Ultrafast Electron Microscopy with Relativistic Femtosecond Electron Pulses

An ultrafast electron microscope (UEM) with a femtosecond temporal resolution is a “dream machine” desired for studies of ultrafast structural dynamics in materials. In this chapter, we present a brief overview of the historical development of current UEMs with nonrelativistic electron pulses to illustrate the need for relativistic-energy electron pulses. We then describe the concept and development of a UEM with relativistic femtosecond electron pulses generated by a radio frequency (RF) acceleration-based photoemission gun. The technique of RF electron gun and physical characteristics of the relativistic electron pulses are described. Demonstrations of UEM images acquired using approximately 100 fs long electron pulses with energies of 3 MeV are presented. Finally, we report a single-shot diffraction imaging methodology in the UEM with a relativistic femtosecond electron pulse for studies of laser-induced ultrafast phenomena in crystalline materials.


Introduction
It is well-known that transmission electron microscope (TEM) is one of the most powerful imaging instruments. Currently, the TEM enables imaging of three-dimensional (3D) structures on the atomic scale. However, the temporal resolution of TEM is limited by the video-camera recording rate (millisecond), as continuous electron beams produced by DC-acceleration-based thermionic or field-emission sources are used in conventional TEMs. In order to overcome this millisecond temporal resolution limit in TEM, in 1987, Bostanjoglo et al. [1,2] proposed a technique with a nanosecond-triggered beam-blanking unit in TEM to produce electron beam flashes and succeeded in observation of laser-induced phase transitions in amorphous Ge films with a nanosecond resolution. Two years later, they developed time-resolved electron microscopy with a laser-triggered photoemission electron gun [3,4] and paved the way for studies and imaging of fast dynamic events with pulsed electron beams. In the time-resolved electron microscopy (pump-probe technique), an initialing pump laser pulse excites the materials (sample) to produce a transient state, and then a later analytical probe electron pulse detects it at a correlated time with the pump pulse, as shown in Figure 1. It is worth noting that the temporal resolution is determined by the durations of the pump laser pulse and probe electron pulse. It is not limited by the speed of the electron detector. Therefore, the generation of short electron pulses is very significant.
In the past decade, both temporal and spatial resolutions of the time-resolved electron microscopy were improved by several research groups [5][6][7][8][9][10][11][12][13][14][15] by developing high-brightness electron sources and optimizing TEM electron optics. Currently, there are two main approaches to time-resolved electron microscopy: (1) single-shot approach, which uses high-charge electron pulses and (2) stroboscopic approach, which uses "single" electron pulses. The first approach, pioneered by Bostanjoglo et al. (described above), aims to generate a sufficient number of electrons in the pulse to form an image with a single shot. The main advantage of this approach is that the studied structural dynamics or processes do not need to be perfectly reversible. This approach has been developed later at the Lawrence Livermore National Laboratory (LLNL) [5,6] using a modified JEOL 2000FX for dynamic transmission electron microscopy (DTEM). Single-shot imaging with spatial and temporal resolutions of 10 nm and 15 ns, respectively, has been achieved using a 15-ns electron pulse containing 5 × 10 7 electrons. DTEM has achieved a spatial resolution of approximately 5 nm and has been applied to various projects, including laser-induced melting of metals, reactions in solid states, and crystallization of amorphous semiconducting materials. However, a serious problem in this approach is the significant space-charge effect due to the Coulomb repulsion of electrons. The high current of the pulses limits the overall temporal and spatial resolutions of the instrument, even with an optimized microscope source, good column, and excellent detector.
The stroboscopic approach uses a femtosecond laser source to generate an extremely low-current electron pulses ("single" electron pulses) at the sample to maintain high temporal and spatial resolutions. A key factor in the stroboscopic approach is to have only a single electron in the column at any time to reduce space-charge effects. Images are constructed from ~10 7 of these single-electron pulses. The first single-electron imaging was demonstrated by Zewail et al. [7][8][9] at the California Institute of Technology (Caltech) using a modified 120-kV TEM as  a first-generation ultrafast electron microscope (UEM). Later, they constructed a second-generation UEM-2, using a hybrid 200-kV TEM, and achieved spatial and temporal resolutions of 3.4 Å and 250 fs, respectively [8,9]. The temporal resolution Δt (root-mean-square (RMS)) in UEM is determined by the laser pulse width Δt hv and temporal broadening Δt KE due to excess energy of electrons emitted from the photocathode. It can be calculated as [9] Δt = √ where e is the electron charge, m 0 is the electron rest mass, ΔE i is the energy spread of electrons emitted from the cathode, E i is the mean energy, and V is the potential across the distance d between the cathode and anode. Δt KE ~ 250 fs at ΔE i = 0.1 eV and 650 fs at ΔE i = 0.5 eV [9]. Recently, there are many research activities [10][11][12][13][14][15] focused on improving the electron source and electron optics inside the microscope to achieve better temporal and spatial resolutions. However, the current UEM has restrictions: (1) the specimen must be pumped ~10 7 times by the laser, which implies that the studied processes must be perfectly reversible, that is, the sample must heal between pulses; (2) the interval between two pulses needs to be longer than the recovery time of the specimen, thus limiting the repetition frequency of laser excitation; and (3) instrumental instabilities such as specimen drift are inevitable at long exposure times. Therefore, for most experiments under realistic conditions, it is necessary to operate with a larger number of electrons per pulse.
All of the current DTEMs and UEMs use a DC-acceleration-based photoemission electron gun to generate electron pulses at energies of 100-200 keV. For such low-energy electron pulses (nonrelativistic electron pulses), the space-charge effect due to the Coulomb repulsion of electrons is a serious problem. It not only broadens the pulse duration but also increases the energy spread and beam divergence during the acceleration (particularly near the cathode) and propagation to the specimen. We can reduce the space-charge broadening in the propagation with a high-energy electron beam, that is, with the use of ultrahigh-voltage electron microscopy. However, the space-charge effect near the cathode can be reduced only by instantaneously accelerating the electrons to high energies with a high electric field. This is very difficult or impossible, as the maximum static electric field in the DC gun is determined by the vacuum breakdown limit of ~10 MV/m. The current state-ofthe-art DC guns have been developed to generate 600-fs electron pulses with up to 10,000 electrons per pulse [16]. An approach of electron pulse compression based on the radio frequency (RF) technology was proposed to control the space-charge effect and generate high-current femtosecond electron pulses at the sample position [17][18][19][20]. However, this approach is not suitable for microscopy, because of the relatively large energy spread of the electron pulses. From the theoretical modeling and experimental study, it is obvious that it is impossible to use the DC electron gun parameters to attain femtosecond or picosecond electron pulses at the sample position with a reasonable electron number of 10 7 (or larger) for the single-shot imaging.
Recently, an advanced accelerator technology of RF-acceleration-based photoemission electron guns has been successfully applied for ultrafast electron diffraction (UED) with a single-shot measurement [21][22][23][24][25][26][27][28][29][30]. The RF gun is usually operated with a high RF electric field equal to or higher than 100 MV/m, which is 10 times higher than those of the DC guns. Therefore, the electrons emitted from the photocathode can be quickly accelerated into the relativistic-energy region to Electron Microscopy -Novel Microscopy Trends minimize the space-charge effects in the pulse, yielding a femtosecond or picosecond pulse containing a large number of electrons. Yang et al. have developed the first prototype of relativistic UEM using the RF gun technology at the Osaka University, have succeeded in generation of high-brightness relativistic electron pulses with a pulse duration of 100 fs containing 10 7 electrons at an energy of 3 MeV [31,32], and have demonstrated the first single-shot imaging using such femtosecond electron pulses [33][34][35][36]. This promising approach has a large potential to study ultrafast dynamics in materials, as there are several crucial advantages over nonrelativistic UEM systems: • The relativistic energy reduces the space-charge effect, which consequently maintains the temporal confinement and beam brightness during the propagation to the sample. It is possible to perform single-shot imaging with femtosecond temporal resolution to observe reversible and irreversible processes in materials.
• Relativistic-energy electrons significantly enhance the extinction distance for elastic scattering and provide structural information, essentially free from multiple scattering and inelastic effects [37]. Our previous UED study of structural dynamics of laser-irradiated gold nanofilms indicates that the kinematic theory can be applied in the case of 3-MeV probe electrons with the assumption of single scattering events [29,30]. This enables to easily understand and explain structural dynamics.
• A thick sample can be used for measurement, thereby obviating the requirement to prepare suitable thin samples. The utilization of the relativistic electron pulse overcomes the loss of temporal resolution due to the velocity mismatch in samples. Furthermore, the relativistic UEM is suitable for in situ observations as there are large area and space inside the objective lens to install various specimens.
In this chapter, we introduce a UEM with relativistic femtosecond electron pulses, including information of an RF photoemission gun, concept of relativistic UEM, and demonstration experiments with relativistic femtosecond electron pulses.

Relativistic UEM
The relativistic UEM consists of a 1.6-cell S-band (2.856 GHz) photocathode RF gun and microscopy column including an electron illumination system, objective lens, and imaging system. Figure 2 shows a prototype of relativistic UEM, which has a height of 3 m and diameter of 0.7 m.

Photocathode RF gun
Photocathode RF gun is a high-brightness electron source in the particle accelerator field, which has been widely applied in free-electron lasers [38,39], and is considered for use in the next linear colliders [40,41]. The RF gun used in our relativistic UEM consists of two RF cavities: a half cell and full cell. The accelerating RF is 2.856 GHz, belonging to the so-called S-band corresponding to a wavelength of λ = 104.969 mm. The length of the full-cell cavity is λ/2 = 52.4845 mm, while the length of the half-cell is 31.49 mm, equal to 0.6 times λ/2, as numerical studies show that more optimal performances are obtained if the half-cell cavity length is 0.6 (rather than 0.5) times the full-cell length. The cross section of the actual RF cavities is shown in Figure 3(b). The shapes of the cavities are optimized to reduce both RF-induced emittance and energy spread. The cavities and other components are carefully fabricated and brazed together to minimize the dark current due to the field emission. A very fine copper photocathode is located at a position of a highaccelerating RF field in the half-cell cavity and is illuminated by the third harmonic of a Ti:sapphire laser (ultraviolet (UV) emission: 266 nm, pulse duration: 100 fs). When the electrons leave the cathode, they are accelerated by a negative electric field in the cavity, as shown in Figure 3(a).
Generally, the RF gun uses the TM 010 transverse magnetic mode with a phase shift of π between the half cell and full cell. The linear components of the electric and magnetic fields in the RF cavities can be assumed to be [42,43]   Electron Microscopy -Novel Microscopy Trends where E 0 ≥ 100 MV/m is the peak accelerating field, k = 2π/λ, ω = ck, c is the velocity of light, and ϕ 0 is the initial RF phase when the electron leaves the cathode surface (z = 0) at t = 0. For short electron pulses with Gaussian distributions in longitudinal and transverse directions, Kim [42] and Travier [44] reported analytical expressions for the following parameters at the gun exit in practical units: electron energy E in MeV, RMS relative energy spread ΔE/E, RMS angular divergence σ' x in mrad, normalized RMS RF-induced emittance ε rf , and normalized RMS spacecharge-induced emittance ε sc in mm-mrad: σ ' x = 0.511 ε sc = 3.76 × 10 3 where E 0 is the peak accelerating field in MV/m, f is the RF in MHz, n is the number of full-cell cavities, Q is the electron charge of the pulse in nC, and σ b and σ x are the RMS pulse duration in ps and RMS transverse beam size in mm, respectively, which are dependent on the laser pulse width and spot size on the cathode. These expressions are useful to estimate the beam parameters for the consideration and design of a new RF gun in other instruments. For example, for a 1.5-cell S-band RF gun at E 0 = 100 MV/m with a 100-fs and 0.1-mm laser, we estimate the following beam parameters: E = 3.9 MeV, ΔE/E = 3.8 × 10 −4 , σ' x = 1.1 mrad, ε rf = 2.2 × 10 −6 mm-mrad, and ε sc = 1.3 × 10 −2 mm-mrad at Q = 0.1 pC. These estimated parameters are in agreement with a particle simulation with the space-charge effect, as described below.
For a short electron pulse with a small beam size, the RF-induced emittance is negligible in the RF gun. In this case, the thermal emittance (initial emittance) at the cathode is dominant. Assuming an isotropic emission into a half sphere in front of the cathode surface, the thermal emittance can be expressed in terms of the RMS incident laser spot size on the cathode σ r and a kinetic energy of the emitted electrons E kin : where hν s the laser photon energy, φ is the work function of the cathode, ϕ schottky is the reduction in the potential wall barrier due to the Schottky effect, and α and β are a constant and field-enhancement parameter, respectively, which are determined by the roughness and clearness of the cathode surface. Finally, the total beam emittance is For a very fine copper photocathode with a 266-nm laser under the conditions of E 0 = 100 MV/m and ϕ 0 = 30°, the measured thermal emittance exhibited a linear relationship with the RMS laser spot size: ε th [mm-mrad] = 0.74 × σ r [mm] [45], yielding an E kin = 0.42 eV.
In electron microscopy, the electron gun is required to generate a low-emittance and low-energy-spread beam (normalized emittance ≤0.1 mm-mrad, energy spread ≤10 −4 ). The beam dynamics in the RF gun can be calculated by a theoretical simulation using the General Particle Tracer (GPT) code [46]. Figure 4 presents the simulation results of relativistic femtosecond-pulsed electron beams at the specimen position in the UEM generated from a 1.6-cell S-band RF gun. The results of the beam dynamics show that (1) the minimum energy spread is obtained at the launch phase of approximately 20°. At ϕ 0 ≥ 60°, the energies of the electrons decrease leading to the large increases in the energy spread due to the space-charge effects during the electron propagation. The slight increase in the energy spread at ϕ 0 < 20° is caused by the space-charge effect near the cathode as the actual RF electric field is decreased by E 0 sinϕ 0 , (2) large increases in both energy spread and pulse duration are observed at an electron energy smaller than 3 MeV, and (3) the transverse emittance of the femtosecond electron pulses generated from the RF gun is dominated mainly by the thermal emittance if the number of electrons in the pulse is 10 6 (or smaller). This allows us to generate low-emittance electron pulses by focusing the laser spot on the cathode, as described in Eq. (9). The increase in the energy spread due to the space-charge effect is also negligible at an electron number smaller than or equal to 10 6 per pulse. The theoretical modeling and particle simulation indicate that the RF gun could generate high-current femtosecond electron pulses with excellent characteristics, including a normalized RMS transverse emittance of 0.02 mm-mrad, energy spread of 10 −4 to 10 −5 , and pulse duration of 100 fs with 10 6 electrons per pulse at an energy larger than or equal to 3 MeV. The peak brightness of such electron pulses B p can be calculated by where β = v/c, v is the electron velocity, and γ is the normalized relativistic energy. From the given parameters, we can calculate the peak brightness, B p = 2 × 10 17 A/m 2 •sr. Recently, the development of a high-repetition-rate normalconducting RF gun at 1000 Hz was proposed in our research group. In the near future using this RF gun, the time-averaged brightness of the femtosecond-pulsed electron beam can be potentially increased to B = 2 × 10 7 A/m 2 •sr, corresponding to the brightness of the 100-kV thermionic emission gun used in modern TEMs. In addition, if we can further reduce the energy spread, the RF gun will pave the way for generation of a practical high-brightness femtosecond-pulsed electron beam for UEM.

Electron illumination system
The electron illumination system comprises two condenser lenses and condenser aperture to control and transfer the electron pulses from the RF gun on the specimen, as shown in Figure 5. An aperture with three pinholes with diameters of 0.5, 1, and 2 mm is made of a 1-mm-thick molybdenum metal and is installed between the two condenser lenses. The distance from the photocathode to the specimen is 0.8 m. However, there are two significant differences from the normal TEMs: (1) there is no gun crossover in the RF gun and (2) we cannot produce a crossover between the two condenser lenses owing to the space-charge effect (i.e., the condenser lenses do not condense). Therefore, in this illumination system, the image of the beam spot on the cathode acts as the object plane of the first condenser lens as the beam size is minimum in the RF gun. It is worth noting that a virtual source image behind the cathode may be better for the object plane of the first lens as the source size is smaller than that on the cathode, as shown in Figure 5. We adjust the first lens to create a parallel electron beam. The aperture stops the large-divergence electrons to further reduce the emittance, yielding a small illumination convergence angle at the specimen. Finally, we used the second lens to create a parallel beam or convergent beam on the specimen. The parallel beam is used primarily for UEM imaging and selected-area diffraction (SAD), while the convergent beam is used mainly for convergent-beam electron diffraction (CBED). In the experiments, a small convergence angle of α = 31 μrad was achieved with the condenser aperture with the pinhole diameter of 0.5 mm in the parallel-beam operation mode.

Objective lens
The objective lens is the most important lens in a TEM. It forms TEM images or DPs, magnified by the other lenses. It is very challenging to construct this lens as the specimen must be located close to its center. In the UEM, two asymmetrical and separable pole pieces (upper and lower) are used for the objective lens. The gap between the pole pieces is 19 mm. It allows us to insert both specimen and aperture between the pole pieces. With the large gap, it is straightforward to design specimen holders for various tasks such as tilting, rotation, heating, cooling, straining, etc. The gap-to-bore ratio is 1.46 for creation of a strong magnetic field and aberration suppression. We carefully designed and produced all of the pole pieces, iron circuits, coils, and water-cooling components. The pole pieces were made of a soft magnetic alloy (Permendur) with an iron-to-cobalt content ratio of 1:1. The saturation magnetic flux density is 2.4 T. The objective lens is a very strong lens. The maximum magnetic field strength at the center of the pole pieces is 2.3 T under the magnetomotive force of 35 kA•turns. The focal length is 5.8 mm for a 3-MeV electron beam. The diameter of the lens is 0.7 m, as shown in Figure 6(a). The specimen is placed close to the center of the pole pieces with a side-entry method and manipulated by a five-axis motorized stage. The sample can be pumped by a pulsed laser beam, as shown in Figure 2. An objective aperture with a pinhole diameter of 0.3 mm is inserted at the back-focal plane of the objective lens to block scattered electrons in the imaging operation mode.

Imaging system
The imaging system uses two magnetic lenses (intermediate and projector lenses) to magnify the TEM image or DP produced by the objective lens and to project it onto a viewing screen (scintillator) through a charge-coupled device (CCD) camera. In the intermediate and projector lenses, two symmetrical and separable pole pieces are used. The gap is 20.8 mm, while the gap-to-bore ratio is ~1. In a time-resolved image measurement with the pump-probe technique, the spread of the detector (recording rate of the video-camera) does not limit the temporal resolution; however, a high-sensitivity detection of electron waves is crucial. In particular, acquisition of images in a single shot is necessary in order to observe irreversible processes. In addition, as mentioned above, the space-charge effect causes increases in the pulse duration, emittance, and energy spread, even in relativistic electron beams. Low-current electron pulses should be used in the UEM. Therefore, the image recording system should be highly sensitive to every electron. In the UEM, in order to achieve a high sensitivity to MeV electron detection with a high damage threshold, we chose a Tl-doped CsI columnar crystal scintillator equipped with a fiber optic plate (Hamamatsu Photonics) to convert the relativistic-energy TEM images or DPs into optical images. The light generated by the scintillator is propagated by a reflective mirror (at 45°) consisting of aluminum deposited on a 5-μm-thick polymer, and finally the optical images are detected with an electron-multiplying CCD (EMCCD) with 1024 × 1024 pixels, as shown in Figure 6(b). The effective detection area of the scintillator is 50 × 50 mm 2 , while the distance from the specimen to the scintillator is 1.8 m. The sensitivity of the whole detection system is 3 × 10 −3 counts/electron.

Femtosecond laser system
A femtosecond Ti:sapphire laser (Spectra-Physics) is used to generate femtosecond electron beam pulses and to excite the specimen. The laser consists of a Ti:sapphire laser oscillator with a pulse width of 90 fs (Tsunami, central wavelength: 800 nm), regenerative amplifier including a pulse compressor, and a wavelength converter. The femtosecond laser oscillator is synchronized to a 79.3-MHz RF signal, corresponding to 1/36 of the 2856-MHz RF used for the electron generation in the RF gun, with a time-to-lock piezoelectric device. The time jitter between the laser pulse and RF phase is 61 fs [36]. The laser pulses generated from the oscillator are fed to the regenerative amplifier and amplified to ~1 mJ per pulse. The regenerative amplifier is driven by a green laser with a highly stable repetition rate of 1 kHz (Empower, wavelength: 532 nm, output: 10 W).
The amplified femtosecond pulses are converted to the third harmonics by a wavelength converter (Tripler) composed of two nonlinear crystals (SHG and THG) and time plate for pulse delay adjustment. The third-harmonic pulses (UV wavelength: 266 nm) with the maximum energy of 70 μJ per pulse are illuminated onto the copper cathode to generate femtosecond electron pulses. The residual fundamental (wavelength: 800 nm) and second-harmonic (wavelength: 400 nm) pulses are used to pump the samples. The time delay between the pump laser pulse and probe electron pulse is changed with an optical delay located on the pump laser beam line for time-resolved experiments. Both laser beams used for the electron generation and sample excitation can be focused to a spot size with a full width at half maximum (FWHM) smaller than 30 μm at the corresponding target.

UEM (imaging mode)
In the imaging operation mode of the relativistic UEM, we adjust the intermediate lens so that its object plane is the image plane of the objective lens and then project the image onto the scintillator with the projection lens, as shown in Figure 5(a). The objective aperture with a pinhole diameter of 0.3 mm inserted at the back-focal plane of the objective lens is used to block the diffraction patterns and other scattered electrons. Figure 7 shows bright-field UEM images of polystyrene latex particles, with diameters of 1.09 μm and gold nanoparticles with diameters of 400 ± 20 nm, dispersed on a carbon film pasted on a copper mesh, observed with a pulse integration measurement [35]. The magnification of the images is approximately 1500×. The energy of the electron pulses used for the observations is 3.1 MeV. The pulse duration is approximately 100 fs. In this experiment, a condenser aperture with a pinhole diameter of 0.5 mm is used to collimate the electron beam. The repetition rate of the electron pulses is 10 Hz. The normalized RMS emittance and electron charge in the pulses are 0.12 mm-mrad and 1 pC at the specimen position, respectively. From these parameters, the estimated peak brightness of the pulses in the observations is B p = 3.5 × 10 16 A/m 2 •sr. For these electron pulses, acceptable images of both polystyrene latex particles and gold nanoparticles can be obtained using our relativistic UEM with 2000-and 500-pulse integrations, respectively.
At a low-magnification observation condition, the single-shot observation of UEM images with a relativistic femtosecond electron pulse is achievable. Figure 8 presents UEM images of single-crystal gold obtained with a single shot and 10-and 100-pulse integrations. The sample is a single-crystalline gold film with a thickness of 10 nm placed on a gold mesh. Although the signal-to-noise ratio is still not sufficient in the single shot, an acceptable image can be obtained with 10 pulses (or more), as shown in Figure 8(b) and (c). This demonstrates that the single-shot observation of UEM images with a relativistic electron pulse is achievable if the brightness of the pulses can be increased by one order of magnitude, B p ~ 10 17 A/m 2 •sr, which can be realized, as described in Section 2.1.

UED (diffraction mode)
In the relativistic-energy electron diffraction measurement (diffraction mode), we adjust the imaging-system lenses so that the back-focal plane of the objective lens acts, as the object plane for the intermediate lens, and then use the projection lens to project the DPs onto the scintillator, as shown in Figure 5(b). It is worth noting that in the diffraction mode, if the electron beam is too intense, it will damage the viewing screen or saturate the CCD camera. Therefore, we could generate a smaller beam to reduce the illuminated area of the specimen contributing to the DP on the screen. The use of a selected-area aperture inserted at the image plane of the objective lens is a better choice to create a virtual aperture in the plane of the specimen, thus yielding only the SAD pattern. In the diffraction mode, the objective aperture is not used. In order to check the contrast of the DPs and resolution, we generate a parallel electron beam with a diameter of 0.5 mm to illuminate the specimen using a condenser aperture with a diameter of 0.5 mm and weakened second condenser lens in the illumination system. The characteristics of the electron pulses are the same as those in the imaging operation mode. Figure 9 presents the DPs of the singlecrystal gold observed by a single shot and 10-and 100-pulse integrations. The sample is a single-crystalline gold film with a thickness of 10 nm placed on a gold mesh. The energy of the electron pulses is 3.1 MeV. The electron charge per pulse is 1 pC. Data in Figure 9 show that (1) sharp DPs and high contrast can be obtained with the relativistic femtosecond electron pulses, (2) higher order spots of (−420) and (4-20) from the single-crystal gold with scattering vectors up to 1.1 Å −1 can be clearly captured with a single shot, and (3) the RMS width of the zeroth-order spot (000) in the single shot is measured to be 0.018 Å −1 , indicating an excellent spatial resolution for the relativistic diffracted beam.
Based on the width of the (000) spot and measured distance of the diffraction spots from the (000) position, the estimated RMS illumination convergence angle α of the electron beam at the specimen is α = 31 μrad. This convergence angle is two orders of magnitude smaller than that of nonrelativistic UED. Additionally, the coherence of the electron source is an important parameter in diffraction imaging, particularly in terms of spatial coherence (transverse coherence), which determines the sharpness of the DPs and diffraction contrast in the acquired images. The spatial coherence length is defined as where λ e is the electron wavelength and α is the RMS illumination convergence angle. Using the obtained illumination convergence angle, the spatial coherence length of the electron pulses generated with the RF gun is d c = 5.6 nm, twice that of the current UED systems. This enables to detect sharp DPs and acquire goodcontrast diffraction images with a single shot, as shown in Figure 9.
The temporal resolution can be characterized in the time-resolved electron diffraction studies. Figure 10 presents an example of time-resolved experiment for observation of UED structural dynamics in a 35-nm thick single-crystalline silicon sample. The sample was pumped by a 400-nm laser beam with a pulse duration of 100 fs and density of 3.5 mJ/cm 2 . The UED patterns were measured with a single shot using a 3-MeV electron pulse with the pulse duration of 100 fs containing 10 5 electrons per pulse. The data elucidate the dynamics in the silicon crystals: the The structural recovery after a change is very slow. Tanimura and Naruse [47] suggested that these dynamics are caused mainly by the lattice distortion due to the laser excitation in silicon crystals, indicating that the timeresolved diffraction methodology in the relativistic UEM could be utilized to obtain an atomic perspective of lattice motion in crystalline materials.
The total temporal resolution of the UEM can be estimated mainly with the probe electron pulse duration σ b , pump laser pulse width σ b , and time jitter Δt j between two pulses as The time jitter is determined by the synchronization of the laser pulse to the accelerating RF phase; therefore, we can define Δt j = 61 fs, described in Section 2.3. In our relativistic UEM, both pump and probe pulse durations are ~ 100 fs (RMS). The estimated total temporal resolution is approximately 150 fs (RMS), corresponding to the experimental results represented by the dashed line in Figure 10

Conclusions
In this chapter, we have introduced a relativistic UEM with femtosecond electron pulses, including the relativistic femtosecond electron pulse generation with an RF-acceleration-based photoemission gun, first prototype relativistic UEM instrument, and demonstrations of UEM image and UED measurements with the Simulation results of diffracted intensity changes due to lattice distortion within a angle of Δθ < 0.1° along the (111)-oriented direction [47]. DOI: http://dx.doi.org /10.5772/intechopen.81405 relativistic femtosecond electron pulses. The electron pulses generated by the RF gun exhibited excellent characteristics, including a low emittance of ≤0.1 mm-nrad, energy spread of 10 −4 , and pulse duration of 100 fs with 10 6 electrons per pulse at an energy ≥3 MeV. These pulses have facilitated (1) the acquisition of high-quality high-resolution diffraction patterns with a single shot, (2) acquisition of acceptable UEM images with pulse integration measurements, and (3) time-resolved experiments with an excellent temporal resolution of 150 fs, suggesting that the relativistic UEM is very promising for studies on ultrafast phenomena in the femtosecond time region.
Ultrahigh-voltage electron microscopes operated in the relativistic-energy region above 1 MeV have attracted significant attention in various research fields, including physics, biology, and materials science. However, the existing system is too large and expensive to be purchased and operated even by large-scale facilities such as universities or national research centers, not to mention smaller research institutions and laboratories. The RF electron gun is capable of acceleration to ≥3 MeV in a length of only 15 cm. Further reductions in the emittance and energy spread, increase in the repetition rate, and suppression of some instabilities are required; however, the improvement in the RF gun and resolution refinement to the angstrom level will enable new electron microscopes based on this RF gun, sufficiently small and inexpensive for general research institutions and laboratories. Furthermore, by providing a femtosecond temporal resolution, such relativistic UEMs will constitute the next-generation electron microscopes, referred to as "dream machines," desired for a long time by material-structure researchers throughout the world.