electron dynamics at metal surfaces università degli studi di trieste dipartimento di fisica and...
Post on 21-Dec-2015
222 views
TRANSCRIPT
Electron Dynamics at Metal Surfaces
Università degli Studi di TriesteDipartimento di FisicaandSincrotrone Trieste (Trieste, Italy)
Fulvio Parmigiani
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 band-structure 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
Introduction
ToF
E kin h EB
k // 2mE kin/2 sin
LINEAR PHOTOEMISSION (h > band mapping of OCCUPIED STATES
TIME RESOLVED MULTI-PHOTON PHOTOEMISSION (h< band mapping of UNOCCUPIED STATES and ELECTRON SCATTERING PROCESSES mechanisms
PHOTOEMISSION SPECTRA ON Ag(100)
Log Scale106 sensitivity
Iabs=13 J/cm2
p-polarized incident radiation30° incidence and 150 fs pulse.
Multiphoton on Ag(100)
M-B distribution “temperature” in atypical range of 0.5-0.7 eV. G. P. Banfi et al., PRB 67, 035418 (2003).
n=1
n=2
h = 3.14 eV
Linear photoemission on Ag(100)
h=6.28 eVF-D distribution at the RT energy
Introduction
Linear Photoemission Process
Experimental Set-up -metal UHV chamber
residual magnetic field < 10 mG
Base pressure <2·10-10 mbar
photoemitted electrons detector:Time of Flight (ToF) spectrometer
Acceptance angle: 0.83°Energy resolution:
10 meV @ 2eVDetector noise:
<10-4 counts/s
ToF
PCGPIB
Multiscaler FAST 7887
PS1 PS2 PS3 PS4
start stop
PreamplifierDiscriminator
Laser
sample detector
G. Paolicelli et al. Surf. Rev. and Lett. 9, 541 (2002)
Non-Linear Photoemission Process
PHOTOEMISSION PROCESSPROBLEMS:
Efermi
Evac
occupied states
emptystates
Φn=1
Upon the absorption of two photon the electron is already free.
Which is the absorption mechanism responsible of the free-free transition?
Keldysh parameter 1500>>1, perturbative regime
Evidence of ABOVE THRESHOLD PHOTOEMISSIONin solids ?
ATP
2 and 3 photon Fermi Edge:
- E = h- Fermi-Dirac edge
Energy-shift with photon energy:
E3PFE = 3·h
3-Photon Fermi Edge: Three experimental evidences...
Non-linearity order:
3-photon Fermi edge vs2-photon Fermi edge
n=2
n=3
ATP
PHOTOEMISSION PROCESSRESULTS:
To evaluate the cross section for an n-photon absorption involving the initial and final states:
Efermi
Evac
occupied states
emptystates
Φn=1
fi and
is proportional to the Transition Matrix Element in the DIPOLE APPROXIMATION
ipEGpnEGpfT iin
fi )(...))1(()(
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 Is another mechanism involved?
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
LEED
Ekin h EB
sin/2 2// kinmEk
*
2||
2
2|| 2)(
85.0),(
m
k
anknE
n = 1
E
n = 2
k//
m/m*=0.97 0.02
m/m*=1.03 0.06
G. Ferrini et al., Phys. Rev. B 67, 235407 (2003)
Image Potential States dispersion measured via two-photon resonant ARPES on Ag(100) along X
n=1
n=2
IPS n=1:h=4.32 eV, p pol.
Fermi EdgeDirect Photoemission
2-Photon Photoemissionwith P-polarized light
2-P Fermi Edge
h= 6.28eV
Ekin= h-
h= 3.14eVEkin= 2h-
h
Efermi
Evac
occupied states
emptystates
n=1
Photoemission Spectra on Ag(100) single crystal
Log Scale106 sensitivity
Iabs=13 J/cm2
p-polarized incident radiation
?
Undirectly Populated IPS on Ag(100)
Image Potential State
Ekin = h-Ebin
Ebin 0.5 eV
n=1
Ag(100)
K||=0
Shifting with photon energy
h=3.15eV
h=3.54eV
Ekin=0.39 eV
eV39.012 hhEkin
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 polarizationsm/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).
EV
n=2Cu(111)
LEED pattern
K
M
Shockley state
d-band
Tammstates
Cu(111)
Cu(111)
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
SS
IPS
bulk
k// (Å-1
)
Ene
rgy
(arb
. uni
ts)
EF
VL≈≈
IPS is located at k//=0 close to the upper edge of the bulk unoccupied sp-band (~200meV)
The energy separation between the IPS and the occupied surface state n=0 (Shockley)is about 4.45 eV
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997
year
m*/
m
Goldmann
Smith
Giesen
Schoenlein
Padowitz
IPS (n=1) m*/m measurements on Cu(111) and Ag(111)
Haight
m*/m measurements
In the phase-analysis model treats the states as electron waves undergoing multiple reflection between the crystal and image potential.
Phase shift model - P.M. Echenique, J.B. Pendry-
Bohr-like quantization condition on the round trip phase accumulation
Ci
Cer
Bi
Ber
1)(exp1 CBCB irr
a pole in this expression denotes a bound states of the surface, i.e. a surface states
Reflected wave from the crystal surface:
Reflected wave from the image potential barrier:
Summing the repeated scattering gives the total amplitude of :
the condition for a surface state is
11 CB rr1BCrrFor the flux conservation
11 CB rr
nBC 2
N.V. Smith, PRB, 32,3549(1985)
J.Phys.C:Solid State Phys., 11, 2065 (1978)
Phase shift model
Even though completely reflected, the wave does extend to the far side of the boundary as the evanescent wave
wave function inside the crystal
)cos( pzezq
wave function outside the crystal
ziiC
zieere C
iqpkz
momentum perpendicular to the surface
where q is the damping factor
1.0
0.5
0.0
-0.5
-1.0
bulk
func
tion
-50 -40 -30 -20 -10 0z (A)
IPS wave functionon Cu(111)
q = 0.2 A-1
The wave functions
N.V. Smith, PRB, 32,3549(1985)
Phase shift model
GAPUnoccupied bands
BC
For a pure image potential, the barrier phase change may be written
14.3 2
1
EE
eV
V
B
In the nearly-free-electron two band model
qpzpC
)tan(2
tan 0
is the electron momentum at k//=0
z0 is the position of the image potential plane
rdE
B 32
The phase B change respect to the energy is connected to the penetration of the wave on the vacuum side of the boundary.
The phases
rdE
C 32
The phase C change respect to the energy is connected to the penetration of the wave in the crystal
The phase B for an image barrier diverges equation is satisfied ad infinitum, Rydberg
series are generated, converging on the vacuum level
nBC 2
Phase shift model
En
The C phase
If C is treated as a constant over the range of the Rydberg series the energies are given by
2)(/85.0 aneVEn
m
kEEkE nV 2
)(2//
2
//
a 1
2(1 C / )
is the quantum defect
When Ev is in the gap
non perfect reflectivity
C <
a ≠ 0
For infinite crystal barrier
perfect reflectivity
C =
a = 0
m free electron mass; n =1, 2, 3…
K. Giesen, et al., PRB, 35, 975 (1987)
K// ( Å-1)
P.M. Echenique, Chemical Physics, 251, 1 (2000)
Phase shift model
a
m
kEEkE nV 2
)(2//
2
//
IPS effective mass on Cu(111) in the phase shift model
An effective mass m*/m different from unit results when the phase C and, consequently En, depends on k//.
At different k// the electron reflected by the surface experiences different phase change
)( //kEE nn )( //kCC
K. Giesen, et al., PRB, 35, 975 (1987)
K// ( Å-1)
3.1*
m
m on Ag(111)
on Cu(111)
Phase shift model
6000
4000
2000
0
Int
ensi
ty (
Cou
nts/
sec/
eV)
5.04.84.64.44.24.0
Kinetic Energy (eV)
60 meV
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
SS
IPS
bulk
k// (Å-1
)
Energ
y (
arb
. unit
s)
Fermi Energy
Vacuum level
5.0
4.9
4.8
4.7
4.6
Kin
etic
Ene
rgy
(eV
)
-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4
k// (Å-1
)
m*=1.26±0.07
m*=0.47±0.04
Resonant Case
The effective mass of the IPS and SS states are in agreement with the litterature.
h=4.45 eV
Cu(111)
Cu(111)
h= 4.71 eV4.90
4.85
4.80
Kin
etic
Ene
rgy
(eV
)
-0.2 -0.1 0.0 0.1 0.2 k// (-1
)
h=4.71 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]
Changing C
To be submitted
4.90
4.85
4.80
-0.2 -0.1 0.0 0.1 0.2
4.25
4.20
4.15
-0.2 -0.1 0.0 0.1 0.2
h eV
h eV
4.65
4.60
4.55
-0.2 -0.1 0.0 0.1 0.2
h eV
Kin
etic
ene
rgy
(eV
)
k// (-1
)
m*=1.28 ± 0.07
m*=2.17 ± 0.07
m*=1.26 ± 0.07
80
70
60
x10-3
-0.2 -0.1 0.0 0.1 0.2
80
60
40
20
x10-3
-0.2 -0.1 0.0 0.1 0.2
k// (-1
)
Intr
insi
c lin
ewid
th (
meV
)
h=4.71 eV
h=4.45 eV
Cu(111)FWHM
3-PPE
m
kEEkE nV 2
)(2//
2
//
2)(/85.0 aneVEn
Log
In
ten
sity
(arb
. u
nit
s)
4.84.64.44.24.03.8
KInetic energy (eV)
4.5
4.4
4.3
4.2
4.1
Kin
etic
Ene
rgy
(eV
)
-0.2 -0.1 0.0 0.1 0.2
k//(Å-1)
m*/m=1.64+/-0.07
m*/m=0.46+/-0.04
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
SS
IPS
bulk
k// (Å-1
)
Energ
y (
arb
. unit
s)
Fermi Energy
Vacuum level
h=4.28 eV
Cu(111)h=4.28 eV
3.5
3.4
3.3
3.2
-0.2 -0.1 0.0 0.1 0.2
k// (Å-1
)
2.0
1.5
1.0
600x109
400200
Photon number per pulse
Cu(111)
Dependence of m/m* on the pump intensity
h=4.71 eV
h=4.71 eV
h=3.14 eV
To be submitted
3.8
3.6
3.4
3.2
3.0
Kin
eti
c Energ
y (
eV
)
-0.2 -0.1 0.0 0.1 0.2
k// (Å-1
)
2.0
1.5
1.0
IPS
eff
ect
ive
ma
ss600x10
9400200
Photon number per pulse
1.0
0.5
0.0
-0.5
-1.0
inte
nsi
ty w
ave
-50 -40 -30 -20 -10 0z (A
-1)
IPS wave functionon Cu(111)
q = 0.2 A-1
1.0
0.5
0.0
-0.5
-1.0
wa
ve
in
ten
sit
y
-50 -40 -30 -20 -10 0z (A
-1)
IPS wave functionCu(111)
q = 0.7 A-1
A B
IPS
k//
unoccupied sp bands
A B
IPS
k//
unoccupied sp bands
h=4.71 eV Cu(111)
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. FerriniC. GiannettiS. PagliaraF. Banfi (Univ. of Geneve)
G. Galimberti E. PedersoliD. Fausti (Univ. of Groningen)