5: Chapter Electron Sources
1. All microscopes need an electron source to illuminate the specimen. There are stringent requirements for the beam of electrons and these are best met by only two types of source: Thermionic sources and field emission sources. 2. Thermionic sources are either tungsten hairpin filaments or lanthanum hexaboride (LaB6) crystal needles, and field emitters are fine tungsten needles. Some field emitters are coated with low working function materials such as zirconium oxide (ZrO2). These types of field emitters are called Schottky emitters. 3. The important points are that in general (a) the two types of electron sources (thermionic or field emission) can not be interchanged within the same microscope due to the vacuum requirement and the lens settings, (b) field-emission sources give monochromatic electrons; thermionic sources are less monochromatic and give white electrons.
For high performance, high spatial resolution, rapid data acquisition, and reliable operation, an electron microscope requires an electron source with the following ideal properties: Small source size, low electron emission energy spread, high brightness (beam current per solid angle), low short-term noise and long-term stability. Schottky and cold-field emission are superior to thermionic sources in terms of source size, brightness, and lifetime. Both are up to 1000 times smaller and up to 100 times brighter than thermionic emitters. However, Schottky emission (SE) is preferred over cold field emission (CFE) because it provides higher stability and is easier to operate.
Schottky Field Emission Sources:
A single crystal tungsten wire with a sharp end etched to a small radius (red in the sketch) is mounted on a tungsten hairpin (also red). A current through the filament is used to maintain the tip at a temperature of 1750 - 1850 K. The tip just penetrates a hole in a cylindrical suppressor electrode mounted around the assembly. Electrons are emitted from the tip due to both thermal excitation and the electric field at the tip due to the potential difference between it and an extractor electrode (not shown). Electrons from the filament are repelled by the potential on the suppressor. Electrons from the tip are used by the subsequent column to form a focused beam.
Beam Noise
Beam noise is the time-dependent fluctuation in beam current. Describing the relationship simply, beam noise is inversely proportional to the emission area. Emission area is dependent on emitter radius. If all conditions are the same, the smaller the emission area, the higher the noise. Cold field emission is more noisy than Schottky emission simply because of the emission area (i.e. radius) size differences. Another contributing factor to noise is emitter temperature. Schottky emission noise is caused by the surface Brownian motion of the W and Zr emitter atoms at 1800 degrees C. The CFE is operated at room temperature, and one might think the noise caused by the surface Brownian motion of the W emitter atoms at 25 degrees C would be less. Unfortunately, in all real vacuum systems, residual gas adsorbs onto the CFE. It is the surface Brownian motion (which can be significant at room temperature) of these absorbed gases that is partly responsible for the noise in cold field emission.
Deformation of the emission area is one of the factors affecting long-term emission stability and usability. In all electron columns, residual gases are present. When a high energy electron hits a residual gas molecule, a positive ion can be created. This ion is accelerated back to the emitter and bombards the emission area. Ion bombardment will mechanically deform an emitter's surface. Because Schottky emitters operate at 1800 degrees C, the surface mobility is high enough to anneal such deformations in a reasonable time. The room temperature CFE will not anneal such deformations. To repair the CFE, it is necessary to periodically "flash" the emitter. The flashing process is simple heating of the emitter to allow deformations to be annealed and to remove the adsorbed molecules, just as occurs automatically with Schottky emitter use. The CFE flashing process not only interrupts work in progress, it eventually leads to end-of-life for the cold field emitter. Each time a CFE is flashed in the absence of an electric field, the emitter radius grows slightly. Ultimately, the tip radius grows so large to the extent that sufficient electric field cannot be achieved. Schottky emitters do not grow at these elevated temperatures because the Schottky emitter endform is in thermal-field equilibrium.
Thermionic Emission
1. If we heat any material to a high enough temperature, we can give the electrons sufficient energy to overcome the natural barrier that prevents them from leaving this material. This natural barrier is termed the work function () and usually has a value of a few electron volts. The physics of thermionic emission is well explained by Richardsons Law in terms of the current density (J) from the source to the operating temperature (T). J = AT2 e-/kT Where J in A/m2, T in Kelvin, and A is Richardsons constant (A/m2K2) From the above equation we can see that we need to heat the source to a temperature T such that energy is greater than . Then electrons will escape from the source and be available to form an electron beam. However, not many materials can withstand this type of heating. The only viable thermionic sources are either refractory (high melting point) materials or those with an exceptionally low work function. For instance: W has a melting point of 3695 K, and LaB6 has a low work function of 2.4 eV.
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Electron Field Emission
The emission of electrons from a metal or semiconductor into vacuum (or a dielectric) under the influence of a strong electric field. In field emission, electrons tunnel through a potential barrier rather than escaping over it, as in thermionic or photoemission. Field emission is most easily obtained from sharply pointed metal or semiconductor needles. The smallest controllable tip radius is about 100 nm. The small optical source size and very high current densities of fieldemission cathodes make them attractive electron sources for electron microscope and microprobe applications because, for focused beam sizes below about 500 nm, field-emission sources provide higher currents than thermionic cathodes. Field-emission sources operate on a fundamentally different principle than thermionic sources. When an electric field is applied to a material with a sharp point, the strength of an electric field E at that point is very strong. Based on E = V/r, where E in V/cm, and r (in cm) is the radius of the point source.
Field Emission
For a metal field emitter at low temperature, the process can be understood in terms of the illustration (Fig. 5.0). The metal can be considered a potential box, filled with electrons to the Fermi level, which lies below the vacuum level by several electronvolts. The distance from Fermi to vacuum level is called the work function, . The vacuum level represents the potential energy of an electron at rest outside the metal, in the absence of an external field. In the presence of a strong field E, the potential outside the metal will be deformed along the line AB, so that a triangular barrier is formed, through which electrons can tunnel. Most of the emission will occur from the vicinity of the Fermi level where the barrier is thinnest. Since the electron distribution in the metal is not strongly temperature-dependent, field emission is only weakly temperature-dependent and would occur even at the absolute zero of temperature.
Metal Fermi level Energy
A
Vacuum level
Tunnel distance
B
Fig. 5.0 Diagram of the energy-level scheme for field emission from a metal at absolute zero temperature.
Continue: Electron Field Emission
The phenomenon of field emission was first reported by R.W. Wood in 1897. Fowler and Nordheim, in 1928, provided the first generally accepted explanation of field emission in terms of the newly developed quantum mechanics (Fowler-Nordheim equation).
J = BE2 exp { - 6.8 x 107 3/2 /E}
B: field-independent constant of dimensions (A/V2) E: applied field (V/cm) : work function (eV) E.W. Muller in 1936 invented the field emission microscope which is very useful for the measurement of heats of desorption, work function changes, and diffusion energies of adsorbates.
J: emission current density (A/cm2)
To allow field emission, the surface has to be free of contaminants and oxide. We can achieve this by operating in UHV conditions (<10-11Torr), in this case, the tungsten is operated at ambient temperatures and the process is called cold field emission. Alternatively, we can keep the surface in a pristine condition at a poorer vacuum by heating the tip. The thermal energy, in fact, assists in electron emission when the electrons dont tunnel through the barrier. For such thermal field emission, surface treatments with ZrO2 improve the emission characteristics, particularly the stability of the source. Such Schottky emitters are becoming popular. To evaluate the quality of the electron beam generated by either thermionic emission or field emission, parameters such as brightness, coherency, and stability are important.
Brightness
Brightness is the current density per unit solid angle of the source. Electron sources differ considerably in their size and, as a result, the electrons leave the source with a range of angles. Brightness is particularly important when we are using very fine electron beams, as we do in analytical and scanning microscopy. To define the brightness, we consider an electron source having the following characteristics: A diameter do Giving off a certain emission current ie
The electrons diverging from the source with a semiangle o
These parameters are actually defined at the gun crossover. See Fig. 5.1 Therefore, the current density = ie/(do/2)2 and the solid angle of the source = o2 The brightness is defined as = ie/(do/2)2 o2 = 4ie/(doo)2, where the units of are usually A/ cm2 Sr.
An important factor embodied in the brightness definition is that increases linearly with increasing accelerating voltage for thermionic sources (J ~ T~ ie). From the definition, obviously, the higher the value of , the more electrons we can put into an electron beam of a given size, and the more information we can extract from the specimen and the more we can damage sensitive specimens. The brightness is very important in analytical electron microscopy, which is the technique of quantitative analysis of the many signals that come from a specimen irradiated by an electron beam. As we go to higher magnification in HRTEM, the screen intensity becomes less because we are viewing only a fraction of the illuminated area of the specimen. The electron density can be increased by using the brightest available source. Then images can be recorded with reasonably short exposure times.
Temporal Coherency and Energy Spread
The coherency of a beam of electrons is a way of defining how well the electron waves are in step (phase) with one another. To get a coherent beam of electrons we must create one in which all the electrons have the same wavelength, just like monochromatic light. We refer to this aspect of coherency as temporal coherency. If the wave packets are all identical they have the same coherence length. A definition of the coherence wave length c is c = h/E Where is electron the velocity, E is the energy spread of the beam, and h is Plancks constant. The above equation suggests that we must have an electron source emitting electrons with small energy spread. It also means that we have to have stable power supplies to the source and a stable high-voltage supply so that all the electrons have a small E, thus giving a welldefined wavelength. In practice, the typical E values for the three sources are in the range 0.1 to 3 eV (which is remarkably small compared with a total energy of 100 to 400 keV).
Spatial Coherency and Source Size
1. Spatial coherency is related to the size of the source. Perfect spatial coherence would imply that the electrons were all emanating from the same point at the source. So source size governs spatial coherence and smaller source size gives better coherency. We can define the distance dc, the effective source size, for coherent illumination to be dc << /2 Where is the electron wavelength and is the angle subtended by the source at the specimen. We can control by inserting an aperture in the illumination system.
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Electron gun The electron beam is generated in the electron gun. Two basic types of gun can be distinguished: the thermionic gun and the field emission gun (FEG). Thermionic guns are based on two types of filaments: tungsten (W) and lanthanum-hexaboride (LaB6) (cerium-hexaboride, CeB6, can also be used instead of LaB6; its performance is roughly the same as that of LaB6). On modern instruments the different types of thermionic filaments can be used interchangeably. The FEG employs either a (thermally-assisted) cold field emitter - as on the Philips EM 400-FEG - or a Schottky emitter - as on the more recent generations of FEG microscopes (CM20/CM200 FEG, CM30/CM300 FEG, Tecnai F20 and F30).
Thermionic gun The thermionic gun (so-called triode or self-biasing gun) consists of three elements: the filament (cathode), the Wehnelt and the anode. The Wehnelt has a potential that is more negative - the bias voltage - than the cathode itself. The bias voltage is variable (controlled by the Emission parameter) and is used for controlling the emission from the filament. A high bias voltage restricts the emission to a small area, thereby reducing the total emitted current, while lowering the bias voltage increases the size of the emitting area and thus the total emission current.
The emitted electrons that pass through the Wehnelt aperture are focused into a cross-over between the cathode and anode. This crossover acts as the electron source for the optics of the microscope.
The size of the cross-over is determined by the type of filament, the electric field between cathode and anode, and by the exit angles of the electrons from the filament. At low bias voltages, electrons are emitted from a larger area of the curved tip of the filament, causing a higher divergence of emission angles and thus a larger source size. Higher emission therefore not necessarily improves the brightness (a performance parameter of the emitter, measured in A/cmSr). In addition, higher emission increases the Coulomb interaction between electrons - the so-called Boersch effect - (some get accelerated, others decelerated) which increases the energy spread.
Field Emission Gun In the case of a Field Emission Gun (abbreviated FEG), electron emission is achieved in a different way than with thermionic guns. Because a FEG requires a different gun design as well as much better vacuum in the gun area (~10e-8 Pa instead of the ~10e-5 Pa necessary for thermionic guns), it is found only on dedicated microscopes (Tecnai F20, F30). The FEG consists of a small single-crystal tungsten needle that is put in a strong extraction voltage (2-5 kV). In the case of a cold FEG or thermally-assisted cold FEG, the needle is so sharp that electrons are extracted directly from the tip. For the Schottky FEG (as used on the Tecnai microscopes) a broader tip is used which has a surface layer of zirconia (ZrO2). The zirconia lowers the work function of the tungsten (that is, it enhances electron emission) and thereby makes it possible to use the broader tip. Unlike the thermionic gun, the FEG does not produce a small cross-over directly below the emitter, but the electron trajectories seemingly originate inside the tip itself, forming a virtual source of electrons for the microscope.
The FEG emitter is placed in a cap (suppressor) which prevents electron emission from the shaft of the emitter and the heating filament (very similar to the Wehnelt of the thermionic gun). Electron emission is regulated by the voltage on the extraction anode. Underneath the extraction anode of the FEG is a small electrostatic lens, the gun lens. This lens is used to position the first cross-over after the gun in relation to the beam-defining aperture (usually the C2 aperture). If the gun lens is strong, the cross-over lies high above the aperture while a weak gun lens positions the cross-over close to the aperture, giving a high current but at the expense of aberrations on the beam. A strong gun lens is therefore used where small, intense and low-aberration electron probes are needed (diffraction, analysis and scanning), while a weak gun lens is used when high currents are important (TEM imaging). In the latter case, the beam is spread and the aberrations do not affect the area within the field of view.
The high brightness of FEGs comes about because of two reasons: 1.The small size of the tip ensures that large numbers of electrons are emitted from a small area (high A/cm). 2.The electrons come out of the tungsten crystal with a very restricted range of emission angles (high A/Sr). FEGs also have a low energy spread due to their low working temperature and emission geometry (small virtual source size, but much larger actual size of the emitting area).
Comparison of Electron Guns
The Reasons for Choosing the Highest kV
The gun is brightest. The wavelength is shortest; the resolution is potentially better. The cross section for inelastic scatter is smaller; the heating effect is smaller. As materials scientists, you should always operate the microscope at the maximum available kV, unless there is a definite reason to use a lower kV. Of these reasons,the most obvious is avoiding beam damage.
Chapter 6: Lenses, Apertures, and Resolution
In an electron microscope, we change the focus and magnification by changing the strength of the lens itself. So electron lenses differ fundamentally from glass lenses in that one lens can be adjusted to a range of strengths.
The Lens Equation, Magnification and Demagnification, and Focus
Newtons lens equation: 1/u + 1/v = 1/f (where u is the object distance, v is the image distance, and f is the focal length) We can use Newtons lens equation to define the magnification of the convex lens as M = v/u Sometimes we may want to demagnify an object (for example, when we want to form a small image of the electron source, to create the finest possible beam at the specimen). If that is the case, we define the demagnification as 1/M
If the lens is too weak and the image forms below the desired image plane, the image will be out of focus and the lens is said to be underfocused. If the lens is too strong and the image forms above the image plane, then we say the lens is overfocused.
Focus
Electron Lenses
Different Kinds of Lenses
The objective lens is the most important lens in the TEM, since it forms the images and diffraction patterns that will be magnified by all the other lenses. It is also the most difficult to construct, since the specimen must be located so close to the plane of this lens. The objective lens is a strong lens. The most flexible objective lens is that in which the upper and lower polepieces are separated and have their own coil, as shown in Fig. 6.8A. This geometry gives the space needed to allow us to insert the specimen and the objective aperture between the polepieces. With this type of polepiece, other instruments such as X-ray spectrometers can have relatively easy access to the specimen. For the same reason, it is straightforward to design specimen holders that do a variety of tasks such as tilting, rotating, heating, cooling, and straining. With split polepieces it is possible to make the upper polepiece behave differently than the lower polepiece. The most common application of this is to excite the upper objective polepiece very strongly. This kind of lens is ideal for an AEM/STEM because it can produce both the necessary broad beam of electrons for TEM and a fine beam of electrons for AEM and STEM. If high resolution is a major requirement, it is essential to keep the focal length of the objective lens short and this means a very strong lens is needed which can be accomplished by an immersion lens.
Image Rotation and the Eucentric Plane
The electrons follow a helical path as they traverse the field along the axis of the lens. Its effects are seen in the routine operation of the TEM because the image, or diffraction pattern, rotates on the viewing screen as you try to focus or if you change magnification. This rotation may require calibration. The manufacturer may have compensated for it by including an extra lens. Fig. 6.4 suggests that if we change the strength of the lens, the position of the focal plane and the image plane will also change. Because of this we have to define a standard object plane for the main imaging lens of the microscope and we call this the eucentric plane. Specimen height should always be adjusted to sit in the eucentric plane because an image of an object in this plane will not move as you tilt the specimen. All other planes in the imaging system are defined with reference to the eucentric plane. If your specimen is in the eucentric plane, then the objective lens strength is always the same when the image on the screen is in focus.
The Electromagnetic Lens
The electrons move through the lens in a helical path, a spiral, not a straight line. One effect is that the image in an TEM will appear to rotate if you vary the accelerating voltage.
Apertures and Diaphragms
Spherical Aberration, Chromatic Aberration, and Astigmatism
Chromatic Aberration
The objective lens bends electrons of lower energy more strongly and thus electrons from a point in the object once again form a disk image. The radius rchr of this disk is given by: rchr = CcE/Eo
Astigmatism
Astigmatism occurs when the electrons sense a nonuniform magnetic field as they spiral around the optic axis. This aberration arises because we cant machine the soft iron polepieces to be perfectly cylindrically symmetrical down the bore. The soft iron may also have microstructural inhomogeneities which cause local variations in the magnetic field strength. Even if these difficulties were overcome, the apertures we introduce into the lens may disturb the field if they are not precisely centered around the axis. Furthermore, if the apertures are not clean, the contamination charges up and deflects the beam. So there are a variety of contributions to astigmatism, which distorts the image by an amount rast where rast = f and f is the maximum difference in focus induced by the astigmatism.
Resolution
The resolution is defined as the minimum resolvable distance in the object. The theoretical resolution is expressed as the distance apart of the two incoherent point sources is defined as the theoretical resolution of the lens rth and is given by the radius of the Airy disk:
rth = 0.61/