Transcript Document

Electron Dynamics at Metal Surfaces
Fulvio Parmigiani
Università degli Studi di Trieste
Dipartimento di Fisica
and
Sincrotrone Trieste (Trieste, Italy)
Introduction
The study of the electron dynamics at surfaces and interfaces
relays on the ability to time-resolve the ultra-rapid scattering
processes which result in energy and momentum relaxation,
recombination and diffusion.
In typical experiments a short-pulsed (10-100 fs) laser can be used
for photoemission experiments in the time-domain, whereas longer
laser pulses (1-5 ps) provided by FT limited coherent sources can
be used for photoemission experiments in the frequency (energy)
domain with unrecorded resolving power.
Experimental techniques must be brought to bear in which bandstructure specificity are combined with time resolution. Angle
resolved photoemission is particularly suited for such experiments.
Introduction
A rather interesting system to study the electron dynamics at
the solid surfaces is represented by the Surface States
(SS) Image Potential States (IPS).
The SS-IPS represents a paradigmatic two-levels system in
solids and can be seen as a playground to study, in the
momentum space,the optical transitions in semiconductors,
insulators and superconducting systems.
•
•
•
•
•
band dispersion
direct versus indirect population mechanisms
polarization selection rules
effective mass ( in the plane of the surface)
electron scattering processes and lifetime
Introduction
LINEAR PHOTOEMISSION (h > F)
band mapping of OCCUPIED STATES
E kin  h  E B  
k //  2mEkin /
2

TIME RESOLVED
 MULTI-PHOTON
PHOTOEMISSION (h < F)
band mapping of UNOCCUPIED STATES and
ELECTRON SCATTERING PROCESSES
mechanisms
 sin
Introduction
PHOTOEMISSION SPECTRA ON Ag(100)
Linear photoemission on Ag(100)
h=6.28 eV
F-D distribution at the RT energy
Multiphoton on Ag(100)
h  = 3.14 eV
n=1
p-polarized incident
radiation
30° incidence and
150 fs pulse.
Log Scale
106 sensitivity
n=2
M-B distribution “temperature” in a
typical range of 0.5-0.7 eV.
G. P. Banfi et al., PRB 67, 035418 (2003).
Iabs=13 mJ/cm2
Linear Photoemission Process
Experimental Set-up
 m-metal UHV chamber
 residual magnetic field < 10 mG
 Base pressure <2·10-10 mbar
 photoemitted electrons detector:
Time of Flight (ToF) spectrometer
ToF
sample
Acceptance angle:
 0.83°
Energy resolution:
10 meV @ 2eV
Detector noise:
<10-4 counts/s
PS1
detector
PS2
GPIB
Laser
start
PS3
PC
Multiscaler
FAST 7887
PS4
Preamplifier
Discriminator
stop
G. Paolicelli et al. Surf. Rev. and Lett. 9, 541 (2002)
Non-Linear Photoemission Process
PHOTOEMISSION PROCESS
PROBLEMS:
Upon the absorption of two photon
the electron is already free.
Which is the absorption mechanism
responsible of the free-free transition?
Evac
n=1
Keldysh parameter g1500>>1,
perturbative regime
g
Evidence of
ABOVE THRESHOLD PHOTOEMISSION
in solids ?
Φ
Efermi
empty
states
occupied
states
ATP
3-Photon Fermi Edge: Three experimental evidences...
2 and 3 photon Fermi Edge:
- DE = h
- Fermi-Dirac edge
Energy-shift with photon energy:
DE3PFE = 3·hD
n=3
n=2
Non-linearity order:
3-photon Fermi edge vs
2-photon Fermi edge
ATP
PHOTOEMISSION PROCESS
RESULTS:
To evaluate the cross section for an
n-photon absorption involving the initial and
final states:
i and f
is proportional to the Transition Matrix Element in
the DIPOLE APPROXIMATION
Evac
n=1
( n)
Ti
f  f p  G( Ei  (n 1))  p  ...G( Ei  )  p i
In this calculation we have to consider the mixing of
the final free electron state with all the unperturbed
Hamiltonian eigenstates but is it difficult to evaluate
the contribution of this mixing to T(3).
Rough Estimate T(3)/T(2)10-6
Experimental Value T(3)/T(2)10-4
Φ
Efermi
Is another mechanism involved?
empty
states
occupied
states
ATP
Image Potential States
In most metals exists a gap in the bulk bands projection on the surface.
When an electron is taken outside the solid it could be trapped between
the Coulomb-like potential induced by the image charge into the solid,
and the high reflectivity barrier due the band gap at the surface.
Ag(100)
U. Hofer et al., Science 277, 1480 (1997).
k// Dispersion
Image Potential States dispersion measured via twophoton resonant ARPES on Ag(100) along GX
LEED
n=1
n=2
E
IPS n=1:
h=4.32 eV, p pol.
m/m*=1.03  0.06
n=2
m/m*=0.97  0.02
G. Ferrini et al., Phys. Rev. B 67, 235407 (2003)
n=1
E kin  h  E B  F
k//

k //  2mE kin /  2  sin 
 2 k||2
0.85
E (n, k|| ) 

2
(n  a)
2m*
Undirectly Populated IPS on Ag(100)
Photoemission Spectra on Ag(100) single crystal
Fermi Edge
Direct Photoemission
h= 6.28eV
Ekin= h-F
Evac
n=1
2-P Fermi Edge
2-Photon Photoemission
with P-polarized light
h= 3.14eV
Ekin= 2h-F
p-polarized
incident radiation
Log Scale
106 sensitivity
?
Efermi
empty
states
occupied
states
h
Iabs=13 mJ/cm2
F
Image Potential State
Ag(100)
Ekin = h-Ebin
n=1
K||=0
Ebin  0.5 eV
Shifting with photon energy
h2=3.54eV
DEkin=0.39 eV
h1=3.15eV
DEkin  h 2  h1  0.39 eV
k// -dispersion of non-resonantly populated IPS
2DEG effective mass
(ARPES)
m/m* = 0.88  0.04,
h = 3.14 eV non resonant
excitation both in p and s
polarizations
m/m*= 0.97  0.02,
h = 4.28 eV resonant
excitation, p-polarization
9% change of IPS effective
mass suggests that the
photoemission process is
mediated by scattering with
the hot electron gas created
by the laser pulse.
G. Ferrini et al., Phys. Rev. Lett. 92, 2568021 (2004).
LEED pattern
Cu(111)
Cu(111)
n=2
EV
GK
GM
Shockley state
d-band
Tamm
states
Cu(111)
The energy separation
between the IPS and the
occupied surface state n=0
(Shockley)is about 4.45 eV
≈
-0.3
≈
IPS
Energy (arb. units)
IPS is located at k//=0
close to the upper edge
of the bulk unoccupied
sp-band (~200meV)
VL
bulk
EF
SS
-0.2
-0.1
0.0
0.1
-1
k// (Å )
0.2
0.3
m*/m measurements
IPS (n=1) m*/m measurements on Cu(111) and Ag(111)
1.6
Smith
1.5
Goldmann
Padowitz
m*/m
1.4
Haight
1.3
Schoenlein
1.2
Giesen
1.1
1
0.9
1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997
year
Phase shift model
Phase shift model - P.M. Echenique, J.B. PendryIn the phase-analysis model treats the states as electron waves undergoing multiple
reflection between the crystal and image potential.
Reflected wave from the crystal surface:
rC eiFC 
Reflected wave from the image potential barrier:
rB eiF B 
Summing the repeated scattering gives the total
amplitude of :
1 rBrC expi(B  C )1
a pole in this expression denotes a bound states of the
surface, i.e. a surface states
the condition for a surface state is
N.V. Smith, PRB,
32,3549(1985)
rC rB  1
rB  1 rC  1
rB  1 rC  1
For the flux
conservation
  C  B  2 n
Bohr-like quantization condition on the
round trip phase accumulation
J.Phys.C:Solid State Phys., 11, 2065 (1978)
Phase shift model
The wave functions
1.0
wave function inside
the crystal
  e cos( pz   )
IPS wave function
on Cu(111)
-1
q = 0.2 A
0.5
bulk function
Even though completely
reflected, the wave does
extend to the far side of
the boundary as the
evanescent wave
0.0
-0.5
Unoccupied
bands
q z
-1.0
-50
momentum perpendicular
to the surface
k z  p  iq
where q is the damping
factor
-40
-30
-20
z (A)
wave function outside
the crystal
 e
 i z
 rC e
 iC i z
e
N.V. Smith, PRB,
32,3549(1985)
GAP
-10
0
Phase shift model
The phases
FB
FC
In the nearly-freeelectron two band model
 
 t an C   p t an(pz0   )  q
 2 
 is the electron momentum at k//=0
z0 is the position of the image potential
plane
2
F C
   d3r
E

The phase FC change respect to the energy
is connected to the penetration of the wave
in the crystal
For a pure image potential,
the barrier phase change
may be written
 3.4eV 

 
  EV  E 
FB
1
2
1
The phase FB for an image barrier diverges equation
is satisfied ad infinitum,   C  B  2 n Rydberg
series are generated, converging on the vacuum
level
2
F B
   d3r
E

The phase FB change respect to the energy is
connected to the penetration of the wave on
the vacuum side of the boundary.
Phase shift model
The FC phase
If FC is treated as a constant over the
range of the Rydberg series the
energies are given by
2
K. Giesen, et al., PRB, 35, 975 (1987)
En
2
//
 k
E (k // )  EV  En 
2m
En  0.85eV / (n  a)2
m free electron mass; n =1, 2, 3…
K// ( Å-1)
1
a  (1 C /  )
2
a is the quantum defect

For infinite crystal
barrier

When Ev is in the gap
perfect
reflectivity
non perfect
reflectivity
FC = 
FC < 
a=0
a≠0
P.M. Echenique, Chemical Physics, 251, 1 (2000)
Phase shift model
IPS effective mass on Cu(111) in the phase shift model
 2 k //2
E (k // )  EV  En 
2m
At different k// the electron reflected by
the surface experiences different phase
change
FC  FC (k// )
En  En (k// )
An effective mass m*/m different from unit
results when the phase FC and, consequently
En, depends on k//.
m*
 1 .3
m
K// ( Å-1)
K. Giesen, et al., PRB, 35, 975 (1987)
on Ag(111)
on Cu(111)
Vacuum level
Cu(111)
Resonant Case
bulk
Fermi Energy
SS
-0.2
-0.1
0.0
0.1
0.2
6000
60 meV
4000
2000
0.3
-1
k// (Å )
0
4.0
4.2
4.4
4.6
4.8
5.0
Kinetic Energy (eV)
5.0
Kinetic Energy (eV)
-0.3
h=4.45 eV
Intensity (Counts/sec/eV)
Energy (arb. units)
IPS
4.9
m*=0.47±0.04
4.8
4.7
4.6
m*=1.26±0.07
-0.4
-0.3
-0.2
-0.1
0.0
-1
k// (Å
0.1
0.2
0.3
0.4
)
The effective mass of the IPS and SS states are
in agreement with the litterature.
Cu(111)
Changing FC
h=4.71 eV
h= 4.71 eV
Kinetic Energy (eV)
m*/m=2.17 ± 0.07 in k//[-0.12, 0.12]
m*/m=1.28 ± 0.07 in k//[-0.2, 0.2]
4.90
4.85
4.80
-0.2
-0.1
-1
k0.0
// ( )
0.1
To be submitted
0.2
Cu(111)
FWHM
80
h eV
m*=1.26 ± 0.07
4.65
h=4.45 eV
-3
60
x10
4.60
4.55
-0.1
0.0
0.1
0.2
h1 eV
m*=1.28 ± 0.07
4.25
3-PPE
-0.2
-0.1
0.0
0.1
0.2
0.1
0.2
h=4.71 eV
80
-3
4.20
20
x10
Kinetic energy (eV)
-0.2
Intrinsic linewidth (meV)
40
4.15
70
-0.2
-0.1
0.0
0.1
0.2
h1 eV
m*=2.17 ± 0.07
4.90
60
4.85
-0.2
-0.1
0.0
-1
k// ( )
 2 k //2
E (k // )  EV  En 
2m
4.80
-0.2
-0.1
0.0
0.1
-1
k// ( )
0.2
En  0.85eV / (n  a)2
Vacuum level
Cu(111)
h=4.28 eV
bulk
h=4.28 eV
Log Intensity (arb. units)
Energy (arb. units)
IPS
Fermi Energy
SS
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
-1
k// (Å )
4.5
4.4
m*/m=1.64+/-0.07
4.3
3.8
4.2
4.1
4.0
4.2
4.4
4.6
KInetic energy (eV)
m*/m=0.46+/-0.04
-0.2
-0.1
0.0
k//(Å-1)
0.1
0.2
4.8
Cu(111)
Dependence of m/m* on the pump intensity
h=4.71 eV
h=3.14 eV
h=4.71 eV
To be submitted
h=4.71 eV
3.8
intensity wave
IPS effective mass
2.0
1.5
0.0
-0.5
1.0
200
400
600x10
9
Photon number per pulse
3.4
-1.0
-50
-40
-30
-1
-20
-10
z (A )
unoccupied sp
bands
3.2
B
A
IPS
3.0
-0.2
-0.1
0.0
-1
0.1
G
0.2
k // (Å )
k//
1.0
0.5
wave intensity
Kinetic Energy (eV)
IPS wave function
on Cu(111)
-1
q = 0.2 A
0.5
3.6
Cu(111)
1.0
0.0
IPS wave function
Cu(111)
-1
q = 0.7 A
unoccupied sp
bands
B
A
IPS
-0.5
-1.0
G
k//
0
Conclusions
•ATP on solid was demonstrated
•Indirect population of the IPS was
shown
•The origin of anomalous electron
effective mass for the IPS has been
clarified
•The possibility to photo-induced
changes of the electron effective mass in
solids has been demonstrated.
Co-workers:
G. Ferrini
C. Giannetti
S. Pagliara
F. Banfi (Univ. of Geneve)
G. Galimberti
E. Pedersoli
D. Fausti (Univ. of Groningen)