SPIE Handbook of Microlithography, Micromachining and Microfabrication
Volume 1: Microlithography
Section 2.2 Elements of Electron Optics
The part of the EBL system that forms the electron beam is normally referred to as the column. An EBL column (Fig. 2.4) typically consists of an electron source, two or more lenses, a mechanism for deflecting the beam, a blanker for turning the beam on and off, a stigmator for correcting any astigmatism in the beam, apertures for helping to define the beam, alignment systems for centering the beam in the column, and finally, an electron detector for assisting with focusing and locating marks on the sample. The optical axis (Z) is parallel to the electron beam, while X and Y are parallel to the plane of the sample.
Electron optics are a very close analog of light optics, and most of the principles of an electron beam column (except for the rotation of the image) can be understood by thinking of the electrons as rays of light and the electron optical components as simply their optical counterparts. In order to operate an EBL machine, generally it is not necessary to understand the underlying math andphysics, so they will not be discussed here although several excellent texts are available should the reader desire more information. [13,14] In addition, computer programs are available that allow easy and accurate design and simulation of optical components and columns. 
Electrons may be emitted from a conducting material either by heating it to the point where the electrons have sufficient energy to overcome the work function barrier of the conductor (thermionic sources) or by applying an electric field sufficiently strong that they tunnel through the barrier (field emission sources). Three key parameters of the source are the virtual source size, its brightness (expressed in amperes per square centimeter per steradian), and the energy spread of the emitted electrons (measured in electron volts).
The size of the source is important since this determines the amount of demagnification the lenses must provide in order to form a small spot at the target. Brightness can be compared to intensity in light optics, so the brighter the electron source, the higher the current in the electron beam. A beam with a wide energy spread (which is undesirable, as will be shown in the section on lenses) is similar to white light, while a beam with a narrow energy spread would be comparable to monochromatic light. Although the energy spread of the source is important, space charge interactions between electrons further increase the energy spread of the beam as it moves down the column (Boersch effect).  An electron source is usually combined with two or more electrodes to control the emission properties, as shown in Fig. 2.5. 
Table 2.1 summarizes the properties of common sources. For many years the standard thermionic electron source for lithography optics was a loop of tungsten wire heated white hot by passing a current it. Tungsten was chosen for its ability to withstand high temperatures without melting or evaporating. Unfortunately, this source was not very bright and also had a large energy spread caused by the very high operating temperature (2700 K). More recently, lanthanum hexaboride has become the cathode of choice; due to a very low work function, a high brightness is obtained at an operating temperature of around 1800 K. The beam current delivered by thermionic sources depends on the temperature of the cathode. Higher temperatures can deliver greater beam current, but the tradeoff is an exponentially decreasing lifetime due to thermal evaporation of the cathode material.
Field emission sources typically consist of a tungsten needle sharpened to a point, with a radius less than 1 um. The sharp tip helps provide the extremely high electric fields needed to pull electrons out of the metal. Although cold field emission sources have become common in electron microscopes, they have seen little use in EBL due to their instability with regard to short term noise as well as long term drift, which is a much more serious problem for lithography than microscopy. The noise is caused by atoms that adsorb onto the surface of the tip, affecting its work function and thus causing large changes in the emission current. Heating the tip momentarily (flashing) can clean it, but new atoms and molecules quickly readsorb even in the best of vacuums. In addition, atoms may be ionized by the electron beam and subsequently accelerated back into the tip, causing physical sputtering of the tip itself. To minimize the current fluctuations, the electron source must be operated in an extreme ultra high vacuum environment, 10-10 Torr or better.
A technology that is now available to EBL (as well as in many electron microscopes) is the thermal field emission source. It combines the sharp tungsten needle of the field emission source and the heating of the thermal source. Because the tip operates at a temperature of about 1800 K, it is less sensitive to gases in the environment and can achieve stable operation for months at a time. Although thermal field emitter is the common name, it is more properly called a Schottky emitter since the electrons escape over the work function barrier by thermal excitation. It features a brightness almost as high as the cold field emission sources, a very small virtual source size, and a moderate energy spread. The tungsten is usually coated with a layer of zirconium oxide to reduce the work function barrier. A heated reservoir of zirconium oxide in the electron gun continuously replenishes material evaporated from the tip. It requires a vacuum in the range of 10-9 Torr, which, although much better than required for the thermionic sources, is readily achievable with modern vacuum technology. (A light bakeout might be required to remove water vapor after the system has been vented.) LaB6 sources are still preferred for shaped beam systems since the total current provided by the thermal field emission source is inadequate for this application.
Electrons can be focused either by electrostatic forces or magnetic forces. Although electron lenses in principle behave the same as optical lenses, there are differences. Except in some special cases, electron lenses can be made only to converge, not diverge. Also, the quality of electron lenses is not nearly as good as optical lenses in terms of aberrations. The relatively poor quality of electron lenses restricts the field size and convergence angle (or numerical aperture) that can be used. The two types of aberrations critical to EBL are spherical aberrations, where the outer zones of the lens focus more strongly than the inner zones, and chromatic aberrations, where electrons of slightly different energies get focused at different image planes. Both types of aberrations can be minimized by reducing the convergence angle of the system so that electrons are confined to the center of the lenses, at the cost of greatly reduced beam current.
A magnetic lens is formed from two circularly symmetric iron (or some other high permeability material) polepieces with a copper winding in-between. Fig. 2.6 shows a cross-section through a typical magnetic lens, along with some magnetic flux lines.
The divergence of the magnetic flux along the optical axis imparts a force on electrons back towards the optical (Z) axis, resulting in focusing action. The magnetic field also causes a rotation of the electrons (and the image) about the Z axis in a corkscrew fashion. Although this does not affect the performance of the lens, it does impact the design, alignment, and operation of the system. For instance, the deflection system must be rotated physically with respect to the stage coordinates. Also, when aligning a column, X and Y displacement in the upper regions of the column will not correspond to the same X and Y displacement at the target. Finally, changes in focus or changes in the height of the sample can cause a slight rotation in the deflection coordinates. This must be properly corrected or stitching and overlay errors will result. Magnetic lenses, particularly the final lens, may be liquid-cooled to maintain a controlled temperature, which is critical for stable operation of a system.
Electrostatic lenses have worse aberrations than magnetic lenses, so they are not as commonly used. They are most often found in the gun region as a condenser lens since they can be combined with the extractor or anode used to pull electrons out of the cathode, and they are easily made for ultrahigh vacuum use and are bakeout compatible. Also, aberrations in the condenser lens tend to be less important; system performance is usually dominated by the aberrations of the final lens. A simple electrostatic lens, as shown in Fig, 2.7, consists of three consecutive elements like apertures, the outer two being at ground potential and the inner at some other (variable) potential that controls the lens strength. The electric potentials set up by such a lens tend to pull an electron that is traveling away from the optical axis back towards the axis, resulting in the focusing action.
Other optical elements include apertures, deflection systems, alignment coils, blanking plates, and stigmators.
Apertures are small holes through which the beam passes on its way down the column. There are several types of apertures. A spray aperture may be used to stop any stray electrons without materially affecting the beam itself. A blanking aperture is used to turn the beam on and off; by deflecting the beam away from the aperture hole, the aperture intercepts the beam when not writing. A beam limiting aperture has two effects: it sets the beam convergence angle [[alpha]] (measured as the half-angle of the beam at the target) through which electrons can pass through the system, controlling the effect of lens aberrations and thus resolution, and also sets the beam current. A beam limiting aperture is normally set in an X-Y stage to allow it to be centered, or aligned, with respect to the optical axis. It is best to have a beam limiting aperture as close to the gun as possible to limit the effects of space charge caused by electron - electron repulsion.
Apertures may be heated to help prevent the formation of contamination deposits, which can degrade the resolution of the system. If not heated, the apertures typically need to be cleaned or replaced every few months. With platinum apertures, cleaning is easily accomplished by heating the aperture orange hot in a clean-burning flame. Shaped beam systems also have one or more shaping apertures, which can be square or have more complicated shapes to allow the formation of a variety of beam shapes, such as triangles, etc.
Deflection of the electron beam is used to scan the beam across the surface of the sample. As with lenses, it can be done either magnetically or electrostatically. The coils or plates are arranged so that the fields are perpendicular to the optical axis, as shown in Fig. 2.8(a). Deflecting the beam off axis introduces additional aberrations that cause the beam diameter to deteriorate, and deviations from linearity in X and Y increase as the amount of deflection increases. These effects limit the maximum field or deflection size that can be used. As with lenses, magnetic deflection introduces fewer distortions than electrostatic deflection. Double magnetic deflection using a pair of matched coils is sometimes used to further reduce deflection aberrations. However, electrostatic deflection can achieve much higher speeds since the inductance of the magnetic deflection coils limits their frequency response, and eddy currents introduced by the magnetic fields may further limit the speed of magnetic deflection. Since deflection systems are frequently placed inside the final lens, care must be taken to prevent the fields from interacting with conducting metal parts. Usually the final lens will be shielded with ferrite to minimize eddy currents. Some tools use multiple deflection systems, where high speed, short range deflection is done electrostatically while long range deflection is magnetic. In either case, the field size of the tool is limited by aberrations of the deflection system; some tools introduce dynamic corrections to the deflection, focus, and stigmators in order to increase the maximum field size, at the cost of additional complexity.
Blanking, or turning the beam on and off, is usually accomplished with a pair of plates set up as a simple electrostatic deflector. One or both of the plates are connected to a blanking amplifier with a fast response time. To turn the beam off, a voltage is applied across the plates which sweeps the beam off axis until it is intercepted by a downstream aperture. If possible, the blanking is arranged to be conjugate so that, to first order, the beam at the target does not move while the blanking plates are activated. Otherwise, the beam would leave streaks in the resist as it was blanked. The simplest way to ensure conjugate blanking is to arrange the column so that the blanking plates are centered at an intermediate focal point, or crossover. In very high speed systems, more elaborate blanking systems involving multiple sets of plates and delay lines may be required to prevent beam motion during the blanking and unblanking processes. 
A stigmator is a special type of lens used to compensate for imperfections in the construction and alignment of the EBL column. These imperfections can result in astigmatism, where the beam focuses in different directions at different lens settings; the shape of a nominally round beam becomes oblong, with the direction of the principal axis dependent on the focus setting, resulting in smeared images in the resist. The stigmator cancels out the effect of astigmatism, forcing the beam back into its optimum shape. Stigmators may be either electrostatic or magnetic and consist of four or more poles (eight is typical) arranged around the optical axis. They can be made by changing the connections to a deflector, as shown in Fig. 2.8(b). With proper mixing of the electrical signals, a single deflector may sometimes perform multiple functions, including beam deflection, stigmation, alignment, and blanking.
A number of other components may be found in the column, which although not important to the electron optics are nonetheless critical to the operation of the system. A Faraday cage located below the final beam limiting aperture is used to measure the beam current in order to ensure the correct dose for resist exposure. It can be either incorporated directly on the stage or a separate movable assembly in the column. The column will also typically have an isolation valve that allows the chamber to be vented for maintenance while the gun is still under vacuum and operational. All parts of an electron beam column exposed to the beam must be conductive or charging will cause unwanted displacements of the beam. Often a conductive liner tube will be placed in parts of the column to shield the beam from insulating components.
Finally, the system needs a method of detecting the electrons for focusing, deflection calibration, and alignment mark detection. Usually this is a silicon solid state detector similar to a solar cell, mounted on the end of the objective lens just above the sample. Channel plate detectors and scintillators with photomultiplier tubes may also be used. Unlike scanning electron microscopes, which image with low voltage secondary electrons, EBL systems normally detect high energy backscattered electrons since these electrons can more easily penetrate the resist film. The signal from low energy secondary electrons may be obscured by the resist.
There are several factors that determine the resolution of an electron beam system. First is the virtual source size dv divided by the demagnification of the column, M -1, resulting in a beam diameter of dg = dv /M -1. In systems with a zoom condenser lens arrangement, the demagnification of the source can be varied, but increasing the demagnification also reduces the available beam current.
If the optics of the column were otherwise ideal, this simple geometry would determine the beam diameter. Unfortunately, lenses are far from perfect. Spherical aberrations result from the tendency of the outer zones of the lenses to focus more strongly than the center of the lens. The resultant diameter is ds = 1/2Csa3, where Cs is the spherical aberration coefficient of the final lens and a is the convergence half-angle of the beam at the target. Using an aperture to limit the convergence angle thus reduces this effect, at the expense of reduced beam current. Chromatic aberrations result from lower energy electrons being focused more strongly than higher energy electrons. For a chromatically limited beam, the diameter is dc = Cc a DV / Vb, where Cc is the chromatic aberration coefficient, DV is the energy spread of the electrons, and Vb is the beam voltage.
Finally, quantum mechanics gives the electron a wavelength L = 1.2/(Vb)1/2 nm; although much smaller than the wavelength of light (0.008 nm at 25 kV), this wavelength can still limit the beam diameter by classical diffraction effects in very high resolution systems. For a diffraction limited beam, the diameter is given by dd = 0.6 L / a. To determine the theoretical beam size of a system, the contributions from various sources can be added in quadrature: d = (dg2 + ds2 + dc2 + dd2)1/2.
The diagram in Fig. 2.9 shows how these sources contribute in a typical column. In systems with thermionic sources, spherical aberrations tend to be the limiting factor for beam diameter, while chromatic aberrations dominate in field emission systems. For a given beam current, there will be an optimum combination of convergence angle and system demagnification. Resolution can generally be improved in most systems by using a smaller beam limiting aperture, at the expense of reduced beam current and throughput. In systems where the demagnification can be varied, increasing the demagnification will also improve resolution, at the expense of reduced beam current.
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This material is based upon work supported by the National Science Foundation under Grant No. ECCS-1542081. Any opinions, findings, conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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