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We perform time-, energy-, and angle-resolved two-photon photoemission
(2PPE) spectroscopy to study electron dynamics at semiconductor
and metal surfaces.
2PPE gives access to the occupied and unoccupied surface and valence
electronic states. As light source we use ultrashort laser pulses.
They are provided by a 200 kHz Ti:Sa regenerative amplifier (RegA
9050, Coherent) and a homebuilt oscillator, which generates 800 nm
pulses of 38 fs duration. Subsequent parametric amplification in two
Optical Parametric Amplifiers (OPA 9400 and OPA 9800, Coherent), pulse
compression by prism pairs and second harmonic generation provide
pump and probe pulses of 30 to 80 fs duration with photon energies
between 0.8 eV and 5.4 eV. An ultra-high vacuum chamber (UHV, pressure
< 3 x 10-11 mbar) is used to prepare and sustain clean,
well-ordered surfaces over several hours (Fig.1).
Fig.1: The UHV endstation consists
of preparation and analyzer chamber (upper and lower part) separated
by a gate valve. The hemispherical electron analyzer can be seen
in the lower left part, the laser system in the background.
The hemispherical energy analyzer PHOIBOS 100 (SPECS GmbH, Berlin)
equipped with a 2D-CCD imaging-detector allows for measuring the intensity
of photoemitted electrons within a sizeable range of emission angles
and kinetic energies at the same time. By introducing a time delay
between the pump and probe pulses, allowqs us to follow the temporal
evolution of the carrier population in surface as well as bulk states.
An important aspect of this experimental setup is that all information
about different electronic states is gathered within one image. There
we can analyze the lifetimes of different states very precisely with
a relative temporal resolution of only a few femtoseconds. As an example
we show a spectrum of the Cu(111) surface in Fig. 2. The 2PPE pump-probe
measurements of the n=0 Shockley surface state, and the n=1 and n=2
image-potential states in Fig. 3 highlight the potential of the set-up
resolving ultrafast dynamics at surfaces.

Fig.2: Left: Schematic of the
Cu(111) projected bulk-band structure including the occupied Shockley
surface state (SS) and the first two image-potential states n=1
and n=2. Right: Energy- and angle-resolved 2PPE-intensity of the
Cu(111) surface at zero pump-probe delay.

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Fig.3: Time-resolved
measurements of the regions marked in Fig. 2 by colored squares.
The red curve gives the cross-correlation of pump and probe
pulses. The shift of the blue and green traces correspond
to the lifetimes of n=1 and n=2 image-potential states, respectively.
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A very recent experiment was performed on the Si(100)
surface. Tuning the photon energy of the pump pulse between 4.5
and 5.4 eV unoccupied states up to the Si(100) vacuum level are
populated, e.g. the image-potential states n=1 and n=2 in Fig. 4.

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Fig. 4: Surface projected
bulk-bandstructure close to the Γ – point of the surface
Brillouin zone, in- cluding the surface states Dup
and Ddown and image-potential states n=1 and n=2
of Si(100).
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Our measurements corroborate the existence of the Rydberg-like series
of image-potential states on the semiconducting silicon surface. Figure
5 shows the first two image-potential states at zero time delay (Td=0
fs) between pump and probe pulses. For Td > 100 fs n=3
and n=4 states are resolvable, due to the longer lifetimes of the
higher image-potential states.
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Fig. 5: 2PPE-intensity
as a function of the kinetic energy of the photoemitted electrons.
For zero delay time between pump and probe pulses n=1 and
n=2 image-potential states can be seen. For increasing delay
Td the n=3 and n=4 image-potential states are observed.
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As we tune the pump-pulse photon-energy across the
Dup to n = 1 and Dup to n = 2 transitions,
significant variation of both the 2PPE peak positions and intensities
are seen (Fig. 6). Below resonance we observe the Dup
initial state with the kinetic energy following the pump-pulse photon-energy.
Above resonance the Dup intensity is significantly reduced
and the peak position reflects the respective image-potential-state
resonances. Around the resonance the lowering in energy of the expected
peak position and the intensity variations can be explained by a
Fano-like resonance, caused by interference between transitions
from Dup to the discrete image-potential-state resonances
and the bulk states of the silicon conduction band.
Fig.6a: False color representation
of the Si(100) 2PPE intensity as a function of pump-pulse photon-energy.
The photon energy of the probe pulse ionizing the system at zero
delay time is kept constant. b: Kinetic
energy of the intensity maxima in a. For the Dup to n=1 and n=2
transitions a clear shift of the maximum to photon energies below
those expected from the kinetic energies of the n=1 and n=2 intermediate
states is observed. This shift and the negligible intensity after
resonance indicate a Fano-like interference. c: Measured
intensity along the inital-state energy (red solid line in b.) and
simulated Fano-profile for q=-3.4.
In future experiments we plan to compare electron
dynamics at silicon and germanium surfaces.
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