Scanning Electron Microscopy

4.2 Topographical imaging

4.2.0 Secondary imaging

4.2.1 Differential imaging

4.3 Compositional imaging

4.3.0 Backscatter electron emission

4.3.1 Auger electron emission

4.3.2 X-ray emission

4.4 Structural imaging

4.4.0 Induced speciment current

4.4.1 Selected area electron channeling

4.5 Property imaging

4.5.0 Voltage contrast

4.5.1 Electron beam induced current (EBIC)

4.5.2 Magnetic contrast imaging

The scanning electron microscope generates a beam of electrons in a vacuum. That beam is collimated by electromagnetic condensor lenses, focussed by an objective lens, and scanned across the surface of the sample by electromagnetic deflection coils. The primary imaging method is by collecting secondary electrons that are released by the sample. The secondary electrons are detected by a scintillation material that produces flashes of light from the electrons. The light flashes are then detected and amplified by a photomultiplier tube.

By correlating the sample scan position with the resulting signal, an image can be formed that is strikingly similar to what would be seen through an optical microscope. The illumination and shadowing show a quite natural looking surface topography.

There are other imaging modes available in the SEM. Specimen current imaging using the intensity of the electrical current induced in the specimen by the illuminating electron beam to produce an image. It can often be used to show subsurface defects. Backscatter imaging uses high energy electrons that emerge nearly 180 degrees from the illuminating beam direction. The backscatter electron yield is a function of the average atomic number of each point on the sample, and thus can give compositional information.

Scanning electron microscopes are often coupled with x-ray analysers. The energetic electron beam - sample interactions generate x-rays that are characteristic of the elements present in the sample. Many other imaging modes are available that provide specialized information.

At Cambridge University in 1948, C. W. Oatley began construction of an SEM based on Zworykin's. Graduate student D. McMullan⁴ described this work in a doctoral dissertation where they had claimed a resolution of 500 Angstroms. Further work, reported by K. C. A. Smith⁵, made large changes to the electron optics. The electrostatic lenses were replaced with electromagnetic coils, a double deflection scanning system was added as were stigmator coils. Additionally, Smith utilized non-linear signal processing (gamma processing) to help improve imaging.

The next major improvements were made to the signal collection process. The original phosphor screen / photomultiplier used by Zworykin was improved by the addition of a light pipe. The light pipe allowed for direct optical coupling between the scintillator and the photomultiplier tube, greatly improving efficiency⁶. This was accomplished by T. E. Everhart and R. F. M. Thornley, and the detector arrangement carries their names as the Everhart-Thornley detector.

All of these improvements were combined in one instrument. Once again at Cambridge University, R. F. W. Pease and W. C. Nixon created the SEM V, utilizing the inverted column, electromagnetic lenses, double deflection scan system, stigmation coils and the Everhart-Thornley detector. This instrument became the basis for the first commercial SEM, the Cambridge Scientific Instruments Mark I, first available in 1965.

The accelerating voltage, generally between -500 Volts and -50,000 Volts DC, is applied to the Wehnelt cylinder. Resistive self-biasing is usually used where an adjustable bias resistance connects the filament to the accelerating voltage. The biasing brings the filament slightly more positive than the Wehnelt. The anode is connected to electrical ground.

Without the Wehnelt and anode, electrons emitted from the filament would tend to stay in the area of the filament. This forms a 'space charge' or a cloud of electrons whose mutual repulsion resists any further emission from the filament. The anode, being at ground potential, is more positive than the filament and attracts the electrons away from the filament - providing the primary acceleration for the electron beam. But the current flow that would result would be very low and dependent on the accelerating voltage. By adding the grid, or Wehnelt, we have a way of controlling the space charge of the filament, shaping the beam and increasing the beam current.

Figure 2 depicts the equipotential force lines between the various parts of an electron gun. The equipotential lines form a contour map of the intensity, or flux, of the electrical field. The gradient, or direction, of the electrical field will always be perpendicular to these lines and is the direction of the most rapid change of the potential. Electrons leaving the filament will be accelerated along the gradient towards the most positive area, the anode. This beam of electrons will be focussed by the shape of the field gradient to a cross-over just before the anode, forming the first optical image of the source and ensuring that a larger percentage of the electrons will pass through the aperture of the anode.

While the plain tungsten wire filament is the most common cathode material in use, there are several variations and different materials used. Oxide and thoriated coatings have been explored to increase the emissivity of tungsten. Such coatings have not found much commercial use.

LaB₆ cathodes are becoming quite common. They use a single crystal LaB₆ rod, of approximately 1 mm in diameter. This cathode can not be heated as directly as a tungsten filament, so a special mount or separate heater is used to provide the 1700 - 2100 degrees Kelvin required. The tip of the rod is polished to a point, then a small angled flat is usually polished at the point. The flat provides a defined area for emission. Without the flat, or if the cathode material evaporates past the flat, emission occurs from a broad undefined area around the point and resolution is decreased.

LaB₆ cathodes provide around an order of magnitude higher brightness than tungsten cathodes. Longer cathode life is also an advantage, but both come at a cost. The LaB₆ cathode requires a higher vacuum to operate (10^-6 to 10^-7 Torr) than the tungsten (10^-5 Torr). This cleaner vacuum requirement can only be attained with different and more expensive vacuum system design and components.

A LaB₆ electron gun uses the same basic cathode / grid / anode configuration used in a tungsten wire gun. Because of the high reactivity of the borides at the cathode temperatures used and their brittle nature, the mounting and heating of the cathode is crucial. Three different methods are in common use.

These two discoveries illustrate two important properties. The first, that field emission results from electrons 'tunneling' past the work function of the metal tip helped by the high electrical field gradients. The second is that while electrons are emitted from the surface, their apparent source is a single point beneath the surface. That is, because of the electrical fields present, electrons tend to be emitted tangential to the surface which, in a hemispherical tip, results in an apparent source at the focus of the hemisphere. This apparent source will actually not be a point because of thermally caused differences in the electron's momentum.

Hibi¹⁰ first suggested in 1954 that a heated tungsten point, rather than a bent tungsten wire, might produce a smaller source size and higher brightness. This cathode actually incorporates both thermionic and field emissions and is referred to as a 'Schottky' or T-F (thermal - field) cathode.

Also in 1954, Cosslett and Haine¹¹ proposed the use of a field emission cathode for electron microscopy. Due to the requirement for an extremely high vacuum, on the order of 10^-9 Torr, no practical use was made until 1966. At that time, Crewe^{12, 13, 14} managed to build a usable system.

At the present time, field emission guns are gaining favor in electron microscopy as the costs of the associated very high vacuum equipment are going down.

Sustaining high electrical field gradients is also essential to emission, so a tip that is well worn might not emit electrons at all.

As with the tungsten filament gun, the voltage difference or bias between the first anode and the accelerating voltage on the cathode determines the emission current. The second anode is at ground potential and the voltage difference from here to the cathode determines the acceleration given the electrons. The shape of the anodes is carefully selected to minimize aberrations.

In general, the smaller and brighter the apparent source, the higher the ultimate resolution. Many other factors are involved, in most cases a well designed modern instrument is limited more by the instrumental aberrations. In practical use, resolution of most instruments is limited by environmental effects - vibrations and electromagnetic fields.

Brightness of a cathode is defined as the current density per solid angle. More specifically:¹³

Vacuum required relates primarily to the cost and complexity of an instrument. While a tungsten filament cathode can be used with a simple diffusion pump, the higher vacuum requirements can mean more exotic vacuum system pumps and seals.

In this discussion, we won't be attempting to relate an electron microscope to an optical microscope since no direct relationship can be made. Rather, we'll study the problem of producing an optical system capable of producing a small, focussed spot of light. This is directly analogous to the actions of the electron optics of an SEM, minus the beam deflection mechanism.

The simplifications of the thin lens calculations come from the ability in many cases to consider the two principal planes to be coincident, or located at the same place. These calculations become more complex in the so called 'thick' lens, particularily in multiple lens systems. In this light optics section, we'll be using only thin lens examples.

To begin with, we must consider the source of the light. In the process of creating as small a final spot as possible, the apparent size of the source will determine the optics required. As an example, a source size of 1mm² will require a magnification in the optics of 0.1x (the magnification of less than one is used here to represent the negative magnification, or de-magnification) in order to produce a final spot size of 0.1mm². At the point of the final spot, an optical image of the source will be formed.

The term apparent size is used here to indicate that there can be many variables that affect the optical appearance of the source. A 1mm wide by 2mm long helical tungsten filament, for example, may appear as a 1mm by 1mm source of visible light when heated. This could be due to the conductive cooling of the outer portions of the coil by the structures that support the coil, thus preventing the emission of visible light from those areas. In this case, the physical size of the source is twice as large as the apparent size.

Refraction is based on the fact that light travels at different rates in different materials. The ratio of the speed of light in a vacuum to that in a particular material is known as the absolute refractive index: n=c/v where n is the refractive index, c the speed of light in a vacuum, and v the speed of light in the lens medium. A refractive index can also be calculated for any two materials, and for practical reasons is often calculated for a lens operated in air. The refractive index varies for a given material based on the wavelength of the light involved, the ratio being larger for blue light than red. However, the speed of light in a vacuum is constant for all wavelengths.

From this example it is clear that the index of refraction and the incident angle are the determining factors in the refraction of light. The incident angle will affect the length of segment A - B and the ratio of the index of refraction for each material will affect the length of segment A' - B'. From this we can derive n'/n=AB/A'B'. By dividing the numerators and denominators by BA', we can bring this formula to trigonometric terms as n'sin I' = nsin I (Snell's Law).

In Fig. 6 the distances U and V are shown equal to each other, and in this case the image magnification would be 1. Magnification is related to these distances by: M=V/U where M is the magnification. Some other ways of determining magnification are:

M=V/U

M=(V-F)/F

M=F/(U-F)

The distances, U and V, and the overall distance D can be determined from:

U=V/M

U=(R*D)/(R+1)

U=D/(M+1)

U=(F*V)/(V-F)

V=U*M

V=U/R

V=(F/R)+F

V=(F*M)+F

D=F*(M+(1/M)+2)

D=(F*(M+1)²)/M

D=F*(R+(1/R)+2)

D=(F*(R+1²)/R

The focal point can also be determined from the parameters shown by:

F=(U*M)/(M+1)

F=(D*R)/(R+1)²

F=(D*M)/(M+1)²

F=U/(R+1)

F=(U*V)/D

F=1/((1/U)+(1/V))

From these equations, we can determine the operating characteristics of simple optical systems. For example, let's say we have a need for a single lens system that will provide the smallest image magnification if the distance D from the object to image is 100mm and the lens can be no closer than 5mm to the image (V). It's clear from M=V/U that putting the lens at the minimum 5mm from the image would give the smallest magnification, in this case 5/95 or a magnification of 0.053.

In order for us to use this setup, and have the image focussed, we'll need to select a lens with an appropriate focal length. Using F=(U*M)/(M+1) we find that a lens with a focal length of 4.78mm would fit.

Obviously, it's not possible to design a single lens system, given these parameters, that would produce a smaller image size. But what if we used more than one lens? For simplicity, let's split the 100mm length we have into two 50mm sections. We'll put one lens into each section, in each case 45mm from the light entrance of each section. Now, using M=V/U we get a magnification of 0.11 for each section.

From the examples above, you can see how we're able to produce a greatly demagnified image of a light source through the use of a multi-lens system. This system could be extended to even more lenses, but there are other considerations that affect any optical design and can place severe constraints, particularily on multiple lens systems. The common definition for aberration is, according to Webster's, "deviation from the normal or usual. In optics, however, aberrations are quite the norm. The term aberration in optics refers to a number of effects that prevent light rays being refracted from acting ideally. Specifically, aberrations are classified into spherical, coma, astigmatism, curvature of field and distortion. Aberrations can be inherent in the design and materials used and they can be caused by imperfections in manufacture. Aberrations will be covered in more detail later.

In practical instruments used today, electrostatic lenses are used only in the electron gun, as described in the previous section. Magnetic lenses are used through the rest of an instrument. Electrostatic lenses require conducting surfaces very close to the path of an electron beam in order to produce an electrical field of high intensity. These surfaces must be accurately formed, extremely smooth and are easily contaminated. Magnetic fields, on the other hand, are usually formed by solenoid coils that are located completely outside of the vacuum system. Therefore, they suffer none of the contamination problems inherent in electrostatic lenses. Electrostatic lenses, however, can be made extremely small and are capable of producing much faster response for beam deflections. For these reasons, they are also used for beam blanking, a technique very useful in the SEM analysis of integrated circuits.

A high electrical field gradient will accelerate a charged particle such as an electron. In a scanning electron microscope, that fact is used in the electron gun assembly to provide the initial acceleration to the beam electrons. Electrical fields can also be used for focussing a beam of charged particles. In Fig. 8 above, a series of three cylinders with their axis coincident with the beam axis, demonstrate the principal of electrostatic focussing (please note that the cylindrical shape of the electrodes is merely representative - they could be the inner surfaces of apertures in disc shaped electrodes). Electrons entering into the system from the left will be affected by the electrical field formed by the large voltage difference between the first two cylinders. The electrons will be given both an impulse towards the cylinder axis and a boost in velocity by the increasingly negative field. As the electrons move into the second cylinder, they receive an impulse towards the walls of the cylinder, but since they are now closer to the axis and traveling faster, the change in direction will be less than from the first impulse.

Entering the second field, the electrons will once again be given an impulse towards the cylinder walls. As they pass through the field, though, they will be de-accelerated by the increasingly positive field. Finally, they will again receive an impulse towards the cylinder axis. When exiting the system, the electron beam will again have it's original velocity, and there will be a net impulse towards the cylinder axis, resulting in a focussing of the beam. If the center cylinder were at a positive voltage in relation to the other two, it would create a diverging lens system.

Magnetic fields can also be used as lenses for beams of charged particles. In an SEM, electro-magnetic lens are used almost exclusively for the condensor and objective lenses (some instruments refer to the objective lens as the final condensor lens, but I prefer using the term objective for this lens which is usually of a considerably different design than the condensors). Electro-magnetic lenses used in commercial SEMs have always been solenoid coils. While so-called 'strong focussing' or multiple pole lenses are theoretically possible, they have not been used primarily due to the increased complexity of accurately manufacturing them.

A solenoid is a cylindrical coil with circumferencially wound wire. In SEMs, the lens is completely encased in a ferromagnetic shroud forming a thick walled cylinder, with a small gap around the inner circumference. The gap confines the external magnetic field to a small area and may be located anywhere on the inner surface. The strength of the magnetic field generated is proportional to the number of turns of wire multiplied by the current passing through the coil (N*I where N = number of wire turns, I = current). Relatively large fields are required for focussing electron beams of the accelerating voltages found in SEMs (up to 50KV).

Fig. 9 represents a number of features of a magnetic lens. Magnetic field lines are shown, as are equipotential lines. These give a visible description of the shape of the magnetic field. The light blue lines represent two possible electron paths. The smaller inset gives an approximation of the magnetic field strength along the optical axis and perdendicular to the optical axis. What can not be faithfully represented in a two dimensional image is the rotation of charged particles about the axis in a uniform magnetic field. This effect is the heart of the cyclic particle accelerators, momentum spectrometer and other instrumental techniques.

In a uniform magnetic flux density B, a moving charged particle will follow a curved path . For a point charge, like an electron, the force imparted on it by electrical and magnetic fields is found in the vector equation F = q(E+v*B) (the Lorentz force) where F is the force, q is the charge on the particle, E is the electric field, v the particle's velocity and B is the magnetic field. In the case of a magnetic lens, there is no electric field and the E term is dropped giving F = qv*B. As an electron comes down the optical path, it first encounters the horizontal component (H_r)of the magnetic field. This causes the electron to begin a rotation about the axis. The strengthening of the vertical field component (H_Z) gives the electron an impulse towards the axis. Finally, as the electron emerges through the bottom horizontal field component, it receives an impulse that stops it's rotation about the axis. Note that unlike the case of electrostatic lenses, no change in velocity takes place along the optical axis.