Ph. D. Thesis – G. Caretto
function of experimental controlled parameters, like the target material, its superficial
morphology, the accelerating voltage, the wavelength and the fluence of the used laser.
During the thesis work, this phenomenon was studied by means of three excimer
UV lasers of short wavelengths: KrF at 248 nm, XeCl at 308 nm and KrCl at 222 nm
wavelength; regarding to the materials used like cathodes in the experiments, they
were mostly yttrium and zinc.
To comprehend the processes concerning the photoemission it is necessary to
develop a fine electron-beam extraction system. It is important to find if, changing the
experimental conditions, there is a real possibility to increase the number of the
extracted electrons from metal target. In particular, the surface morphology variations
of the cathode and its influence on the charge yield were analyzed.
Samples with natural and induced surface roughness were examined. Micro
superficial irregularities were simply created and their effect on photoemission process
studied in detail.
Using a fast oscilloscope the pulsed current signals and the incident laser
waveforms were recorded; measurements and analyses have been carried out on
photo-emitted current, temporal quantum efficiency, electron spatial distribution, and
temporal behavior under laser action.
Moreover, a theoretical model has been formulated, which allows one to estimate
the results for a real surface profile and to predict the current and the efficiency for
particular morphologies that will be realized and used in the future.
To confirm the performed calculations, simulation code OPERA 3D was used.
Using this one it is possible to plan the anode-cathode gap and to let the different
4
Ph. D. Thesis – G. Caretto
voltages on the surfaces; starting the estimation process, several experimental
parameters were evaluated and confronted with the real ones.
Future work could be the realization of finer superficial roughness, one-two order
lower, hoping to increase more and more the electron-beam intensities.
In the Chapter 1 there is the development of the equations that govern the electron
photoemission process. In particular, thermionic emission, field-effect emission and
photo-emission will be treated; the reduction of the work function of the metal
(Schottky effect) plays a fundamental role in the photocurrent calculation.
In the Chapter 2 the whole experimental apparatus is described in details: the
vacuum chamber, the targets, the diagnostic system, and the way to record the laser
and current pulses. Complete description of the characteristics of excimer lasers are
made: the active medium, the laser chamber, the pumping systems used, the duration
and the shape of the laser pulses.
In the Chapter 3 the experimental results concerning the efficiency and the
photocurrent for different metal targets, irradiated by different excimer lasers are
reported.
In the Chapter 4 a theoretical model and an electronic simulation of an extraction-
acceleration system is presented. Choosing appropriate parameters, it is possible to
correlate the results obtained to the ones carried out from the experimental
measurements, in order to confirm the given interpretation of phenomena that govern
the photoemission process.
5
Ph. D. Thesis – G. Caretto
In the Chapter 5 there is a discussion of all the results and a comparison between
different types of cathodes (changing work function, thickness, and superficial
morphology) and different laser wavelength.
Furthermore, during the Ph. D. course several publications on paper and
proceedings for conferences participations have been made:
I. F. Belloni, G. Caretto, A. Lorusso, V. Nassisi, M.V. Siciliano, “Photo-emission studies
from Zn cathodes under plasma phase”, Radiation Effects and Defects in Solids, 160, p
587-594, 2005.
II. G. Caretto, D. Doria, V. Nassisi and M.V. Siciliano, “Photoemission studies from metal
by UV lasers”, Journal of Applied Physics, 101, 73109-73116, 2007.
III. G. Caretto, L. Martina, V. Nassisi, M.V. Siciliano, “Behavior of photocathodes on
superficial modification by electrical breakdown”, Nuclear Instruments and Methods B,
2007 (in press).
IV. G. Caretto, L. Martina, V. Nassisi and M.V. Siciliano, “Temporal behavior of
photoemission for Yttrium cathodes” Radiation Effects and Defects in Solids, 163,
2008.
V. G. Caretto, P. Miglietta, V. Nassisi, A. Perrone and M.V. Siciliano, “Photoelectron
performance of Y thin films and Y smooth bulk”, Radiation Effects and Defects in
Solids, 163, 2008.
VI. F. Belloni, G. Caretto, A. Lorusso, V. Nassisi, A. Perrone and M.V. Siciliano, “Photo-
emission studies from Zn cathodes under plasma phase”, PPLA II, Giardini Naxos,
Catania, Italy, June 8-11, 2005.
VII. F. Belloni, G. Caretto, D. Doria A. Lorusso, V. Nassisi, A. Perrone, M.V. Siciliano,
“Studio dell’evoluzione temporale dell’efficienza quantica di un fotocatodo metallico”,
XCI Congresso Nazionale SIF, Catania, Italy, September 26 - October 1, 2005.
VIII. V.Nassisi, G.Caretto, A.Lorusso, D.Doria, F. Belloni and M.V.Siciliano, “Temporal
quantum efficiency of a micro-structured cathode”, EPAC 06, Edimburgh, Scotland,
June 26-30, 2006.
IX. D. Doria, F. Belloni, A. Lorusso, G. Caretto, V. Nassisi and M.V. Siciliano, “Plasma
influence on photoemission from metal by UV lasers”, ESCAMPIG XVIII, Lecce, Italy,
July 12-15, 2006.
6
Ph. D. Thesis – G. Caretto
X. F. Belloni, G. Caretto, D. Doria, A. Lorusso, V. Nassisi, P. Espositivo, V. Nicolardi,
“Compressori di corrente e tensione e nuovi circuiti di amplificazione con linee di
trasmissione”, XCII Congresso Nazionale SIF, Torino, Italy, September 18-23, 2006.
XI. G. Caretto, L. Martina, V. Nassisi and M.V. Siciliano, “Temporal behavior of
photoemission for Yttrium cathodes”, PPLA III, Scilla, Reggio Calabria, Italy, June 14-
16, 2007.
XII. G. Caretto, P. Miglietta, V. Nassisi, A. Perrone and M.V. Siciliano, “Photoelectron
performance of Y thin films and Y smooth bulk, PPLA III, Scilla, Reggio Calabria, Italy,
June 14-16, 2007.
XIII. G. Caretto, V. Nassisi, M.V. Siciliano, “Role of plasma in temporal behaviour for Y
cathodes”, ICPIG XXVIII, Praga, Czech Republic, July 15-20, 2007.
XIV. G. Caretto, V. Nassisi and M.V. Siciliano, “Electron emission performance of yttrium
cathodes by UV lasers”, HEP 07, Manchester, England, July 19-25, 2007.
XV. G. Caretto, L. Martina, V. Nassisi and M.V. Siciliano, “Behavior of photocathodes on
superficial modification by electrical breakdown”, ECAART IX, Firenze, Italy,
September 2-5, 2007.
XVI. G. Caretto, P. Miglietta,
V. Nassisi, A. Perrone, M.V. Siciliano, “Studio di
fotoemissione da catodi di ittrio”, XCIII Congresso Nazionale SIF, Pisa, Italy,
September 24-29, 2007.
7
Ph. D. Thesis – G. Caretto
1 Electron emission from metals
____________ ____________
1.1 Introduction
In this chapter the fundamental physical laws that govern the electron emission
from solids and, in particular, from metals are presented. In details, thermionic effect,
field effect and photoelectric effect will be discussed and analyzed; Schottky effect
will be considered, being it responsible of tangible variations of the extracted electrons
number.
1.2 Metals properties
According to the “free electron model” [1], it is possible to consider the external
electronic shells of metal atoms like free fermions gas. In fact, these ones can move in
the whole solid and feel less the interaction with the nuclei, because of the shield effect
due to the internal shells. Macroscopically, one can suppose that the metal forms an
almost equipotential structure for the conduction electrons, that suffer only little
8
Ph. D. Thesis – G. Caretto
perturbations of their free path, because of interactions with the lattice ions and the
others electrons. In this model the electron energy is due simply to its kinetic energy
and it is feasible to think the metal like a potential hole deep E
s
: the electron is able to
leave the metal surface if its kinetic energy is greater than E
s
(figure 1.1).
The free electron energy distribution ),( TEρ is defined like the electron number
for energy unit and for volume unit at T temperature. The knowledge of this quantity is
important because allows to establish if inside of the metal there are fermions able to
overcome the potential barrier.
Figure 1.1 - Schematic representation of the potential hole in the free-electron model.
E
s
is the minimum energy necessary for electron to get out from the metallic surface,
φ
0
is known like the metal work function.
By quantum calculation, being the electron a half integer spin particle (fermion),
one can write the energy distribution as
( ) ( ) ( )TEfENTE ,, =ρ (1.1),
where is the state density and ()EN ( )TEf , is the Fermi-Dirac distribution, namely
the probability that a fermion has got energy E at the temperature T ; all the energy
values have to be referred to the bottom of the potential hole.
9
Ph. D. Thesis – G. Caretto
The expression for the Fermi-Dirac distribution is
Tk
EE
F
e
TEf
−
+
=
1
1
),( (1.2),
where k is the Boltzmann constant, T is the solid temperature and E
F
is the Fermi level,
that corresponds to the energetic state that has probability ½. In opposition to the
classical theory, at temperature T = 0 K some electrons may have no-zero energy; this
fact is due to the Pauli Exclusion Principle. For T >0 K the levels with energies higher
than E
F
begin to populate; the level E
F
can be interpreted like the fermionic maximum
energy reached at the absolute zero temperature.
Figure 1.2 - Fermi–Dirac distribution function for different temperature values.
The state density is the number of the electrons per volume unit at fixed energy; it
can be written as
() ()
2
1
2
3
3
2
8
Em
h
EN
π
= (1.3),
10
Ph. D. Thesis – G. Caretto
where m is the electron mass and h is the Planck constant. Utilizing the expressions
(1.2) and (1.3) it has been obtained the final formula for the energy distribution of free
electrons
() ()
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
+
=
−
Tk
EE
F
e
E
m
h
TE
1
2
8
,
2
1
2
3
3
π
ρ (1.4),
as plotted in figure 1.3.
The function ),( TEρ shows a small dependence with the temperature; the only
effect due to the temperature is the changing of the electron concentration in the
neighborhood of Fermi energy from lower to higher energetic levels. E
F
can be
considered like a constant depending on little temperature changing.
Figure 1.3 - State density as a function of the energy for a free electron gas.
One of the most important property for the solids and in particular for the metals is
their work function
Fs
EE −=
0
φ (figure 1.4), defined like the minimum energy
11
Ph. D. Thesis – G. Caretto
necessary for an electron to overcome the potential barrier at 0 K temperature. It is of
the order of few eV and depends on the material that composes the solid.
(a) (b)
Figure 1.4 - (a) State density for two different values of temperature.
(b) Potential wall onto the metal surface.
The work function is not fixed; it depends on the roughness and on the presence of
imperfections in the crystal lattice. It plays a fundamental role in the phenomena
correlated to the emission of electrons from the surface of a solid: photoemission,
thermionic effect, field emission or electron transfer from a metal to the other (contact
potential).
1.3 Thermionic emission
This process allows to get electrons by increasing the target temperature. In this
way the (TE, )ρ function assumes high values for E > E
F
and electrons can leave the
metal surface.
12
Ph. D. Thesis – G. Caretto
Also for temperatures near to the melting point of metal (~ 10
3
K) few electrons are
extracted, therefore at room temperature (≅ 300 K), the probability that an electron is
able to rise above the potential barrier is very low.
The expression for the current density by thermionic emission is
Tk
o
e
h
Tkem
J
0
3
22
4
φ
π
−
=
(1.5).
If one lets
120
4
3
2
≈=
h
kem
A
π
⎥
⎦
⎤
⎢
⎣
⎡
22
Kcm
A
,
the equation (1.5) can be simply written as
Tk
o
eATJ
0
2
φ
−
=
(1.6),
well known like Dushman–Richardson equation [2].
The space-charge effect in the area of emitted electrons is the primary responsible
of a significant reduction of the current density for all the extraction processes.
The (1.6) formula is effective in the saturation regime, namely the state with high
electric fields applied, in order to annihilate the space-charge effect.
13
Ph. D. Thesis – G. Caretto
1.4 Schottky effect
If an external electron is near a metallic surface connected to the ground, the metal
polarizes itself and induces attractive forces on the electron. Until the distance z
electron-surface is greater than the interatomic dimension, image charge method can
be used in order to calculate its potential energy [3]
z
e
V
img
4
2
−= (1.7),
represented by AB curve plotted in figure 1.5.
The model proposed by Schottky supposes that this potential energy is valid for
distances z > z
o
, assuming a constant force for 0 < z < z
o
, where z
0
is a critical
distance, function of the material; in this region the potential energy of the electron is a
linear function of z (CA line in figure 1.5).
Figure 1.5- Surface potential wall for field-effect.
14