial resolution
• vs. x-ray diffraction
• table-top instrument
• compact source
• easier manipulation of beam
• stronger interaction
• 106 electrons vs. 1012 x-ray for diffraction
• thickness comparable to optical depth
• nuclear information
• rather than charge density
• disadvantages
•
•
•
•
•
space-charge effect
poor coherence
aberration
multiple scattering
sample preparation
• requires thin specimen
•
•
requires high vacuum
unselective
• atomic rather than molecular
Transmission electron microscopy
• high resolution
• atomic detail
• Cs and Cc aberration correction
• versatile
• diffraction (parallel & converged)
• imaging (transmission & scanning)
• spectroscopy (plasmon & atomic)
- combinations
momentum-selected imaging
energy-filtered TEM
• specimen
• <100 nm thick, nm to μm size
• in situ (real time, temperature, field, ...)
Ultrafast electron microscopy
p
e
• stroboscopic, time-resolved , pump-probe electron microscopy
•
modified TEM (FEI, Tecnai)
•
•
•
•
photoemission gun and specimen photoexcitation
UEM-1: 120 keV Wehnelt geometry with 50 μm LaB6 flat cathode
UEM-2: 200 keV FEG geometry with 16 μm LaB6 flat cathode
pump-probe set up
•
ultrafast laser pulses to initiate
•
•
•
•
ultrashort electron pulses to probe
•
•
•
~500 fs in low current mode
10 ns in nanosecond mode
spatial resolution
•
•
SpectraPhysics Tsunami HP (Ti:sapphire, 800 nm, 110 fs, 6 W, 80 MHz)
Coherent Talisker (Nd:YAG, 1064 nm, 16 ps, 80 μJ, 0 – 200 kHz)
Clark MXR Impulse (Yb-fiber, 1038 nm, 250 fs, 20 W, 100 kHz – 25 MHz)
up to conventional TEM resolution (albeit signal limited)
versatility
•
•
•
•
imaging
diffraction
spectroscopy
combinations
UEM-2
Design considerations
in situ
DTEM
aberration
correction
energy filter
cathode size
electron density
energy
spread
compression
spatial
resolution
signal
temporal
resolution
pulse length
radiation
damage
acquisition time
repetition rate
TEM
UEM
drift
stability
specimen
dynamics
Resolutions vs. signal
• Stroboscopic signal
• total number of electrons per acquisition
• Temporal resolution
• electron pulse duration
photoemission density ↔ repulsion
cathode size ↔ emittance
condenser thruput ↔ aberration
repetition rate ↔ specimen recovery
acquisition time ↔ specimen drift
← laser duration plays little role for < 1 ps
• photoemission energy spread
• space charge effect (number of electrons per pulse)
• compression
• Spatial resolution
• Cs aberration
• cathode size & condenser settings
• Cc aberration
• energy spread (space charge effect & compression)
• specimen stability
• repeated dynamics
Electron phase space characterization
Dispersion: electrons disperse due to energy spreads.
ΔEε = 1.82 eV
1
Cross ocrrelation: PINEM temporally selects coincident electrons while
discretely changing energies.
0
We can characterize intrinsic duration and dispersion coefficient.
-0.3
total electron duration
∂t∂E
-1
-2
-6
-4
-2
0
2
4
electron energy, E' (eV)
6
2
slope, ∂t/∂E (ps/eV)
time delay, τ (ps)
2
 t

t  t  
E 
 E

-0.2
2
-0.1
δt = 580 fs >> 250 fs
∂t/∂E = -180 fs/eV
0.0
1
1
1.0
-1
-2
2
3
energy width, ΔE (eV)
4
4
Δte
δte
∂t∂E*ΔE
0.8
total energy spread, ΔEε (eV)
electron time width, δte (ps)
time delay, τ (ps)
0
0
0.6
intrinsic
0.4
0.2
-4
-2
0
2
4
electron energy, E' (eV)
6
Park, Kwon, Zewail, New J. Phys. 14, 053046 (2012)
~100 e- at cathode
3
1.82 eV
2
1
0
0.0
-6
2
2
0
1
2
3
energy width, ΔE (eV)
4
0
0.2
0.4
0.6
pulse energy (nJ)
0.8
1
Versatility in UEM
spectroscopy
diffraction
imaging
Cu[TCNQ]
7×7×0.7 μm
-60 ps
MWCNT
004
100
002
+60 ps
0.96
X
60
Y
40
20
0
relative peak position
position (pixel = 1.9 nm)
80
c002
002
c100
100
0.97
c004
004
c110
110
0.98
0.99
1
-20
-1
0
1
2
time (μs)
3
4
5
-60
-40
-20
0
20
time (ps)
40
60
Versatility (combinations)
• momentum selected imaging
diffraction contrast
momentum selection
dark field imaging
Fe(pz)Pt(CN)4
605×605×20 nm
200 nm
• energy filtered imaging
bright field image
energy filtering
dark field imaging (PINEM)
graphite 4 nm step
1 μm
8
6
4
2
0 -2 -4
electron energy (eV)
-6
-8
Part II: Plasmons
Photon-induced near field electron microscopy
Visualization of plasmons
• Plasmon
• collective oscillation of free electrons
Can we see it ?
• localized surface plasmons (LSP) in nanoparticles
• field confinement and enhancement
• geometry dependent
Can we see where and how strong ?
How do we visualize plasmon modes ? E, P, or ρ ?
EELS spectral imaging
SI
HAADF
78 x 10 nm
A
C
STEM/ADF
STEM/EELS/MVSA
192 x 20 nm
B
STEM-EELS
EELS
Nelayah, Nat. Phys. 3, 348 (2007)
Guiton, Nano Lett., 11, 3482 (2011)
EEGS imaging in (S)TEM
electron energy gain spectroscopy in electron microscopy
• Photon-induced near field electron microscopy (PINEM)
•
•
•
•
plasmons are excited by laser.
In EELS, probe electrons excite plasmons.
electrons interact w/ plasmon fields and gain/lose energies.
energy-filtered image w/ electrons that have gained energies
measures/maps the “electron interaction” w/ the field
TEM bright field image
silver wire
of carbon
nanotube
“PINEM”
field image
“PINEM”dark
image
ofofsilver
wire
carbon
nanotube
Electron energy selection
0.6
Δt = -2 ps
244000
Δt = 0 ps
246000
0.4
gain
Energy
domain
loss
Space
domain
0.2
0
30
20
10
0
-10
electron energy (eV)
-20
-30
E
Degree of interaction in EEGS
Probability
𝐼+1 𝑥, 𝑦 ∝ 𝐹
Interaction
𝑊
=𝐹≡
𝑞
Electric field
+∞
𝑑𝑧 𝐸𝑧 𝑧, 𝑡
for 𝑧 = 𝑣𝑡 at 𝑥, 𝑦
−∞
𝐄 𝐫, 𝜔 by plasmon (from light scattering)
𝐄 = 𝐸𝑥 , 𝐸𝑦 , 𝐸𝑧
I (EELS)
Ez at t = 0
“field integral”
2
𝛁 ∙ 𝐄 = 𝜌/𝜖0
|E| (DDA)
I (EELS)
z = vt
I (simulation)
Garcia de Abajo, New J. Phys. 10, 073035 (2008)
Park, et. al., New J. Phys. 12, 123028 (2010)
Guiton, Nano Lett., 11, 3482 (2011)
|E| (DDA)
Mirsaleh-Kohan, J. Phys. Chem. Lett. 3, 2303 (2012)
Near field approximation
in Coulomb gauge
+∞
Field integral
𝑑𝑧 𝐸𝑧 𝑧, 𝑡 for 𝑧 = 𝑣𝑡 at 𝑥, 𝑦
𝐹≡
−∞
near field = Coulomb field of instantaneous charges
Electric field
Coulomb potential
Induced charge
Polarization
𝜕𝐀
𝐄 = −𝛁𝑉 −
𝜕𝑡
𝑉 𝐫, 𝑡 =
σ=𝐧∙𝐏
𝜌 = −𝛁 ∙ 𝐏
near field approximation
𝜎 𝐫′, 𝑡
𝑑𝐴′
+
𝑟"
linear material
𝜌 𝐫′, 𝑡
𝑑𝑉′
𝑟"
Evaluating the field integral
total electric field
total field integral
volume integral
mechanical work
charge
fields
charge
near
fields
𝐄=
convolution
charge field integrals
𝐫"
𝑑𝐴′𝜎 2
𝑟"
+∞
𝑑𝑧
−∞
𝑧 −𝑖∆𝑘𝑧
𝑒
= −2𝑖∆𝑘 𝐾0 ∆𝑘𝑏
𝑟3
induced charge density
𝐄 ≅ −𝛁
𝑑𝐴′
𝜎
𝑟"
induced polarization
incident light
light scattering
+∞
𝐹≡
𝑑𝑧 𝐸𝑧 𝑧, 𝑡
−∞
Near field integral
+∞
Mechanical work
𝐹=
𝑣𝑑𝑡 𝐸𝑧 𝑣𝑡, 𝑡
−∞
+∞
Fourier transform of electric field
𝑑𝑧 𝐸𝑧 𝑧, 0 𝑒 −𝑖∆𝑘𝑧
=
−∞
∆𝑘 ≡ 𝜔
𝑣
+∞
F.T. of Coulomb potential
𝑑𝑧 𝑉 𝑧, 0 𝑒 −𝑖∆𝑘𝑧
≅ −𝑖∆𝑘
−∞
Convolution of projected charge
∝ 𝐾0 ∆𝑘𝑏 ⨂ 𝜎𝑥𝑦
σxy = all the charges in electron trajectory along z at (x,y).
𝑏=
𝑥2 + 𝑦2
𝜎𝑥𝑦 ≅
𝐽𝐴′ 𝜎
𝑥𝑦
𝑧′∈𝐴′
K0 = (long-range) Coulomb field interaction of each charge oscillation.
Convolution accounts for contributions from all the charge densities.
Park and Zewail, Phys. Rev. A (submitted)
100 nm
Evaluating
thethe
field
integrals
Convoluting
charge
density
y
x
E
E z
Ez z
Ez
z
field integral
x
-Im[F0]
Px
radiation



dz E z e ikz
polarization
σ=n·P
near field integral
induced charges
σxy
F is a blurred map of charges.
-Im[F ]
c
σ
 K 0 kb
projection
100 nm
y
Multipole case:
silver nanorod (192×20 nm)
e-
x
1E+3
y
X
Y
1E+2
Qextinction
z
1E+1
1E+0
1E-1
1E-2
1E-3
0
Px
|E| at z=0
σxy
-Im[Fc]
|Fc|2
1
2
3
photon energy (eV)
4
5
charge density is the direct source of the E field and the PINEM signal.
1.10 eV
2.54 eV
Coulomb field
convolution
charge blobs
3.10 eV
Comparisons to F
• E maximum (Ex at z=0)
• Ez maximum (Ez at z=h)
F
|F|2
Ex(0)
|E(0)|
Ez
• V maximum (V at z=0)
V(0)
• σ and ρ
σxy
•P
Px
𝐄 ≈ −𝛁𝑉
𝑉 0 ~𝐹
𝐹 ∝ 𝐾0 ⊗ 𝜎𝑥𝑦
Part II summary
• EEGS measures the electron-plasmon interaction.
• “PINEM image” spatially maps the interaction (not the field itself).
• PINEM field integral = mechanical work by electromagnetic wave (Ez)
• “PINEM” visualizes charge density via Coulomb interaction.
• PINEM field integral = K0-convolution of projected charge density.
• K0[Δkb] describes Coulomb interaction of an oscillating charge density.
• Convolution accounts for the total interaction.
• PINEM can visualize the plasmon mode:
• convoluted charge density projection
also applicable to EELS
• plasmon is a collective oscillation of free electrons.
• related to Coulomb potential
• |E| is correlated to the slope, not the absolute intensity, of PINEM image.
• correlated to Ez maximum (≠ |E| maximum)
Acknowledgement
• Advisor
• Prof. Ahmed H. Zewail
• UEM-1
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Dr. Vladimir Lobastov
Dr. Ramesh Srinivasan
Dr. Jonas Weissenrieder
Dr. David Flannigan
Dr. Petros Samartzis
Dr. Anthony Fitzpatrick
Dr. Ulrich Lorenz
• Funding
• Moore foundation
• NSF
• AFOSR
• UEM-2
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PINEM experiments
Dr. J. Spencer Baskin
Dr. Hyun Soon Park
Dr. Oh-Hoon Kwon
Dr. Brett Barwick
Dr. Volkan Ortalan
Dr. Aycan Yurtserver
Dr. Renske van der Veen
Dr. Haihua Liu
Dr. Byung-Kuk Yoo
Dr. Mohammed Hassan