Generation of X-Rays in the SEM specimen The electron beam generates X-ray photons in the beam-specimen interaction volume beneath the specimen surface. Some X-ray photons emerging from the specimen have energies specific to the elements in the specimen; these are the characteristic X-rays that provide the SEM s analytical capabilities (give information about composition). Other photons have no relationship to specimen elements and constitute the continuum background of the spectrum. We can distinguish Production of bremsstralhung X-rays Production of characteristic X-rays The X-rays we analyse in the SEM usually have energies between 0.1 and 20 kev
Continuum X-ray production (bremsstralhung) Beam electrons can undergo deceleration in the Coulombian field of the specimen atoms which corresponds to a loss in electron energy E. E is emitted as electromagnetic radiation, that is as a photon ( E = hυ, υ = frequency of the electromagnetic radiation). Thi radiation is referred to as bremsstalhung or braking radiation Since the interactions are random, the electrons may lose any amount of energy in a single deceleration event. Therefore, the bremsstalhung can take on any energy value from zero up to the original energy of the incident eletron (from 0 to E 0 ), forming a continuous electromagnetic spectrum.
The intensity of the continuum increases with beam current and energy. Moreover, although the bremsstralhung radiation is generated by beam electrons and it doen t present specimen characteristics, its intensity increases with specimen atomic number, because of the increased Colulombian field of the nuclei (more charge). The intensity of the continuum radiation is important in analytical X-ray spectrometry because it forms a background under the characteristic peaks. The dependence of intensity upon Z can cause artifacts in the spectra; for this reason the identification of characteristic peaks should be difficult and ambiguous.
Characteristic X-rays production A beam electron can interact with tightly bound inner shell electrons of a specimen atom, ejecting an electron from a shell. The atom is left as an ion in an excited, energetic state. The incident beam electron leaves the atom having lost at least E K (the binding energy of the electron to the shell K) The ejected orbital electron leaves the atom with a kinetic energy of a few ev to several kev, depending on the interaction The atom is left in an excited state with a missing inner shell electron. Then the atom relaxes to its ground state within approximately 1 ps through a limited set of allowed transitions of outer shell electrons filling the inner-shell vacancy.
The energy of electrons in the shells (atomic energy levels) are sharply defined with values characteristic of a specific element. So the energy difference between electron shells is a specific value for each element. The excess energy can be released from the atom during relaxation in one of 2 ways: In the Auger process, the difference in shell energies can be transmitted to another outer shell electron, ejecting it from the atom with a specific kinetic energy. In the characteristic X-ray process, the difference in energy is expressed as a photon of electromagnetic radiation which has a sharply defined energy.
X-ray involving the filling of a vacant state in the innermost electron shell (K-shell) with an electron transition from outer shells are indicated as K-series X-rays Thus, as an example the energy of a Kα X-ray is equal to the difference in energy between K and L shell. In fact the situation is more complicated because the L and M shells are splitted into subshells, as we will see shortly. The partioning of the de-excitation process between X-ray and Auger branches is described by the fluorescence yield (ω coefficient). As an example, for the production of K radiation the fluorescence yield is: ω K = # K _ photons _ produced # K shell _ ionization
X-ray and Auger are competitive, anyway X-ray emission prevails at high atomic number (Z), against the Auger electron emission. For example: for the carbon K shell ω K 0.005, whereas for the germanium K shell ω K 0.5, increasing to near unity for heaviest elements. In the figure ω L ed ω M are shown, too.
Electronic shells Electrons of an atom occupy electron shells around the atom that, in order of increasing distance from the atomic nucleus, are designed with K, L, M, (related to quantum numbers of atomic physics). The shells beyond K shell are divided into subshells: for example the L shell is composed of three subshells (that are closely spaced in energy), the M shell has five subshell,. Electrons populate these subshells in a definite scheme (see below)
Energy-level diagram In the figure below a representative energy level diagram is reported. The diagram originate from the solution of the Schrödinger equation. The possible transitions are shown.
Electron transitions Characteristic X-ray lines result from transition between subshells; however, atomic theory tells us that only transitions between certain subshelles are allowed (only those indicated with x in the table). For example, for the K series, only those electrons coming from L III and L II subshells can fill the vacancy in the K shell, so only the Kα 1 and Kα 2 X-rays are emitted
Critical ionization energy Because the energy of each shell and subshell is sharply defined, the minimum energy to remove an electron from a specific shell has a sharply defined value as well. This energy is called critical ionization or excitation energy, E c, which is function, for each shell or subshell, of atomic number.
As an example, consider the wide range in E c for the K, L and M shells and subshells of platinum (Pt, Z = 78) A 20-keV beam can ionize the L and M shells, but not the K shell. As Z decreases decrease. (Z(Nb)=41 and Z(Si)=14), the critical ionization energies The critical ionization energy is an important parameter in calculating characteristic X-ray intensity and to have quantitative information about the elemental composition of the specimen. For X-ray microanalysis the SEM typically operate at energies two to three times E c of the element of interest.
Moseley s law The energy of the electron shells vary in a discrete fashion with Z. In particular the difference in energy between shells changes in regular steps when Z changes by one unit. This law was discovered by Moseley and can be expressed in the form of an equation: E = A ( Z C) 2 where E is the energy of the X-ray line, and A and C are constant which differ for each series (for example: C = 1.13 for the K series and approximately 7 for the L series). Thus Moseley s law may be used to find the energy of any element K or L line and forms the basis for qualitative analysis, that is, the identification of elemental constituent.
Families of characteristic lines For elements with Z 11 (sodium), the shell structure is sufficiently complex that when an ionization occurs in the K shell, the transition to fill the vacant stage can occur from more than one outer shell. Following ionization of a K-shell electron, a transition to fill the vacant state can occur from either L or M shell. X-rays resulting from transition of electrons from the M shell are designed Kβ X-rays; for transitions from the L shell the X-rays are designed Kα X-rays. Because the difference of energy between the K and M shells is larger than between K and L shells, the Kβ rays energy is larger than that of the Kα.
Within the SEM beam energy range, each element can emit X-rays, of the K series only (light elements), the K and L series (intermediate elements) and L and M series (heavy elements) Kα Kβ Some series (L series) are not resolved because their energies are very close and the resolution of the instrument is low. When a beam electron has sufficient energy to ionize a particular electron shell in an atom to produce characteristic X-ray lines, all other characteristic X-ray of lower energy for the atom will also be excited, provided there are electrons available for such transition. Typical EDS spectra for increasing Z This occurs because of 1 direct ionizazion 2 propagation of the vacant state as the atom returns to groud state
Weights of lines Although many possible electron transitions can occur giving rise to the families of X-rays, the probability (called weight of lines ) for each type of transition vary considerably. The weights of lines are dependent upon atomic nimber and vary in a complex fashion, but, in general: The greater the energy difference in the electron transition The less probable and less intense is the X-ray line Thus the Kα lines are more intense than the Kβ lines.
Although the values in the table are not exact for a specific element, these wieights are a useful guide in interpreting spectra and assigning peak identification in energy dispersive X-ray spectrometry. Anyway peaks belonging to different elements cannot be compared on the basis of the emission probability (weights of line) because intensity depends on a variety of factors (including the fluorescent yield, absorption and excitation energy)
Cross section for inner shell ionization Numerous cross sections expressing the probability for inner shell ionization can be found in literature; anyway the basic form is that derived by Bethe: Q = nsb UE 20 S 6.51 10 2 c ln ( c U ) S n S is the number of electrons in a shell or subshell (e.g., n S = 2 for K shell) b S e c S are constant for a particular shell E c is the critical ionization energy (kev) U is the overvoltage U = E 0 /E c Cross section for the K-shell ionization for silicon (it has a maximum at U 3, that is E 0 3E c )
X-ray peak-to-backgroud ratio The most important factor in determing the limits of detection in X-ray spectrometric analysis is the presence of the continuum background, whose contribution can be calculated by: I I Peak Background = 1 Z E0 E Ec c n 1 It would seem to be advantageous to make E 0 as large as possible to increase the peak signal with respect to tha background. In fact, beam electrons penetrate deeper into the specimen as the beam energy E 0 increases. Correspondingly, X-rays are produced deeper into the specimen. As a consequence, there are a) the degradation of the spatial resolution of analysis and b) the increasing of X-ray absorption, which reduces the measured X-ray intensity. For a thick, bulk specimen there is an optimum beam energy beyond which further increases in beam energy actually degrade analytical performance. This limit depends on the energy of the characteristic X-ray and the composition of the specimen. An overvoltage of 2-3 is usually optimum for a given element.
Characteristic X-rays can be produced in almost all the interaction volume, in particular within that portion of the electron trajectories for which the energy exceeds E c for a particular X-ray line, whereas bremsstralhung X- rays continue to be produced until the electron energy equals zero. Scheme of the interaction volume and of the regions from which the electron beam induced signals come
Energy and wavelength of the most intense X-rays
X-ray fluorescence For some element pairs (A, B) in the specimen, the primary X-ray of element A created by the electron beam can generate a secondary X-ray of element B by fluorescence (photoelectric effect) : An electron of element B absorbs a primary photon from A and is ejected leaving B atom in an excited state. Then B follows deexcitation, producing either Auger electrons or (secondary) characteristic X-ray (SECONDARY FLUORESCENCE). Secondary radiation can be generated also by bremsstrahlung photons. Because the X-ray photon causing fluorescence must have at least as much energy as the critical excitation energy of the atom in question, the energy of secondary radiation will always be less than energy of the photon that is responsible for ionizing the inner shell.
X-ray detectors Chemical analysis in the SEM is performed by measuring the energy and intensity distribution of the X-ray signal generated by a focused electron beam There are two main kinds of spectrometers: Energy Dispersive Spectrometer (EDS) Wavelength Dispersive Spectrometer (WDS)
Energy Dispersive Spectrometer (EDS) They are the most common, althoug the most recent. The spectrometer is composed of a Silicon crystal (doped with Litium) covered with a Gold evaporated layer. Each photon, penetrating inside the crystal, generates electron-hole pairs. The number of pairs is proportional to the energy photon. The electrons, produced in the detector are collected and converted, through an amplification circuit, in an electric signal with intensity proportional to the number of electrons, and, consequently, to the photon energy. The output, is an energetic spectrum with peaks in correspondence of the photon energy and height (intensity) dependent on the number of detected photons.
The Au layer is very thin (about 20 nm) in order to minimize the X-ray absorption. The detector is protected by a Be window, to prevent possible contaminations. To reduce the noise due to the thermal agitation, the detector is held at about 77 K (liquid nitrogen) or, in the latest, is cooled by Peltier method. The Be window, although is only of some microns, absorbs a significant fraction of the low-energy photons that go through it. So it is impossible to detect X-rays with energy lower than 1 kev and, therefore, to analyse elements having Z lower than that of Na. Nowadays, detectors without window or with very thin polymeric windows are avilable; so it is possible to broaden the analysis down to Boron.
This state solid detector is very efficient (about 100% of X-rays entering the detector produce a pulse is detected). Anyway, the main drawback is the resolution that is very low (about one hundred of ev); therefore the spectra are characterized by broaden peaks and not by narrow lines. This can make ambiguous the identification of the peaks, and of the elements to which they belong, but, above all, precise quantitative analyses are very difficult.
Wavelength Dispersive Spectrometer (WDS) Differently from EDS detectors, WDS detectors can reveal without problems light elements and are characterized by a high energetic resolution. The detector geometry is shown in figure: The X-rays emitted from the sample are reflected by the analyzing crystal (dispersive element) and sent towards the detector. If d is the distance between the crystal planes and θ the angle that X-rays form with the crystal surface, only the photons with λ = 2d sinθ n are sent to the detector. The crystal behaves like a filter which selects a well-defined wavelenght. By varying θ, the wavelenght of the photon impinging the detector changes. The detector doesn t distinguish photons with different energy, but counts the number (proportional counter). Detector, specimen and crystal stay on a circle (Rowland circle).
This spectrometer is bulky, with a very complex mode of operation and very often θ can vary only in a narrow range. So, to cover all the X-ray wavelenght range, more crystals, with different d, are necessary. Some instruments are equipped with different spectrometers or with one spectrometer, but with interchangeable crystals Another drawback is that, being the collecting angle very small, the efficiency is almost low (< 30%). Morever the cost is quite high. Finally, although the detector is very fast, the fact that it reveals one wavelenght at a time makes this technique lengthy and complex. Anyway, as analytical instrument it is interesting because of the: high spectral resolution high peak/background ratio possibility to reveal light elements
In conclusion: The Energy Dispersive Spectrometers are faster and suitable for qualitative analyses, the Wavelenght Dispersive Spectrometer are more lengthy but give more precise information for quantitative analyses.