High brightness picosecond electron gun

REVIEW OF SCIENTIFIC INSTRUMENTS 76, 085108 共2005兲

High brightness picosecond electron gun M. Merano,a兲 S. Collin, P. Renucci, M. Gatri, S. Sonderegger, A. Crottini, J. D. Ganière, and B. Deveaud Institut de Photonique et d’ Electronique Quantique, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

共Received 2 April 2005; accepted 7 July 2005; published online 4 August 2005兲 We have developed a high brightness picosecond electron gun. We have used it to replace the thermionic electron gun of a commercial scanning electron microscope 共SEM兲 in order to perform time-resolved cathodoluminescence experiments. Picosecond electron pulses are produced, at a repetition rate of 80.7 MHz, by femtosecond mode-locked laser pulses focused on a metal photocathode. This system has a normalized axial brightness of 93 A / cm2 sr kV, allowing for a spatial resolution of 50 nm in the secondary electron imaging mode of the SEM. The temporal width of the electron pulse is 12 ps. © 2005 American Institute of Physics. 关DOI: 10.1063/1.2008975兴

I. INTRODUCTION

Laser-driven picosecond electron guns have been developed in recent years.1–3 A picosecond or femtosecond laser pulse is used to create an electron pulse with a comparable time duration. The photoelectrons are then accelerated and focused by a suitable electron optical system. Picosecond electron pulses are used in time-resolved electron diffraction experiments to investigate the nuclear dynamics of laserexcited molecules, the structural rearrangement of transient species during photochemical reactions,4 or transient surface effects on crystal surfaces.5 Laser-driven electron guns have also been used for free electron laser setups6 and other electron accelerator systems.7 We have developed and fully characterized a high brightness picosecond electron gun to perform time-resolved cathodoluminescence experiments. With this gun we have replaced the thermionic electron gun of a commercial scanning electron microscope 共SEM兲共JEOL 6360兲. Electron pulses 12 ps long are focused down to 50 nm, keeping the capability to get structural information through the secondary electron imaging mode of the microscope. The time resolution of the system is obtained via a streak camera.8 This new spectroscopic tool allows performing time-resolved experiments on single nanostructures such as semiconductor quantum dots, carbon nanotubes, or polymers.9 In this article we provide a complete description of the high brightness picosecond electron gun, we characterize the electron optical properties of this system, and we report the temporal width of the electron pulse produced. The main properties of this electron gun are as follows: • A normalized gun brightness of the order of 100 A / cm2 sr kV. At 20 kV acceleration voltage this corresponds to a probe current 共i.e., the current focused on the sample by the SEM electron optical column兲 of 10 pA 共⬃1 electron per pulse兲 with a probe diameter of 50 nm. a兲

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• An electron pulse width of ⬃12 ps. • A high repetition rate 共80.7 MHz兲 for fast luminescence detection with a streak camera system.

II. ELECTRON GUN DESCRIPTION

Our high brightness picosecond electron gun is shown in Fig. 1. The photocathode is a 20-nm-thick gold film deposited on a quartz window by conventional evaporation techniques. It is used in the transmission mode. A circular aperture, 1 mm in diameter, located 2.5 mm from the cathode, is used as an extraction electrode and is followed by the anode 共diameter 5 mm兲 at a distance of 15 mm. When installed on the microscope column the anode is replaced by the anode of the SEM. The electron gun is mounted in a vacuum chamber at a pressure of 10−6 mbar. The laser system used for the generation of picosecond electron pulses is a femtosecond mode locked Ti:sapphire laser. Infrared radiation at 800 nm is first doubled and then tripled in a frequency harmonic generator 共FHG兲 system. The FHG provides 0.6 nJ pulses at 266 nm and a pulse width of 200 fs. The repetition rate is 80.7 MHz. The light from the tripler system goes through a beam expander and a microscope objective, enters in the vacuum chamber through a sapphire window, and is focused on the cathode surface. The spot size 共defined as the radius at which the intensity drops by the factor 1 / e2兲 is 2.5 ␮m. Pure metal photocathodes seem to be better candidates for laser-driven electron guns because of high damage threshold, large free electron density, almost instantaneous time response, and the ease of preparation.10 Gold has the advantage that is transferable in air without any problem, and has a work function 共4.3 eV兲 well suited for our laser system. The thickness of the cathode film is a compromise between quantum efficiency and roughness. Photocathodes of 20 nm have a good quantum yield and are rugged enough to withstand many days of operation.2 Once the photocathode is mounted in the vacuum chamber, it can be exposed to UV radiation. Initially the current

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FIG. 1. Picosecond electron gun. Electron pulses are produced by a photoelectric effect 关cathode 共C兲兴 and are accelerated by an extraction electrode 关pinhole 共P兲兴 and the anode 共A兲. The blade and the Faraday cup are used to measure the gun brightness. FIG. 3. Electron beam profile at the blade level. Dots are experimental values, the line is a Gaussian fit.

produced for a constant amount of light increases over time. To activate the cathode the surface is irradiated with 266 nm radiation for several hours. After the activation process, as long as the cathode remains under vacuum, his quantum efficiency is reproducible for days of operation. In Fig. 2 an aging test for the gold cathode is reported. We have been focusing 48 mW of UV radiation onto the cathode for several hours. The cathode was kept at −1 kV, and the pinhole and the anode were grounded. The stability of the emitted current is rather good and a quantum efficiency ␩ of 3.8 ⫻ 10−6 is obtained. Published data for gold cathodes quantum efficiency, tested with ultraviolet laser pulses in reflection mode operation, report values of 4.7⫻ 10−5.11 Considering the fact that we are working in the transmission mode and we have a 10% UV transmission through the 20 nm gold film, our results are in good agreement with previously performed experiments.

III. OPTICAL PROPERTIES A. Crossover and magnification

In this section we suppose that the photocathode is grounded while the pinhole and the anode are at a positive potential V P. The C-P distance is ␹ and the P-A distance is ␰.

The electric field in the C-P region is E1 = −V P / ␹ and in the P-A region E2 = 0 V. Electrons are supposed to have all the same initial energy ¯E. For the sake of simplicity we can divide the system into three parts: the region in which electrons experience a constant electric field E1, the pinhole, and the region at null field E2. Such a system is an example of an electrostatic immersion lenses. It is possible to compute the electron trajectories 共ray tracing method兲 in the three different parts of the gun and to derive its optical properties.12 In the pinhole proximity the electric field is inhomogeneous and contains a radial component. It can be shown13 that the pinhole is equivalent to a thin lens of focal length f = − 4␹.

共1兲

The pinhole is thus a diverging lens. The effective source point of the cathode 共crossover兲 is placed behind the cathode at a distance d from the anode12 given by d = 2␹ M + ␰ ,

共2兲

where the lateral magnification M is 2 M= . 3

共3兲

B. Gun brightness

FIG. 2. Aging test. Photocurrent produced for a constant amount of incident light. The stability of the emitted current is rather good.

With the aim of measuring the gun brightness, we examined the electron beam profile after the anode 共Fig. 1兲. Electrons, freely expanding in the vacuum chamber, were collected in a Faraday cup. By cutting the beam with a blade and plotting the measured current derivative as a function of the blade displacement we obtained the beam profile 共Fig. 3兲. The blade was placed in the middle of the vacuum chamber, at a distance d = 106 mm from the cathode. For 24 nA extraction current, the cathode at −1 kV, pinhole and anode grounded, and a laser spot size of 2.5 ␮m, we found a Gaussian beam with a radius Rb = 6.5 mm. The main parameter for electron microscopy is axial brightness.14 Only electrons leaving the center of the crossover with a small emission angle are relevant. If we assume


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that the current density j共␳兲 at the cathode surface has the same Gaussian profile than the laser beam, the current density at the crossover is j共␳兲 = I0

2␳2 2 , 2 exp − ␲␴ ␴2

共4兲

where I0 is the total current, ␴ = MRl 共Rl laser radius兲 and ␳ the distance from the beam axis. The fraction of electrons emitted from a disk of radius r Ⰶ ␴ in the center of the crossover is 2r2 / ␴2. We consider now a small disk of radius r⬘ Ⰶ Rb placed on the axis of the vacuum chamber at the blade level. The fraction of electrons propagating in the solid angle 2 ⌬⍀ = ␲r⬘2 / 共d + 31 ␹兲 ⯝ ␲r⬘2 / d2 defined by r⬘, are 2r⬘2 / R2b. Axial brightness is given by the number of electrons emitted from the disk of radius r in the solid angle ⌬⍀ per unit surface per unit solid angle:

␤ = I 02

4I0d r r⬘ 1 d 2 = . ␴2 R2b ␲r2 ␲r⬘2 ␲2R2b␴2 2

2

2

2

共5兲

For 1 kV acceleration voltage the brightness of our laserdriven electron gun is 93 A / cm2 sr. The maximal possible brightness ␤th for an electron gun was given by Langmuir15 as

␤th =

jV , ␲⌬V

共6兲

where j is the source current density, V the acceleration voltage, and ⌬V is the initial photoelectron energy spread divided by the electron charge. For a gold photocathode and 266 nm incident light we have e⌬V = 0.3 eV. A discrepancy between the theorical brigthness ␤th = 2.9⫻ 102 A / cm2 sr and the measured one suggests that we are facing space-charge effects.16 Formula 共6兲 has a very general value and does not depend on the optical system employed. In particular, the linear relation between brightness and acceleration voltage is valid as long as relativistic corrections can be neglected. It is then possible to define17 the normalized axial brightness 共␤norm兲:

␤norm =

␤ . V

共7兲

For our laser-driven electron gun we have ␤norm = 93 A / cm2 sr kV. This value is 100 times smaller than the normalized brightness of a thermionic electron gun 共共0.2 − 1兲 ⫻ 104 A / cm2 sr kV兲.14 Modern SEMs with a thermionic electron gun can achieve a spatial resolution of 3 nm. This means that the electron beam can be focused on the sample over a spot diameter d p 艋 3 nm still having enough current to obtain a clear image. With our gun, we have the same current over a spot 10 times bigger, which means that a spatial resolution of 50 nm is possible. We get a confirmation of this by evaluating the probe current with the formula that relates it to brightness: I p = ␤normV␲2

d2p 2 ␣ , 4

共8兲

where ␣ is the probe aperture angle.14 Typical values for ␣ are between 5 and 20 mrad. Choosing V = 20 kV, ␣ = 10 mrad, d p = 50 nm, it gives an I p of 10 pA, still sufficient

FIG. 4. Pulse width: setup. In the same experimental configuration, first electrons and then UV light are focused on a GaAs:Si sample. The TRCL and the TRPL signals are compared.

to have a secondary electron image. Such a current corresponds to 0.8 electrons per pulse. This excitation current is largely sufficient also for cathodoluminescence 共CL兲 analysis, since a single electron per pulse may generate, depending on the acceleration voltage, a few thousand electron-hole pairs into a semiconductor sample. Until now we have considered the continuous brightness ␤. Indeed we intend to use the standard Everhart-Thornley secondary electron detector mounted on a commercial SEM in order to obtain secondary electron images. Such a detector operates in continuous mode so that ␤ is the relevant parameter. Anyway, since we are working with pulses it is interesting to give also the brightness per pulse ␤pulse = ␤ / ␯␶. With ␯ = 80 MHz the repetition rate of our laser system and ␶ = 12 ps the estimated electron pulse width 共see below兲 we obtain a normalized brightness per pulse of 9.7 ⫻ 104 A / cm2 sr kV. IV. PULSE WIDTH

The temporal width of the electron pulses has been measured by an indirect method. The electron beam is focused over a semiconductor material and the CL signal is collected with a 2 ps resolution streak camera 共Fig. 4兲. We compare the time-resolved cathodoluminescence 共TRCL兲 emission, produced by electron pulses, with the time-resolved photoluminescence 共TRPL兲 signal obtained with the 200 fs UV laser pulses. The electron pulses are focused by an electrostatic lens placed after the anode. A lens 共L1 f = 20 cm兲 collimates the luminescence signal that is focused on the streak camera with a 31 cm focal-length lens 共L2兲. A filter is inserted in the light beam path in order to stop the residual laser light. An electrostatic lens is mounted after the pinhole. It consists of three circular 2-mm-thick electrodes with a circular central aperture of diameter ␾ = 2 mm. The distance between the first electrode and the pinhole is 2 mm and the distance between two consecutive electrodes is also 2 mm. The cathode is placed at a negative potential, pinhole, anode, and electrode 1 and 3 are grounded. By varying the potential V2 of electrode 2 we have a converging lens. The system is simulated with Simion software for an acceleration potential of −1 kV and −2.5 kV. We find that electrons are focused at the center of the vacuum chamber for V2 equal to −558 V and to −1428 V. An experimental test of the lens is carried


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Several causes contribute to the temporal broadening 共⌬t兲 of the electron beam: the photocathode time response, the initial energy spread, the electron path difference, and the 45° sample position. It is well known that the photocathode time response 共⌬t1 = 100 fs兲 is not relevant at the time scale we are concerned. The ⌬t2 due to initial energy spread is only relevant in the acceleration region and is given by ⌬t2 =

FIG. 5. Dots are the experimental TRCL data. Crosses are the TRPL data. Lines are the two fitting curves. The two signals were normalized and superposed in order to evidence the same exponential decay.

out as well. Using the blade and the Faraday cup we find optimal focalization for V2 = −554 V and −1385 V, respectively, and spot sizes of 279 ␮m and 178 ␮m. The semiconductor sample, used to generate cathodoluminescence, is GaAs:Si with an impurity concentration of 1019 / cm3. It is mounted at the center of the vacuum chamber 共distance from the cathode d = 106 mm兲 at 45° with respect to the electron beam direction. The CL signal is collected at 90° and directed towards the streak camera by a lens collecting system. The acceleration potential for the electrons is chosen to be 2.5 kV. We excite the sample with a current of 22 nA. In the same experimental configuration we focus the femtosecond laser pulses over the sample and we obtain the time-resolved photoluminescence signal 共TRPL兲 also. Experiments are carried at room temperature. We observe that the TRCL and the TRPL signals have different rise times and the same decay time of 16 ps 共Fig. 5兲. We can regard the TRPL signal as the response of the system to a ␦ of Dirac excitation 共200 fs兲. It is then possible to obtain the pulse width of the electron beam as the deconvolution of the TRCL signal with the TRPL one. A very good fit of the photoluminescence spectrum is given by the convolution h共t兲 = Ag1共t兲 ⴱ f共t兲

共9兲

of a Gaussian g1共t兲 with a full width half maximum 共FWHM兲 of 6 ps and an exponential f共t兲 = exp共−t / 16兲. The TRCL is fitted with y共t兲 = Bg2共t兲 ⴱ f共t兲,

共10兲

where g2共t兲 is a Gaussian of FWHM= 16 ps and f共t兲 the same exponential found previously 共A and B are normalization factors兲. In the frequency domain the deconvolution is simply given by x共␯兲 =

y共␯兲 Ag1共␯兲f共␯兲 A = = g3共␯兲, h共␯兲 Bg2共␯兲f共␯兲 B

共11兲

where g3共␯兲 is a Gaussian function. The Fourier transform of x共␯兲 is still a Gaussian of FWHM= 14.8 ps. We identify it with the pulse width of our electron excitation.

1 E

冑

m 冑⌬V = 0.92 ps, 2e

共12兲

where E is the electric field between the cathode and the pinhole, and m and e are the electron mass and charge, respectively. It is important to remind that electrons obey the Maupertuis principle and not the Fermat principle. Electrons that travel different paths from one point in the object plane to the image plane take different times ⌬t3: 1 ⌬t3 = 共␣21d1 + ␣22d2兲/v = 0.81 ps. 2

共13兲

In this formula d1 and d2 are the E2 distances from the pinhole and the sample, ␣1 is the aperture angle of the beam divergind towards E2, ␣2 the aperture angle of the beam focused on the sample, and v the mean electron velocity. In 共13兲 we do not consider the acceleration region because the initial energy dispersion is relevant there and not the different electron paths. One main cause of temporal broadening is the 45° sample position with respect to the electron beam incident direction and, consequently, to the image plane of our optics system. The electron beam FWHM 共210 ␮m兲 at the sample level introduces indeed an equal optical path difference. At 2.5 keV kinetic energy this corresponds to a time delay of 7 ps. If we deconvolve this contribution from the measured pulse width, we obtain a FWHM pulse of 12 ps. This is the electron pulse broadening of our electron gun. We suppose it to be mainly due to space-charge effects. V. SPACE-CHARGE EFFECTS

The effects of space charge on the propagation dynamics of the electron packet are investigated by a mean-field model developed by Siwick et al.18 to treat longitudinal pulse broadening due to Coulomb repulsion. We generalize the equations they derive to the case of an electron pulse propagating in a position-dependent external electric field. As in the article just cited, we model our electron packet as a disk of charge. This is a very good approximation at least in the cathode proximity. For a laser pulse width of 200 fs and an electron velocity of 3.5⫻ 105 m / s 共fixed by the initial energy spread兲, we have a pulse length l of 70 nm. This length must be compared to the radius of the electron pulse at the cathode 共laser spot size兲. With this approximation the force felt by an on-axis electron at the leading edge of a pulse can be written18 F=

冉

冊

Ne2 l 1− 2 冑l + 4R2b , 2⑀0␲R2b

共14兲

where N is the number of electrons in one pulse 共1700 in our case兲, Rb is the beam radius, e is the electron charge, and ⑀0 is the permittivity of free space. If the electron packet propa-


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FIG. 6. Electron pulse broadening due to space-charge effects. The curve concavity is negative in the cathode-pinhole region and positive in regions of null electric field. Inset: focus in the cathode-pinhole region.

gates in an external field, the equations of motion for leading 共subscript 1兲 and trailing 共subscript 2兲 electrons are m

dz1 = F + Fext共z1兲, dt

dz2 = − F + Fext共z2兲, m dt

l = z1 − z2 ,

共15兲

where m is the electron mass and the external force Fext depends on the axial position of the particle z. For our system we have Fext共z兲 = 兩eE1兩, =0

0 艋 z 艋 2.5 mm

2.5 mm 艋 z 艋 d,

共16兲

where E1 is the constant electric field in the C-P region and d the cathode-sample distance. For simplicity we can neglect in our calculation the electric field in the lens that introduces a difference in the time of flight of electrons from the cathode to the sample of only 40 ps 关assuming a constant electric field 共directed along the z direction兲 between electrodes 1 and 2 and electrodes 2 and 3兴, over a time of flight of 3.7 ns. The radius of the electron beam as a function of the electron packet position 共Z = 共z1 + z2兲 / 2兲 is determined by our experimental data and simple ray tracing considerations 共as suggested also in Ref. 18兲. For instance, from the measure of the brightness we know the electron beam radius 共Rb兲 at the sample level when we do not insert the lens in the beam trajectory. This measure furnishes the aperture angle of the beam 共␪ = Rb / d + 31 ␹ ⯝ Rb / d兲共see Sec. II兲 up to the lens. In the C-P region the trajectory of the electron beam is assumed to be parabolic with a radius at pinhole 共153 ␮m兲 fixed by ␪. In our model, in the region between pinhole and electrode 2, electrons expand freely 关the radius at electrode 2 is Rb = 共583 ␮m兲兴. The radius beam at the sample useful to find the electron beam trajectory after electrode 2 has been experimentally measured 共see previous section兲. Equations 共15兲 can be easily solved numerically. Figure 6 reports the electron pulse width ⌬tsp due to space-charge effects as a function of the electron packet position. The pulse width is defined as

FIG. 7. Velocity difference between leading and trailing electrons. When the electron packet crosses the pinhole the external force still accelerates the trailing electrons while the leading electrons are already in a region of null electric field. Due to space-charge effects trailing electrons spend a longer time with respect to leading ones 共⬃4 ps, see Fig. 6兲 in the acceleration region. Indeed, the electron pulse is generated at the cathode in 200 fs only.

l ⌬tsp = , v

共17兲

where v = dZ / dt is the electron packet velocity. We can see that the pulse width increases fast in the cathode proximity 共inset兲 and then continues to increase during all the time of flight. The final value of ⌬tsp is found to be equal to 10.1 ps. This value can be considered in good agreement with the experimental value of 12 ps if we consider that the streak camera resolution is 2 ps and the simplicity of our model. In order to have a rough idea of the error done in the estimation of the Coulomb interactions between electrons when l is of the same order of magnitude than Rb, we can compare the value obtained from formula 14 with that given by assuming a spherical distribution of radius Rb. By choosing 共l = Rb兲 it is found that the error is ⯝10%. We can conclude that the error done to model the electron packet as a disk of charge in the entire electron trajectory introduces an error on ⌬tsp 艋 1 ps. Finally, in formula 共15兲 external forces depend on the position of the particles. This is the correct formulation of the problem. Our calculation shows that the dynamics of the electron pulse length l is not only governed by the force F, as it usually happens for a two-particle system in which the external forces on the two particles are always the same. Indeed, when the electron pulse crosses a region of inhomogeneous electric field 共for instance, when it crosses the pinhole兲 the external force is relevant on the dynamics of l. To illustrate this fact we report dl / dt 共the velocity difference between the leading and the trailing electrons兲 as a function of the electron packet position 共Fig. 7兲. It is evident that when the electron packet crosses the pinhole, dl / dt varies. The length of the electron pulse at the pinhole is indeed 120 ␮m and the external force still accelerates the trailing electrons while the leading ones are already in a region of null external electric field. The variation of dl / dt in crossing the pinhole is of one order of magnitude. Neglecting this fact introduces an important error on the final value of ⌬tsp.


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VI. DISCUSSION

In a SEM electrons from a thermionic, Schottky, or field emission cathode are accelerated toward the anode. The smallest beam cross section at the gun—the crossover—is demagnified by a two- or three-electron lens systems so that an electron probe, of diameter d p = 1 nm to 1 ␮m, carrying an electron probe current 10−12 − 10−8 A, is formed at the specimen surface. We can define the electron microscope magnification M as M = d p / d, where d is the crossover diameter. A SEM electron optical column is designed to have a magnification factor M that varies according to the crossover size and hence for the different types of electron guns. The crossover diameter of a thermionic gun, being between 10 and 50 ␮m, requires an electron optical column with a magnification factor M ⬃ 1 / 5000, in order to have a final spot size d p of 10 nm. Conversely the crossover of a Schottky or field emission gun is 艋15 nm, and the magnification factor of the electron optical column designed for these electron guns is M ⬃ 1 / 15.14 The crossover diameter of our electron gun is ⬃5 ␮m 共Sec. II兲. The gun brightness is high enough to allow for a probe spot diameter of 50 nm still having enough current to obtain a secondary electron image 共Sec. III B兲. The magnification factor we require from an electron optical column is at least M 艋 1 / 100. For this reason we have chosen the column of a thermionic SEM to develop our original time-resolved cathodoluminescence setup.8 ACKNOWLEDGMENTS

The authors thank Roger Rochat and Nicolas Leiser for their help and technical support. We are also indebted to

Nguyen Hoan and Jean Paul Hervé from OPEA 共Vincennes, France兲 for scientific discussions of our results. This work was supported by the Swiss National Science Foundation, NCCR project “Quantum Photonics.” 1

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