SEM

ASSIGNMENT I

SCANNING ELECTRON MICROSCOPY

SUBMITTED BY:-

RITU DAS

SCH-08193

MRC SUBMITTED TO:- RAVISHANKAR SIR

Q1.Based on Richardson equation, plot the variation in current density as a function of temperature for a material with a work function of 4.5 eV. Repeat the same for a material with a work function of 2.5 eV (on the same graph). Compare the maximum theoretical brightness at 20 kV and 2000 K for both these source materials. Use the appropriate values of constants

Ans-:The Richardson-Dushman equation relates the current density of a thermionic emission to the work function (W) and temperature (T) of the emitting material:

js = A T2 exp(-W/kT)

where js is the current density of the emission (mA/mm2) A is Richardson's constant. A = 4*πmek2/h3 ~ 1202 mA/mm2K2, where m is the mass of electron, e is elementary charge, and h is Plank's constant. In practice, A may be multiplied by a correction factor that depends on the material

T is temperature (K) W is the work function of the cathode material (J) k is the Boltzmann constant (1.38066E-23 J/K)

Tungsten – work function is 4.5 and Richardson constant – 60 A*b (A cm-2 K-2 (b is material correction factor)

LaB6 work function is 2.5 and Richardson constant – 29 A*b (A cm-2 K-2 (b is material correction factor)

Brightness(A/cm2sr) Brightness(A/cm2sr)

Temperature (K)

4.5 eV 2.5eV

0 0 0

200 0 0

400 0 0

600 6.38E-27 4.15E-10

800 3.25E-17 0.000133

1000 2.4E-11 0.294445

1200 2.1E-07 53.58747

1400 0.000144 2312.961

1600 0.019997 40370.19

1800 0.954003

2000 21.48238

2200 279.6465

2400 2409.746

2600 15101

For Tungsten,

js.t = 60* 20002 exp(-4.5/( 1.38066E-23*2000))

js,t= 3.5 A/cm2

For LaB6

js,l = 70 A/cm2

Theoretical brightness is , B = (js eV0)/(3.14*K*T)

E=1.69e-190C

Q2.An immersion lens configuration is better than the asymmetric pin-hole lens for obtaining high resolution. Why? Ans- OBJECTIVE LENS-: This is the final lens in the column that focuses the electron probe onto the sample surface and contributes additional demagnification. It contains the scanning coils, the stigmator, and the beam-limiting aperture. The basic designs of objective lens are (1).the pinhole lens, where the specimen is placed outside the lens and its magnetic field. (2) the immersion lens, where the specimen is placed inside the lens and its magnetic field. In immersion lens a specimen is placed directly inside the lens gap, giving a focal length in the range 2-5 mm. Because lens aberrations scale with focal length, this design yields the lowest aberrations. the smallest probe size, and the highest image resolution. With this configuration the specimen should be very small (<5 mm to place inside the lens). This limits the selection of sample. As the sample is inside the lens there is no choice of working distance, and also the depth of focus. Where as in asymmetric pin hole lens the sample is kept below the objective lens, in this configuration focal length depend on the working distance( i.e. distance from the center of the lens to the specimen plane). Because both the objective lens focal length and its aberrations increase with the working distance, this design have higher aberration, enlarge probe size and lower magnification. Here with comprise on resolution, the specimen size is limited only by the size of the specimen chamber. Working distances up to 40 mm can be employed to produce images with high depth of field.

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

0 500 1000 1500 2000 2500 3000

4.5 eV

2.5eV

(a) Asymmetric pinhole lens, where a large specimen may be placed

outside the lens and lens aberrations are large. (b) Symmetric immersion lens, where a small specimen is placed inside the lens and lens aberrations are small.

Q3.The three key parameters for controlling the resolution are the probe size, probe current and the convergence angle. How will you determine these parameters experimentally? Ans= The probe size/ the Beam Diameter

The measurement of d, the beam diameter, is not so straightforward. It can either calculate d or measure it experimentally. The former is easy but imprecise, the latter is difficult and can be equally imprecise. Here mentioning both methods. Gaussian Probe Diameter/ calculated d To understand how probe size varies with probe current, we need to calculate the minimum probe size and the maximum probe current. We start with a calculation of the aberration-free Gaussian probe diameter dG which is the full-width at half-maximum height (FWHM) of the intensity distribution of dG. If the emitter source size is known, then the Gaussian probe size may be calculated from the total demagnification as described above. However, to compare field-emission with thermionic sources, another,

more general method is needed to estimate dG. Because electron optical brightness is constant throughout the electron column, we can use it to estimate dG by rearranging the brightness equation, as applied at the final probe spot:

Brightness

The definition of the full width at half maximum (FWHM)

The current in the final probe can be estimated by rearranging the brightness equation to solve for current:

increase the convergence angle α p to increase the probe current at a constant probe diameter. However, because of the aberrations present in the

electron optical system, αp must be kept small, and the current available for a given probe diameter is thus limited. Beam diameter experimentally:- The probe diameter is measured by sweeping the beam across a sharp, electron opaque edge and observing the tting to electron. These change in signal as function of the beam position. The edge must be clean smooth and non-transmitting to electron. These condition are easy to satisfy for large probe, it is difficult to fabricate suitable edge for small probe diameter. Convergence Angle:- The beam is focused on sharp edge, and the intial probe diameter di is measured. Without changing the focus the test edge is moved vertically upward a distance z. the large final diameter df is measured. The convergence angle α may be found αp= (df-di)/2z Beam Current Tthe beam current ib can be measure at the specimen ib directly using a Faraday cup in a specimen holder. A Faraday cup consists of a small aperture above a relatively deep hole in an earthed metal block. If the aperture is small enough (e.g., ~50 mm) and the metal block enough (~2mm), and made of something light like Al to minimize backscatter, then it is a reasonable assumption that no electrons escape back out of the entrance aperture. All the electrons going into the aperture therefore go to earth, and you can measure the electron current using a picoammeter in the earth line. Q4. Write down an expression for the effective probe size for a probe limited by spherical aberration, chromatic aberration and diffraction limit. Assuming negligible contribution from chromatic aberration, derive expressions for the optimum aperture size (αopt), minimum probe size (dmin) and the maximum current (Imax) under a given set of conditions. Will these expression be valid for low kV operation? Ans-: Lens Aberrations All lenses suffer from a number of defects or aberrations in their performance. In electron optics, the effects of aberrations cannot be canceled by using combinations of lenses. The only recourse therefore is to try to minimize these effects. Spherical Aberration Spherical aberration arises because electrons in trajectories further away from the optic axis are bent more strongly by the lens magnetic field than

those rays near the axis. This results in a disk rather than a point where all rays converge. The smallest disk occurs just in front of the Gaussian plane and is often called the spherical aberration disk of least confusion. The diameter of this disk d, can be written as

Where Cs is the spherical aberration coefficient and α is the angle of the outer ray through the lens. The contribution of d, to the final probe diameter can be reduced by limiting a with an objective lens aperture. Unfortunately, a very small aperture significantly reduces the current in the probe and introduces aperture diffraction. Aperture Diffraction For very small apertures, the wave nature of electrons gives rise to a circular diffraction pattern instead of a point at the Gaussian image plane. Electrons emerging from point P diffract at the edge of the small aperture and appear in the image plane as a broad "Airy disk" intensity distribution surrounded by smaller subsidiary maxima. Half the diameter of the Airy disk taken as the diffraction contribution to the spot size dd given by

where A, is the wavelength of the electrons and a is the beam convergence. The wavelength X (in nanometers) for electrons of energy E0 (in electron volts) can be calculated with only a small error as

(a) spherical aberration and (b) aperture diffraction in a lens cause a point object at P to blur into an enlarged spot at the Gaussian image plane. The disk of minimum confusion cis and one-half the Airy disk dd are used in calculations of probe size. Chromatic Aberration Electrons from point P of slightly different energies E0 and E0 – δE will be focused at different locations in the image plane. This again results in a disk rather than an ideal point. The diameter dc of the disk of least confusion formed in front of the image plane is

where Cc is the chromatic aberration coefficient, α is the convergence angle, and δE/Eo is the fractional variation in the electron beam energy.

chromatic aberration, where electrons of differing energy are focused at different locations, The chromatic disk of minimum confusion d, is only important at low accelerating voltages. Minimum Probe Size Calculations of the probe size assume that d p is the quadrature sum of the diameters of the Gaussian probe and the various aberration disks, that

Q5. You are looking at a fracture specimen. What conditions would you use for the following to be able to simultaneously observer all the regions of the surface. a) working distance, b) aperture size. How do these parameters affect the resolution? Ans- Working distance-: the objective lens can focus the final probe at various working distance ( i.e. distance from the center of the lens to the specimen plane). To simultaneously view the overall region the working distance must be increase, this will increase the scan length that the beam traverses on the specimen.

Effect of working distance in a two-lens system. (a) Small working distance, (b) large working distance. The working distance W may be increased by lowering the specimen stage with the z-control and refocusing the beam on the increased, making q2 larger and the demagnification m2 = p2/q2 smaller. Increasing the working distance produces a larger spot size d2 at the specimen and a consequent degradation of the image resolution, although the beam current remains about the same. The convergence angle a2 decreases giving an improved depth of focus. Weakening the objective to focus at a long W increases both the focal length f 2 and the aberrations of lens. Aperture size:- A real objective aperture placed in the gap of the probe-forming lens (usually 50-500 ,µm in diameter). This aperture decreases the beam angle α1 diverging from the condenser lens to a smaller angle αa for the electrons entering the objective lens. The final convergence angle controls the

image depth of focus, smaller α2 produce the greater depth of focus. Smaller the aperture, focal length f2 will be large, and the area that beam traverses will be large. For small aperture the image resolution will reduce. Q6.You want to separate the effects of SEI and SEII contribution to the image. How would you do this? Ans- Relative Contributions of SE1 and SE2

Experimentalists have been able to distinguish the relative contributions of SEI and SE 2 to the total secondary emission by careful experiments on thin foils, where the backscattered electron component can be

Schematic illustration of 5 λ the origin of two sources of secondary electron generation in the sample. Incident beam electrons (B) generate secondary electrons (SE 1 ) upon entering the sample. Backscattered electrons (BSE) generate secondary electrons (SE2) while exiting the sample. λ is the mean free path for secondary electrons.

The SE2 component depends on a sample's backscattered coefficient, η, which reflects chemical differences well below the surface. This effect increases with increasing penetration depth, so the sample will appear more

"transparent" at higher E0, and less so at low E0. Finer surface structure images can generally be obtained with lower accelerating voltages, At high E0, the SE2 and SE3 signals are larger, reducing image contrast and veiling fine surface structures. Hence to reduce the effect of SEII the voltage should be low (5kV) thereby reducing the back scattering yield. In low voltage mode beam interaction with the specimen is confined to regions very close to the surface. This provides an image which is rich in surface information compared to those obtained at higher accelerating voltages (15-30 kV), where the beam penetrates beneath the surface and the emerging signal electrons mostly carry information about the interior of the sample. But the resolution is poor in low voltage mode.

Q7. What is the typical current value required for imaging in the SEM?

What type of electron source would you select to get the highest current? The beam current is usually in the range from nanoamps to picoamps. A typical SEM runs at a few nA probe current at 30kV.

Ans-To achieve highest current for a smaller probe size is obtained by changing the filament material (to LaB6) or the mechanism of emission (to field emission).

LaB6 has a lower work function than tungsten, meaning that more electrons are emitted for the same heating temperature. Sharp emitters have the highest brightness, but the shortest lifetime; blunt or truncated tips exhibit slightly lower brightness, but longer lifetimes. LaB6 emitters are generally more expensive to operate than the conventional tungsten hairpin gun.

Field emission gun.

The disadvantages of low brightness, limited lifetime, and large energy spread. In the normal thermionic source can be changed by having a Field emission gun.The field emission cathode is usually a wire fashioned into a sharp point (100 nm or less in radius) and supported by a tungsten hairpin. When a negative potential is applied to the cathode, the electric field is concentrated by the tip. When the field at the tip reaches a magnitude of about 10 V/nm, the potential barrier is lowered in height and also becomes so narrow that electrons can "tunnel" directly through it and leave the cathode.

Two forms of field emitter are now in common use in the SEM.The first one is the Cold Emission gun (CFE)in which a high applied field causes electrons to tunnel out of the cathode wire and has its name because the magnitude of

emission is independent of the temperature of the tip. The emission current is 1-10 uA.

The second class of sources includes Schottky ( SFE) and thermal (TFE) field emitters. A TFE has the same properties as a CFE, but is operated at an elevated temperature. This helps to keep the tip clean, reducing noise and instability even in degraded vacuum conditions. In the Schottky emitter the field at the tip is mostly-used- to reduce the effective work function barrier. To still further lower, thework function, Zr02 is deposited on the flattened tip from a small dispenser As a result, although the SFE is a thermionic_source, its brightness and emission density are comparable with those of a CFE. SFE guns are generally similar to those for other field emitters, but include a suppressor grid to eliminate unwanted thermionic emission from regions outside the tip. Emission currents in the range 30-70 uA are available.

Q8. You are given the Monte Carlo simulation results under two different sets of conditions. One shows a very large interaction volume while the other shows a small interaction volume. What could be the conditions used if you were told that a) the atomic number was varied, b) accelerating voltage was varied?

Ans-: The electron scattering is an interaction between the probe electron and the specimen atoms that results in a change in the electron trajectory and/ or energy. In terms of scattering a key concept is that of the cross section, which is the measure of the probability that an event will take place. The cross section for scattering can be conveniently describe by the Rutherford expression

Where Q is called the cross section (cm2 ) for elastic scattering (i.e., probability of elastic scattering). The Monte Carlo simulation technique has developed into a highly useful tool for SEM/microanalysis ranging from applications in interpreting SEM images to the x-ray microanalysis of complex structures. To construct a Monte Carlo electron trajectory simulation the effects of elastic and inelastic scattering are calculated from appropriate models to determine scattering angles, distances between scattering sites ("step length"), and the rate of energy loss with distance traveled. From these parameters and equations of analytical geometry that relate the scattering angles and step length to successive electron locations, the electron trajectory can be simulated in a stepwise fashion from the location at which it enters the specimen to its final fate. The size of the interaction volume is a strong function of the energy with which the beam electrons interact with the target and the anomic number. Influence of Beam Energy on the Interaction Volume

The cross section for elastic scattering has an inverse dependence on the square of the energy, Q~1/E2. Thus. as the beam energy increases, the electron trajectories near the surface become straighter and the electrons penetrate more deeply into the solid before the cumulative effects of multiple elastic scattering events cause some of the electrons to propagate back toward the surface. 'The rate of energy loss with distance traveled, as Oven by the Bethe expression, is inversely related to the energy. dElds ~1/E . As the beam energy is increased, the electrons can penetrate to greater depths -because they enter the specimen with more energy and lose it at a lower rate. The lateral dimensions of the interaction volume 'are scale with energy in a similar fashion to the depth. Influence of Atomic Number on the Interaction Volume

Monte Carlo calculation reveal that the linear dimensions of the interaction volume decrease with increasing atomic number at a fixed beam energy. This is the direct consequence of the increase in the cross section for elastic scattering with atomic number. Q~Z2. In targets of high atomic number, the electrons undergo more elastic scattering per unit distance and the average scattering angle is greater than for low-atomic-number targets. The electron trajectories in high-atomic-number materials thus tend to deviate out of the initial direction of travel more quickly, increasing backscattering and reducing penetration the solid. In low-atomic-number materials, elastic scattering is less likely and the trajectories deviate less from the initial beam path. allowing for deeper penetration into the solid. Because the rate of energy loss is lower in low-Z materials. this also contributes to a larger interaction volume. The shape of the interaction volume also changes

significantly as a function of atomic number. The dense region of trajectories changes from the pear shape seen in low-atomic-number materials to a more nearly hemispherical shape truncated by the plane of the surface for high-atomic-number materials. Atomic number varied:- For high atomic number material the interaction volume is small, hemispherical shape. For low atomic number material the interaction volume is large and pear shape. Accelerating voltage varied- As accelerating voltage increase the electron trajectory deviate out of the initial path reducing penetration, and for low accelerating voltage the electron trajectory deviate less from its initial path penetrate deeper in specimen. For high accelerating voltage the interaction volume is large where as for low acceleration voltage the interaction volume is small. Q9.The wavelength of electrons accelerated to 20 kV is ~ 0.08 A implying that sub-angstrom level resolution should be possible in the SEM. Of course, this is nowhere near the resolution that is actually obtained. Why? Discuss all possible reasons for this. Ans-: There are various reason due to which resolution of SEM degrades. 1.A source(Electron gun) for producing a beam of electrons. The ability to achieve a small probe diameter is directly related to the source size or the diameter of the electron beam exiting the gun. An electron beam emanating from a small source size is said to have high spatial coherency. Electron beams can also be characterized in terms of temporal coherency. A beam with high temporal coherency will have electrons of the same wavelength. In reality there is a certain “Energy Spread” associated with the beam. The lower energy spreads result in better resolution and are particularly important in low accelerating voltage imaging. This energy spread results in electrons with different wavelength leading to chromatic aberrations, resulting in lowering the resolution.

2.A series of lenses (condenser and objective) which act to control the diameter of the beam as well as to focus the beam on the specimen

These lenses suffer spherical, chromatic aberration and astigmatism which results ina disk of minimum confusion than a clearly defined focal point. Spherical aberration is the principle limiting factor with respect to the resolving power of the SEM. The further off the electrons from the optical axis the more is the magnetic force and thus more is the electrons bent towards the axis. Chromatic aberration is not something we can do much about as an operator and it becomes particularly problematic when imaging at low accelerating voltages. The electron beam generated by the gun will have a certain energy spread. Electrons of different energies at the same location in the column will experience different forces. An electromagnetic

lens will “bend” electrons of lower energy more strongly than those of higher energy. As with spherical aberration, a disk of minimum confusion is produced Astigmatism is due to the lens errors. The electromagnetic lenses used in the SEM can not be machined to perfect symmetry. If the fields produced by the lenses were perfectly symmetrical, a converged beam would appear circular.A lack of symmetry would result in an oblong beam: the narrower diameter due to the stronger focusing plane; the wider diameter due to the weaker focusing plane. The net effect is the same as that of the aberrations above—a disk of minimum confusion rather than a well defined point of focus.

3.All these aberrations ultimately lowers the resolution.

A series of apertures (micron-scale holes in metal film) which the beam passes through and which affect properties of that beam To reduce the effects of spherical aberration, apertures are introduced into the beam path. Apertures are circular holes in metal disks on the micron scale. The net effect of the aperture is to reduce the diameter of the disk of minimum confusion. However the positive effect comes at the price of reduced beam current. Also, a very small aperture will display diffraction effects (dD). The wave nature of electrons gives rise to a circular diffraction pattern rather than a point in the Gaussian image plane. The diameter of the aperture used will also affect the convergence angle of the beam and this in turn will affect image properties such as depth of focus. Hence due to the diffraction effects of the aperture the resolution is limited.

4.The interaction volume and the pixel size that generates several types of signals that can be detected and processed to produce an image or spectra; The beam is raster scanned from left to right and top to bottom. There is a one-to-one correspondence between the rastering pattern other specimen and the rastering pattern used to produce the image on the monitor. The resolution we choose to imagwill obviously affect the number of pixels per row as well as the number of rows that constitute the scanned area. If the interaction volume is so large and the probe size is very small, then pixels overlap and there is a lot of overlap of interaction volume will take place resulting in blurring of images. If the interaction volume is less and the probe size is large then lot of information is missed, leading to loss of information and reduced resolution. Q10. The collection efficiency of backscattered electrons in a negatively-biased E-T detector is very low while that of secondary electrons in the positively-biased E-T detector is close to unity. Discuss in terms of how the electrons are collected in each case. Ans:- Everhart-Thornley Detector

The electron detector most commonly used in scanning electron microscopy is the combined secondary/backscattered electron detector developed by Everhart and Thornley (1960), Operation:- When an energetic electron (-10 keV energy) strikes the scintillator material, light is emitted. (The scintillator may be a doped plastic or glass target, or a crystalline compound such as CaF2 doped with europium. The light is conducted by total internal reflection in a light guide (a solid plastic or glass rod) to a can pass through a quartz glass window, which forms a vacuum barrier, to the first electrode of a photomultiplier. At this photocathode, the photons are converted back into electrons, and the electrons are accelerated onto the successive electrodes of the photomultiplier, producing an ever-increasing cascade of electrons until the final collector is reached. The typical gain of the photomultiplier is 105-106, and is adjustable by selecting the voltage on the electrodes. The photomultiplication process provides high gain with little noise degradation and high bandwidth. A large fraction of the backscattered electrons that originate from incident beams with energies from 10 to 30 keV carry sufficient energy to directly excite the scintillator. even in the absence of post-specimen acceleration. To collect the low-energy secondary electrons with higher geometric efficiency than simply collecting the fraction defined by the line-of-sight solid angle, a separate bias potential is applied to the Faraday cage, typically selectable in the range +50 V to +250 V. Everhart-Thornley Detector, Negative Bias, When the E-T detector is biased negatively, only backscattered electrons are detected. All secondary electrons are rejected, including those that are emitted from the specimen in the direction of the E-T detector within the line-of-sight solid angle for direct geometric collection. Those high-energy backscattered electrons that leave the specimen with trajectories directly toward the face of the scintillator are collected (that is within the "line-of-sight" cone of solid angle); all other back scattered electrons emitted from the specimen are lost. For a specimen at 0° tilt (normal beam incidence), the E-T detector usually views the specimen from a take-off angle of approximately 30°. The collection efficiency also depends on the angular distribution of the emitted signal. Because the cosine angular distribution for 0° tilt favors BSE trajectories near the surface normal, when the E—T detector is placed at a low detector take-off angle, the fraction of the BSE collected is even less than that given by the simple geometric efficiency. The negatively biased E-T detector is thus a highly directional. asymmetrically placed, low-geometric-efficiency detector for BSEs.

a) Relative collection of backscattered electrons emitted in a cosine distribution by negatively biased E—T detectors placed at various take-off angles. (b) Relative collection of backscattered electrons emitted from a highly tilted surface Everhart—Thornley Detector, Positive Bias. The positively biased E—T detector behaves in a markedly different manner. The direct effect of the positive bias is to attract secondary electrons to enter the Faraday cage for subsequent acceleration by the bias on the scintillator. In addition to those secondaries emitted from the specimen into the solid angle of collection of the E—T detector (identical to the solid angle for BSE), the action of the attractive positive bias is to cause a deviation of the trajectories of SE emitted from the specimen over a much wider range of solid angle into the detector. Calculations of the trajectories of SE under the positive field of the E—T detector reveal that SE can be collected even if there is not direct line of sight from the specimen to the detector. From a flat surface, the collection efficiency can approach 100%. The positively biased E—T detector accepts both this i direct component as well as the indirect component, which is effectively collected over a much larger solid angle approaching 2ᴨ sr. The positively based E- T detector must

thus be thought of as a combined secondary backscattered electron detector. Another advantage of the positively biased E—T detector is its performance at low beam energy. The positive Faraday cage bias results in efficient collection of direct SE and BSE as well as remote SE (equivalent to BSE).

Schematic illustration of deflection of trajectories of secondary electrons of various energies by positive potential on the Faraday cage.

Q11. Fig. A and B are secondary electron images of an electric bulb coil (next page). You are told that the conditions that the images were obtained are as follows: i) 5 kV, Mag x540, Objective aperture 200 mm, Working distance 10 mm and

ii) 5 kV, Mag x540, Objective aperture 200 mm, Working distance 38 mm. Match the conditions with the image and justify your statement.

Ans-: 1)5kV, Mag x540, Objective aperture 200 mm, Working distance 10 mm-A 2)5 kV, Mag x540, Objective aperture 200 mm, Working distance 38 mm.- B The picture A have working distance of 10mm, less the working distance results in reduced depth of focus. As seen in picture A the background is blur, out of focus. Due to less working distance, the scan length that beam traverses on specimen is also less this increase the magnification as seen. On the other hand the picture B have 38mm working distance it is having increase working distance, Increasing the working distance produces a larger spot size at the specimen, although the beam current remains about the same. The convergence angle decreases giving an improved depth of focus. As seen the background in picture B the background is also in focus. The longer working distance also increases the scan length that the beam traverses on the specimen and in this way reduces the magnification. Q12. Backscatter coefficient is sensitive to difference in atomic number but is relatively insensitive to the accelerating voltage. Why? Ans- . Backscattered Electrons Backscattered electrons (BSE) are beam electrons whose trajectories have intercepted a surface usually, but not necessarily the entrance surface and which thus escape the specimen. They undergone numerous elastic scattering events to accumulate enough deviation from the incident beam

path to return to the surface. Backscattered electrons remove a significant amount of the total energy of the primary-beam which in the absence of the backscattering effect would contribute to the production of additional secondary radiation products. Backscattering is quantified by the backscatter coefficient which is defined as

where nB is the number of beam electrons incident on the specimen and n BSE is the number of backscattered electrons (BSE). The backscatter coefficient can also be expressed in terms of currents, where ib refers to the beam current injected into the specimen and iBsE to the backscattered electron current passing out of the specimen. The backscatter coefficient ( η ) is the ratio of the number of BSEs to the number of beam electrons incident on the sample. η and atomic number: η shows a monotonic increase with atomic number. This relationship forms the basis of atomic number (Z) contrast. Areas of the specimen composed of higher atomic number elements emit more backscatter signal and thus appear brighter in the image. This is because the slope of the line, Z contrast is relatively stronger at lower atomic numbers.

The slope of η versus Z is initially steep, but decreases with increasing

Z, becoming very shallow above Z = 50. The practical effect of this behavior is

that atomic number contrast between adjacent pairs of elements is strong at

low atomic number and weak at high atomic number.

η and accelerating voltage: There is only a small change in η with accelerating voltage (< 10% in the -50 keV range). As the accelerating voltage is reduced toward the very lower end (1 keV), η increases for low Z elements

and decreases for high Z elements. Although the η range increases as approximately the 1.67 power of the beam energy, the bethe energy loss expression shows that the rate of energy loss decreases with increasing energy. Compare an average electron at the limit of the envelope of the interaction volume for an incident energy of 10 keV with an average electron at the same absolute depth in the interaction volume that started with 20-keV incident energy. In the 10-keV case, the electron loses virtually all of its energy and becomes captured by the specimen. For the 20-keV case, an electron at the same depth still has at least 10 keV of its energy remaining because it started with twice the energy and lost it at a lower rate. The electron thus has the possibility of continuing to travel and scatter, so that a significant fraction of these electrons can eventually reach the surface and escape as backscattered electrons. The backscatter coefficient is thus relatively insensitive to the beam energy. At beam energies below 5 kcV the behavior of the back- scatter coefficient is more complicated. As the beam energy is reduced toward 1 keV.The back scatter coefficients of light elements apparently increase, whereas those for heavy elements decrease.

Backscattered electron coefficient as a function of atomic number plotted for a range of beam energies from 5 to 49 keV.