Detection of Signals
Wavelength dispersive spectrometry (WDS)
Wavelength spectrometers are used to select the X-ray of interest for analysis. This selection is made by Rayleigh scattering of the X-rays from a systematic crystal located between the sample and X-ray detector. By changing the angle of incidence, a crystal can be made to constructively diffract X-rays of different wavelengths. The diffracted X-rays are counted using X-ray detectors that must be moved to accommodate the changing incident angles on the crystal.
Scattering and diffraction of a coherent beam of X-rays can occur from parallel planes of atoms spaced distance, d, apart. For a given angle, θ, in order for constructive interference to occur, the extra distance traveled by a wave diffracting off the lower layer (CBD in the figure below) must be an integer number of wavelengths.
the conditions necessary for constructive diffraction of X-rays (and light) by a crystal are:
where n = integer (1, 2, 3 ...). X-rays with other wavelengths will produce destructive interference. Note, however, that the wavelengths 1λ = 2(λ/2) = 3(λ/3) ... Thus, specific shorter wavelengths will also experience constructive interference. These are called higher-order wavelengths (abbreviated 2°, 3°, etc.) because their diffraction occurs when n > 1; the value of n specifies the "order" of the diffraction. Higher order diffracted wavelengths generally have lower intensities than those produced by first order (1°) diffractions.
Spectrometer Scan. Wavelength dispersive spectrometer scan of an augite pyroxene using a TAP crystal. Note the high-order peaks at high sinθ values.
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The WDS spectrometers on the microprobe and JEOL-6480LV SEM use what are termed linear-focusing drives. For efficient X-ray focusing, the sample, crystal, and detector must lie on a circle called the Rowland circle and remain on it for all wavelengths of interest. Since the sample is fixed in place, the crystal and detector must both move to remain on the Rowland circle. This arrangement is mechanically complex, since to maintain the appropriate geometry the crystal must rotate as source-crystal distance changes. However, because the Rowland circle radius and the take-off angle do not change, the mechanical problems are not insurmountable. Precision internal gearing controls the movement of the detector along a complex path and rotation of the detector. Crystal and detector movement are driven by a worm gear connected to a stepping motor. Each step corresponds to 10000 x sinθ on the MBX microprobe. Thus a position where sinθ = 0.45 corresponds to a motor value of 45000.
Spectrometer Geometry. The geometry of a linear, fully focusing X-ray spectrometer. This type of spectrometer is used in most commercial wavelength-dispersive electron microprobes (after Williams 1987).
A larger diameter Rowland circle is more efficient than a small diameter circle in providing peak separation at given angle. The diameter of the Rowland circle of all Cameca microprobes is 16 cm, whereas, the JEOL 733 Superprobe has a 14 cm Rowland circle. Thus, the Cameca microprobes provide better peak resolution. However, larger Rowland circles require larger spectrometer housings with the attendant vacuum and positioning problems. A very large Rowland circle could provide better peak resolution, but it is not practical.
MBX Microprobe Spectrometer. (left) The armature and gearing that move the detector are visible in the center of this photograph of a Cameca SX-50 vertical spectrometer; (upper right) Detail of the crystal holder and flipping motor; (lower right) X-rays from the sample come through the X-ray window (circular hole into the column) and are diffracted by the analyzing crystal into the detector. The high voltage feed and gas-flow lines trail off from the detector towards the lower right corner.
Oxford WDS spectrometer on the JEOL-6480LV SEM.
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Spectrometers may be mounted vertically or inclined relative to the top surface of the sample. The NAU microprobe has one inclined spectrometer (#1) and two vertical spectrometers (#2, #3). An inclined Oxford spectrometer is attached to the JEOL-6480LV SEM.
MBX spectrometer mountings. (a) Vertical spectrometer mounting with part of the the Rowland circle shown dashed; (b) Inclined spectrometer mounting (the secondary-electron detector is shown beneath the spectrometer). X-ray paths are shown in green.
Inclined spectrometers are less sensitive to changes in sample focus and topography, but, because of their orientation, only a few can be mounted together around the electron column. A small variation in sample height simply displaces the X-rays to a different portion of the analyzing crystal.
Focusing in an inclined spectrometer. The effect of a small variation in sample height on the focusing of the crystal is very small in an inclined spectrometer, as is the corresponding variation of the Bragg angle. For clarity, only the front part of the Rowland circle is shown (after Maurice et al. 1979).
Vertical spectrometers are more sensitive to changes in focus, but many can be mounted together. For example, the old Smithsonian microprobe had 12 vertical spectrometers!
Focusing in a vertical spectrometer. The effect of a small variation in sample height on the focusing of the crystal produces a correspondingly large variation of the Bragg angle (after Maurice et al. 1979).
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The angle between the surface of the sample and the detecting crystal is termed the "take-off" angle, a. High take-off angles decrease absorption of the X-rays and other effects produced in the sample and yield in higher count rates. Low take-off angles increase absorption because the X-rays must traverse more material. Thus, a low φ take-off angle is more sensitive to topographic effects. For this reason, secondary electron counters are located at low angles to enhance the topographic resolution of secondary electron images.
Take-off angle. Schematic illustration of the take-off angle. For a given angle of electron incidence, the length of the absorption path is directly proportional to the cosecant of the take-off angle,φ.
Absorption increases rapidly for take-off angles under 25°, but is relatively constant for angles greater than 35°. All Cameca and JEOL microprobes have take-off angles of 40°, old ARL machines have angles of 52.5°, and MAC and ETEC machines angles of 38.5°. Count rates on ARL microprobes are about 30% higher than on MAC microprobes simply due to the higher take-off angle.
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Space constraints limit the range of Bragg angles possible in a wavelength dispersive spectrometer. The incident angle, θ ranges from 12.5° to 56° in the MBX microprobe; the range is slightly larger in a JEOL 733 microprobe (12.5° to 65°). The range for the Oxford wavelength dispersive spectrometer attached to the JEOL-6480LV SEM is 16.5° to 67.5°. Thus, crystals with different d-spacings are necessary to cover the entire range of X-ray wavelengths of interest (~1 to 20 Å). Many microprobes have multiple crystal in each spectrometer to increase analytical flexibility; the NAU microprobe has pairs of crystal that can be flipped. The most commonly used crystals are:
- LIF 200, lithium fluoride, LiF
- PET 002, pentaerythritol, C(CH2OH)4
- TAP 1011, thallium acid pthalate, TlHC8H4O4
- ODPB, lead sterate or lead octodecamoate
- PC0, W and Si
LIF is an ionic solid, whereas PET and TAP are organic crystals. ODPB is a pseudo-crystal, in which Pb atoms are interlayered with a fatty-acid salt to produce regularly spaced planes equivalent to interplanar crystal spacing. PC-0, also a pseudo-crystal, uses W and Si to create regularly spaced layers. ODPB and PC-0 are periodic in only one direction. There are many other types of large d-spacing synthetic "crystals," For example, the JEOL-6480LV has an LSM-060 crystal, made of W and Si, with a d-spacing of ~61 Å.
A given X-ray line can be diffracted using any crystal, but spectrometer mechanical limits will restrict which crystals can actually be used. For example, Fe-Kα with a wavelength of 1.937 Å, is located at θ of 28.75° on LIF, 12.8° on PET, and 4.3° on TAP. Fe-Kα radiation is very near or beyond the mechanical limits of the MBX spectrometers for PET and TAP, necessitating use of a LIF crystal.
Recall that although a spectrometer may be able to reach a certain elemental peak, insufficient overvoltage may make the peak unusable. In cases where a
spectral line can be observed on multiple crystals, choose the crystal according to the criteria below.
- Always measure Si-Ka
- Use the crystal with the best peak-to-background
ratio. In general, K-lines have the best P:B ratios (vs. L-lines) as do larger
sine-theta values on a given crystal. Sharper peaks (lower 2d crystals)
generally have lower count rates.
- However, major elements don’t need the best P:B ratios
and count rates because the peaks are so large. In this case, pick the crystal
with the best reproducibility, i.e., one with the smallest sine-theta value.
It is best to distribute the elements on the spectrometers as evenly
as possible, so that one spectrometer in not idle while another does the bulk
of the work. In general high-pressure detectors will have higher
count rates (PET on 2 has better count rates than PET on 1). Use high-pressure
detectors for lower abundance elements.Back to top.
Not every regular crystal makes a good analyzing crystal.
- Analyzing crystals must be chemically stable; for example, although NaCl has a useful 2d-spacing, it dissolves in humid air
- A crystal must also not be too perfect. If a spectral peak is too sharp, its position is difficult to reproduce consistently.
- Low X-ray absorption is also critical. An analyzing crystal is constantly bombarded with X-rays; while much radiation is diffracted, some is absorbed and re-emitted as secondary fluorescence radiation, which may reach the detector.
- Analytical crystals must effectively separate adjacent spectral lines, something called dispersion efficiency. Dispersion efficiency may be expressed as:
Note that higher order reflections are better dispersed and that the 2d-spacing of the crystal is an important factor. Where high resolution is desired, it is best to avoid low θ and large 2d-spacings even at the loss of peak intensity. For example, an LIF crystal will separate the peaks for Ti-Kα (4508 eV) and Ba-Lα (4466 eV) better than a PET crystal.
- Such conditions pertain when analyzing trace amounts of V in Ti-bearing materials and the analysis of rare earth elements (REE).
- Crystals also must have high reflection efficiency. Reflection efficiency depends on the number of electrons in orbitals of atoms in the crystal, the angle of diffraction and the wavelength of the X-rays.
- Finally, crystals should not be sensitive to temperature fluctuations, having a low coefficient of thermal expansion. The effect of thermal expansion is most pronounced at higher diffraction angles. Of the commonly used crystals, PET is most sensitive to changes in temperature, but the effect is not a problem if temperature is adequately regulated.
Effect of temperature on analyzing crystals. The effect of thermal expansion is most pronounced at high diffraction angles with PET showing the greatest changes (after Jenkins & de Vries, 1967).
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The efficiency of an X-ray spectrometer, in part, depends on the crystal design and crystals are bent and/or ground to improve their efficiency. This can be done in two ways:
- Johann optics, where the dispersing crystal is bent to a radius equal to the diameter of the Rowland circle, R. This results in some broadening and asymmetry of the focusing 'point'.
- Johanson optics, where the crystal is bent as in Johann optics but also ground to a radius of R/2, resulting in focusing over the entire range of angles.
Crystal optics. The essential geometry of fully focusing Johanson (left) and semi-focusing Johann (right) X-ray spectrometer optics. These diagrams are not drawn to scale and exaggerate the loss of resolution in a semi-focusing spectrometer. The effect is much less pronounced than the diagrams indicate; semi-focusing spectrometers are used in microprobes (after Williams 1987).
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Detectors convert X-rays photons through ionization into voltage pulses which can be counted. There are three types of proportional detectors used in microprobes to detect X-rays: gas-flow, sealed-gas and semiconductor. In a "proportional" counter the size of pulse is proportional to the energy of the X-ray that produced it. however, the first two types have poor energy discrimination and must be used with an analyzing crystal to preselect the X-ray energy. Semiconductor detectors have excellent energy discrimination and are used without analyzing crystals. They will be discussed in the Energy Dispersive Spectrometry section.
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Gas-flow and sealed detectors
Gas-flow and sealed-gas detectors have identical designs except that in the first case the detector gas is constantly changed and replenished while in the latter the gas is static. Both detectors consist of a cathode tube with a thin (20-100 mm thick) W-wire anode running through the center. A 1-2 keV voltage is applied between wire and tube. Sealed-gas detectors were first developed to a high degree of reliability by H. Geiger and W. Muller in 1928.
Gas-flow detector. A gas-flow proportional detector (after Goldstein et al. 1981).
The detector tube has a window through which X-rays from the analyzing crystal enter the detector. The window is usually made of either Mylar (polyethylene tetrapthalate) or polypropylene window. Unfortunately, whatever the thickness of the window, it will still absorbs a significant portion of the X-rays from the analyzing crystal. For example, a 5.5 mm Mylar window absorbs ~50% Al-Kα, ~70% Mg-Kα, ~85% Na-Kα and ~98% F-Kα X-rays. Thinner polypropylene windows absorb about 60% less than Mylar windows and are routinely used for light element detectors. The NAU microprobe uses a 1 mm polypropylene window for the light element spectrometer (TAP crystal) and 6 mm Mylar windows for more energetic X-rays (PET and LIF).
X-ray absorption properties of various materials. Elements indicate wavelengths of Kα lines (after Potts 1987).
Detectors usually have a second window opposite the one that allows the X-rays from the crystal to enter. These allow high-energy X-rays to exit, preventing them producing secondary radiation from the detector itself. All MBX detectors have thicker (25 mm) Be windows in their backs, as does the light element detector of the Oxford spectrometer on the JEOL-6480LV microscope.
In a gas-flow detector, a mixture of 90% argon and 10% methane, called P-10, continuously flows through the detector. The detector tube is not just sealed with P-10 gas inside, because some gas escapes through the thin windows and must be constantly replenished. The detector gas must be ultra-pure to avoid reaction with the wire and subsequent loss of detector sensitivity. Electronegative impurities like O2- and CO- are especially bad. The efficiency of a gas-flow detector can be improved by increasing the pressure and most probes have high and low pressure detectors.
Sealed detectors filled with Xe or Kr gas are used for higher energy X-rays since these gases are ionized more efficiently than Ar by shorter wavelengths. Since they are used for more energetic X-rays, the detector windows can be thicker to prevent loss of the gas by diffusion. A window ~25 mm thick made of Be or Al is commonly used because the high-energy X-rays gradually destroy Mylar or polypropylene windows.
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In gas-flow and sealed detectors, the X-rays ionize an inert detector gas, ejecting an outer shell electron to produce an electron-ion pair: The first ionization potentials of the inert gases are small (less than 25 eV); however, the effective ionization potential required to produce an electron-ion pair is somewhat higher due to competing processes which absorb incident photon energy without causing ionization.
| ||1st Ionization|
The average number of electron-ion pairs, n, produced by an X-ray is:
where E = incident X-ray energy (eV) and ei = effective ionization potential of the detector gas (eV). Consider a Cu-Kα X-ray, which has an energy of 8.04 keV. With Ar detector gas, n = 8040/26.4 = 304 primary electron-ion pairs. This number is too small to detect by itself, but placing a potential across the gas from wire to tube wall will produce amplification. The electrons produced by the incoming X-ray are accelerated towards the anode wire by the detector voltage and can in turn ionize other Ar atoms producing another electron-ion pair and so on. The resulting electron avalanche is still proportional to the initial signal.
Electron avalanche. Principle of detection of an X-ray photon. Incident X-rays ionize the Ar detector gas (purple spheres) losing an average of 26.4 eV, then continue to ionize other Ar atoms. The resulting secondary electrons are accelerated toward the detector wire, gaining sufficient energy to ionize other Ar atoms, producing an electron avalanche. The Ar ions are neutralized by electrons donated by methane molecules in the detector gas mix.
The chain of ionizations causes a momentary voltage across the detector producing a pulse. The amount of amplification produced by the gas depends on the amount of voltage applied to the detector. At very low voltages in the region of "undersaturation", the detector potential difference is too small to prevent recombination of electron-ion pairs formed by incident X-rays before they reach the collecting wire. At slightly higher voltages in the ionization chamber region, the potential is just sufficient to counter recombination so that the number of electron-ion pairs produced by X-rays equals the number reaching the anode wire; the resulting amplification (gain) is 1. Further increases in the detector voltage produce the avalanche effect and significant amplifications. At voltages in the proportional counter region, the pulse height is proportional to the energy of the incident X-ray. Too high a voltage drives the detector out of the proportional region and into the Geiger region.
Effect of detector voltage. The effect of increasing the applied anode voltage on (a) the gas amplification factor and (b) the observed count rate for a gas proportional counter. Note the rapid increase in observed count rate at the threshold of Geiger breakdown (after Potts 1987).
Gain is defined as:
where N = number of electrons reaching the anode wire, n = number of electrons produced by X-ray ionization. Detector gains are typically on the order of 104 to 105. With a gain of 104, the 304 electron-ion pairs formed by a Cu-Kα X-ray yield 3.04 x 106 electrons at the anode wire. The size of the resulting pulse can be calculated from:
where ce = charge on the electron (1.6022 x 10-19 coulomb), C = capacitance of the detector (typically 10-10 farad). Thus, the Cu-Kα photon will generate a voltage, V,of:
or, 4.87 mV. Recall that we've assumed a gain of 10,000! The resulting pulse is still very small and needs further electronic amplification by a preamplifier located near the detector on the spectrometer housing.
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If the energy of the incoming X-rays is greater than the absorption edge of the detector gas, it can produce characteristic X-rays from the gas and produce what is termed an escape peak. The name derives from the fact that some energy of the incoming X-ray is escaping as characteristic X-rays from the detector gas.
For example, Ec for Ar is 3.2 keV and any X-rays with higher energy can excite Ar-Kα X-rays (E = 2.95 keV). The production of characteristic X-rays from the gas decreases the apparent energy of the incident X-ray and yields a separate peak offset towards lower energy by 2.95 keV. The size of the escape peak is a function of fluorescent yield, ω, and is generally smaller than the characteristic peak because relatively few X-rays excite the gas compared with the number detected; however, in some cases its size can be quite large.
Examples of escape peaks. (A) Iron escape peak in argon (ωK = 0.12); (B) Molybdenum escape peak in krypton (ωK = 0.65) (after Maurice et al. 1979).
Escape peaks can be a problem if they interfere with peaks of elements of interest.
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All detectors suffer from deadtime due to the physical constraints on X-ray detection. The time between X-ray entry and electron-ion pair avalanche production is on the order of 3 x 10-7 seconds. The avalanche produces a sharp voltage drop that requires ~10-4 seconds to decay back to zero. The rate-limiting process in this decay is the slow movement of Ar+ ions to the cathode tube, which is about 103-104 times slower than electron movement. This slow neutralization of the Ar+ ions prevents production of another electron-ion avalanche and produces what is called a deadtime, an interval during which the detector is inoperative and cannot detect incoming X-rays.
To counter the effect of the slow movement of Ar+ ions, methane is added to the detector gas (P-10 indicates 10% methane). Methane is an electron donor and provides "quench" electrons to the Ar+ ions, allowing the detector to rapidly reset, decreasing deadtime, because neutralization of the Ar+ ions is not dependent on them actually reaching the cathode tube. In addition, the electronics are often set to "clip" the decay pulse after about 10-6 seconds. Deadtimes are usually about 1 to 2 µsec.
Effect of deadtime. Plot of output count rate as a function of input count rate, for four deadtime constants.
All X-ray count rates are corrected for the effect of deadtime by the analysis software. Such deadtime corrections become very important at count rates exceeding 3000 cps. The detector deadtime correction is:
where It = true counts, Im = measured counts, and td = deadtime. For example: if Im = 105 and td = 2 x 10-6 seconds, then It = 1.25 x 105 (25% higher than observed). Deadtime constants can be determined by accumulating a series of intensities, I, at different beam currents, i. For any current, i, the measured intensity is proportional to the current:
Thus we can rewrite the deadtime correction equation:
Plotting Im/i against Im will yield a straight line; the value K can be determined by extrapolating the line to Im = 0. Once K is known td can be obtained from any point on the line by:
where A = (Im/i). Values calculated from higher values of Im will generally be more accurate because of better counting statistics.
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The statistical process of pulse formation yields a Poisson distribution of voltages coming from the detector.
Detector Resolution. Peak shape and energy resolution of the detected X-ray peak (A) and of the proportional counter (B). Resolution of the X-ray peak includes the additional effects produced by the analyzing crystal, whereas, resolution of the proportional counter reflects the effects of the detector electronics.
At sufficiently high count rates a Poisson distribution approaches a normal distribution and the relative standard deviation may be expressed as:
where K = constant (close to 16 for Ar-filled detectors), and E = energy of incident X-rays (keV). The pulse height distribution is wider for longer wavelengths (lower E). For example, the standard deviation is 13.1% for Al-Kα and 6.3% for Fe-Kα.
A more refined way of calculating theoretical resolution is expressed by:
where EFWHM = full width at half maximum of the energy distribution (eV), E = energy of incident X-rays (eV), ei = effective ionization potential (eV), and F = Fano factor that depends on gas type. The Fano factor is required because it has been demonstrated that the resulting variance is only a fraction of what would be expected. This factor ranges from 0.5 to 0.22 for Ar/methane mixtures. The 2.355 factor in the formula relates 1 standard deviation (1σ) to the FWHM of the pulse-height distribution. For example, with F = 0.22, the Al-Kα energy distribution is 218 eV (14.7%) at FWHM.
It is usually better to not rely on theoretical expressions and simply measure the detector resolution, expressing the result as a percentage of the X-ray energy. The observed resolution is defined as the full width in energy units of the peak at half-maximum, EFWHM, divided by the energy of the X-ray, E:
Once the resolution of a detector has been established for given energy the relative resolutions for other energies may be calculated:
where R1 = observed resolution at E1, E2 = energy of interest, and R2 = resolution at energy of interest.
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Single channel analyzer
Recall that the amplitude of the pulse from gas-flows detectors is proportional to the energy of the incident X-ray photon. This permits the electronic circuitry to select for a specific X-ray photon by excluding anything but the desired amplitude. A single-channel analyzer (SCA) selects pulses of interest and outputs pulses suitable for the counting electronics.
The SCA can be set to reject pulses of lower energy than a certain threshold (baseline) and higher than the baseline plus a "window." Sometimes, these discrimination values are expressed as "lower" and "upper" limits, EL and EU, rather than as a baseline and window. Selection of desired pulse energy is termed pulse-height analysis, and SCAs are commonly called "pulse height analyzers" (PHAs).
Schematic representation of pulse height analyzer behavior. (a) Main amplifier output; (b) single channel analyzer output with EL = 5V and EU = 7V. Pulses I and III are rejected. These limits could also be described as a baseline of 5V with a 2V window. Figure after Goldstein et al. 1981.
When both baseline and window are in use, the PHA is in "differential" mode. The baseline is usually used to eliminate low-energy electronic noise. The upper limit (window) may be used to eliminate the interference from higher order peaks of other undesired elements which also satisfy Bragg's Law. In addition to the desired wavelength, an analyzing crystal will also diffract 2(λ/2), 3(λ/3), etc. However, only the desired wavelength has energy of E; the 2° peak has an energy of 2E, the 3° peak has energy of 3E, etc. Setting the window (upper limit) to screen out these higher energies insures that only photons with the correct intensities are counted.
As an alternative, the PHA can be set in "integral" mode with the window wide open to accept all pulses greater than a given baseline. The use of integral mode is recommended in most cases to limit the problems associated with a narrow window caused by drift in the detector electronics, and changes in P-10 gas pressure and room temperature. The significance of the high-order interference depends on how much of the interfering element is in the sample and the effective intensity of its X-ray line. For the elements most abundant in geological samples, high-order interferences are rare, because elements with twice (or three times, etc.) the energy of the element of interest are rare. Obviously, in trace element work, where the peaks of interest are very small, very careful evaluation of interferences is required.
One important example of interference is that of Ca-Kβ1 (2°) on P-Kα1, which affects analysis of the mineral apatite. Fortunately, the effect is essentially uniform in all apatites and can be ignored, as long as apatite unknowns are analyzed using apatite standards. Another important case is that of analyzing Hf-Lα1 in zircon, owing to an interfering Zr-Kα1 (2°) peak; here, setting an upper limit is essential.
High-order peak. In this example, the 2° Zr-Kα1 peak also appears in the voltage spectrum of the Hf-Lα1 peak. Pulse-height analysis should be used to exclude it and include the Hf-Lα1 (Ar) escape peak. The red bar shows the range of voltages that should be included by pulse-height analysis. Modified from image source: http://www.bruker-axs.de/fileadmin/user_upload/xrfintro/sec1_8.html.
In summary, the operator user must consider three possibilities:
- If the X-ray of interest has energy exceeding Ec of Ar (2.96 keV), escape peaks can be a problem but high-order diffractions are not. The baseline may be used to eliminate the escape peak and the PHA run in integral mode.
- If the X-ray energy is less than Ec of Ar and greater than about 30 times the ionization potential of Ar (30 x 26.4 eV = 0.8 keV), there are neither escape peaks nor higher-order diffractions. Again, integral mode is appropriate.
- If the X-ray energy is less than 0.8 keV, there are likely to be wavelength shifts and higher-order peaks can cause significant interferences. Differential mode, with carefully selected baselines and windows is appropriate.
Energy dispersive spectrometry (EDS)
The semiconductor detectors used in energy dispersive spectrometry (EDS) are proportional detectors like the gas-flow detectors used in WDS analysis. However, in contrast to the gas detectors, a semiconductor has good energy discrimination by itself and can be used without preselecting energies using analyzing crystals. It might be worth reviewing the discussion of semiconductors in the Cathodoluminescence section.
Semiconductors detectors are made of single crystals of either Si or Ge. If the crystal structure were perfect, there would be no local abundances or shortages of electrons; however, all crystal have imperfections (lattice defects, impurities, etc.) that result in electron-deficient areas (termed "holes") and extra free electrons within the crystal lattice. These holes and free electrons will act as charge carriers when an electrical field is applied across the crystal. Thus, a pure crystal, with fewer holes and free electrons, allows less current to pass than an impure crystal.
X-ray analyzing instruments use Si semiconductor detectors; Ge detectors are generally used for γ-ray counting (e.g., in instrumental neutron activation analysis, INAA). Pure Si is an intrinsicsemiconductor, providing a excellent material for a detector; however, even purest available Si contains some residual impurities such as B of Al, causing it become a conductor by creating holes in the valence band of Si (B has fewer valence electrons than Si). These holes become charge carriers, allowing current to flow; the result is called a p-type semiconductor. Addition of Li or P to the Si crystal adds electrons to conduction band (more valence electrons than Si) and swamp out the effects of B impurities; this is termed an n-type semiconductor. Addition of trace impure such as Li to a crystal is called "doping." P-type and n-type semiconductors are also termed "extrinsic" semiconductors, because their semiconductive properties result from the introduction of impurities into the lattice.
Types of semiconductors. Schematic diagram showing the only the valence electron shell to illustrate intrinsic, p-type and n-type semiconductors. Images' sources:http://britneyspears.ac/physics/basics/basics.htm.
Different types of semiconductors can be combined to yield useful electronic devices. For example, a p-n junction (also called a diode), will only allow current to flow in one direction. Placing a voltage across a diode causes the electrons in the n-type zone to move across the contact and towards the positive terminal and the holes in the p-type zone to move the opposite way across the contact towards the negative terminal. When the electrons and holes reach each other they recombine causing a current flow to through the diode. Although the electrons and holes flow in opposite directions, the current only flows one way because the charge carriers have opposite polarities.
PN junction (diode). A forward-bias (voltage) situation applies when the p-type silicon is connected to the positive terminal of a battery and the n-type silicon is connected to the negative terminal; a current will flow. With a reverse bias (p-type silicon is connected to the negative terminal of a battery, etc.), no current will flow. Image modified from images at: http://www.mpoweruk.com/semis.htm.
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Detector crystals are doped with Li (an electron donor) in a process called "drifting." Li drifting makes Si a better semiconductor by swamping out the effects of impurities. Li-drifted crystals are called "silly" for Si(Li) and "jelly" for Ge(Li). A detector crystal consists of 2-5 mm thick Si crystal, with gold contacts on its ends. A bias is applied across the crystal causing a current to flow. The Si crystal consists of a "Li-drifted" intrinsic region facing the specimen (p-type) and an adjacent Li-free region (intrinsic). The front contact, Li-free region and Li-drifted intrinsic region form a p-i-n junction. The crystal is maintained at low temperatures to prevent diffusion of Li from the intrinsic region to the Li-free region. In general, the diffusion of Li is only a problem when there is a voltage across the detector.
Cross section of a typical lithium-drifted silicon detector. X-rays create electron-hole pairs in the intrinsic region of the semiconductor; these charge carriers then migrate to the electrodes under the influence of an applied bias voltage (after Kevex Corporation 1983).
Immediately beneath the gold surface facing the sample is a "dead-zone" where the Li drifting is inadequate to deal with impurities. In this zone there is a large excess of holes, that trap charges produced by X-ray interaction in the crystal and produce a low-energy "tail" on the side of the peak.
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When an X-ray hits the detector crystal, it is absorbed and produces a high-energy photoelectron. The photoelectron knocks a valence band electron into the conduction band producing a electron-hole pair. This interaction uses up some of the energy of the photoelectron, and the slightly less energetic photoelectron continues to produce more electron-holes pairs until its energy is dissipated. On average for a Si crystal, 3.8 to 3.9 eV are dissipated per electron-hole pair created. Thus, X-rays with energy more than 1 keV make many holes. The bias placed across the detector crystal causes the electron-hole pairs to migrate and increases the conductivity of the crystal. The more holes created, the greater the increase in conductivity and the associated drop in resistance. The total charge conducted is directly proportional to the energy of the absorbed X-ray; Unlike a gas-flow detector there is no internal gain. Baseline conductivity due to thermal excitation of electrons in the detector crystal produces a leakage current and increased signal noise. Consequently, the crystal is sheathed in a liquid-N2-filled cryostat producing a temperature of about 77 K (-209°C) to decrease thermal noise.
The X-ray detection process in the Si(Li) detector. The energy of incident X-ray is absorbed by production of Auger electrons and by electron-hole pairs. Incident X-rays may cause ionization in the Si of the detector. Escape peaks in a Si(Li) detector occur 1.84 keV lower in energy (Ec for Si-Ka) than the incident X-rays, and will be present for all parent peaks above 1.84 keV. However, the magnitudes of the escape peaks are usually just a few percent of the parent peak (after Goldstein et al. 1981).
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Although the number of electron-hole pairs created is a function of the energy of the X-ray, it is a statistical process and there is a normal distribution around the actual X-ray energy. Detection is a statistical process and resolution is treated as for gas-flow detectors. Fano factor for Si(Li) semiconductor detector ranges from 0.1 to 0.13. Resolution depends not only on the detector but also the electronics. The standard industry EDS resolution test is on Mn-Kα radiation (5.9 keV) at 1000 cps with an 8 msec time constant; resolutions are ~150 eV. WDS systems can handle a much higher count rates without loss of resolution than EDS systems. For WDS the limit is about 50000 cps, whereas EDS functions best at 2000 cps.
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Signal amplification and processing
The pulses produced by the Si(Li) crystal require amplification before they can be shaped, analyzed and measured. The preamplifier is located physically near the detector crystal to minimize stray electronic noise. It incorporates a field-effect transistor (FET) that is used to reset the pulse amplification circuitry. Both the preamplifier and FET are cooled with liquid N2 to decrease electronic noise. The resulting signal is sent to a main amplifier, which provides linear, low noise amplification of the preamplifier signal. Most importantly, the main amplified must be able to recover quickly after processing one pulse to be ready for the next, because pulses are produced rapidly.
At high count rates, a second pulse may reach the amplifier before the first has been fully processed and pulse pileup results. This results in a total pulse that is a combination of two pulses and thus meaningless. Pulse pileup rejection circuitry, which assures that processing of one pulse is finished before accepting another, is used to avoid this. Unfortunately, the pulse pileup circuitry significantly increases the deadtime.
Pulse Pileup. Failure to discriminate pulses 1 and 2 leads to an anomalously large pulse (1+2) being recorded (after Kevex Corporation 1983).
A multichannel analyzer (MCA) processes the pulses from the main amplifier. Recall that the amplitude of the pulse is proportional to the energy of the incident X-ray photon. The MCA contains an analog-to-digital converter (ADC) and as each pulse is received it is converted into a number. Large pulses are converted into larger numbers. The resulting ADC output is used as the address of a memory location and one is added to the value at that location. In effect, the memory acts as a set of independent counters, each covering a narrow range of energy. Counts are accumulated into these "bins" or "channels" for a preset "live" time (counting time corrected for deadtime) and the results can then be displayed.
The EDS system on the Cameca MBX microprobe consists of a Quantuum detector system connected to an 4Pi MCA board, which is located in the G3 computer. The MCA board and has a 1024-channel memory and can accumulate up to 16,777,215 (224-1) counts in each channel. Each channel is approximately 10 eV wide. The system can be calibrated using known energies to allow the use of a set of KLM marker lines. The INCA system on the JEOL-6480LV is similar.
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The resulting energy spectra can be used qualitatively or qualitatively. Commonly available software allows the analyst to rapidly identify the X-ray lines present in an accumulated spectrum. In general, elements with concentrations of about 0.5 wt. % produce distinct identifiable EDS peaks. Peak heights can be used as a rough proxy for the element abundances, although the effect of variable fluorescent yields makes this problematic. For example, the heights of the Si-Kα and Fe-Kα peaks in a fayalite spectrum have similar heights, but the concentration of Fe is about three times that of Si in this mineral. However, for a given spectra line, variation in peak height have an approximately linear correlation with concentration. Thus, if the Fe-Kα peak is twice as high in a mineral when compared with another mineral, the concentration of Fe is also about twice as high.
Quantification of the spectrum requires a procedure called "peak fitting," in which reference peaks are used in variable proportions to recreate the spectrum. The reference peaks are acquired on reference materials using identical operating conditions. Peaks sizes are adjusted to minimize the least-squares deviation of the modeled spectrum from the actual one. This process is sometimes termed "deconvolution."
Peak fitting (deconvolution). Acquired rare-earth element spectrum compared with the modeled spectra of all elements determined with the deconvolution. Note how each element has numerous L peaks that overlap. Image source: http://microanalyst.mikroanalytik.de/info5.phtml.
The spectra used in the fit and the unknowns spectrum should be collected long enough to eliminate the effects of noise; this is especially critical for the quantification of minor elements. Acquisition times of ~200 seconds (at count rates of ??) yield generally excellent spectra. Perhaps the biggest problem with quantitative analysis is the presence of unresolved peak overlaps. Although many potential overlaps are trivial in geological materials, a few make absolute identification and quantification impossible. For example, there is an almost exact overlap between Pb-Mα and S-Kα, making analysis of Pb in sulfides impossible. Other geologically significant overlaps include:
- F-Kα and Fe-Lα
- Na-Kα and Zn-Lα
- Si-Kα and Sr-Lα
- P-Kα and Zr-Lα
- Cr-Kβ and Mn-Kα
- Ti-Kβ and V-Kα
- Fe-Kβ and Co-Kα
Backscattered electron detection
Backscattered electrons are detected using PN junctions positioned at the base of the objective lens at a high take-off angle. Current flows when backscattered electrons strike the semiconductor chips imparting energy. The size of the current (signal) is proportional to the number of electrons hitting the PN junctions. The BSE detectors are sensitive to light and cannot be used when the sample illumination is on.
Backscattered electron detector.
The BSE detector system for the MBX microprobe consists of four semiconductors (PN junctions) located at the bottom of the column at a 40º take-off angle. The JEOL-6480LV SEM has two semicircular plates at the base of the objective lens and one offset plate.
Backscattered electron detectors. (left) Location of BSE detectors in the JEOL-6480LV SEM; lower picture shows BSE unit removed from the objective lens. (right) Bottom of the MBX electron column showing the SEM detector (large brass assembly on the right). The BSE detectors are mounted at the end of the objective lens (hidden behind the chrome anti-contamination plate inside the red circle).
The spatial resolution of BSE images is poor (usually ~1 μm; at best ~0.1 µm) because BSE are produced from the entire upper half of the interaction volume; however, BSE provide valuable information because of their sensitivity to atomic number variations. BSE images are displayed on the MAC 3 computer and acquired using the NIH imaging software.
Example MBX image. Backscattered electron image of exsolution of orthopyroxene lamellae in large iron-rich meteoritic pigeonitic pyroxene.
Example JEOL-6480LV image. Backscattered electron image of a chondrule from an ordinary chondrite meteorite with large zoned olivine crystals and glassy matrix with tiny quench crystals. The strong iron enrichment in the rims of the olivine is easily observed in the backscattered image.
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The BSE signal reflects two parameters: specimen composition (average Z) and specimen topography. The JEOL-6480LV uses paired detectors to combine signals to emphasize these two signal components. In TOPO mode the signals are processed to emphasize topography (TOPO), in COMPO mode to emphasize composition. THe SEM also has a shadow mode, which further enhances topographic effects. The quadripole BSE detectors of the MBX microprobe were designed to allow the instrument to act as a scanning electron microscope; the signal are simply summed when used as a microprobe.
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Secondary electron detection
Secondary electrons emitted from the specimen are detected using a scintillator-photomultiplier, "Everhart-Thornley," detector. Low energy secondary electrons are emitted from the sample in all directions. They are gathered by a charged collector grid (or cage), which can be biased from -50 to +300 V. This draws the secondary electrons towards the scintillator. The scintillator is a thin plastic disk coated with a short-persistence phosphor that is highly efficient at converting the energy contained in the electrons into ultraviolet light photons (4000 Å). The response time of the phosphor is fast and permits high resolution scanning. The outer layer of the scintillator is coated with a thin layer [10-50 nm] of aluminum, positively biased at approximately 10 KeV, which accelerates the electrons to the scintillator surface. The charged collector grid, in addition to collecting secondary electrons from the sample, helps to alleviate some of the negative effects of the scintillator aluminum layer bias, which can actually distort the incident beam.
Secondary Electron Detection. Low-energy secondary electrons (trajectories shown by dashed lines) are collected by applying a suitable bias to the Faraday grid. These electrons are further accelerated in order to give them sufficient energy to scintillate the phosphor (after Potts 1987).
The aluminum layer also acts as a mirror to reflect the photons produced in the phosphor layer down the light pipe, which consists of a Plexiglas or polished quartz pipe, and out through the specimen chamber wall. The photoelectrons strike a photocathode that converts the UV photons back into electrons. The electron multiplier consists of a series of dynodes, each held at a more positive voltage than the previous one. The tube interior is a vacuum. Electrons are accelerated towards the first dynode, strike it, and emit more low energy electrons. These in turn are accelerated towards the second dynode, and so forth. The dynodes are coated with a material with high SE yield so at least two (sometimes as many as ten) secondary electrons are emitted for each photoelectron. The result is a cascade of electrons that eventually strike the anode; a single photon produces ~106 final electrons.
The number of cascade electrons produced by the PMT depends on the voltage applied across the cathode and anode of the PMT, in a manner analogous to how a gas-flow X-ray detector works. One can increase the gain by increasing the voltage to the PMT (this is essentially what is accomplished when adjusting the contrast). The amplified electrical signal is sent to further electrical amplifiers, which increase the electrical signal thus increasing brightness.
Photomultiplier tube. Modified from the image at: http://en.wikipedia.org/wiki/Image:Photomultipliertube.svg.
The topographical aspects of a secondary electron image depend on how many of electrons actually reach the detector. When the incident electron beam intersects the edges of topographically high portions of a sample at lower angles, it puts more energy into the volume of secondary electron production. Thus, high points produce more secondary electrons, generating a larger signal. Faces oriented towards the detector also generate more secondary electrons. Secondary electrons that are prevented from reaching the detector do not contribute to the final image and these areas will appear as shadows or darker in contrast than those regions that have a clear electron path to the detector. It should be noted that those backscattered electrons directed at the scintillator will also contribute to the signal that reaches the scintillator and form part of the the secondary electron image.
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A photomultiplier tube is also used to detect the cathodoluminescence signal, but rather than converting electrons into photoelectrons before amplification, photons are amplified directly. The CL signal contains two types of information: intensity and wavelength; however, most CL detectors respond only to the former, combining photons of all wavelengths to generate an intensity signal.
Information in CL Signal. (left) The actual CL signal produced from a sample includes both color and intensity information. Colors reflect the nature of the activating elements. (right) The same image processed to remove the color information. Although different phases can be distinguished by intensity variations, but the activator information is gone. Original image source:http://serc.carleton.edu/images/research_education/geochemsheets/cathodoluminescence_2.jpg.
Some CL detectors can also access the wavelength information. This is accomplished by using a diffraction grating (monochromator) to select a particular wavelength in a manner directly analogous to that using X-ray analyzing crystals, separating the wavelength of interest from other wavelengths emitted from the sample. A grating is a reflective surface, scored either mechanically or holographically with parallel grooves.
Design of a typical monochromator. It consists of the diffraction grating (dispersing element), slits, and spherical mirrors). Note how the blue light is diffracted into the exit slits, whereas, other wavelengths (such as red) are not. Image source: http://weather.nmsu.edu/Teaching_Material/SOIL698/Student_Reports/Spectroscopy/monochromator_files/image002.gif.
The resulting intensities are different wavelengths of light yield a spectrum that can be deconvolved into individual peaks using a computer.
Example of multiple Gaussian curves fit to CL spectrum. Note how the bumps in the spectrum result from the addition of several peaks with variable intensities and widths. Image source:http://www.gatan.com/images/monocl3_gaussiancurve.giff.
The Gatan CL unit attached to the JEOL SEM in the Geology Department detects only intensity variations. It must be inserted manually into the sample chamber after carefully checking that the stage and sample are not in the way. Once inserted the sample is brought as close as possible to the light pipe and tilted to face it by approximately 20° to direct more photons into the light pipe. In addition, there is a parabolloidal collecting mirror attached to the end of the pipe to capture even more phonons. The resulting phonon signal is amplified using a photomultiplier tube controlled by the CL controller box. Increasing voltage on the tube increases the overall intensity of the resulting image and contrast enhances variations in signal intensity.
Gatan MiniCL Detector. (left) Gatan MiniCL detector showing end of light pipe and parabolloidal collecting mirror. (right) View outside of the sample chamber. The detector electronics are housed in the cylinder with the logo.
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