Generation, Characterization and Applications of Femtosecond Electron … · 2014-01-22 · Abstract Generation, Characterization and Applications of Femtosecond Electron Pulses Christoph

Generation, Characterization and Applications of

Femtosecond Electron Pulses

by

Christoph Tobias Hebeisen

A thesis submitted in conformity with the requirementsfor the degree of Doctor of Philosophy

Graduate Department of PhysicsUniversity of Toronto

Copyright c© 2009 by Christoph Tobias Hebeisen

Abstract

Generation, Characterization and Applications of Femtosecond Electron Pulses

Christoph Tobias Hebeisen

Doctor of Philosophy

Graduate Department of Physics

University of Toronto

2009

Ultrafast electron diffraction is a novel pump-probe technique which aims to determine

transient structures during photoinduced chemical reactions and other structural tran-

sitions. This technique provides structural information at the atomic level of inspection

by using an electron pulse as a diffractive probe. The atomic motions of interest happen

on the 100 fs = 10−13 s time scale. To observe these atomic motions, a probe which

matches this time scale is required. In this thesis, I describe the development of an

electron diffractometer which is capable of 200 fs temporal resolution while maintaining

high signal level per electron pulse. This was made possible by the construction of an

ultra-compact photoactivated 60 keV femtosecond electron gun.

Traditional electron pulse characterization methods are unsuitable for high number

density femtosecond electron pulses such as the pulses produced by this electron gun. I

developed two techniques based on the laser ponderomotive force to reliably determine

the duration of femtosecond electron pulses into the sub-100 fs range. These techniques

produce a direct cross-correlation trace between the electron pulse and a laser pulse. The

results of these measurements confirmed the temporal resolution of the newly developed

femtosecond electron diffractometer. This cross-correlation technique was also used to

calibrate a method for the determination of the temporal overlap of electron and laser

pulses. These techniques provide the pulse diagnostics necessary to utilize the temporal

ii

resolution provided by femtosecond electron pulses.

Owing to their high charge-to-mass ratio, electrons are a sensitive probe for electric

fields. I used femtosecond electron pulses in an electron deflectometry experiment to

directly observe the transient charge distributions produced during femtosecond laser

ablation of a silicon (100) surface. We found an electric field strength of 3.5 × 106 V/m

produced by the emission of 5.3×1011 electrons/cm2 just 3 ps after an excitation pulse of

5.6 J/cm2. This observation allowed us to rule out Coulomb explosion as the mechanism

for ablation under the conditions present in this experiment.

iii

Acknowledgements

I would like to thank my research supervisor R. J. Dwayne Miller for his boundless

enthusiasm for science, his creativity and his optimism. He has been a constant source of

motivation and energy for the work that led to this thesis. His insistence to aim for the

impossible has been my driving force to explore the limits of the possible throughout my

years at the University of Toronto. In this process, I very much appreciated the freedom

Dwayne gives his students to develop their own ideas and to perform their research in a

largely self-directed manner.

Bradley J. Siwick, Jason R. Dwyer and Robert E. Jordan laid the foundations of

femtosecond electron diffraction in the Miller group. It was a privilege to work along-

side them; their ideas and their theoretical and experimental work provided the basis

from which I started my research. I spent countless hours discussing setups, performing

experiments and puzzling over data with Maher Harb, Ralph Ernstorfer and German

A. Sciaini. Their expertise was essential and it has been a pleasure working with them.

I would also like to thank John E. Sipe and Ania M. Michalik from his research group

for many helpful discussions about the dynamics of femtosecond electron pulses.

A large part of my work involved building apparatus for ultrafast electron diffraction

experiments. John Ford, Johnny Lo, Ahmed Bobat and David Heath produced precise

and beautiful pieces and provided helpful suggestions and modifications to my drawings.

I want to thank my parents for teaching me the value of knowledge and education and

for ensuring that I could always live comfortably throughout my university education.

Last but most importantly, I would like to thank my beloved wife Sadia A. Khan for

her unwavering support, her encouragement and most of all for her patience, which has

– no doubt – been taxed heavily during the writing of this thesis.

iv

Contents

1 Introduction 1

2 The Electron Diffractometer 11

2.1 Optical Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 Ultra-Compact Femtosecond Electron Pulse Source . . . . . . . . . . . . 14

2.2.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.2 The Photocathode . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.3 Electron Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2.4 Beam Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.3 Sample Manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.4 Electron Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.5 Vacuum Chamber Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3 Characterization of Femtosecond Electron Pulses 37

3.1 Laser Pulse-Electron Pulse Temporal Overlap Determination . . . . . . . 42

3.2 Laser Pulse-Electron Pulse Cross-Correlation . . . . . . . . . . . . . . . . 45

3.2.1 Experimental Setup for the Laser Pulse-Electron Pulse Crosscor-

relation Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.2.2 Results and Data Analysis . . . . . . . . . . . . . . . . . . . . . . 51

3.2.3 Calibration of the Temporal Overlap Determination . . . . . . . . 57

v

3.2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.3 Grating Enhanced Ponderomotive Scattering for Characterization of Fem-

tosecond Electron Pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.3.1 Grating Enhanced Electron Pulse Characterization Setup . . . . . 63

3.3.2 Results and Data Analysis . . . . . . . . . . . . . . . . . . . . . . 67

3.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4 Femtosecond Electron Deflectometry 76

4.1 Experimental Setup for the Observation of Transient Charge Distributions 79

4.2 Experimental Results and Analysis . . . . . . . . . . . . . . . . . . . . . 81

4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

5 Future Directions 94

Bibliography 97

vi

List of Figures

1.1 Demonstration of the effect of the probe pulse duration . . . . . . . . . . 4

2.1 Optical setup of an electron diffraction experiment . . . . . . . . . . . . . 13

2.2 Principle of a DC femtosecond electron gun . . . . . . . . . . . . . . . . 15

2.3 Simulated electron pulse shapes . . . . . . . . . . . . . . . . . . . . . . . 19

2.4 Simulated pulse durations for different electron gun configurations . . . . 20

2.5 Performance of the magnetic lens . . . . . . . . . . . . . . . . . . . . . . 28

2.6 The femtosecond electron pulse source . . . . . . . . . . . . . . . . . . . 31

2.7 The vacuum chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.1 Principle of a streak camera . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2 Laser pulse-electron pulse temporal overlap measurement . . . . . . . . . 43

3.3 Simulated electron beam images after scattering by a laser pulse . . . . . 49

3.4 Setup of the laser pulse-electron pulse crosscorrelation experiment . . . . 50

3.5 Electron pulse characterization beam images . . . . . . . . . . . . . . . . 52

3.6 Line profiles through detected electron beam shapes . . . . . . . . . . . . 53

3.7 Electron pulse characterization signal traces . . . . . . . . . . . . . . . . 56

3.8 Calibration of the grid t = 0 measurement . . . . . . . . . . . . . . . . . 58

3.9 Enhancement of the ponderomotive force in a standing wave . . . . . . . 61

3.10 Simulated beam images after grating enhanced ponderomotive scattering 63

vii

3.11 Setup of the grating enhanced electron pulse characterization experiment 64

3.12 Beam images of the grating enhanced electron pulse characterization ex-

periment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.13 Line profiles through beam images of the grating enhanced electron pulse

characterization experiment . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.14 Signal traces of the grating enhanced electron pulse characterization ex-

periment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.15 Laser power dependence of the signal in the grating enhanced electron

pulse characterization experiment . . . . . . . . . . . . . . . . . . . . . . 72

3.16 Experimentally determined electron pulse durations and simulations . . . 74

4.1 Femtosecond electron deflectometry experiment setup . . . . . . . . . . . 79

4.2 Fabrication of the silicon strips . . . . . . . . . . . . . . . . . . . . . . . 80

4.3 Femtosecond electron deflectometry beam images . . . . . . . . . . . . . 81

4.4 Charge distribution model for fitting of the beam images . . . . . . . . . 85

4.5 Measured and calculated probe beam intensity maps . . . . . . . . . . . 89

4.6 Time traces of the fit results . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.7 Probe electron deflection for different laser fluences . . . . . . . . . . . . 92

viii

Chapter 1

Introduction

Nunc age, quo motu genitalia materiai

corpora res varias gignant genitasque resolvant

et qua vi facere id cogantur quaeque sit ollis

reddita mobilitas magnum per inane meandi,

expediam: tu te dictis praebere memento. 1

Lucretius, De Rerum Natura 2:62-66

The concept that all matter is made up of small particles or “atoms” (�tomon = indi-

visible) was developed in the framework of religious and natural philosophies in ancient

India and Greece. The mythical founder of the V aise˙sika system of Hindu philosophy

Ka˙nada (possibly “atom eater”), who lived somewhere between the 6th and 2nd cen-

turies BC, taught that atoms exist, are spherical and have no cause [1]. Democritus

(Dhmìkrito ) of Abdera (*460 BC) and his teacher Leukippus (LeÔkippo ) of Miletus

thought that only atoms and the void are real and that different macroscopic substances

could be explained by different shapes and arrangements of the atoms [2]. Democritus’

atoms are solid without any internal structure. They are in constant motion and can

undergo “chemical reactions” when they collide, by forming clusters when hooks that

1“Now then, I will explain through which motion the seeds of substance produce the different thingsand dissolve the produced, further by what force they are compelled and through which vessels each isgiven the speed to travel through the vast void: remember to live by these words.”

1

Chapter 1. Introduction 2

they carry on their surface get entangled [3].

These early atomistic views were not supported by observations of any effects related

to actual atoms and even made some untenable assertions (e.g. the lack of internal struc-

ture), yet the basic concept of matter consisting of discrete particles inspired modern

atomism and is still valid even though the limits of what is considered indivisible have

shifted. In the early 1800s, John Dalton published his observation that in chemical re-

actions, elements combine in certain fixed proportions. He was able to derive atomic

weights in relation to hydrogen from these observed proportions [4]. This is generally

seen as the beginning of modern atomic theory, which underlies all modern natural sci-

ences and applied science and has become a pervasive scientific concept – even outside of

academia. Computer-generated renderings of ball-and-stick models of complex biological

molecules have become a staple not only in scientific publications but also in the science

section of newspapers, providing a concrete and intuitive (as well as aesthetically pleas-

ing) illustration to experts and laypeople of what a molecule or crystal structure “looks

like”.

The static structures of crystalline matter and of many molecules – even very large

ones – are known from electron diffraction, x-ray diffraction or nuclear magnetic reso-

nance spectroscopy. Crystal structures can also be observed by transmission electron

microscopy (TEM), and scanning tunnelling microscopy (STM) allows the detection of

even single atoms on a surface. Despite the seeming ease of observing atomic structure

and locating even single atoms, none of these techniques allows the observation of atomic

structure at arguably the most interesting time, i.e. during a chemical reaction in real

time. This limitation is mostly due to the timescales involved in structural changes on

the atomic level. Chemical bonds are made or broken on the timescale of 100 fs, the

approximate time it takes two atoms to move far enough apart to break a bond, or the

periods of the most highly damped motions along structural relaxation coordinates [5].


The time it takes to obtain structural data from any of the above-mentioned methods is

on the order of seconds to milliseconds at best, which is many orders of magnitude larger

than the timescale required to resolve motions involved in structural changes.

In order to record the progress of any process, one usually obtains a series of “snap-

shots”. These snapshots can be literal images (e.g. in the case of video rate microscopy),

or a single or multiple observables (e.g. reflectivity or absorptivity of a sample) that

are defined for each point in time. Cameras or other detectors fast enough to observe

changes on the 100 fs timescale are not available. However, if the measurement of a

quantity involves a “probe” (e.g. the illumination of the sample with a femtosecond laser

pulse), a short pulse probe can be used to obtain the same effect. In the absence of the

probe, the detector (which integrates the signal over a time much longer than the desired

timescale) does not receive any signal. A pulsed probe allows one to obtain a snapshot

of the process at the exact time of the probe pulse. Since the detector is much slower

than the process to be observed, only one snapshot can be taken at a time. To obtain

the time-series, the measurement has to be repeated many times with different delays

between the initiation of the process and the probe pulse. The initiation of the process

is accomplished by another pulse called the “pump” pulse. Hence, techniques based on

this principle are called time-resolved pump-probe techniques.

The duration of the probe pulse fundamentally limits the temporal resolution of any

pump-probe technique. Since the detector integrates the observable of interest over the

duration of the probe pulse, the measured quantity does not reflect the state of the

observed system at one point in time but its average state over the duration of the probe

pulse weighted with the intensity profile of the probe. This is analogous to the shutter

speed of a camera when trying to obtain a picture of a moving object (Fig. 1.1).

Since only one snapshot can be taken at a time, the experiment has to be repeated

for every time step. Beyond that, every time step may require multiple pump-probe


Figure 1.1: The probe pulse duration in a pump-probe experiment is analogous to the

shutter speed of a camera; when a changing state is recorded, the result is integrated

over the duration of the probe pulse / exposure time, respectively. The progress of the

state during the exposure time cannot be resolved. This becomes clear when comparing

these images. The left image was taken with a shutter speed of 1/80 s compared to 1 s

in the right image. The duration of a measurement causes an uncertainty in the position

measurement of moving objects.

cycles or “shots” in order to acquire enough signal. Hence, the number of pump-probe

cycles the sample has to undergo is the product of the number of time steps and the

number of shots needed to obtain a single measurement. This makes sample reversibility

an important consideration for pump-probe experiments. If the sample is fully reversible,

i.e. it can go through an arbitrary number of pump-probe cycles without changing any

of its properties, this is not a major concern. However, many if not most interesting

processes are not reversible or not fully reversible. Additionally, the probe pulse can

also damage the sample in some cases. Even transitions we normally consider reversible

may not be reversible for the purpose of these experiments. As an example, consider the

melting of a metal as a transition. While the metal will resolidify, there is no guarantee

that it will do so in the same crystal structure and shape. Since the available amount of


sample is often limited, it is important to maximize the signal that can be acquired with

a single shot, ideally to the limit where no integration beyond a single shot per time step

is necessary.

Laser pulses in the femtosecond range are now readily available and have been used

extensively to probe chemical reactions in a time-resolved manner. The wavelength of

the light used in these experiments is three orders of magnitude longer than typical

interatomic distances so atomic structure cannot be probed directly by optical means.

Spectroscopic methods can yield information about the potential energy surface in the

vicinity of a transient configuration; however, in all but a few relatively simple cases [6],

the atomic structure of the sample cannot be inferred from this information. Hence, if

we want to fully understand conformational changes on the atomic level, it is necessary

to combine the spatial resolution of a diffraction technique with the temporal resolution

of ultrafast optical spectroscopy. Both x-ray diffraction and electron diffraction can in

principle be used to achieve this aim. In the last few years, enormous strides have

been made in making such experiments possible, using ultrafast laser excitation pulses

to trigger structural changes and either x-ray or electron probes to follow the induced

atomic motions [7, 8, 9, 10, 11].

X-rays, as a form of electromagnetic radiation, almost exclusively interact with the

electrons of an atom making x-ray diffraction a probe of the electron density of the

sample. Electrons, on the other hand, are scattered by the electric potential in the

sample, which is formed by both the electrons and the nuclei. While x-ray diffraction is

by far the more prevalent technique for static structure determination, both can and have

been used successfully to determine structures. There are some important differences

[12] in the way x-rays and electrons interact with a sample. The elastic mean free

path for 1.5 A x-ray photons is 105 − 106× longer than for 80 − 500 keV electrons. In

transmission geometry, this means that solid samples for electron diffraction must be


thinner by this factor than samples for x-ray diffraction. This can be both an advantage

or a disadvantage depending on the affinity of the sample to form thin films or “large”

(≥ 10 µm) crystals, respectively. In experiments that involve an excitation beam, thin

samples are advantageous since it is easier to illuminate them evenly and thereby to obtain

even excitation conditions throughout the probed volume. Even metals, usually thought

of as completely opaque for visible light, have skin depths longer or roughly the same as

the thickness of thin film samples used in transmission electron diffraction (on the 10 nm

scale) for 10 − 100 keV electrons. On the other hand, ultrafast x-ray diffraction with its

thicker samples may suffer from “contamination” of the desired diffraction pattern from

the excited sample with the diffraction pattern of non-excited parts of the sample. This

so-called ground-state contamination must be subtracted from the recorded patterns,

decreasing the signal-to-noise ratio (SNR). Due to the large scattering cross-section,

electron diffraction is also naturally more suitable for low-density, i.e. gas-phase, samples

[13].

Both electrons and x-ray photons can scatter elastically (coherently) or inelastically

(incoherently) from the sample. While elastically scattered electrons / photons form the

diffraction pattern, inelastic scattering leads to a mostly featureless background. Also,

inelastic scattering events deposit much more energy into the sample than elastic scat-

tering events, leading to sample deterioration. The ratio of elastic vs. inelastic scattering

events is about three times higher for electrons while the deposited energy per inelas-

tic scattering event is 1000 times higher in the case of x-rays [12]. Sample damage of

biological specimens during x-ray diffraction is a well-known issue.

Ultrashort x-ray pulses can be generated in a number of different ways. Synchrotrons

produce very bright x-ray pulses in the 100 ps range. While these pulses have been used

for dynamic structure determination [14], they are three orders of magnitude longer than

the timescale of interest. Shorter pulses can be produced by so-called femtoslicing [15], at


the cost of the number of x-ray photons. This compromises the main advantage of syn-

chrotron sources, their brightness. Laser plasma sources [16] generate x-rays by focusing

a femtosecond high-intensity laser onto a solid. Fast electrons generated in the resulting

plasma produce x-rays by bremsstrahlung when they hit the solid sample and eject inner

shell electrons of the atoms in the target plasma, giving rise to characteristic-line radi-

ation [17, 18]. While laser plasma x-ray sources have been built using table-top lasers,

sources capable of producing a sufficient number of photons per pulse to follow structural

changes in x-ray diffraction require terawatt lasers [19]. Accelerator-based x-ray sources

[8] are capable of reaching 100 fs time resolution. These will be superseded by x-ray

free electron lasers, which are currently under construction in multiple countries. The

necessary accelerators are kilometres long and require enormous investments in infras-

tructure and personnel. Current free electron laser demonstration facilities operate at

variable wavelengths down to a minimum of 17 nm [20], which is too long for atomic-level

structure determinations.

Femtosecond electron pulses for electron diffraction are currently produced by laser-

driven DC electron guns. In these electron guns, the electron pulse is created via the

photoelectric effect when a laser pulse hits a metal photocathode. The photocathode

is biased at a high negative voltage and mounted across from a grounded anode. The

electrons are accelerated by the electric field between the cathode and the anode. Since

the electrons repel each other by Coulomb interaction, the pulse inevitably spreads lat-

erally and along the propagation direction as it propagates towards the sample. In order

to minimize the duration of the electron pulses, either the time between the generation

of the electron pulse and its interaction with the sample or the number of electrons per

pulse need to be minimized [21]. The reduction of the number of electrons is not desirable

because of the proportional reduction in useful signal. Hence, we have minimized the

pulse propagation distance to produce short, high electron number pulses. Currently,


systems are being developed that use radio frequency (RF) acceleration and compression

schemes [22] to counteract space charge broadening of the electron pulse. These systems

hold the promise to produce electron pulses containing 105 electrons in a pulse below

100 fs.

The main advantage of ultrafast electron diffraction over ultrafast x-ray diffraction is

that UED experiments are table-top experiments and can be operated using an off-the-

shelf chirped-pulse-amplified laser system. Compared to x-ray diffraction setups, they

deliver better value and they can be financed, built, and operated by a single research

group.

The first photoactivated electron gun for electron diffraction was built by Williamson

and Mourou [23, 24] from a modified streak camera. This setup produced about 100 ps

electron pulses and used a thin film solid sample. The setup of Ischenko et al. [25]

used a molecular beam as a sample for time resolved electron diffraction, which is very

practical as it provides a steady stream of fresh sample, avoiding reversibility issues.

This concept was also adopted by others [26, 27], although it became clear early on

that the time resolution of this technique would be limited to the picosecond regime by

the velocity mismatch between the electron beam and the laser beam [28]. Ultrafast

RHEED (reflection high energy electron diffraction) [29, 30, 31, 32] suffers from a very

similar limitation to its time resolution, which has only recently been addressed by using

tilted wavefronts for the excitation laser [33]. However, even with this improvement in

the time resolution of ultrafast RHEED, sub-picosecond time resolution has yet to be

demonstrated. Since the first UED experiment with sub-picosecond resolution [7], the

UED experiments with the highest time resolution have all been conducted on thin-film

samples with transmission electron diffraction [34, 35, 36].

Our approach to reducing the electron pulse duration has been to reduce the size of

the electron gun to minimize the electron pulse propagation time. This concept led to


the first compact electron gun for UED [21], which allowed for a useful time resolution

of ≈ 600 fs [37]. In chapter 2 of this thesis, I report on the design and construction of an

improved electron diffractometer with an ultracompact electron gun to replace this setup.

The design goals were shorter, more intense electron pulses; better sample handling; and

simpler, more reliable operation.

Since its commissioning, the femtosecond electron diffractometer has been used for

the following UED studies:

• Photo-induced bond-hardening under strong excitation in gold [38]. Un-

der femtosecond illumination, the electrons in a material reach very high tempera-

tures before equilibration with the lattice is reached. While this excitation leads to

softening in most materials, lowering the melting threshold, the rate of disordering

was found to be retarded in gold. This is evidence of increased lattice strength at

high electronic temperatures, as predicted in recent theoretical work [39, 40].

• Carrier relaxation and lattice heating dynamics in silicon [35]. Electron-

phonon relaxation was observed at a carrier density of 2.2×1021 cm−3. The process

was found to be strictly thermal at this excitation level and, in agreement with

theoretical predictions and all-optical measurements, carrier screening was observed

to slow the relaxation process significantly.

• Electronically driven melting of silicon [36]. At a carrier excitation level of

more than 6% of the valence electrons (1.2 × 1022 cm−3), the electronic structure

of silicon collapses in less than 500 fs, which is faster than expected for a phase

transition in which the lattice is heated by electron-phonon scattering. While this

transition had been observed with all-optical methods, this study confirmed for the

first time that the lattice actually disorders on this timescale.

• Electronic acceleration of atomic motions and disordering in bismuth [41].


Under strong electronic excitation, the potential energy surface of bismuth changes.

After femtosecond laser excitation, the nuclei are still close to their original position

while their equilibrium positions have shifted. At excitation levels above 4%, the

bismuth lattice was found to disorder non-thermally and in an accelerated manner

due to the modified potential energy surface.

In addition to designing and constructing the electron diffractometer, I developed

and demonstrated two new methods for the characterization of femtosecond electron

pulses based on the laser ponderomotive force [42, 43]. These methods are capable of

performing pulse duration measurements on electron pulses below 100 fs in a well-defined

position along the electron beam propagation direction. They also provide a means to

determine the exact temporal overlap of pump and probe pulses independent of any

material constants. These methods and their application to the performance analysis of

the electron diffractometer are described in chapter 3.

I also used femtosecond electron pulses to detect and map the transient electric fields

produced during laser ablation from a solid surface on the sub-picosecond timescale [44].

This new technique delivers insights into the earliest stages of femtosecond laser ablation

and plasma generation. This work is described in the final chapter of this thesis.

Chapter 2

The Electron Diffractometer

The obvious design goals for a femtosecond electron diffractometer are to produce high

quality diffraction patterns with the highest time resolution in as few shots as possible.

It is clear that Coulomb repulsion between the electrons automatically leads to temporal

broadening if the number of electrons is increased under otherwise identical conditions.

Hence, there is an obvious trade off between the temporal resolution and the amount of

signal that can be acquired with one probe pulse. By reducing the time the electron pulse

takes from its birth at the photocathode until it reaches the sample, an improvement can

be reached in this tradeoff. However, this gain comes at the cost of beam quality because

a shorter cathode-to-sample distance constrains the placement of beam-forming elements

such as a magnetic lens for collimating the beam. One of the main challenges in the

design was to find workable solutions for these tradeoffs that did not compromise the

functionality of the setup.

Many features were introduced in this setup to address specific problems that were

encountered in the practical operation of the previous setup [37]. In some instances, I

will elaborate on these problems to make certain design features more transparent. The

current electron diffraction setup has undergone a large number of small, evolutionary

11

Chapter 2. The Electron Diffractometer 12

changes from my original design. Unless otherwise stated, I am referring to the latest

state of the setup.

2.1 Optical Setup

The optical setup of the electron diffractometer is shown in Fig. 2.1. The laser pulses

are produced by a chirped pulse amplified laser system (not shown). The seed laser is a

mode-locked erbium fibre laser (λ = 1550 nm, 180 fs pulse duration, 40 MHz repetition

rate). The output of the fibre laser is frequency doubled to 775 nm by a periodically poled

lithium niobate (PPLN) crystal and stretched. The stretched pulse is then amplified by

a Ti:sapphire (titanium sapphire) regenerative amplifier, which is pumped by an intra-

cavity doubled, Q-switched, flash lamp pumped Nd:YAG (neodymium-doped yttrium

aluminium garnet) laser, operating at 1 kHz. The amplified pulse is then compressed

into a 200 fs, 700 µJ pulse. To facilitate single or few shot measurements, the regenerative

amplifier can also be operated at lower repetition rates, down to single shot mode.

The laser pulse is split into a pump arm and a probe arm. The pump arm first

traverses a λ/2 wave plate that controls the linear polarization of the laser beam. In

combination with a polarizing beam splitter, the wave plate provides control over the

pulse energy in the pump arm. The setup shown in the figure is the case of a frequency-

doubled (388 nm) pump pulse. The specific wavelength of the pump pulse depends on

the sample and can be changed using a combination of nonlinear optical subsystems. For

the illustrated case, the second harmonic is produced by a BBO crystal cut for type I

doubling of 775 nm light. Some experiments have also used the fundamental wavelength

in which case the BBO crystal would be removed. The addition of a noncollinear optical

parametric amplifier (NOPA) in the pump arm to obtain tunable wavelength and shorter

laser pulses has been planned as a future modification of the setup. The pump beam is


NOPA

Harmonicseparators

Delayrail

ShutterBeam dump

Shutter

BBOPrism compressor

BS

PBS775 nmµ700 J

200 fs

500 nm50 fs

Vacuum pump

Vacuum pump

−55 kV

Electron gunSample

λ/2

Variableattenuator

Figure 2.1: Optical setup of an electron diffraction experiment. BS = beam splitter; λ/2

= half wave plate; PBS = polarizing beam splitter; BBO = b-barium borate crystal (cut

for frequency doubling).

focused by a lens mounted on a three axis translation stage outside the vacuum chamber.

Translation of the lens along the laser propagation direction can be used to modify the

spot size of the laser on the sample and translation in the lateral directions allows moving

the laser spot on the sample to facilitate the overlap of laser pump and electron probe

beam on the sample.

The laser pulse in the probe arm drives a NOPA that produces a 500 nm pulse,

which is then compressed to 50 fs by a prism compressor. A computer controlled variable


delay stage provides the delay between pump and probe pulse and a variable attenuator

serves to control the number of electrons created per pulse. The laser pulse for the

probe arm then excites the photocathode to produce the electron pulse via two photon

photoemission.

The placement of the last mirror in the pump arm inside the chamber directing the

pump beam towards the sample is crucial for the temporal resolution of the experiment.

While the electron pulse hits the sample at normal incidence, the laser pulse arrives at an

angle α with the sample surface normal, therefore exciting different parts of the sample

at different times. The broadening effected by the non-normal incidence is τ = we

csinα.

Here, we is the width of the area probed by the electron beam in the plane spanned by

the sample surface normal and the pump beam. Note that α cannot be made arbitrarily

small because the mirror would have to be placed inside the cone of the diffraction pattern

recorded on the detector. Given the size of the detector (4 cm at 20 cm from the sample)

and practical problems such as the size of mirror mounts, in practise α ≈ 8◦. With a

150 µm diameter electron beam, τ ≈ 70 fs. For a 200 fs pump pulse, this causes only

about 6% broadening but for future experiments with shorter pump and probe pulses,

this broadening could become significant.

2.2 Ultra-Compact Femtosecond Electron Pulse

Source

The electron gun is the heart of the electron diffractometer. It is responsible for producing

the electron probe pulses and delivering them to the sample while keeping them as short

as possible. The electron gun also determines the beam quality of the electron beam and

therefore it is a deciding factor in the quality of the diffraction pattern.


Photocathode

Anode

Magnetic lens

E

GND

−V0

Laser pulse Electronpulse

Figure 2.2: Principle of a DC femtosecond electron pulse source.

The basic setup of a DC, photoactivated electron gun is shown in Fig. 2.2. A fem-

tosecond laser pulse hits the thin film photocathode and produces an electron cloud via

the photoelectric effect. The cathode is biased with a negative voltage with respect to

the anode. The resulting electric field between cathode and anode accelerates the elec-

tron pulse towards the anode. After acceleration, the electron beam is collimated by a

magnetic or electrostatic lens before it hits the sample.

2.2.1 Simulations

Space charge broadening of electron pulses is a well-established fact in electron accel-

erators and streak cameras. Intuitively, it acts to broaden the electron pulse in the

longitudinal as well as in the transverse direction. Obviously, the higher the number

density of electrons in the pulse, the stronger the broadening. The force acting on an


electron due to the presence of the other electrons is

~Fn =∑

m 6=n

e2

4πε0 |~rn − ~rm|3(~rn − ~rm) (2.1)

where ~rn is the position of the n-th electron in the pulse. To calculate this force, N − 1

evaluations of the Coulomb force are required for each of the N electrons. Since the force

electron n experiences due to electron m and the force electron m experiences due to

electron n have the same magnitude and opposite directions, the forces inside the pulse

can be calculated in N(N − 1)/2, i.e. O(N2), operations. This leads to computationally

very expensive simulations as the number of particles grows. While there are models that

allow to calculate the evolution of an electron pulse analytically [45] or by solving a set of

differential equations [46] by assuming a continuous charge distribution, these methods

are very pulse-shape specific. Simulations, on the other hand, allow calculations with

arbitrary pulse shapes. The obvious way to make this problem computationally tractable

is to lump the mass and charge of several electrons into a so-called macroparticle at the

position of the centre of mass of the electrons represented by the macroparticle. While the

quantization error introduced by this method may be small for 106 ( 3√

N = 100) particles,

it does not necessarily seem acceptable at 103 − 104 particles where 3√

N = 10 − 22.

The consolidation of multiple charges into one particle is obviously a problem for the

force calculation in the vicinity of the macroparticle. However, for charges that are

much further away than their distances from each other, i.e. that occupy a small solid

angle all at very similar distances, a single particle containing all their charge is a very

good approximation. This approach is taken by the Barnes-Hut tree algorithm [47],

first introduced to calculate N-body problems arising in astrophysics. This algorithm

reduces the computational complexity of the N-body problem to O(N log N) by sorting

the particles into a hierarchical tree of cubic cells. Cells containing multiple particles,

which are sufficiently far away, are represented by a single particle with the total mass and


charge of the particles contained in the cell. The tree is recreated for each integration

step. Thus, the composition of the groups of particles that are lumped together for

the force calculations changes in each step according to the evolution of the system, as

opposed to the fixed groupings imposed by macroparticles. The equations of motion are

then solved by a simple leapfrog integrator. While the code was written for gravitational

forces with gravitational mass equal to inertial mass, a particular choice of units allows

the use of the code with electrical charges, as long as the charge of all of them has

the same sign, once the sign in the force calculation is switched to turn the attractive

gravitational force into the repulsive Coulomb force between electrons [21].

The Barnes-Hut tree code uses classical mechanics without relativistic corrections.

At 55 keV electron energy, the electron velocity is 43% c and γ = 1.108. No attempt was

made to modify the code to accommodate relativistic corrections since such modifications

would have been extensive and would have required rewriting a large part of the code base.

While relativistic effects cause a significant deviation from non-relativistic mechanics at

the electron velocity, the simulations can still serve as a tool for estimating electron

pulse durations; relativistic effects act to slow the spread of the electron pulse, causing

the non-relativistic simulations to overestimate the pulse durations. In recent years,

commercial programs [48] have become available, which treat the N-body problem fully

relativistically.

This Barnes-Hut tree code is useful for calculating the free propagation of the electron

pulse, but in its original form, it is not able to simulate the electron pulse acceleration.

Space charge effects during this time are particularly important because at this time

the electron pulse is most dense. This is partly because at this time the pulse has the

shortest duration, and partly because it is moving much more slowly at the beginning

of the acceleration, i.e. the electron pulse is shorter in space for a given pulse duration.

Together, this leads to higher electron density and increased space charge. To allow the


simulation of an electron pulse in the acceleration region of a DC electron gun, I modified

the force calculation code to add a homogeneous electric field. Since the simulation

proceeds in discrete time steps, a problem arises at the injection into the region with

the field (i.e. at the photocathode) as well as at the anode, where the electrons leave the

electric field. At the photocathode, the electrons of the pulse are “created” at different

times over the duration of the laser pulse but in the same plane. Note that this situation

cannot be emulated by creating an electron distribution in space that mirrors the laser

temporal shape because the electrons at the leading edge have acquired more energy

from the electric field than electrons further behind. In order to construct an electron

distribution that corrects for this problem, we assume that an electron is to be emitted

from the photocathode at t = τ at ~rτ with a velocity of ~vτ while the time step of the

simulation starts at t = 0. Assuming a homogeneous electric field ~E, we get

~r0 = ~rτ − τ~vτ − τ 2 e

2me

~E and ~v0 = ~vτ + τe

me

~E (2.2)

for the position ~r0 and velocity ~v0 at t = 0 (note that e is the elementary charge i.e. the

charge of an electron is −e). Space-charge was disregarded in this calculation. An infinite

plane with a charge density of 1.3 × 108 electrons/cm2 (104 electrons per 100 µm circle)

gives rise to a field of 115 V/cm, which is about 1/1000 of the typical acceleration field.

Hence, for short τ , the influence of space-charge is negligible. A similar problem, which

arises at the anode where the electron pulse crosses from the acceleration region into the

field free drift region, requires an analogous correction of position and velocity of the

individual electrons. A pinhole in the beam path was implemented by stripping away

all electrons outside a certain radius and a mesh was modeled by removing all electrons

whose lateral positions are within the width of the grid wires. The magnetic lens was not

implemented for the simulations since in practise, it is usually placed close to the sample

in an effort to minimize the total electron propagation distance and therefore has only


0 mm9 mm

18 mm27 mm36 mm45 mm

−400 −300 −200 −100 0 100 200 300 400

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

−800 −600 −400 −200 0 200 400 600 800

Ele

ctro

n de

nsity

[arb

itrar

y un

its]

t [fs]

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

−800 −600 −400 −200 0 200 400 600 800

Ele

ctro

n de

nsity

[arb

itrar

y un

its]

t [fs]

N=2000N=3900N=7800

N=15000N=28000N=51000

Figure 2.3: Simulated electron pulse shapes. The main graph shows the temporal shape

of electron pulses containing different numbers of electrons (55 kV, 6 mm acceleration,

150 µm pinhole as anode, 23 mm drift region). The inset shows the evolution of the

temporal envelope of an N = 7700 electron pulse from the anode to a 45 mm drift.

minor influence on the pulse duration.

For practical reasons, such as electrical safety and cost, I decided to design the electron

source at a maximum of 60 keV. While it has reached and operated at the design voltage,

normal operation is performed at 55 keV for reasons of electrical vacuum breakdown

stability (vide infra). The current electron pulse source setup is constructed with a 6 mm

cathode-to-anode distance and with a pinhole as the anode. While further shortening of

the acceleration region is very difficult for DC electron guns because of breakdown, the

“drift region” between the anode and the sample can be optimized.

Simulated electron pulse shapes are shown in Fig. 2.3. As expected, the pulse duration

increases as the number of electrons per pulse increases and as the propagation time


0 20000 40000

0

200

400

600

800

1000

1200

1400

1600

1800

0 5000 10000 15000 20000 25000 30000

Pul

se d

urat

ion

[fs]

Electrons per pulse

electron pulse sourcePrevious 30 kV

45 mm

36 mm

23 mm

12 mm

0 mm

800

600

400

200

0

Figure 2.4: Pulse durations vs. number of electrons per pulse for various electron gun

configurations from simulations. The black dotted line describes the previous 30 kV

electron gun while the solid blue line describes the current setup (also shown in the inset

for higher electron numbers). The dashed lines stand for the same setup with different

drift region lengths. All configurations use a 150 µm pinhole.

increases. More surprisingly, the pulse shape also changes, becoming more and more

flat-top. This effect is also space-charge related since it occurs more strongly and earlier

in pulses with higher electron densities.

The most commonly used measure for the pulse duration is the full width at half

maximum with FWHM = 2√

2 ln 2σ ≈ 2.35σ for a Gaussian. This conversion technically

does not apply to other pulse shapes, but in practise it is a useful value to estimate the

effect of the pulse shape on the temporal resolution of a pump-probe experiment. We use

this conversion to calculate pulse duration from the simulation results. Electron pulse

durations for different lengths of the drift region are shown in Fig. 2.4.


It is obvious from Fig. 2.4 that even for relatively long drift regions the current setup

outperforms the old electron pulse source by a significant margin. In the previous electron

gun, the cathode as well as the anode were executed as Rogowski profiles (vide infra) at

a distance of 3 mm. The electric field was terminated on the anode side by a TEM mesh.

After 11 mm, the electron beam was stripped by a pinhole after which the electron pulse

propagated for another 28 mm through the magnetic lens before striking the sample. The

cathode was biased at −30 kV. The higher acceleration voltage (55 kV) in the current

setup reduces the time the electron pulse spends in the drift region and also increases

the spatial length of the electron pulse for the same duration, thereby reducing the effect

of space charge. Also, in the previous setup the mesh at the anode and the pinhole

11 mm downstream from it increased the number of electrons that were necessary at the

cathode to produce a given number of electrons in the pulse that reached the sample.

These improvements in combination with the shortened drift region allow the dramatic

improvement of the pulse duration evident in Fig. 2.4.

2.2.2 The Photocathode

The electron pulse is generated by a laser pulse impinging on the photocathode, creating

a cloud of photoelectrons. Ideally, the photocathode would be a single crystal bulk

material to guarantee a homogeneous work function across the size of the beam. Given

the geometry of the electron gun (vide infra), front-side illumination of the photocathode

is not possible. Instead, we use back-side illumination of a thin-film photocathode on a

transparent substrate. The substrate of the photocathode is a 12.5 mm diameter sapphire

disk. Since the electrical contact to the photocathode needs to be made from the back

side, a relatively thick layer (usually 500 nm) of chromium is deposited on that side of

the disk, overlapping one edge. A 20 nm gold layer is then deposited on the other side


of the photocathode, overlapping the same edge and therefore making electrical contact

with the chromium layer.

The electrons are produced by the photoelectric effect. If the energy delivered by a

photon is higher than the energy required to free the electron from the solid (the work

function), the electron is emitted with excess kinetic energy [49]. This initial kinetic

energy can lead to broadening of the electron pulse [21]. By choosing the wavelength of

the laser pulse so that the energy of the photons is very close to the work function, this

effect can be minimized. The work function of a freshly deposited, clean gold surface is

4.83 eV (λ = 257 nm) [50]. Our photocathodes are produced in a deposition chamber

which is used for various metals and which uses an oil pump. It is transferred to the

electron gun under normal atmospheric conditions. This treatment likely changes the

surface, and the operating wavelength needs to be determined empirically. The NOPA

in our setup produces visible light, so that two-photon photoemission has to be used to

produce electrons. In practise, the NOPA is operated at a wavelength just below the

two-photon cutoff (500 nm or 2.48 eV), at which no electron pulse is observed any more.

2.2.3 Electron Acceleration

As explained in section 2.2.1, space charge effects are strongest during the early stages

of the electron pulse acceleration and hence the electron pulse needs to be accelerated as

quickly as possible. Hence, the electric field between the photocathode and the anode is

maximized. The electric field at the surface of a charged conductor is increased where

the radius of curvature is small, which is particularly the case at any sharp corners.

These electric field spikes can lead to field emission and breakdown. Breakdown not

only disrupts the experiments by discharging the high voltage power supply but also

can do serious damage to the photocathode. The extreme current transients that occur


during breakdown may even lead to transient malfunction and permanent damage in

electronic equipment not related to the high voltage part of the experiment by inducing

damaging voltages in signal wires. These effects can be mitigated by careful shielding

and grounding. While macroscopic edges can be avoided in the design of the electrodes,

microscopic roughness can only be reduced by polishing of the electrodes. Despite all

measures to ensure smooth surfaces, some sparking will usually occur. Moderate sparking

can condition the surface by melting or evaporating the roughness on the surface.

In practise, the maximal practical electric DC field that can be obtained is on the order

of 10 kV/mm. Since the electrodes have finite size, some curvature is required. If we do

not want to compromise on the field strength in the centre of an electrode, the electrode

can be made according to a so-called Rogowski profile [51]. This shape ensures that

the electric field has its maximum value in the flat, centre part of the electrode. While

usually both the cathode and the anode are shaped to obey Rogowski profiles, the same

condition for the electric field can be satisfied when making one of the electrodes plane

and designing the Rogowski profile of the other electrode with different parameters. Since

the electrons have to travel through the anode, like all parts along the electron path, it

should be optimized for minimal length. Hence, the anode of the electron diffractometer

is flat while the cathode was originally designed to have the shape of a Rogowski profile.

However, this cathode design is not without problems: since the photocathode itself is a

thin sapphire disk and cannot be made in the shape of a Rogowski profile without undue

technical complexity, the photocathode is usually embedded into a metal piece that has

the shape of a Rogowski profile with a cut-out that fits the photocathode. The obvious

disadvantage of this solution is the seam between the photocathode and the metal profile.

It occurs necessarily in a high-field area and roughness is unavoidable. A different design

ultimately proved to be more practical and stable. The photocathode of the current

setup is mounted inside a macor tube with a lip at the end that covered the edges of


the photocathode disk. Macor is a vacuum-compatible, machinable ceramic with a high

bulk dielectric strength. In this design, only the flat part of the photocathode is exposed

while the edges are covered by the dielectric, which prevents breakdown. In practise, this

turned out to be much more stable and easier to handle for photocathode exchanges. In

contrast to the Rogowski profile design, which required gluing the photocathode into the

metal profile, the photocathode is held by a mechanical retaining ring in the macor tube

design.

The original design of the anode used a TEM mesh to allow the electron pulse through

the anode. Besides the limited transmission of the TEM mesh, meshes that separate two

regions of different electric field also distort the electric field around the grid lines, leading

to defocusing of the passing electron beam [52]. Since this effect is much less pronounced

when a pinhole is used instead, significantly improving the beam quality, we use a pinhole

as the anode (typically 150 µm). The size of the pinhole also limits the size of the electron

beam.

High Voltage Power Supply

The output of the high voltage power supply ultimately defines the kinetic energy of the

electrons and hence their velocity. At V0 = 55 keV, the time the electron pulse takes to

propagate from the photocathode to the sample is 271 ps and changes by 2 fs per 1 V

change in the high voltage. Therefore, the stability of the high voltage power supply

must be better than 0.1% in order to keep the timing error introduced by the power

supply below 100 fs. The power supply used in the electron diffractometer 1 guarantees

a drift of less than 0.01% per hour after warm up and 0.02% ripple.

1Glassman - FC60N2


2.2.4 Beam Conditioning

In order to obtain a high quality diffraction pattern on the detector, the electron beam

size at the detector needs to be minimized. The electron pulses created by photoemission

and acceleration in a DC field spread during their propagation. Without any measures to

control the electron beam divergence, the electron diffractometer would produce very poor

diffraction patterns. Electrostatic or magnetic solenoid lenses can be used to counteract

this spread and focus the electron beam. Since this focusing element needs to be placed

between the anode and the sample, it is critical to build it as short as possible to keep

the total pulse propagation time short.

The focal length f of the electron lens needs to be similarly short. The smallest elec-

tron spot on the detector is achieved by imaging the electron cloud on the photocathode

onto the detector. The necessary focal length is given by the thin lens equation

1

f=

1

lobject

+1

limage

(2.3)

where lobject is the distance from the object to the lens and limage is the distance from the

lens to the image or the detector in our case.

Since the distance from the lens to the detector is much larger than the distance

from the photocathode to the lens, the latter is crucial for the determination of the focal

length of the electron lens. Neglecting relativistic effects, electrons that emanate from a

point source at x = 0 in the plane of the photocathode with a lateral velocity vx at t = 0

arrive at the anode at t = 2d/vz where d is the distance between the cathode and the

anode and vz is the velocity of the electron resulting from the acceleration in the electric

field. Since the velocity in x-direction is unaffected by the acceleration in z direction,

the offset in x direction at the anode is twice the offset the electron would have had it

travelled at vz. Hence, the point source looks like a point source of accelerated electrons

at a distance 2d before the anode, twice the actual cathode-anode distance.


The size of the lens itself also increases the pulse propagation distance. As a rule of

thumb, stronger (i.e. shorter focal length) lenses are larger. The challenge is to build a

lens that will not unduly increase the pulse propagation distance but that will also be

strong enough to image the photocathode onto the detector from its position very close

to the anode.

Electrostatic Lens

A simple electrostatic lens is the so-called einzel2 lens. The lens consists of three di-

aphragms through which the electron beam passes. The first and the last diaphragms

are at ground potential while the middle diaphragm is biased at a high voltage. The lens

effects no net acceleration of the electrons but it first accelerates and then decelerates

(or vice versa, depending on the polarity of the centre diaphragm) the electrons passing

through it. The actual focusing is caused by the radial fields present due to the geom-

etry of the lens. The mathematical treatment of these electrostatic lenses can be found

in the literature [53, 54] and is beyond the scope of this thesis. The focal length for

the same geometry and voltage is shorter when the centre electrode is biased negatively.

However, this configuration is not desirable since it results in the electron pulse getting

compressed longitudinally, increasing space charge broadening. The distance between

the diaphragms is subject to the same limitations as the anode-cathode distance for a

given potential difference. Given these technical limitations, a focal length of less than

50 mm is very difficult to obtain with an electrostatic lens for 60 kV electrons.

Magnetic Solenoid Lens

The basic design of a magnetic solenoid lens is shown in Fig. 2.2. The magnet wire

windings (shown in black in the figure) are wrapped around the electron beam aperture.

2German: einzel = individual, single


They are shielded by a soft iron material with high magnetic permeability (µ > 200)

(shown in grey), which increases the magnetic field in the gap in the magnetic shield

placed inside the aperture and prevents the magnetic field from “leaking” outside the

magnetic lens. The magnetic solenoid lens is similar to the electrostatic lens in that the

focusing effect is also caused by the inhomogeneities of the field. The focal length of a

magnetic solenoid lens [54] is

f =4m2v2

z

e2∫

B2zdz

(2.4)

where the electron beam propagates along the z direction with a velocity of vz and Bz is

the magnetic field in z direction. The magnetic field in the gap is

B =µ0IN

d + lµ

(2.5)

where I is the current in the coil, N is the number of windings, d is the width of the gap

and l is the length of the shield from pole piece to pole piece.

Electrostatic lenses can be constructed from metal diaphragms and a vacuum com-

patible insulator, making them completely vacuum compatible. Magnetic lenses, on the

other hand, require large amounts of magnet wire. Magnet wire is not desirable inside

a UHV environment since it increases the area and the varnish used as insulation on

magnet wires is not considered vacuum compatible. The current in the magnet wire also

heats up the magnetic lens, which can become a serious problem in the absence of con-

vective cooling. For these reasons, magnetic lenses are often placed around a beam tube

so that the electromagnet is actually located outside the vacuum. However, this setup

requires additional vacuum seals, which would lengthen the anode-to-sample distance

by centimetres. It is therefore advantageous to build a magnetic lens for in-vacuum use

despite the obvious problems.

A large volume in the lens is taken up by the magnet wire windings. To keep the

electron beam path through the lens short I designed the magnetic lens so that the


0.0 A 0.2 A 0.4 A 0.6 A 0.8 A 1.0 A

2.2 A2.0 A1.8 A1.6 A1.4 A1.2 A

2.4 A 2.6 A 2.8 A 3.0 A 3.2 A 3.4 A

10 mm

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.5 1 1.5 2 2.5 3 3.5

Bea

m F

WH

M a

t det

ecto

r [m

m]

Magnetic lens current [A]

16000 electrons / pulse5000 electrons / pulse

Figure 2.5: Magnetic lens performance. Top: Diffraction pattern of single crystalline

(001)-oriented Si for different magnetic lens currents. At low lens currents, the “shadow”

of the supporting Si “mesh” is visible in the diffraction spots. Bottom: Width (FWHM of

Lorentzian) of the undiffracted electron beam at the detector vs. magnetic lens current.


bulk of the windings is placed away from the electron beam path, wrapped around the

electron gun. Note that because of the magnetic shield around the lens, the electron gun is

magnetic field free except for the small region around the gap in the magnetic lens shield.

This is where the actual focusing happens. Since the focal length is increased i.e. the

lens can be weaker when it is placed further from the electron source, the gap in the

shield was placed as far downstream as possible. The lens was constructed with a 5 mm

gap whose centre is placed 14.5 mm from the anode. With a gun-to-detector distance of

about 20 cm, the focal length of the lens needs to be f ≈ 23 mm. For the design electron

energy of 60 keV, the required magnetic field is B = 0.154 T = 1540 Gauss, produced by

700 A Turns.

The performance of the magnetic lens is demonstrated in Fig. 2.5. Obviously, the

best focusing occurs at around I = 2.4 A. Note that while the size of the focus for

the different electron densities is the same, when the beam is not properly focused, the

pulse with the higher number of electrons displays more lateral broadening due to space

charge. At the optimal focusing current, the voltage drop across the magnetic lens is

about 6.2 V. The dissipated power is about 15 W. To keep the magnet wire within

its operating temperature range, cooling is required. Water cooling inside a vacuum

chamber is problematic because of the potential of leaks in water cooling lines. This is

especially true in the presence of high voltages in the same vacuum chamber. I avoided

this problem by designing the magnetic lens to be bolted to a Conflat flange which can

be water-cooled without the need for in-vacuum water lines. The windings of the magnet

wire are wound on a copper yoke for better thermal conductivity. The yoke is Ni plated

for better vacuum compatibility. Layers of indium foil between the yoke and the magnetic

lens shield and between the shield and the flange could improve thermal contact but were

not implemented for convenience.

As mentioned above, the magnet wire used in the magnetic lens is technically not UHV


compatible. While magnet wire with Kapton insulation is sold as vacuum compatible

wire, it did not perform any better in our tests than off-the-shelf low-outgassing magnet

wire. On the contrary, pump-down time was increased with Kapton insulated wire over

standard magnet wire and the Kapton insulation seemed to severely hamper the heat

conduction between the wire and the yoke.

Heat can speed up the outgassing process of contaminants on surfaces such as water

or hydrocarbons. This is usually done in a process called “baking” in which the entire

vacuum chamber is heated to over 100◦ C. While this is not possible for the electron

diffractometer because the detector as well as the sample manipulation stages are heat

sensitive, the pump down process can be significantly accelerated by heating the magnetic

lens. This is achieved by running hot (55◦ C) water through the cooling lines for several

hours. A residual gas analyzer (RGA) indicated that the outgassing of the magnetic

lens is almost exclusively water vapour and should therefore not be harmful to other

components inside the vacuum chamber.

2.3 Sample Manipulation

The ability to move the sample accurately and quickly is particularly important for large

area irreversible samples in which every shot has to be performed on a separate spot on

the sample. The techniques we employ for overlapping the electron beam with the laser

beam as well as profile measurements of the electron pulse also require precisely controlled

in-vacuum motion. However, the magnetic fields associated with electrical motors are

not acceptable since even relatively small magnetic fields can deflect the electron beam.

Worse still, the magnetic field of motors that employ permanent magnets in the rotor

changes depending on the rotor position. Hence, the electron diffractometer is equipped


6.75" conflat flange

Cathode retaining ring

Cathode contact diskPhotocathode

Cathode holder

Anode

Pinhole

Magnetic lens shield

Yoke Anode mountCooling lines

Figure 2.6: The electron pulse source. Top: electron gun assembly with laser and electron

beams shown. Bottom: exploded electron gun.


with a pair of stainless steel translation stages driven by piezoelectric motors3. The stages

are equipped with optical encoders for closed loop operation and are controlled by the

experiment computer. These translation stages allow for the sample motion in the plane

normal to the electron beam propagation.

If the sample plane is not parallel to the motion of the stages, the sample is offset in

z-direction as it is moved to a new spot. This motion causes changes in timing because

it modifies the distance between the electron gun and the sample and it also changes the

distance the pump pulse has to travel. The change in the pump-probe delay due to a

change in z-position ∆z is

∆τ = ∆z

(1

vz

+1

c

). (2.6)

This problem is particularly serious for non-reversible samples. Experiments with these

samples require a large area sample to provide enough space for the many shots necessary

to obtain a complete time series of diffraction patterns. In order to keep the deviation

below 100 fs over a 2 cm long sample, the sample surface has to be parallel to the axis of

motion of the sample manipulation stages within 0.03◦. The sample holder is mounted on

a kinematic tip-tilt mount since this accuracy is far beyond regular machining precision.

The necessary corrections to the tip and tilt angles are determined by using the sample

frame as a mirror in one arm of an autocorrelator, and then measuring the change in

timing for different positions of the translation stage.

A condition for these corrections to be successful is the flatness of the sample. If

the sample is not plane but has some curvature, this curvature produces a local tip/tilt

even if the global orientation of the sample has been corrected. For this purpose, we

use silicon square meshes made from a commercial silicon wafer through Bosch etching

to support the thin sample film [38]. The sample surface is then defined by the surface

3Nanomotion - Yokneam, Israel


of the wafer which is very flat (2 nm flatness from wafer specification). Since these

sample supports could still deformed when mounted on a deformed sample frame, I

designed the sample frames to be in contact with these sample supports in three points

only, thereby preventing any stress on them. The sample frame is mated to the tip-tilt

stage by a specially built mount that allows rapid sample frame exchanges with high

reproducibility. In this mount, three spring-loaded ball bearings press the polished side

of the sample frame against a polished stainless steel surface. This setup allows the

sample frame to be inserted and removed easily. Through quick sample exchanges, the

exposure of the vacuum chamber to the atmosphere can be kept at a minimum.

2.4 Electron Detection

Spatially resolved electron detection is usually achieved by means of a phosphor or a scin-

tillator followed by detection of the produced photons by a CCD camera. The coupling

between the phosphor and the CCD camera can either be achieved by a free-space optical

system, in which a lens images the phosphor onto the CCD chip or by a fibre-optic plate,

which is placed directly between the phosphor and the CCD chip. While the former is

much simpler to implement, it suffers from poor optical efficiency

OE ≈ 1

16N2

(b

g

)2

(2.7)

with the f-number N of the lens used to image the detector on the CCD chip and

the magnification b/g of the imaging system. Given a lens with N = 2, the chip size

b = 13.3 mm and a detector size of g = 40 mm, the theoretical efficiency is OE ≈ 2×10−3.

This efficiency is further reduced by reflections on optical surfaces. Fibre optic systems,

on the other hand, can reach efficiencies in the 10−1 range (somewhat less for tapered

fibre plates). The high complexity and cost of a fibre-coupled detection system led to the

decision to use a lens-coupled system despite the obvious advantages of fibre coupling.


A 55 kV electron striking a suitable phosphor screen produces on the order of 103

photons. The noise floor (dominated by readout noise for typical exposure times at a

detector temperature of −20◦ C) of the CCD camera4 is about 10 electrons and the

detection efficiency is > 90%. Hence, the detection efficiency of the entire system is

significantly below the goal of every-electron detection. The detection system currently in

use employs a chevron pair of microchannel plates (MCPs) together with a P20 phosphor

screen5. The MCPs act as an array of electron multipliers with an amplification of up

to 104 per plate [55]. In the electron diffractometer, the MCPs are typically operated

at 1.3 kV and the phosphor screen is biased at 4.6 kV, resulting in an electron energy

of 3.3 keV at the phosphor screen. While this detector configuration certainly increases

the intensity so that every primary electron is detected far above the noise level, the

efficiency of the MCPs in the detection of primary 55 keV electrons is estimated to be

only about 10%, i.e. only 10% of the primary electrons trigger an avalanche of secondary

electrons in one of the electron multiplier channels. This efficiency dictates the overall

detection system efficiency.

While every-electron detection has been reached in lens coupled systems for electron

microscopes [56], such systems operate on the margins of every-electron detection. For

future electron diffractometers, fibre optic coupling between the phosphor screen and

the CCD chip is recommended owing to the robust every-electron-detection capability of

such a setup without any additional amplification. More exotic detection systems, such

as direct bombardment of radiation-hardened CMOS active pixel sensor chips [13] have

so far failed to materialize but may play a role in UED in the future.

In order to measure the electron beam current, the vacuum chamber also contains a

Faraday cup, which can be moved in front of the detector by a linear motion feedthrough.

4Apogee Instruments - Alta U475Photonis - APD-30-40-12/10-8-FM-I-60:1-P20


The electron beam currents that need to be measured are very low; a fairly typical

configuration of 5000 electrons/pulse at a laser repetition rate of 500 Hz correspond to

a beam current of 0.4 pA. To measure these beam currents reliably, the Faraday cup is

connected to a sensitive electrometer6.

2.5 Vacuum Chamber Design

The vacuum chamber (see Fig. 2.7) consists of two almost completely separate sections,

each of which is pumped out by a separate turbomolecular pump. One section contains

the electron gun, while the other section contains the sample, sample manipulation and

the pump beam optics. The electron gun is very sensitive to the quality of the vacuum

– arcing is much more likely at higher pressures. By venting the magnetic lens to the

sample chamber, the surface area in the gun chamber can be kept quite small and the

gun chamber can reach 10−8 Torr after a few hours of pumping. The pressure in the

sample chamber drops much more slowly due to the larger surface area and the magnetic

lens. However, for the reliable operation of the electron diffractometer, a pressure of

10−6 − 10−7 Torr in the sample chamber is sufficient. This pressure is reached after

6 − 8 h of pumping.

The separation of the vacuum chamber into two sections also shields the electron gun

from pressure increases due to the pump laser, which had caused significant difficulties

in the previous 30 kV electron diffractometer. On the other hand sensitive parts inside

the sample chamber, such as the MCPs and the optical encoders are protected from the

electromagnetic pulse produced by the electron gun during an arc.

6Keithley - Model 6514


Laser windows

Ion gauges

Phosphor screento turbo pumps

ViewportSample chamber

60 kV feedthrough

Electron gun section

Faraday cup manipulator

Electron gun flange

Figure 2.7: The vacuum chamber of the electron diffractometer. The gun flange with

the electron gun (shown in detail in Fig. 2.6) separates the vacuum chamber into two

almost completely separate sections. The laser window on the electron gun section is for

the laser pulse that drives the electron gun. The pump beam in UED experiments enters

through the laser window in the sample chamber closer to the detector. The nominal

size of the top and bottom flanges of the sample chamber is 10”.

Chapter 3

Characterization of Femtosecond

Electron Pulses

The duration of the probe pulse is the dominant contribution to the time resolution of

the electron diffractometer. Simulations of the electron pulse propagation provide useful

estimates for the electron pulse duration but they need to be verified experimentally. The

experimental verification of the electron pulse durations is particularly important since

the actual electron pulse duration depends on some experimental parameters (e.g. the

number of electrons before the anode), which are difficult to verify directly.

The conventional method for measuring electron pulse durations is a streak camera.

In a streak camera, a pair of deflection plates are positioned along the electron pulse

path and a voltage ramp is applied to them as the electron pulse passes between them

(see Fig. 3.1). The resulting time-dependent electric field deflects electrons by a different

amount depending on their arrival time. When the electron pulse hits the detector, it is

Parts of this chapter have previously been published in the following articles: [42] Christoph T.Hebeisen, Ralph Ernstorfer, Maher Harb, Thibault Dartigalongue, Robert E. Jordan and R. J. DwayneMiller, Optics Letters 31, 3517 (2006). Copyright 2006 by the Optical Society of America. [43] ChristophT. Hebeisen, German Sciaini, Maher Harb, Ralph Ernstorfer, Thibault Dartigalongue, Sergei G. Kruglikand R. J. Dwayne Miller, Optics Express 16, 3334-3341 (2008). Copyright 2008 by the Optical Societyof America.

37

Chapter 3. Characterization of Femtosecond Electron Pulses 38

Voltage rampGenerator

vz

Unstreakedspot

Streakedspot

Streaking plates

lDetector

E(t)

L

Figure 3.1: Principle of a streak camera.

streaked across the detector i.e. the temporal dimension of the electron pulse is projected

into a spatial dimension, which is easily measured.

In order to calculate the length of the streak on the detector, we assume an electron

initially moving in z direction with velocity vz. The electron enters the streaking field

~E(t) = (0,−st, 0) at t = 0. The velocity in y direction vy(t) is then

vy(t) =

t∫

0

−eEy(T + τ)

medT =

es

me

(t2

2+ τt

). (3.1)

I introduced a time offset τ in the electric field ramp in order to account for the different

arrival times of the electrons in the pulse. When the electron leaves the field at z = l,

vy

(l

vz

)=

esl

mevz

(l

2vz

+ τ

)(3.2)

and

y

(l

vz

)=

l

vz∫

0

vy(t)dt =esl2

2mev2z

(l

3vz

+ τ

). (3.3)

If the detector is placed at distance L after the end of the streaking plates, the offset of

the electron at the detector is

Y (τ) = y

(l

vz

)+

L

vz

vy

(l

vz

)=

esl

mev2z

[l

2vz

(L +

l

3

)+ τ

(L +

l

2

)]. (3.4)


The derivative of this offset at the detector with respect to the arrival time of the electron

at the streaking plates is called streaking speed

us =dY (τ)

dτ=

esl

mev2z

(L +

l

2

). (3.5)

The streaking speed is an important measure of the performance of a streak camera

because it determines directly how long the streak of a given electron pulse is on the

detector screen. The intensity profile of the streak along the streaking direction is a

convolution of the lateral electron pulse intensity profile and the temporal pulse profile.

Hence, the instrument response of a streak camera is given by w/us where w is the lateral

size of the electron beam. While a sub-picosecond system response has been achieved

for special streak camera designs [57], there are severe problems with streak cameras

that limit their ability to measure the high number density electron pulses used in FED.

The measurement of femtosecond electron pulses requires a very high streaking speed.

According to Eq. 3.5, the simplest way to increase the streaking speed is to increase the

length of the streaking plates. Usually, streaking plates for electron pulses in the tens of

keV range are a few centimetres long. Such a setup has been used e.g. by Cao et al. [58].

However, as shown by simulations in the previous chapter, the electron pulse duration

would drastically change over such a length. The measured temporal profile would be

ill-defined and only poorly reflect the duration of the electron pulse that would arrive at

a sample. An increase in the length of the drift region L leads to a corresponding increase

in the lateral electron beam size at the detector and hence does not improve the streak

camera resolution. The ramp speed of the electric field s is limited by technical properties

like the capacity of the streaking plates. An RF cavity could be used instead of the

streaking plates but such a setup requires extensive (and expensive) RF synchronization

circuits and amplifiers and only partially solves the problems with respect to the required

interaction length and the changing electron pulse duration.


The problem of characterizing electron pulses is analogous to earlier problems in

determining optical pulse shapes. With the introduction of passive mode-locking [59],

laser pulses became too short to be characterized by fast photodiodes or photoactivated

streak cameras. The only probe short enough to probe laser pulses were the laser pulses

themselves. In response to this problem, autocorrelation [60] and cross-correlation of

laser pulses were widely adopted to characterize femtosecond laser pulses. Given the

problems in characterizing femtosecond electron pulses with streak cameras, it is clear

that a similar solution is necessary for electron pulses.

Optical correlation techniques rely on nonlinear effects in a material e.g. sum fre-

quency generation (SFG). In cross-correlation, two different laser pulses are overlapped

inside a non-linear crystal. The non-linear signal is a function of the overlap integral of

the envelopes of the two laser pulses. By scanning the relative delay between the laser

pulses, a cross-correlation function can be obtained. In the case of auto-correlation, the

two pulses are copies of the same pulse.

An interaction between an electron pulse and another short pulse would enable a

similar cross-correlation scheme for electron pulses. We proposed a laser-electron cross-

correlation scheme based on electron scattering by the laser ponderomotive force [61] and

demonstrated a technique based on this proposal in a proof-of-principle experiment [42].

We also developed a related practical technique with improved performance that can be

adopted in any UED lab [43]. These two techniques are described below in sections 3.2

and 3.3, respectively.

Several other techniques for measuring electron pulse durations have been demon-

strated. A method developed by Wang et al. [62] uses an RF cavity with the electric

field along the pulse propagation direction. The field is timed so that the pulse passes

the cavity at the zero-crossing of the field i.e. when the time derivative of the field is

at its maximum. The integrated electric field the electrons are exposed to during their


traversal of the cavity is proportional to their longitudinal (temporal) position in the

electron bunch. The cavity is followed by a spectrometer which spreads the electrons in

the pulse according to their energy. This approach is closely related to the principle of

a streak camera described above and suffers from similar limitations. Another technique

uses the coherent transition radiation emitted when an electron passes an interface be-

tween two media of different dielectric constants [63]. This method works best with large

numbers (N ≈ 107) of relativistic (107 eV) electrons and requires a priori knowledge of

the temporal pulse shape. Electro-optical sampling of the electron pulse shape [64] does

not suffer from this limitation since it determines the pulse shape through the measure-

ment. This method exploits the fact that the electric field of a highly relativistic electron

bunch is almost completely perpendicular to its motion. This electric field can induce

birefringence in an electro-optical crystal near the electron beam via the Pockels effect.

The shape of the electron pulse envelope is then encoded in the polarization of a chirped

laser pulse co-propagating parallel to the electron pulse through the crystal. While this

method, too, is suitable only for highly relativistic electrons and therefore unsuitable for

UED setups, it is useful for x-ray free electron lasers and time resolution down to 60 fs

has been shown [65].

Two electron pulse characterization techniques for electron pulses used in UED have

been proposed but not demonstrated. An electron pulse-electron pulse cross-correlation

scheme has been proposed by Baum et al. [33]. This scheme relies on the space-charge

interaction between two electron pulses and therefore its effectiveness strongly depends

on the number of electrons per pulse. It also requires extensive modelling to extract

the electron pulse duration and modifications of the electron beam path, such as an

additional magnetic lens to focus the electron beam in the sample position. Another

laser-based measurement whose principle is based on impact-ionization induced Auger

electron emission has recently been proposed [66].


To date, electron pulse-laser pulse cross-correlation by means of the ponderomotive

force is the only proven method to measure femtosecond electron pulses with pulse pa-

rameters as used in UED.

3.1 Laser Pulse-Electron Pulse Temporal Overlap

Determination

In order to take meaningful and accurate measurements of time constants of processes

observed with UED, which are on the same order of magnitude as the instrument response

of the electron diffractometer, the exact coincidence of the pump and probe pulses or

t = 0 has to be determined with good precision [5] independently of any changes of the

observed diffraction patterns. In gas-phase studies, photoionization-induced lensing has

been used for this purpose [67]. In these measurements, a distortion of the electron beam

due to the charge separation caused by the photoionization of the gas target by the laser

beam is observed if the electron pulse arrives after the laser while no such distortion is

observed if the electron pulse passes the target before it is excited by the laser pulse.

A similar technique can be used with a solid target instead of the molecular beam.

Electrons emitted from a needle tip [68, 69, 13] or a TEM mesh [5] after femtosecond

laser illumination can deform the electron beam, allowing for a t = 0 determination.

These measurements are performed by replacing the sample in a UED experiment by

a fine TEM mesh and increasing the pump pulse intensity so that it is just above the

ablation threshold. The physics of the electron emission from surfaces after intense laser

pulse illumination, which underlies this effect is discussed in chapter 4.

Beam images from such a t = 0 determination are shown in Fig. 3.2. Before taking

an image with the pump laser pulse present, we take a reference image under the same


−0.5 0.5 1.0 1.5 2.0 2.50.0

0

0.2

0.4

0.6

0.8

1

−10 −5 0 5 10

RM

S d

iffer

ence

Pump−probe delay [ps]

Figure 3.2: Top: Difference images of the pulse shapes with and without laser illumina-

tion in a laser pulse-electron pulse temporal overlap measurement. The number in the

lower right corner of each image indicates the delay time in picoseconds. Bottom: RMS

difference signal between the before and during images with some example during images.

Inset: Sketch of the experimental setup. The electron pulse (blue) passes through the

TEM mesh, which is excited by the laser pulse (red).


conditions but with the pump laser beam blocked. We refer to these images as “before

images” and the images with the pump beam present are called “during images”. The

images are usually analyzed by subtracting the before image of each time step from its

corresponding during image and calculating the RMS value of each difference image. The

choice of the RMS of the difference image is somewhat arbitrary and was chosen as a

convenient measure of the deformation the probe pulse has undergone.

The time zero position is usually taken to be the onset of the rise of the RMS signal.

Obviously, this choice is somewhat sensitive to the signal-to-noise ratio (SNR). It could

also be skewed by the pump pulse duration if e.g. the leading edge of the pump pulse

already causes an appreciable change to the detector image. Although it was not known

if the observed changes in the electron beam shape started exactly at the maximum

overlap of the laser pulse, this technique has been used in several UED studies. The

dynamics of this effect are rather complex and are known to evolve on the 100 fs to ps

timescale in a highly surface-dependent and excitation-dependent manner. In contrast,

the scattering of electrons by the ponderomotive force is basically instantaneous and

therefore provides a perfect marker for the t = 0 position of the laser pulse-electron pulse

overlap in time. The beam path for this measurement is different from that of a UED

experiment and hence a calibration of the path length difference is necessary. The much

simpler measurement using a TEM mesh can be performed in both geometries. This can

be used to quantify the delay between the actual laser arrival time as determined by the

ponderomotive electron characterization and the observed change in beam shape in the

mesh-based experiment. This comparison can then serve as a calibration for the t = 0

measurement.


3.2 Laser Pulse-Electron Pulse Cross-Correlation

Charged particles naturally interact with electromagnetic fields through the Lorentz force

~F = q(

~E + ~v × ~B)

. (3.6)

Here, ~E is the electric field, ~B the magnetic field, ~v the velocity of the particle and q its

charge. In the oscillating field of a plane wave, the Lorentz force leads to a quiver motion

of the particle that does not lead to any net displacement over a full cycle. The electric

and magnetic fields of a plane wave in vacuum are

~E =1

2

(~E0e

iωt + ~E∗0e

− iωt)

with ~E0 = Ee− i~k·~r and (3.7)

~B =1

2

(~B0e

iωt + ~B∗0e

− iωt)

with ~B0 = Be− i~k·~r , (3.8)

respectively, where ~k is the wave vector of the plane wave, ω =∣∣∣~k∣∣∣ c and E and B with

∣∣∣B∣∣∣ = 1/c

∣∣∣E∣∣∣ are the amplitudes of the fields where E, B, ~k are mutually orthogonal

and form a right handed system. For light intensities I ≪ 1018 W/cm2 the quiver motion

of an electron is much slower than the speed of light and we can neglect the magnetic

field for the calculation of the quiver motion:

m~r =q

2

(~E0e

i ωt + ~E∗0e

− i ωt)

. (3.9)

We integrate this to yield

~r = − i q

2mω

(~E0e

i ωt − ~E∗0e

− i ωt)

and ~r = − q

2mω2

(~E0e

i ωt + ~E∗0e

− i ωt)

. (3.10)

Charged particles undergoing an accelerated motion lose energy by radiation. However,

the energy classically radiated by an electron undergoing an oscillation corresponding

to the peak laser intensity used in this experiment for the entire laser pulse duration is

much less than the energy of a single photon (0.04 eV vs. 1.55 eV). Therefore, radiation

losses are neglected in this derivation.


If we replace the constants E and B by slowly varying functions (i.e. add an envelope

to the light intensity), there is an additional slow drift component ~R in the particle

motion [70, 71]. We rewrite Eq. 3.6 as

m(

~R + ~r)

=q

2

{E0

(~R)

eiωt + E∗0

(~R)

e− iωt+

(~r · ∇)[E0

(~R)

eiωt + E∗0

(~R)

e− i ωt]

+ ~r ×[B0

(~R)

ei ωt + B∗0

(~R)

e− iωt]}

. (3.11)

Since E and B vary slowly and the amplitude of the quiver motion is small (18 nm for

1017 W/cm2 at 800 nm), we expanded E0 to first order and used only one term for B0.

Substituting Eq. 3.10 into Eq. 3.11 and we obtain an equation for ~R

m~R = − q2

4mω2

{[(~E0e

i ωt + ~E∗0e

− i ωt)· ∇] (

~E0eiωt + ~E∗

0e− i ωt

)

+ iω(

~E0ei ωt − ~E∗

0e− i ωt

)×(

~B0ei ωt + ~B∗

0e− iωt

)}. (3.12)

Since ~R describes the slow drift motion, we can discard the terms oscillating at 2ω:

m~R = − q2

4mω2

[(~E0 · ∇

)~E∗0 +

(~E∗0 · ∇

)~E0 + i ω

(~E0 × ~B∗

0 − ~E∗0 × ~B0

)]. (3.13)

Using Maxwell’s equations we find ~B0 = i /ω∇× ~E0. Hence, after applying ( ~E0 ·∇) ~E∗0 +

( ~E∗0 · ∇) ~E0 = ∇( ~E0 · ~E∗

0) − ~E0 × (∇× ~E∗0) − ~E∗

0 × (∇× ~E0) we get

m~R = − q2

4mω2∇∣∣∣ ~E0

∣∣∣2

(3.14)

or, written as a function of the light intensity I

~F = − q2λ2

8π2mε0c3∇I . (3.15)

~F is called the ponderomotive force, λ is the wavelength of the light and ε0 is the per-

mittivity of free space. Given the mathematical form of Eq. 3.15, it can be rewritten as

the result of an effective scalar potential ~F = −∇Φ where the ponderomotive potential

is

Φ =q2λ2

8π2mε0c3I . (3.16)


Neutral atoms experience a similar force in inhomogeneous laser fields, which can

be used to trap cold atoms [72]. For a free electron, the instantaneous position of the

quiver motion (see Eq. 3.10) is 180◦ out of phase from the electric field. The phase of the

oscillation of the dipole moment of an atom, on the other hand, changes from in phase

at frequencies far below resonance to out of phase above resonance. Hence, a laser beam

whose wavelength is red-shifted with respect to the resonance produces an attractive

potential, i.e. the resulting force on the atom is directed towards higher laser intensity.

In the case of a blue-shifted laser, the force is directed towards lower intensity [73], as in

the case of a free electron. The potential for an atom in an inhomogeneous laser field is

given by the ac Stark shift [73].

3.2.1 Experimental Setup for the Laser Pulse-Electron Pulse

Crosscorrelation Experiment

The objective of this measurement is to determine the electron pulse duration of the

electron diffractometer as it impacts the system response function. Hence, it is important

to perform the measurement as closely to the normal UED sample position as possible.

Since the ponderomotive force interacts with the electron pulse in vacuum, the beam

paths of the laser and electron pulses just need to be crossed at the position at which the

electron pulse duration is to be measured. The ponderomotive force of the laser pulse will

then deflect electrons that traverse the high intensity laser pulse, modifying the shape of

the electron beam at the detector. The relative delay between the electron pulse and the

laser pulse can then be scanned, similar to a pump-probe experiment, to probe different

parts of the electron pulse sequentially.

One of the factors contributing to the system response of the measurement is the

time that the electron pulse takes to cross the laser beam (see section 3.2.2). For this


reason and to maximize the intensity gradients of the laser pulse, the laser beam needs

to be focused. For 55 keV electrons, there is a transit-time broadening of 100 fs for

a laser beam diameter of 13 µm. However, since the lateral electron beam size at the

intersection between the two beams is much larger than the laser beam waist, only a

small percentage of the electrons would interact with the laser pulse, leading to a large

background of unscattered electrons and a poor SNR. Furthermore, the crossing time

of the laser beam through the electron beam also broadens the system response of the

measurement. To mitigate these problems, a pinhole is introduced in the laser beam

path to strip the electron pulse of its outer electrons just before its crossing point with

the laser beam. We used a 30 µm diameter pinhole to limit the time broadening due to

the laser pulse transit time through the finite size of the electron beam to 100 fs. To

prevent damage to the pinhole by the intense laser beam, the laser focus was moved 5 mm

downstream from the usual sample position along the electron propagation direction.

Calculations show that for reasonable laser pulse parameters (100 fs, 20 µm beam

waist), a laser pulse energy on the order of millijoules is needed to deflect an electron at

the detector by the size of the electron beam. Simulated electron beam shapes at the

detector are shown in Fig. 3.3. The simulations were performed by using the Barnes-

Hut tree code (see section 2.2.1) to produce an electron pulse and to propagate it to

a position just before its interaction with the laser beam. For about 1 mm along the

electron beam path centred around the laser beam-electron beam crossing, the electron

pulse propagation was calculated without Coulomb interaction between the electrons

by velocity Verlet integration under consideration of the ponderomotive force of the

crossing laser pulse. After that, the Barnes-Hut tree code was used again to propagate

the electrons to the detector.

The required pulse energies are not available from table-top laser systems and hence

experiments were performed using the beam line 2B of the Advanced Laser Light Source


1 mm

4 mm

−800 −600 −400 −200 0 200 400 600 t [fs]

Figure 3.3: Simulated electron beam images on the detector after interaction with a

10 mJ, 100 fs laser pulse. Top row: The electron beam (100 µm) is being scattered

by a laser pulse with 25 µm beam waist. The image intensity is scaled to make the

depletion of electrons along the laser beam path visible. Bottom row: the electron beam

is stripped by a 30 µm pinhole before interacting with a 15 µm laser beam waist. The

image intensity is scaled to make the scattered electrons visible.

(ALLS) at the Institut National de la Recherche Scientific (INRS) in Varennes, QC. The

beam line consists of a Ti:Sapphire oscillator followed by a regenerative amplifier and two

multi-pass amplifiers which produce laser pulses with up to 40 mJ with a bandwidth of

40 nm at a repetition rate of 100 Hz. For the electron pulse duration measurements, we

detuned the compressor to produce 90 fs pulses. The scattering laser pulse had a pulse

energy of 14.9 mJ at the focus and the electron gun was operated at V = 55 kV. Due

to beam time limitations, the pulse characterization was only performed for one electron

number density (3100 electrons per pulse, 100 µm extraction pinhole).

The experimental setup is shown schematically in Fig. 3.4. The optical setup is very

similar to a UED setup that uses the fundamental laser wavelength as its pump pulse.

However, the beam geometry was changed so that the laser beam crosses the electron

beam at 90◦. Due to the high pulse energy of the laser, a beam dump was necessary to


PhotocathodeV= −55 kV

ElectronPulse

AnodeV=0

Laser Pulse

Pinhole

Detector

Laser267 nm

(a) (b)

RailDelay f=250 mm

Prism Comp.

SHG SFG

Beam Splitter

Attenuator

Telescope (8:1)

10%

90%

Figure 3.4: (a) Optical setup of the laser pulse-electron pulse crosscorrelation experiment.

The incoming laser pulse is split into two arms with 90% of the pulse energy focused to

scatter the electron beam. The remaining 10% is further attenuated, sent through a

variable delay line, tripled and then compressed before entering the electron gun. (b)

Schematic view of the experiment geometry. The electron pulse is stripped of its outer

electrons by a 30 µm diameter pinhole before it is scattered by the ponderomotive force

of the laser pulse.

absorb the laser pulse after its interaction with the electron pulse to prevent damage to

the vacuum chamber and background signal in the recorded beam images.

At the time these experiments were done, a UV pulse was used to drive a silver

photocathode by single photon photoemission. For this purpose, the third harmonic

(267 nm) of the fundamental Ti:Sapphire laser pulse was produced by two BBO crystals.

They were cut for type I second harmonic generation (SHG) and type II sum frequency

generation (SFG), respectively. They were followed by a prism compressor to compresses

the resulting UV pulse. The spatial separation of the different wavelengths in the prism

compressor also facilitated the extraction of the tripled light from the collinear beams of


fundamental, second harmonic and third harmonic light.

One of the main challenges of this experiment was to obtain overlap in space and time

between the laser pulse and the electron pulse. In order to facilitate this task, I designed

an alignment tool consisting of a thin stainless steel foil with two micromachined features.

The first feature was a long, narrow horizontal slit (1 cm × 30 µm), the second was a

rectangular pinhole, machined to appear circular (30 µm diameter) when viewed at 45◦

which was in line with the slit. By moving this tool with respect to the electron beam

or the laser beam with respect to the alignment tool in vertical direction, the long slit is

located, by then moving in the horizontal direction, the pinhole can be found. Through

this procedure, the time consuming two-dimensional search for a pinhole can be turned

into two one-dimensional searches. This alignment tool was mounted so that it could be

inserted at the intersection of the electron and laser beams at 45◦ with respect to both

the electron beam and the laser beams. Rough temporal overlap was established by using

the method described in section 3.1.

3.2.2 Results and Data Analysis

A series of electron distribution maps for different time delays between the electron pulse

and the scattering laser pulse is shown in Fig. 3.5. In the images without a stripping

pinhole, the propagation of the laser pulse through the electron pulse (right to left) can

be directly observed, strikingly demonstrating the broadening of the observed signal by

the lateral width of the electron pulse. Also note that while the scattered electrons are

spatially well-separated from the undisturbed beam in the lower row, they are mixed

with the largely undeflected outer parts of the beam in the case without the pinhole.

A potential disadvantage of the setup with the stripping pinhole is the high sensitivity

of the stripped beam setup to laser beam pointing instability. In the series of images


Figure 3.5: Series of images of the beam on the detector without (upper row) and with

(lower row) the stripping pinhole (30µm) in place. An image of the undisturbed beam

has been subtracted from each of the images to highlight the scattering of electrons due

to the ponderomotive force of the laser pulse. Hence, dark regions are in the image are

depleted of electrons due to the interaction with the laser while bright regions receive

more electrons than in the undisturbed image. The images in the upper row are integrated

over 720 pulses while the ones in the lower row are integrated over 4000 pulses due to the

much lower number of electrons that reaches the detector when the pinhole is in place.

Both series of images are taken at steps of 300 fs between adjacent images.


−2 −1.5 −1 −0.5 0 0.5 1 1.5 2Vertical position [mm]

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2Vertical position [mm]

Inte

nsity

[A.U

.]

Figure 3.6: Line profiles through electron beam shapes recorded without (left) and with

(right) stripping pinhole in place. The dashed lines are with laser interaction, the solid

lines without.

taken with the stripping pinhole in place, it is obvious that the scattering laser beam

moved upwards during the measurement. However, it should be noted that the laser,

the compressor and the experiment were set up on three separate, uncoupled optical

tables and only the laser was mounted on a stiff, floating table. Hence, such behaviour

is expected and should not occur on the same scale in a permanent setup. Line profiles

through these images are shown in Fig. 3.6. The depletion of electrons in the centre of

the pulse is clearly visible as well as the broadening of the electron distribution by the

scattered electrons.

While the number of frames that contain significant distortion of the electron beam

can serve as an estimate for the duration of the electron pulse, for an accurate measure-

ment it is essential to find a quantity that is related to the profiles of the electron pulse

and the laser pulse in a simple way, like a cross-correlation trace.

The laser pulse propagates along the x-axis in positive direction and the electron

pulse propagates along the z-axis also in positive direction at velocity v. Since the size

of the laser focus is small compared to its distance from the detector, the change of the

position of an electron in the detector plane due to deflection by the laser ponderomotive


force can be written as

[X,Y ] =T

me

∫[Fx(~r(t)), Fy(~r(t))] dt. (3.17)

Here, T is the time the electrons take to propagate from the intersection with the laser

to the detector and ~F is the force the electron experiences at its position ~r(t) due to the

laser field. The component of the ponderomotive force in z-direction has no significant

effect due to the high initial velocity of the electrons in this direction. For a short time

around the overlap of the electron and laser pulses, we assume that the envelopes of both,

the electron pulse and the laser pulse are constant. They are described by the number

density of the electron pulse ρ(x, y, z − vt) and the ponderomotive force profile of the

laser pulse ~F (x−ct, y, z). According to Eq. 3.15, the ponderomotive force is proportional

to the gradient of the intensity of the applied laser field. While there is also a deflection

of electrons in x-direction due to the gradient of the temporal envelope of the laser pulse,

the deflection in y-direction caused by the spatial envelope is more useful for the these

measurements, since it is proportional to the temporal intensity envelope itself. In the

detector plane, this deflection for an electron initially incident at (x, y, z − vt) is

Y =T

me

∫Fy(x − ct, y, z + vt)dt (3.18)

as long as the lateral motion of the electron while crossing the laser focus is negligible.

As a practical signal to quantify the scattering of the electrons by the laser pulse, we

choose the product of the absolute value of this vertical displacement and the detected

electron number density D(X,Y ) integrated over the detector area:

S =

∫|Y | D(X,Y ) dX dY . (3.19)

Using the force profile and the electron number, this can be rewritten as

S(τ) =

T

me

∫ρ(x, y, z) |Fy(x − c(t − τ), y, z + vt)| dtdx dy dz . (3.20)


Here, we also introduced the delay τ between the electron pulse and the laser pulse.

The force profile of the laser beam can be rewritten as |Fy(x − c(t − τ), y, z + vt)| =

f0 ft(x/c − t + τ) fy(y) fz(z + vt) for a Gaussian pulse assuming Eq. 3.15. If the laser

beam diameter is small compared to the electron beam diameter, the spatial profile of

the electron beam can be approximated as ρ(x, y, z) = ρ0 ρx(x) ρy(y) ρt(z/v) in the laser-

electron interaction volume.

S(τ) =ρ0f0T

me

(∫fy(y)ny(y)dy

)×

∫ [∫ρx(x)ft

(x

c− t + τ

)dx

∫ρt

(z

v

)fz(z + vt)dz

]dt (3.21)

which is a convolution of fz(tv), ρx(−ct), ft(t) and the sought after ρt(t). Hence, the

signal can be viewed as a cross correlation between the temporal pulse shapes of the laser

and electron pulses with additional broadening caused by the spatial pulse shape of the

electron pulse traversed at the speed of light and the spatial pulse shape of the laser pulse

traversed at the speed of the electrons.

Each of the beam images is normalized with respect to its total intensity before

calculating S(τ) in order to reduce noise from intensity fluctuations brought about by

small intensity fluctuations in the laser. This is necessary since even relatively small

intensity fluctuations can have significant effects on the number of electrons per pulse

because of the nonlinearity of the third harmonic generation.

Signal traces and their respective Gaussian fits for pulse duration measurements with

and without the stripping pinhole in place are shown in Fig. 3.7.

To recover the pulse duration from these traces, the spatial contributions to the

convolution Eq. 3.21 have to be determined. Since the stripping pinhole is much smaller

than the diameter of the electron beam, the resulting stripped electron beam should not

have any notable structure normal to the propagation direction and can be treated as a

top-hat profile with its width equal to the size of the pinhole. The spatial laser beam


0

2

4

−750 −500 −250 0 250 500 750

Sig

nal [

arbi

trar

y un

its]

Delay [fs]

Figure 3.7: Signal traces without (top) and with (bottom) stripping pinhole. The full

width half maximum of the Gaussian fits (dashed curves) are 815± 49 fs and 438 ± 22 fs,

respectively.

profile is assumed to be Gaussian and was determined to be 11.9 ± 0.3 µm FWHM. The

temporal profile of the laser beam is assumed to be Gaussian as well. It was measured

to be 90 fs at the overlap position by autocorrelation. The convolution of these three

contributions is approximated well by a Gaussian with a FWHM of 147 fs. Hence, from

the measurement of the stripped beam, we can determine the pulse duration of the

electron pulse to be 410 ± 30 fs.

Since the determined pulse duration is very close to the width of the measured trace,

this measurement should be largely independent of the exact shape of the spatial con-

tributions to the trace. Errors in the estimates have little effect on the calculated pulse

durations. In contrast, the measurement with the complete electron beam can at best de-

liver a rough estimate of the pulse duration unless the exact lateral shape of the electron


beam, which dominates the duration of the signal trace, is known with good accuracy.

By further reducing the various contributions to the system response and increasing the

signal-to-noise ratio, it should be possible to not only determine the pulse duration but

also to measure the temporal shape of the electron pulse with this method.

3.2.3 Calibration of the Temporal Overlap Determination

By fitting the signal with a Gaussian, the centre position of the cross-correlation curve,

i.e. the t = 0 position, can be determined to a precision on the 10 fs scale. A signal trace

with a Gaussian fit is shown in Fig. 3.8 (blue) together with a trace of a grid measurement

as described in section 3.1 (green). Because of the 90◦ crossing of the two beams a metal

wire was used instead of a TEM mesh. It is essential that the wire surface be exactly

in the middle of the electron beam since any change in position in the direction of the

laser pulse propagation would change the t = 0 position. The wire was positioned by

monitoring the electron beam current reaching the detector and moving the wire to obtain

50% electron transmission of the unobstructed electron beam. The two measurements

were taken in the same position along the electron beam path and in direct succession

with no changes except for the removal of the wire from the path of the electron and

laser beams in order to minimize systematic errors. In order to avoid using the SNR-

dependent appreciable onset, I chose a different method to find the tentative t = 0 point

of the grid measurement signal. Since the signal initially seems to rise linearly I used the

intersection of the first order fit to the linear section of the signal with the zero order fit

to the baseline. Both fits take a number of points into account and hence this analysis

should be much more reproducible than the single-point onset, used in section 3.1. The

crossing point of the two fit lines is at t = 30 ± 30 fs, i.e. well within the duration of the

electron probe pulse, which limits the time resolution. Hence, this method is adequate


Sig

nal [

A.U

.]

Laser pulse−electron pulse delay [ps]−1 −0.5 0 0.5 1 1.5 2

Figure 3.8: Signal traces and fits for ponderomotive electron pulse-laser pulse cross cor-

relation and grid measurement. The slight drift in the baseline of the grid signal may be

caused by a pump pulse pedestal.

to determine the t = 0 position for UED experiments on this timescale.

3.2.4 Discussion

While the ponderomotive laser pulse-electron pulse cross correlation is perfectly capable

of measuring electron pulse durations on the 100 fs scale, it is not a suitable diagnos-

tic tool for every UED lab due to its laser pulse energy requirements. An electron

diffractometer could be taken to a user facility with a suitable laser and the instrument

could be characterized. However, changes in operating parameters and the potential of

malfunctions, especially in light of possible future RF based electron pulse compression

technologies make this scenario a problematic proposition. What is really needed is an


electron pulse characterization that can be undertaken with the means that are available

in a typical UED lab so that measurements can be done in situ and the setup can be

tweaked to change electron pulse characteristics as needed.

3.3 Grating Enhanced Ponderomotive Scattering

for Characterization of Femtosecond Electron

Pulses

In 1933, Kapitza and Dirac proposed using a light intensity grating produced by inter-

ference of two light waves to diffract electrons [74]. This was not experimentally realized

until 2001 [75]. Incoherent scattering of electrons off a standing wave was achieved 13

years earlier [76]. Both of the above experiments used relatively low energy electron

beams compared to the energies used in UED. Here, we use a standing wave produced by

two colliding femtosecond laser pulses to scatter sections of an electron pulse. In addi-

tion to this electron pulse characterization, another application of an intensity grating for

UED has been proposed in which the grating is used to generate trains of sub-laser-cycle

electron pulses [33].

As opposed to the case of a propagating light wave described in section 3.2, in a

standing wave the electric and magnetic field are 90◦ out of phase in space and time.

For a two plane waves polarized in y-direction, propagating in the positive and negative

x-direction, respectively, we have

Ey =1

4E(ei(ωt−krx) + c.c.

)+

1

4E(ei(ωt+krx) + c.c.

)= E cos ωt cos krx (3.22)

and

Bz =1

4B(ei(ωt−krx) + c.c.

)− 1

4B(ei(ωt+krx) + c.c.

)= B sin ωt sin krx. (3.23)


E and B are the scalar real amplitudes of the electric and magnetic fields, respectively

i.e. we chose the phase at x = 0, t = 0 to be zero. A charge in this field undergoes a

quiver motion in y-direction due to the oscillating electric field:

mry = qEy −→ ry =Eq

mωsin ωt cos krx . (3.24)

Since the magnetic field is 90◦ out of (temporal and spatial) phase with the electric field,

it is in phase (in time, not in space) with the velocity of the quiver motion of the charge.

As a result, the Lorentz-force does not cancel out over a cycle of the light. The Lorentz

force due to the magnetic field is

~F = q~r × ~B = q

0

ry

0

×

0

0

Bz

=

EBq2

mωcos krx sin krx sin2 ωt

1

0

0

. (3.25)

Averaged over a cycle of the electromagnetic field we get [77]

Fx =E2q2

2mωccos krx sin krx . (3.26)

Analogous to the case of the ponderomotive force of a travelling wave, we can introduce

an effective potential Φ so that ~F = −∇Φ

Φ =q2

4mω2

(E cos krx

)2

. (3.27)

Note that although the derivation of this force is somewhat different from the case of a

travelling wave, treated in section 3.2, the result is very similar to Eq. 3.16 or actually

identical, if one assumes I = cε0/2(E cos krx

)2

despite the phase shift between the

electric and magnetic fields.

The crucial difference between the two cases is that the intensity variations that

produce the ponderomotive force happen over very different distances. In the case of

the propagating wave, the intensity gradient that causes the ponderomotive force is a


I [A

.U.]

(a) (c)(b)

0

0.5

1

1.5

2

−200 −150 −100 −50 0 50 100 150 −150 −100 −50 0 50 100 150 −150 −100 −50 0 50 100 150 200l [A.U.]

Figure 3.9: Intensity profiles of (a) a single laser pulse, (b) two counterpropagating laser

pulses, not overlapping in time and (c) two counterpropagating pulses overlapping.

result of the spatial envelope of the laser pulse. In the standing wave case, an intensity

grating is formed with a distance of λ/2 between the maximum and the minimum of the

intensity. Obviously, this leads to an enhancement in the ponderomotive force. Under

otherwise identical conditions, the peak force of two counterpropagating waves along the

propagating direction is about 100× stronger than that of a single propagating pulse

in the lateral direction if we assume half of the intensity of a single beam in each of

the counterpropagating beams, a 10 µm FWHM Gaussian beam and λ = 800 nm. This

situation is schematically shown in Fig. 3.9. Each of the laser pulses in the two pulse case

has half the energy of the pulse in the case of a single pulse. The drastically enhanced

intensity gradients along the propagation direction are obvious in the standing wave case

(c).

According to the van Cittert-Zernike theorem, the transverse coherence width of the

electrons is λe−/θsource where λe− is the de-Broglie wavelength of the electrons and θsource

is the angle the electron source (the laser spot on the photocathode) subtends at the

sample [78]. In our current setup, the coherence length is therefore ≈ 1 nm i.e. much

shorter than the periodicity of the intensity grating ≈ 400 nm. Hence, we do not expect

diffraction of the electrons off the laser intensity grating but purely classical scattering

of the electrons off the ponderomotive potential.

For two counterpropagating Gaussian laser pulses, each with a peak intensity of I0/2,


propagating in the positive and negative x-directions, the intensity equivalent is

I(~r, t) =I0

2

∣∣∣∣∣exp

(i(−ωt + kx) −

(t − x

c

)2

4w2t

)+

exp

(i(−ωt − kx) −

(t + x

c

)2

4w2t

)∣∣∣∣∣

2

exp

(−y2 + z2

2w2f

), (3.28)

where I0 is the peak intensity of each laser pulse, k = 2π/λ, ω = ck, and 2√

2 ln 2wt and

2√

2 ln 2wf are the FWHM laser pulse duration and the beam waist, respectively. The

x-component of the ponderomotive force takes the following form:

Fx(x, y, z, t) = − I0e2λ2

16π2meε0c3exp

(−y2 + z2

2w2f

)×

∂

∂x

[exp

(−(t − x

c

)2

2w2t

)+ exp

(−(t + x

c

)2

2w2t

)+

2 exp

(− t2

2w2t

)exp

(− x2

2w2t c

2

)cos(2kx)

]. (3.29)

The first two terms of the expression to be derived describe the laser pulses travelling

in opposite directions and the last term describes the standing wave produced where the

two pulses overlap. Note that the standing wave has the same duration as the original

pulses. Its spatial envelope in x-direction has the width 2√

2 ln 2wtc. Since λ/2 ≪ is

much smaller than this envelope, the derivative is dominated by the former.

Fx(x, y, z, t) ≈

− I0e2λ

2πmeε0c3exp

(−y2 + z2

2w2f

)exp

(− t2

2w2t

)exp

(− x2

2w2t c

2

)sin(2kx) , (3.30)

It is obvious from Eq. 3.30 that the force varies from a maximum in one direction to its

maximum in the opposite direction within λ/4. Since the diameter of the electron beam

is much larger than λ/2, we expect equal numbers of electrons deflected in the positive

and negative x-directions. This is confirmed by simulations of the electron beam shape

at the detector shown in Fig. 3.10. The simulations were performed analogously to the


2 mm

0 fs−200 fs

−400 fs−600 fs−800 fs

200 fs

400 fs 600 fs 800 fs

Figure 3.10: Simulated beam images at the detector after interaction with the standing

wave produced by two counterpropagating 200 fs laser pulses (175 µJ per pulse, 30 µm

beam waist.

simulations of the single beam case described in section 3.2.1. Note that the laser pulse

energy in this simulation is 2× 175 µJ while 10 mJ were required to produce good signal

in the previous measurements.

3.3.1 Grating Enhanced Electron Pulse Characterization Setup

The setup is shown in Fig. 3.11. The optical setup of the arm of the laser beam path,

which drives the electron gun is identical to the standard UED setup. The beam path that

delivers the pump pulse to the sample in a UED setup has been modified to accommodate

the pulse duration measurements. The setup requires two counterpropagating laser pulses

to collide at the overlap of their beam paths with the electron beam path. For this


PhotocathodeV= −55 kV

AnodeV=0

ElectronPulse

Laser Pulses

f=50 cm

Detector

BS

(b)

Pinhole

BS

NOPA

(a)

1:3 telescope775 nm210 fs

50 fs500 nm

z

x

y

Figure 3.11: (a) Optical setup of the grating enhanced electron pulse characterization

experiment. (b) Schematic view of the experiment geometry.

purpose, the laser beam is split by a 50/50 beam splitter. One of the resulting beams is

sent through a delay stage to permit balancing of the two arms. Due to the long beam

path of one of the beams inside the vacuum chamber, a relatively long (50 cm) focal

length lens has to be used to focus the scattering pulses. In order to still obtain a small

beam waist, the laser beam first had to be expanded from its usual diameter (2.7 mm)

by a 1:3 telescope. In practise, the size of the laser spot at the electron beam position

was 41 ± 10 µm.

Alignment

The two laser pulses used to create the ponderomotive force profile need to overlap

in space as well as in time with each other and with the electron pulse to produce a

scattering signal. Since the scattering laser pulses are propagating in opposite directions

at the overlap position, beam pointing variations in the laser cause them to move in

opposite directions if the sum of the numbers of reflections the two beams undergo after


the beam splitter (i.e. not counting the beam splitter itself) in the horizontal or vertical

plane is odd. Hence, we use three mirrors in the horizontal plane on the relative delay

stage to make the setup self-compensating for small beam pointing instabilities. The

spatial and temporal alignments of this experiment are somewhat challenging. Note that

there is no observable signal even very close to perfect spatial and temporal overlap of

both laser pulses and the electron pulse, as long as there is not at least significant partial

overlap of all three pulses. In order to facilitate the alignment, an alignment tool similar

to the one described in section 3.2.1 with slit and pinhole widths of 50 µm instead of

30 µm was used.

The alignment of the setup was performed as follows:

• The focus of the scattering laser pulse transmitted through the beam splitter (pri-

mary beam) is optimized by scanning the laser focus with the top edge of the

alignment tool using the in-vacuum translation stages. The focus is adjusted by

moving the lens along the beam propagation direction.

• The focus of the scattering laser pulse reflected by the beam splitter (secondary

beam) is optimized in an analogous fashion but the focus is now changed by moving

the relative delay stage. Since the two arms are focused by the same lens, the

coincidence of the focus also indicates the coincidence in time. This method is

accurate to about ±1 mm (±3 ps).

• The pinhole is centred on the electron beam using the in-vacuum x/y stages.

• The primary beam is aligned on the pinhole by moving the focusing lens in the

lateral plane.

• The secondary beam is overlapped with the transmitted primary beam on the last

mirror in the secondary beam path by adjusting the last mirror on the relative


translation stage.

• The last mirror in the secondary beam path is used to align the secondary beam on

the pinhole. The electron beam, and both laser beams are now spatially overlapped.

• A TEM copper mesh is moved to the intersection of the electron beam and the

laser beams. By blocking the secondary beam, rough temporal overlap between the

electron pulse and the primary laser pulse is established using the “grid effect”.

• The primary beam is blocked and the temporal overlap between the electron pulse

and the secondary laser determined in the same manner. The relative delay stage

is then moved to compensate for the differences in the temporal overlap of the

primary and secondary beams.

While this procedure should in principle establish perfect spatial and temporal overlap,

in practise there were unforeseen problems. A minor and somewhat predictable problem

is that the last step of the alignment procedure may lead to the loss of spatial overlap of

the laser beams because the mirrors on the delay stage are not perfectly aligned. This

can easily be corrected by repeating the spatial alignment procedure for the secondary

beam. A more severe problem is that the use of the alignment tool in practise led to a

systematic deviation in the spatial overlap of the laser beams. This problem was solved

by using the primary beam to burn a small hole into the edge of the copper TEM mesh

in situ and using that to correct the spatial alignment. While the exact cause of the

deviation is unclear, it is likely related to the thickness of the stainless steel foil that was

used to make the alignment tool since the problem did not appear when using the hole in

the much thinner TEM mesh. Once the signal has been established, it can be optimized

in real time while watching the electron beam image on the detector.


3.3.2 Results and Data Analysis

A series of images of the electron beam on the detector is shown in Fig. 3.12. As expected

from the simulations, symmetric scattering along the horizontal (laser pulse propagation)

direction is observed. Fig. 3.13 shows beam profiles through the electron beam images

are shown in. The horizontal beam profile at t = 0 is clearly a sum of the unbroadened

electron beam and a significantly broadened part. This highlights the fact that only the

(temporal) centre section of the pulse has been scattered while the electrons at the front

and back of the pulse continue on a nearly unaltered trajectory. The vertical line profile

through the electron beam image only displays a reduction in amplitude while changes

to its profile due to the vertical envelope of the laser pulses are small since the laser beam

waist is wider than the electron beam after the stripping pinhole.

In analogy to section 3.2.2, the images taken at different electron pulse-laser pulse

delays τ are analyzed to give a time trace

S(τ) =

∫|X|Dτ (X,Y ) dX dY , (3.31)

where X and Y are the horizontal and vertical coordinates on the detector screen (origin

at electron beam centre) and Dτ (X,Y ) is the number density of electrons detected in

the image at time delay τ . A number of these time traces for different electron numbers

per pulse are shown in Fig. 3.14.

To illustrate that this time trace is a direct cross-correlation of the electron and laser

pulses, we assume that the displacement that electrons experience due to the pondero-

motive force is negligible over the size of the laser focus and therefore the force acting

on an electron can be integrated along a straight line. This condition will be further

discussed below.

The distance from the beam crossing point to the detector is much longer than the


µ400 m

0 fs−160 fs

−320 fs−480 fs−640 fs

160 fs

320 fs 480 fs 640 fs

Figure 3.12: Detector images of the electron beam at different electron pulse-laser pulse

delays. The black spot in the electron beam is caused by detector damage. Conditions:

10,000 electrons per pulse, 135 µJ laser pulse energy, images are integrated over 4000

pulses.

X [ m]−400 −200 0 200 400

Y [ m]µ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

−400 −200 0 200 400

Inte

nsity

[A.U

.]

µ

Figure 3.13: Horizontal (left) and vertical (right) line profiles through the detector images

at −640 fs (solid line) and at 0 fs (dashed line).


τS

( )

28800

56001750

15700

electrons per pulse:

[fs]τ−1000 −500 0 500 1000

Figure 3.14: Time traces with Gaussian fits. Vertical offset for clarity. While a Gaussian

appears to be a good fit for traces of pulses with relatively few electrons, there are

systematic deviations between the data and the fit for pulses with more electrons. The

fits have widths of 1005 fs, 757 fs, 546 fs and 404 fs FWHM, respectively.

laser spot size and therefore, the deflection of an electron at the detector is given by its

velocity after its interaction with the laser:

X =Td

me

∫Fx(x, y, z, t) dt . (3.32)

Td is the propagation time of the electron pulse from its intersection with the laser to the

detector. According to Eq. 3.30 with the lateral envelope of the laser beam, Fx can be

written as a product of a constant F0 and of four functions, each of which only depends


on one of the variables t, x, y, z:

ft(t) = exp

(− t2

2w2t

), fx(x) = exp

(− x2

2w2t c

2

)sin(2kx),

fy(y) = exp

(− y2

2w2f

), fz(z) = exp

(− z2

2w2f

). (3.33)

Eq. 3.31 can be interpreted as the sum of |X| over all electrons in a pulse. Using the elec-

tron density in the electron pulse at the beam crossover position ρ(~r, t) = ρxy(x, y)ρt(t +

τ − z/v) with v being the velocity of the electrons in z-direction and Eqs. 3.32 and 3.33,

we rewrite 3.31 as

S(τ) =

∫F0ft(t)fx(x)fy(y)fz(z)×

ρxy(x, y)ρt

(t + τ − z

v

)dtdx dy dz

∝∫

fz(z)ft(t)ρt

(t + τ − z

v

)dz dt . (3.34)

S(τ) can therefore be identified as a convolution of the temporal profiles of the electron

pulse and the laser pulse and of the transverse spatial profile of the laser pulse as it is

crossed by the electron pulse. As opposed to the earlier experiments (see section 3.2.2),

the scattering potential is not moving through the electron beam, thereby eliminating

the transverse spatial profile of the electron pulse from the convolution.

In this derivation, we used the assumption that an electron propagates through the

standing wave with only a negligible deviation from the z direction. This condition is

much stricter than in the case of a single laser pulse since the ponderomotive force in this

experiment changes drastically over very short distances, defined by λ/2 (the wavelength

of the intensity profile of the standing wave) as opposed to the spatial envelope of the

laser beam. A “short” distance, for this purpose, is therefore a distance ≪ λ/2. If

an electron moves a significant fraction of this distance in x-direction while still inside

the standing wave, the linearity of S(τ) with respect to the laser intensity could be

compromised. Electrons that experience the strongest force also experience the strongest


deflection while crossing the standing wave. These electrons would then encounter a

weaker ponderomotive force as they are deflected towards the intensity minimum of the

standing wave and may even enter a region in which the force is inverted with respect

to the force experienced initially. This would lead to a reduced cumulative acceleration

along the trajectory, primarily for strongly deflected electrons. This “saturation” effect

would flatten the signal trace around its maximum and broaden time trace, leading to

an overestimation of the pulse duration. Hence, even if slight saturation occurs, a pulse

duration determined in the measurement is still guaranteed to be an upper limit to the

actual pulse duration.

To obtain an estimate for the upper limit of the deflection an electron might experience

while still inside the standing wave, we calculate the deflection it would experience if it

were exposed to the maximum possible force

Fmax =I0e

2λ

2πmeε0c3. (3.35)

While the duration of the standing wave is determined by the laser pulse duration wt,

the electron experiences it for a shorter time we since it traverses the beam spatially and

therefore the intensity envelope experienced at the electron position is the product of the

temporal envelope and the spatial envelope crossed at v:

1

w2e

=1

w2t

+

(v

wf

)2

. (3.36)

For the parameters used in this experiment, the FWHM of the resulting profile is 170 fs.

If the electron were exposed to Fmax for this duration, its offset from its initial trajectory

would be

Fmax

2me

(2√

2 ln 2we

)2

≈ 150 nm . (3.37)

Since this is on the same order of magnitude as λ/2, we verified the linearity of the signal

vs. the laser pulse energy experimentally. The measurement of the signal amplitude S(0)


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Sig

nal [

A. U

.]

Scattering Laser Pulse Energy [mJ]

Figure 3.15: Laser power dependence of the ponderomotive scattering signal vs. scattering

laser pulse energy. A straight line is a good fit and demonstrates the linear dependence

of the effect on the laser intensity over the entire accessible range.

vs. the laser pulse energy (see Fig. 3.15) did not show any deviations from the expected

linear response within the range of pulse energies accessible in our setup.

As expected, the width of the time traces shown in Fig. 3.14 and hence the electron

pulse duration increases with the electron number density. Particularly for pulses con-

taining large numbers of electrons i.e. long electron pulses whose shape dominates the

corresponding time trace, the Gaussian fits shown in the graph are not a suitable fit

function. The centre portion of the pulse is flatter and the edges somewhat steeper than

expected for a Gaussian pulse, as expected from the simulations described in section

2.2.1.

The actual temporal shape of the electron pulse cannot be directly deconvolved from

noisy experimental time-traces unless the other contributions to the convolution are small.


However, since the variance σ2 of the convolution of multiple functions is the sum of their

individual variances, the variance σ2ρ of the temporal shape ρt(t) of the electron pulse can

be extracted from the experimental trace without prior knowledge of the non-Gaussian

pulse shape by

σ2ρ = σ2

trace − σ2t − σ2

f/v2 (3.38)

where σ2trace, σ2

t and σ2f are the variances of S(t), ft(t) and fz(z), respectively.

The most common measure for pulse durations is the full width at half maximum.

For a Gaussian, FWHM = 2√

2 ln 2σ. This conversion technically does not apply to other

pulse shapes but in practise, it is a useful value to estimate the effect of the pulse shape on

the temporal resolution of a pump-probe experiment. Therefore, we calculate the electron

pulse duration T as T = 2√

2 ln 2σρ. The contributions that need to be deconvolved from

the trace are the temporal laser pulse shape (210 ± 10 fs FWHM sech2) and the spatial

profile of the laser pulse at the focus in z direction (41 ± 10 µm = 310 ± 80 fs FWHM

Gaussian for 55 keV electrons). Fig. 3.16 shows the deconvolved electron pulse duration

as a function of the number of electrons per pulse.

The measured pulse durations are shown together with simulations performed with

the general particle tracer [48] software package. The parameters used in the simulations

correspond to the setup used in these pulse duration measurements: electrons are emitted

from a gold photocathode by two-photon photoemission with a 50 fs, 500 nm, 200 µm

FWHM diameter laser pulse. In order to account for the two-photon process, the effective

pulse duration used in the simulations is 35 fs and the diameter is 141 µm. An excess

energy distribution of 0.1 eV width is assumed. The electrons are accelerated over a 6 mm

gap to 55 keV. The anode is a 150 µm diameter pinhole and the electrons propagate

freely for 26 mm after that. A 30 µm diameter pinhole strips the electron pulse followed

by another 7 mm of free propagation before the laser interaction. Note that this setup

adds 9 mm in total to the propagation length of the electron pulses over the setup used


GPT simulationsmeasurement

0

200

400

600

800

1000

0 5000 10000 15000 20000 25000 30000

T [f

s]

number of electrons per pulse

Figure 3.16: Electron pulse duration T vs. number of electrons per pulse; general particle

tracer (GPT) simulations and measurements obtained in the described experiments.

in UED experiments. This is not a limitation of this pulse characterization technique

but was chosen to minimize the complexity of the setup caused by the introduction of

the stripping pinhole.

3.3.3 Discussion

The observed electron pulse durations are in reasonable agreement with calculations

both with respect to duration and dependence on electron number. The systematic

deviation seen in the Fig. 3.16 may have been caused by imperfections of the experiment,

e.g. pedestals in the temporal profile of the laser pulse or stem from assumptions used

in the simulations such as the initial momentum distribution of the photoelectrons at

the photocathode, which have not been experimentally verified. The experimental errors

could be reduced and the system response could be improved by using shorter, cleaned


up laser pulses to scatter the electron pulse. Currently, the intrinsic system response is

determined mostly by the electron transit time across the focus (310 fs presently). A

10 µm focus and 20 fs laser pulse would give a system response of 80 fs and a similar

scattering strength as presented here, with only 10 µJ laser pulse energy.

The grid measurement for t = 0 determination together with the presented pondero-

motive force electron pulse characterization methods constitute a comprehensive set of

practical tools for the characterization of electron pulses for UED and for the performance

analysis of femtosecond electron pulse sources.

Chapter 4

Femtosecond Electron Deflectometry

Given their high charge-to-mass ratio, electrons are easily deflected when they traverse

electric or magnetic fields. This property makes them a sensitive probe to measure these

fields. Hence, femtosecond electron pulses can be used as probes for rapidly changing

fields. This fact is exploited in the grid t = 0 determination (see section 3.1) on a

day-to-day basis but little attention had been paid to the physics behind the observed

electron beam deflections. Using the electrometer connected to the faraday cup in the

vacuum chamber, we had observed negative as well as positive currents during these t = 0

measurements and hence we were aware that electrons as well as ions were being emitted

from the target i.e. laser ablation was taking place. As demonstrated in section 3.2.3,

there is not appreciable delay between the arrival of the laser pulse and the onset of the

deflection of the electrons. Hence, these measurements are a sensitive time-resolved probe

of the electric fields produced during the earliest stages of femtosecond laser ablation.

Femtosecond laser ablation of solids has attracted much attention due to its applica-

tions in laser micromachining [79], laser surgery [80] and matrix assisted laser desorption

Parts of this chapter have previously been published in [44] Christoph T. Hebeisen, German Sciaini,Maher Harb, Ralph Ernstorfer, Sergei G. Kruglik, and R. J. Dwayne Miller, Physical Review B 78,081403 (2008). Copyright 2008 by the American Physical Society.

76

Chapter 4. Femtosecond Electron Deflectometry 77

[81]. There are many different processes that lead to the removal of material after ex-

citation with an intense laser pulse. These processes largely fall into two groups [82].

Thermal processes happen after energy relaxation between the electrons and the lattice

has taken place. Melting, evaporation, phase explosion and thermal plasma generation

are examples of thermal processes. In non-thermal ablation processes, disintegration

of the lattice occurs before the electrons and the lattice have reached thermal equilib-

rium. Non-thermal processes include non-thermal melting and Coulomb explosion. For

a non-thermal process to take place, the energy required to drive the process needs to be

deposited within less than the relaxation time. Non-thermal processes are therefore only

possible with ultrashort excitation pulses. Laser pulse parameters and properties of the

material being ablated determine which process ultimately dominates.

Transient electric fields play an important role in laser ablation processes. When an

intense laser pulse hits the surface of a solid, multi-photon photoemission, avalanche and

field ionization lead to the emission of large numbers of electrons and charging of the

surface. Electron escape, recapture, ion emission and transport processes within the solid

modify the spatial charge distributions and the resulting electric fields over time. The

trajectories of electrons and ions emitted during ablation are subject to these fields. If

the charge density in the lattice is high enough, Coulomb repulsion between the ions can

even cause the lattice to disintegrate, possibly aided by the additional pull of the cloud

of emitted electrons above the surface, a process referred to as Coulomb explosion [83].

Even below the ablation threshold of a given material, large numbers of electrons

can be emitted from a sample. Over time, the positive counter charge on the sample is

compensated by recapture of some of the emitted electrons and influx of electrons from

non-excited parts of the sample [84]. Because of electron recapture, the magnitude of the

initially emitted charge is often underestimated when the total charge of the irradiated

sample is measured in the long time limit. However, a transient electron deficit can


lead to equally transient changes in the material properties of the excited sample, a

fact often ignored in ultrafast high excitation experiments which could lead to incorrect

interpretations of measurements. These surface charging effects can also be detected with

the method presented here.

Usually, ablation is studied by analyzing the energy, charge and direction of the pro-

duced electrons, ions and neutral particles using time-of-flight or other mass spectrometry

methods [85, 83, 86, 82]. These methods yield valuable data allowing identification of dif-

ferent ablation regimes. Assuming a model for the ablation process, certain parameters

of the actual ultrafast process can be extracted. However, these measurements inherently

integrate over the ultrashort timescales of the microscopic processes during ablation and

as a result, the dynamics have to be implied from a model or need to be determined us-

ing a different method. Alternative all-optical methods like time-resolved shadowgraphy

[87, 88] can detect ablation plumes in a time-resolved manner but are not sensitive to

electrical charge. Okano and coworkers [89] used electron pulses to detect electric fields.

The temporal resolution of their study was limited by the 64 ps duration of the electron

probe pulses. By using a femtosecond electron pulses to probe the electric fields during

femtosecond laser ablation, we achieve subpicosecond resolution on the visualization of

transient electric fields [44]. This technique opens the door to a more detailed view of the

ablation process since it provides insights into the spatial distributions and behaviour of

charged particles at the earliest stages of ablation. After we had completed and submit-

ted this work for review, we learnt of a study [90], which used electron pulses to study

plasma generation by a femtosecond laser pulse in a nitrogen gas jet. The temporal reso-

lution these experiments is limited to several picoseconds by the duration of the electron

pulses and the velocity mismatch between the laser pump and electron probe pulses.


Figure 4.1: The experiment geometry. The sample is placed inside the electron beam

and the laser pump pulse hits the sample surface within the trace of the electron beam.

4.1 Experimental Setup for the Observation of Tran-

sient Charge Distributions

The setup of this experiment is based on the basic UED setup described in chapter 2.

However, the sample in this experiment is not a thin film and is hence completely opaque

for the electron pulse. In order to probe the electric fields near the sample surface, the

sample is placed inside the beam path of the electron pulse so that it partially blocks the

beam (Fig. 4.1) and that the surface on which the ablation will take place is parallel to

the electron propagation. The laser pump pulse is aligned to strike the sample surface

at normal incidence inside the electron beam trace on the sample surface.

The probe electrons in the unblocked part of the electron beam pass the excited

sample surface at close distance. Transient electric fields present when the probe pulse

passes the sample impart momentum on the probe electrons, which impacts their spatial

distribution at the detector. Electrons contained at different positions within the electron


Silicon

Silicon nitride Photoresist

StrippingExposing,developing

Spin coating,baking etching

Dry (plasma) Wet (KOH)etching

Bufferedoxide etch

Silicon strip

Figure 4.2: Fabrication of the silicon strip samples (layer thicknesses not to scale).

beam probe the field at different positions and are therefore deflected differently.

We obtain a time-series of the resultant probe electron distributions by repeating this

measurement for different pump-probe delays. Each of the recorded images is a snapshot

containing information about the electric field present at the moment when the electron

pulse passed the excited part of the sample. For reference, an electron beam image

without the laser beam is taken before each frame with the laser beam present under

otherwise identical circumstances. We refer to these images as “before images”.

The fabrication process of the samples is shown schematically in Fig. 4.2. The silicon

strips were produced starting from a commercial wafer ((100) orientation) with a 40 nm

silicon nitride layer deposited on both sides. Stripe features were patterned in the silicon

nitride layer using photolithography and reactive ion (plasma) etching. This was followed

by wet etching in KOH to produce strips of Si. Finally, the nitride layer was removed

using 10 : 1 buffered oxide etch and the sample surface was cleaned with methanol. The

resulting Si strips were 330 µm thick.

As the excitation laser pulse, we used the frequency-doubled (λ = 388 nm) laser

pulse. The pulse duration was 150 fs and the beam size was 17 µm FWHM at the sample

position. The electron pulse duration was 300 fs. Each beam image was integrated

over 40 shots. Inspection of the sample after the experiment revealed that ablation had

taken place at all investigated fluences. Hence, potential surface contamination has no


30 ps 100 ps 300 ps 1000 ps9.5 ps

3 ps

100 mµ

0.5 ps 1 ps 2 ps0 ps

Figure 4.3: Probe electron density maps at the detector. Each frame is averaged over 40

laser shots. In these images, the laser beam is incident from the right side, the sample

surface is indicated by the yellow line. The scale indicates size in the sample plane, the

image on the detector appears 5.9× larger due to electron beam divergence. Peak laser

fluence: 5.6 J/cm2.

significant effect on these experiments since the surface contaminants would be removed

after the first or very few laser shots. The sample was moved vertically to a new position

for each image to prevent deep crater formation and to ensure identical conditions for

the images taken at each time step.

4.2 Experimental Results and Analysis

Selected images from the time series are shown in Fig. 4.3. The detected number of

electrons was constant throughout the time series i.e. no time-dependent absorption of

probe electrons by material ejected from the sample or high angle deflection outside the

detector range was observed.

Qualitatively, we interpret the beam shapes shown in Fig. 4.3 as follows: The probe


electrons that pass near the excited part of the sample are initially strongly deflected

away from the sample surface due to the emission of a large number of electrons from the

sample. These emitted electrons are initially very close to the surface and form a dipole

with the countercharges at the surface. Despite the attraction of the countercharge on

the surface, electrons that are sufficiently far away from the sample surface experience a

net force in the opposite direction due to space charge of the emitted electron cloud [84].

By 9.5 ps, this self-acceleration has caused the electron cloud to expanded so far that the

probe beam is split into two lobes. At this time, the probe electrons above and below the

excitation spot are visibly deflected into the sample shadow by the attractive field of the

counter charge. This deflection towards the sample becomes more and more pronounced

at 30 ps and 100 ps. However, a localized electron cloud still partially shields the Coulomb

attraction to the center part of the probe beam, causing a persistent indentation in the

middle of the electron beam profile. As more of the emitted electrons continue to escape

or get reabsorbed, the negative charge density near the surface reduces. At 300 ps and

later, the attractive force of the ions clearly dominates. Even at that time, the positive

charge on the sample surface is strongly localized, leading to a slight contraction of the

probe beam in y-direction.

Probe Electron Deflection for a Given Charge Distribution

In order to extract quantitative information about the charge distributions we calculate

the effect of a given charge distribution on the probe electron beam. The momentum

change a probe electron experiences due to a charge Q at the origin is

∆~p =

∫ −Qe

4πε0 |~r(t)|3~r(t)dt . (4.1)

Here, ~r(t) = (x, y, z) is the position of the probe electron, e is the elementary charge and

ε0 is the permittivity of free space. We assume a “frozen” charge distribution, i.e. that


the charge Q is not moving in the period during which the probe electron traverses the

region of significant electric field caused by Q. Given the size of the excitation beam

(17 µm) and the kinetic energy of the probe electrons (55 keV), the probe electron

passes the excited region of the sample in 130 fs. At least at early times i.e. before the

charge distribution has any time to spread significantly beyond the excited region, the

assumption of a frozen charge distribution is therefore justified. If the angle of deflection

and the longitudinal momentum transfer are small, we can rewrite Eq. 4.1 as

∆~p =−Qe

4πε0vz

∫~r

|~r|3dz (4.2)

for an electron initially propagating parallel to the z-axis with velocity vz. The deflection

∆(X,Y ) of the probe electron at the detector is then

∆(X,Y ) =∆ (px, py) l

mevz

=−Qel

2πε0mev2z

(x, y)

(x2 + y2), (4.3)

where me is the mass of the electron and l is the distance between the sample and

the detector. If the charge distribution is concentrated in a short section along the

electron beam path, we can integrate Eq. 4.3 over the charge distribution to calculate

the cumulative effect that the charge distribution has on the probe electrons i.e. a three-

dimensional charge distribution ρ(x, y, z) can be collapsed into an area density

ρ′(x, y) =

∫ρ(x, y, z) dz . (4.4)

For such a charge distribution, Eq. 4.3 can then be rewritten as

∆(X,Y ) =−el

2πε0mev2z

∫ ∫ρ′(x′, y′)(x − x′, y − y′)

((x − x′)2 + (y − y′)2)dx′ dy′ . (4.5)

Eq. 4.5 allows us to numerically calculate the positions of probe electrons on the detector

for a given charge distribution at the sample, but we still cannot calculate the charge

distribution from the detected electron beam shapes because the “origin” (x, y) of an

electron detected in a given detector position (X,Y ) is not known. If this information


were available, the electric field integrated along z experienced by an electron while

passing the sample at (x, y) could be directly calculated.

Another factor complicating the analysis of the acquired images further is the imper-

fect correlation between the radial position and momentum in the electron pulse even

before it reaches the sample. If the electron beam emanated from a point source or were

perfectly parallel, the radial momentum of paraxial electrons would be directly propor-

tional to their radial position. However, in practise the electrons are produced by a finite

size laser beam and with an initial lateral momentum distribution. Other imperfect ele-

ments of the electron gun may further contribute to this problem through inhomogeneous

electric and magnetic fields. The result is image blur. This can be easily seen in Fig. 4.3:

the left edge of the electron beam is created by the sharp edge of the sample and without

blur would therefore be a step function, not a smooth (albeit steep) gradient as seen

in the measurement. However, if a distribution of deflecting charges is known from a

physical model, the resulting image can be relatively easily calculated and compared to

the experimental results using a blurring function to imitate the imperfections of the

electron beam.

Fitting to a Model Charge Distribution

A full quantitative model of the ablation process treating free electrons and carriers in

the sample could be used to predict the probe beam images. Given such a model, these

experiments could serve as a direct qualitative as well as quantitative test. Lacking a

detailed microscopic model, we fit the experimental data using a phenomenological model

for the charge distribution, which makes no assumptions about dynamics. This model

charge distribution consists of two parts: positive charges on the sample surface and a

cloud of emitted electrons above the surface (see Fig. 4.4). Both parts of the charge

distribution are radially symmetric around the x-axis and the model assumes that the


Excitationlaser

Electronprobe pulse

Emittedelectrons

z

SampleSurface charge

Figure 4.4: Schematic view of the charge distribution model used to fit the data.

radial distributions are Gaussian. The positive charge on the sample is contained in

a plane on the sample surface while the electron density in the charge cloud near the

sample falls off exponentially with increasing distance from the surface.

The parameters of the model were the amount of positive charge on the sample

surface Qs, the radial size (FWHM) of that charge distribution Hs, the (negative) charge

contained in the electron cloud above the sample surface Qc, the thickness (1/e) of

the electron cloud Wc and the radial size of the electron cloud Hc. For the fit, the

vertical position of the two charge distributions Ys had to be introduced as an additional

parameter to compensate for electron beam pointing instability. We also set Qc = −Qs

because in fits we performed with Qc as an independent fit parameter, Qs + Qc was

consistent with 0 for the range of delay times for which the fits delivered meaningful

results. However, the fits with the additional independent parameter were slower and

their outcome was noisier.

We calculated the probe beam shapes resulting from such a charge distribution as


follows. The electron distribution is simulated on a grid where each vertex contains a

certain amount of charge. For convenience, the pitch of the grid was chosen to coincide

with the size of one pixel on the detector CCD image i.e. 12.6 µm on the phosphor screen.

Owing to the divergence of the electron beam, there is a scaling factor between the size

of the buckets at the sample position and their size at the detector. First, the lateral

distribution of the probe pulse had to be determined by fitting the before images. As a

functional shape of the electron beam just before the sample, I assumed

ρ′(r) =

(1 − r

R

)A r < R

0 r ≥ R

with r2 = (x − xb)2 + (y − yb)

2 (4.6)

where A and R are parameters that describe beam amplitude and size, respectively and

xb and yb are the centre position of the beam. The electrons that hit the sample do not

reach the detector. Hence, the charge on each vertex with |x− xs| < ws/2 is set to 0 (xs

is the sample position and ws is the sample width). Finally, a two-dimensional Gaussian

blur is applied on the array. This model was used to fit the before images using a simplex

downhill [91] algorithm with the parameters A, R, xb, yb, xs and ws. The parameter ws

gives the width of the “sample shadow” on the detector. By using the actual thickness of

the sample, the scaling factor for the bucket size at the sample position vs. the detector

position was determined to be 5.9.

While the functional form of the electron beam described in Eq. 4.6 gives only a

very crude desription of the electron pulse envelope, it works well because only the outer

part of the tail of the electron beam passes the sample and only that part needs to be

approximated.

Each of the frames taken with the pump laser pulse present was then fit using the

charge distribution model and the electron probe beam parameters determined from the

before images. A genetic search algorithm (similar to [92]) was used to perform the fits.


In this algorithm, an “individual” is defined by a set of parameters (called “genes”) of the

model and the “population” is the set of n individuals currently being considered. For

each individual, the probe electron map at the detector is simulated according to Eq. 4.5

followed by a Gaussian blur function. The fitness of an individual is determined as the

inverse of the RMS difference between the simulated and the detected probe electron

maps. After the fitness of all individuals has been calculated, the m fittest individuals

are selected as the “mating pool” (m is called the “mating pool size”). From these m

individuals, a new population, the next “generation”, is created. There are several ways

by which a new individual is created from one or two parent individuals:

• “Cloning:” an exact copy of an individual in the mating pool is created. While this

method obviously does not lead to any improvements of fitness, it may sometimes be

desirable to keep the fittest individual(s) of the mating pool in the next generation

to ensure that the best combination of genes found so far is not lost.

• “Mutation:” similar to cloning except that every gene has a certain probability

Pmut. of mutating during the copy process. If gene number i mutates, a random

variable with a Gaussian probability distribution with width σi is added to the

value of the gene. While Pmut. is constant throughout the fit and identical for each

gene, ~σ is a vector containing a value for each gene and changes from generation to

generation.

• “Recombination:” each gene is chosen with equal probability from one of the two

parents.

After the production of the next generation, the fitness of each individual in the new

population is calculated. The fitness of all individuals created by mutation is compared

to the fitness value of their parents. The percentage of “successful” mutants (i.e. mutants,

whose fitness is higher than that of their parent) is compared to a threshold value ηc.


If the number of successful mutants is smaller than ηc, the mutation width vector ~σ is

multiplied by a factor q (this corresponds to a decrease since 0 < q < 1), otherwise

it is divided by q. After the selection of the new mating pool, the next generation is

produced and the process begins anew. The convergence criterion for this algorithm is

the reduction of ~σ below a given fraction of its initial value.

For our fits we used a population size of n = 64 and a mating pool size of m = 8.

New individuals were exclusively created by mutation, i.e. each individual in the mating

pool was used to create 8 new individuals by mutation. The probability for each gene to

mutate was Pmut. = 0.2, the threshold for the increase of ~σ was ηc = 0.6 and the factor

q = 0.8.

These parameters were found by experimentation. The main aim was to speed up

convergence and to prevent runaway solutions and local maxima (this search maximizes

fitness). Recombination of individuals did not produce high fitness individuals because

the different genes (parameters) of the model are not orthogonal and the fitness surface is

complicated. Hence, no recombination of genes is used. Cloning was abandoned because

it favours local maxima in the fitness surface.

The charge distribution model we used obviously places restrictions on the shapes of

the charge distributions and ignores escaping electrons, emitted ions and charge refilling

from the bulk. While all of these effects modify the charge distribution after some time,

the model can still deliver an estimate of the size of the charge distributions as well as the

amount of charge for times shortly after excitation. Up to about 10 ps, the experimental

results are reproduced well by the fits to this model. Measured and fitted beam images

are shown in Fig. 4.5. The deviations for later times are likely caused by the escape

of some of the emitted electrons well beyond the envelope of the probe beam as well as

shortcomings of the assumptions about the charge density distributions in our model. We

attempted to add a separate escaping charge distribution to the above model, however,


0 ps 1 ps 3 ps 5 ps 9.5 ps

Figure 4.5: Measured and calculated probe beam intensity maps. Experimental beam

maps are shown in the top row, the corresponding fit results using the model are shown

in the bottom row.

the large number of parameters, some of them with weak dependence, made the fits

unstable.

The time series of Qs and Wc are shown in Fig. 4.6. The emission of electrons starts

at t = 0, which was expected since the onset of change in the electron probe beam was

used as the t = 0 marker for this experiment. This assumption is backed up by the

direct comparison of the grid t = 0 measurement with the ponderomotive electron pulse

characterization in section 3.2.2. The amount of emitted charge reaches a plateau after

3 ps, after which Wc starts to grow rapidly. The speed of this expansion of the electron

cloud is about 2% of the speed of light corresponding to a kinetic energy of 100 eV.

The model does not treat crater formation of the multi-shot ablation process. Crater

formation may contribute to the delay in the rise of Wc and lead to an underestimation

of Qc, especially at early times. Our implementation of the charge distribution model


−2 0 2 4 6 8t (ps)

W ( m

)µ

c

Q

W

s

c

s

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

10

35

40

45

5

15

0

20

25

30

Q (

10 e

)6

Figure 4.6: Total amount of positive charge on the sample Qs and width of the electron

cloud Wc vs. time. Data points for Wc before t = 0 have been omitted as they have no

meaning in the absence of charge i.e. before the laser excitation.

requires a non-zero minimum for Wc, masking the dynamics of Wc before about 4 ps. If

most of the electrons are very close to the countercharges on the surface, the effect of the

electrons and the countercharges on the probe beam largely cancel, similar to a situation

in which less charge is present. Hence, for early times at which Wc is overestimated due

to this minimum, Qc may be underestimated by these fits.

While there is some evidence for the occurrence of Coulomb explosion in semicon-

ductors [86, 82], its role has been disputed [93, 94]. According to calculations [95], the

initiation of Coulomb explosion in Si requires the emission of electrons on the order of

1014 electrons/cm2. Direct plasma generation, on the other hand, is estimated [96] to

happen at a free electron density of 1012 cm−2 nm−1. Given that only a fraction of these

electrons are expected to escape, our results are consistent with the latter. This is the

expected behaviour in a multi-pulse ablation scenario [83]. Incubation [97] during the


first few pulses causes defects near the surface of the solid, which then lead to increased

absorption, favouring phase explosion. By using only one or few pulses per sample posi-

tion, this method could be used to determine if Coulomb explosion exists as an ablation

pathway in semiconductors.

The calculation of the probe electron displacement at the detector according to Eq. 4.5

neglects magnetic fields. Since the charge distribution model is static, it does not include

magnetic fields, while the moving electrons in practise certainly produce a magnetic field.

However, this field only has a negligible effect on the probe electron distribution at the

detector since the velocity of the cloud of emitted electrons is much smaller than the speed

of light. Hence, the force exerted on the probe electrons by the magnetic field is much

smaller than the force from the electric field. In addition, the current produced by these

electrons points in x-direction. Hence, the magnetic field lies in the yz-plane. To a first

approximation, the z-component of the field has no effect on the probe electrons moving

along z, while the y-component is symmetric with opposite sign around the middle of

the emitted charge distribution. Therefore, the force of the magnetic field approximately

cancels itself out over the crossing of the whole charge distribution.

Determination of the Average Electric Field Strength

A much simpler analysis of the probe beam images allows to calculate the electric field in

x-direction 〈Ex〉 experienced on average by the probe electrons over their path through

the charge distribution. Using Eq. 4.3, the average deflection 〈∆X〉 is

〈∆X(t)〉 =l

vz

× ∆px

me

=le 〈Ex(t)〉 dz

v2zme

(4.7)

where d is the distance along z over which the electric field acts on the probe electron. The

size of the “dent” in the probe electron distribution at 3 ps is dy = 16 µm in y-direction

(very close to the laser beam size) and for symmetry reasons, dz = dy. Time traces of


2

2

2

2

2

2

0 2 4 6 8 10

100

80

60

40

20

Fluence (J/cm )

Max

. Def

lect

ion

( m

)µ

2

µ

−60

−40

−20

0

20

40

60

80

100

−10 −5 0 5 10 15

horiz

onta

l def

lect

ion

( m

)11.2 J/cm 5.6 J/cm 3.4 J/cm 1.7 J/cm

0.5 J/cm 1.1 J/cm

pump−probe delay (ps)

Figure 4.7: Probe electron deflection for different laser fluences. The main graph shows

the time dependence of the probe deflection whereas the inset shows the maximum de-

flection for each fluence as determined by a Gaussian fit to the deflection time trace.

〈∆X〉 at the centre of the probe beam for a range of excitation fluences are shown in

Fig. 4.7. Using the measured maximum deflection at 5.6 J/cm2, 〈∆X(3 ps)〉 = 108 µm

we obtain 〈Ex〉 = 3.5 × 106 V/m for the electric field at this point in space and time.

For fluences above 1.7 J/cm2, 〈∆X〉 peaks at the same time. At 1.1 J/cm2, the

peak is clearly delayed, an effect even more obvious at 0.5 J/cm2. The plasma formation

threshold [85] for 100 fs, 620 nm pulses is ≈ 1 J/cm2. Below this threshold, ablation

occurs through the emission of neutrals. As opposed to the massive ionization through

avalanche ionization or field ionization, which occur at higher fluences, only a moderate

number of electrons is emitted through multi-photon photoemission for excitation below

the plasma formation threshold. The lower number of emitted electrons also results in


weaker self-acceleration of the emitted electron cloud. The amplitude of the deflection

increases with the intensity of the incident laser pulse, however there appears to be a

saturation value which is reached for excitations above 4 J/cm2.

4.3 Discussion

We have used femtosecond electron pulses to observe the transient charge distributions

produced during femtosecond laser ablation from a Si (100) surface on the subpicosecond

timescale. We determined the electric field strength from the maximum deflection of

the probe electrons (3.5 × 106 V/m for 5.6 J/cm2 pump fluence). Fits to a simple

charge distribution model reveal that this field is produced by the emission of 1.2 × 106

electrons (5.3×1011 electrons/cm2). As expected for multi-pulse ablation, this number is

consistent with direct plasma generation but cannot be explained by Coulomb explosion.

By reducing the number of shots, this method will be capable of verifying the existence of

Coulomb explosion in semiconductors and metals. With a detailed microscopic theory,

these experiments will enable effectively a direct observation of the dynamics of the

charges emitted in the ablation process.

Chapter 5

Future Directions

Femtosecond electron diffraction has made enormous progress towards resolving atomic

motions directly even though the ultimately desired sub-100 fs time resolution is not

practical yet with the current generation electron pulse sources. The tradeoff between

the number of electrons per pulse and the electron pulse duration, i.e. between the signal

level and the temporal resolution, limits the potential of compact electron guns to achieve

this goal without confining UED experiments to the small class of fully reversible samples.

A nascent femtosecond electron pulse source design uses an RF electron pulse com-

pression scheme to create sub-100 fs electron pulses at the sample position with 104−105

electrons per pulse [22]. In this design a DC electron gun, similar in principle to the

one used in the setup described in this thesis, is used to create the initial electron pulse.

This pulse is then deliberately propagated over a distance of several centimetres while it

spreads and develops a chirp. If an ellipsoidal electron pulse envelope is used, this chirp

is highly linear [45]. After developing this linear chirp, the electron pulse is sent through

an RF cavity whose electric field is along the electron propagation direction. The RF

field is timed such that the electrons pass at the zero crossing at which the force created

by the electric field switches from decelerating to accelerating. While the electron pulse

94

Chapter 5. Future Directions 95

enters the cavity with the fast electrons at the leading edge of the pulse and the slow

ones trailing behind, this field slows down the electrons that arrive early and speeds up

the later ones, effectively inverting the chirp of the electron pulse. Hence, as the elec-

tron pulse continues to propagate, it recompresses and the sample can be placed at the

position of minimum pulse duration [22]. Due to the longer propagation distances, this

scheme allows for convenient placement of beam forming elements like magnetic lenses.

Obviously, this compression scheme requires very high phase and amplitude stability

of the RF field. These problems have been solved and efforts to build such systems

are underway. Combined with an every-electron detector (see section 2.4), an electron

diffractometer using such a femtosecond electron pulse source could acquire a diffraction

pattern in a single shot without compromising its sub-100 fs time resolution.

The longer electron pulse propagation in this future electron pulse source also pro-

duces electrons with higher lateral coherence [98]. This is crucial for the success of UED

on crystals with large unit cells; a typical unit cell size for protein crystals is 5 nm [99]

and good quality diffraction patterns are only produced if the coherence length spans at

least several unit cells (for comparison, the coherence length of the electrons produced

by the current compact electron gun is 1 nm at the sample position). With photoactive

proteins that maintain their function when crystallized (see e.g. Ref. [100]), this devel-

opment will enable the direct observation of protein function at the most fundamental

level. The remaining challenge will be the preparation of suitable samples.

Vanadium dioxide (VO2) undergoes a phase transition from its high-temperature

metallic phase to its low temperature insulating phase at T = 340 K [101]. This change

is accompanied by a structural transition from rutile to monoclinic [102]. If the low

temperature phase is excited strongly by a femtosecond laser pulse, the transition to the

metallic phase takes place in under a picosecond, suggesting a non-thermal pathway [10].

The driving mechanism of this ultrafast phase transition has not been identified uniquely

Chapter 5. Future Directions 96

despite numerous studies using different methods, including ultrafast spectroscopy [103],

terahertz spectroscopy [104], ultrafast x-ray diffraction [10], and UED [105]. While the

latter two studies probed the structure directly, their time resolutions were limited by the

probe pulse durations of more than 300 fs. However, the optical and terahertz studies

suggest a significantly faster initial structural change of 75 fs or 130 fs, respectively. Since

even thin film samples of VO2 undergo this phase transition reversibly, our compact-gun

electron diffractometer could be used with a low number of electrons per pulse (n ≈ 1000)

to observe the atomic motions with 100 fs time resolution.

As an improvement to the electron deflectometry technique presented in chapter 4,

a mesh could be introduced in the electron beam before the sample, following a method

used in proton radiography [106]. This would divide the electron beam into small sub-

beams. By identifying each sub-beam in the electron beam distorted by the emitted

charges, the “whence problem” for the probe electrons can be solved on the scale of the

pitch of the mesh. Such images would contain a large amount of additional information

over the current data. This would allow the direct calculation of an electric field map with

a pixel size of the mesh pitch. Also, the additional information would impose stronger

constraints on the fits to the charge distribution model, which would allow the use of a

more complex and more realistic model for the charge distribution.

Femtosecond electron pulses have become a versatile tool to probe atomic structure on

the timescale natural to structural transitions, and to map transient charge distributions.

With diagnostic techniques to measure the electron pulse duration and to calibrate the

timing between the electron pulse and a laser pulse, the tools are now in hand for current

and future UED setups to fully realize the potential of this powerful technique.

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