EFFECTIVE MASS AND
MOMENTUM RESOLVED
INTRINSIC LINEWIDTH
OF IMAGE-POTENTIAL
STATES ON Ag(100)
Claudio Giannetti
INFM and
Università Cattolica del Sacro Cuore
Dipartimento di Matematica e Fisica, Via Musei 41
Brescia.
INFM
DMF
INFMeeting, Genova 23-25 Giugno 2003
INTRODUCTION
•Femtosecond Laser and
tunability of photon energy
→ Non-Linear Photoemission
•Study of image-potential states on Ag(100)
at different photon energies: effective
masses and lifetimes.
•WHY IMAGE POTENTIAL STATES?
Relaxation of electrons into bulk states
can be studied directly in the timedomain with pump-probe techniques.
U. Höfer et al., Science 277, 1480 (1997).
W. Berthold et al., Phys. Rev. Lett. 88, 056805 (2002).
It is a many body interesting problem.
A.García-Lekue et al., Phys. Rev. Lett. 89, 096401
(2002).
J. Kliewer et al., Science 288, 1399 (2000).
Interplay between image-potential states
and dynamics of molecules at surfaces.
A. D. Miller et al., Science 297, 1163 (2002).
INFM
DMF
INFMeeting, Genova 23-25 Giugno 2003
LASER APPARATUS
Ti:Sapphire laser system:
Amplified Ti:Sapphire oscillator
Tunability: 750-850nm
Pulse width: 150fs
Rep. rate: 1kHz
Average Power: 0.5W
Travelling-wave optical parametric generation
(TOPG):
Tunability:
1150-1500nm
(0.8-1.1 eV)
4th (3.2-4.4 eV)
Average power 30mW
INFM
DMF
INFMeeting, Genova 23-25 Giugno 2003
ULTRA-HIGH-VACUUM SYSTEM
 m-metal UHV chamber
 B<10 mG
 Base pressure <2x10-10
mbar
 photoemitted electrons
detector:
time of flight
spectrometer (TOF)
TOF: ToF length = 432 mm
Temporal resolution = 0.5 ns
Acceptance angle =  2.6°
Energy resolution about 30 meV @ 2eV
PS1
PS2
GPIB
Laser
start
PS3
PS4
PC
Preamplifier
Discriminator
Multiscaler
FAST 7887
stop
INFM
DMF
INFMeeting, Genova 23-25 Giugno 2003
IMAGE-POTENTIAL STATES ON METALS
Coulomb potential due to
electronic image-charge:
V(z)1/z
forbidden gap in bulk states
Image-charge of an electron
at a metal surface.
2-D electron gas
Ag(100)
n=1
n=2
Rydberg
series:
En 
U. Hofer, I.L. Shumay, Ch. Reuß,
U. Thomann, W. Wallauer, Th. Fauster,
Science 277, 1480 (1997).
INFM
DMF
INFMeeting, Genova 23-25 Giugno 2003
 0.85eV
(n  a)2
DISPERSION OF IS
Band structure of Ag(100)
2
2
 k //
E (k // )  En 
2m*
En: binding energy
m*: effective mass
INFM
DMF
INFMeeting, Genova 23-25 Giugno 2003
IS SPECTRA
Ebin=
0.5eV
2-photon
photoemission
Ekin = h-Ebin
Ag(100)
h=4.32 eV
n=1
FWHM:
62meV
n=2
FWHM:
52meV
Efermi
RADIATION:
Polarization: P
Incident angle: 30°
INFM
DMF
INFMeeting, Genova 23-25 Giugno 2003
SELECTION RULES
DIPOLE SELECTION
RULES:
Ag(100)

n
S
P
J=0
J≠0
in S-polarization
in P-polarization
J is the current density
associated to image-potential
states
INFM
DMF
INFMeeting, Genova 23-25 Giugno 2003
IS DISPERSION
2-Dimensional
electron gas: DISPERSION
k|| 
2mEKin sin
2
 2 k //
E (k // )  En 
2m*
Intensity (log scale)
n=1
n=2
Ag(100)
Ekin (eV)
G.Ferrini, C.Giannetti, D.Fausti, G.Galimberti,
M.Peloi, G.P.Banfi, F.Parmigiani,
PRB 67, 235407 (2003).
INFM
DMF
INFMeeting, Genova 23-25 Giugno 2003
EFFECTIVE MASS
m* 
d
2
E / dk||2 
n=2
n=2
n=1
n=1
Measured values
n=1
n=2
0.99±0.02
0.97±0.02
1.15±0.1*
2
1.06±0.09
1.03±0.06
Calculated values
n=1
n=2
0.95*
1.03**
1.03**
* K.Giesen et al., PRB 35 975 (1987).
** Z.Li and S.Gao , PRB 50 15349 (1994).
INFM
DMF
INFMeeting, Genova 23-25 Giugno 2003
IS LIFETIMES
FITTING: Gaussian-Lorentzian convolution
Gaussian: experimental resolution
FWHM45meV
Lorentzian: intrinsic linewidth 14meV @ k//=0
LIFETIME
  /
Measured values (fs)
n=1
n=2
47±7
55±5#
≥55
160±10#
  658meV  fs
Calculated values (fs)
n=1
n=2
55##
132##
#
# I.L.Shumay et al., PRB 58 13974 (1998).
## A.García-Lekue et al., Phys. Rev. Lett. 89, 096401 (2002).
### E.V Chulkov et al., Surf. Sci 391 L1217 (1997).
Linewidth dependance on k//
INFM
DMF
INFMeeting, Genova 23-25 Giugno 2003
FIRST OBSERVATION OF IMAGE STATES
OUT OF RESONANCE
e-
E
EV
h3.14eVDE
0.5 eV
n=1
e-

 DE=3.8 eV
EF
intensity
intensity
Fermi edge
Fermi edge
LOG
LIN
SCALE
SCALE
Ekin
kin (eV)
Ekin= h-Ebin= (3.14-0.5)eV 2.7eV
INFM
DMF
INFMeeting, Genova 23-25 Giugno 2003
DISPERSION AND SELECTION RULES
Fermi edge
n=1
m*/m0.95
Ekin= h-Ebin
Dh=0.39eV
h=3.15eV h=3.54eV
EV
Ebin
n=1
eEF
INFM
DMF
INFMeeting, Genova 23-25 Giugno 2003
SELECTION RULES
Ag(100)

n
S
P
DIPOLE SELECTION
RULES:
J=0 in S-polarization
J≠0 in P-polarization
WHICH IS THE POPULATION AND
PHOTOEMISSION MECHANISM?
We can exclude:
Role of surface roughness
Ponderomotive and tunnel
effects at the surface,
because the radiation
intensity is too low.
(I~0.1GW/cm2)
INFM
DMF
INFMeeting, Genova 23-25 Giugno 2003
CONCLUSIONS
•Non-linear photoemission on image-potential
states in Ag(100).
• Improvement of the precision in the
measurement of the effective masses and
lifetimes.
• Observation of image-potential states also
when hE1-Efermi. In this case the imagepotential states can be populated and
photoemitted also in S-polarization.
INFM
DMF
INFMeeting, Genova 23-25 Giugno 2003
Responsibles:
Co-workers:
F. Parmigiani,
G. Ferrini.
F. Banfi,
D. Fausti,
G. Galimberti,
S. Pagliara,
M. Peloi.
INFM
DMF
INFMeeting, Genova 23-25 Giugno 2003