The height of the Characteristic X-ray peaks in an ED spectrum, or the X-ray intensity, may be given in X-ray counts or count rate (counts per second or cps). It is tempting to assume that the height of the X-ray peak in the spectrum will be proportional to the concentration of the element in the sample. For spectra generated from a TEM this is largely true but for spectra generated from an SEM it is not the case. Factors related to the sample, the system used to generate the X-rays and the detector used to measure the X-ray spectrum can all influence the height of the X-ray peaks.
While the intensities of the peaks in an X-ray energy spectrum are not directly proportional to element concentration, it is true that the concentration of the element in the sample will influence the height of the X-ray peak. Elements present in major amounts (> 10 wt%) will have major peaks in the spectrum while elements present in minor (1-10 wt%) or trace amounts (<1 wt%) will have small or undetectable peaks in the spectrum.
Beam current, probe current or spot size
The beam current (probe current) or spot size reflects the number of electrons in the primary beam of the electron microscope. It is controlled by the condenser lens or the spot size control knob. The number of electrons in the primary electron beam is directly proportional to the number of X-rays generated from the sample and the number of X-ray counts (intensities) recorded in the X-ray spectrum. Increasing the beam current will increase the number of X-rays generated from the sample but will not change the relative heights (intensities) of the Characteristic X-ray peaks in the spectrum.
Accelerating voltage or overvoltage ratio
The accelerating voltage used in the electron microscope controls the energy of the electrons in the primary beam. In the SEM, accelerating voltages are typically 5-30 keV but in TEMs much higher accelerating voltages, 100-400 keV or more, are used. In order to generate Characteristic X-rays the electrons in the primary beam must have enough energy to overcome the ionization energy, also called the critical ionization energy, of the inner-shell electrons in the atoms of the sample. With the high accelerating voltages used in TEMs this is not a problem, but in SEMs care must be taken to use a sufficiently high accelerating voltage to stimulate X-rays from all elements in the sample.
Figure: If the energy of the electrons in the primary beam is less than the critical ionization energy then no X-rays will be generated. If the accelerating voltage is 15 kV, both K and L family X-rays will be generated from Fe. If the accelerating voltage is 5 kV, no K family X-rays will be produced
The overvoltage ratio is the ratio of the energy of the electrons in the primary beam, Eo, to the critical ionization energy, Ec, needed to ionize an inner shell of an atom in the sample. For example, if the accelerating voltage is 15 kV, the energy of the electrons in the primary beam is 15 keV. The critical excitation energy of the Fe Kα X-ray is 7.11 keV, and therefore the overvoltage ratio, U = Eo/Ec, is 2.11. For efficient generation of X-rays, the overvoltage ratio should be at least 2 (the optimum value is ~2.7).
Remember that the production of Characteristic X-rays is a two-stage process: ionization followed by relaxation with the production of an X-ray photon. However, this is not the whole story, and there is a competing process, the generation of Auger electrons, that can also lead to stabilization of the ionized atom. In this case, when an electron from an outer shell fills the vacancy in the ionized inner shell, the x-ray produced is internally absorbed by the atom and an electron is ejected from an outer shell. The ejected electron is known as an Auger electron and it has an energy equal to the difference between the ionization energies of the two shells involved in the initial transition minus the ionization energy of the shell from which the Auger electron is ejected. So the energy of the Auger electron is also related to the electronic configuration of the atom from which it came and is characteristic of the element concerned.
Figure: After inner shell ionization, the atom may relax by emitting a Characteristic X-ray or an Auger electron. The energy of the Auger electron is related to the electronic configuration of the atom that was ionized by the primary electron beam.
(See Auger animation.)
The fluorescence yield is the relative yield or ratio of X-rays to Auger electrons. Elements with low ionization energies, i.e. the lighter elements (Z<11), have low fluorescence yields. That is, when an inner-shell ionization occurs it is more likely that an Auger electron will be produced rather than an X-ray photon. The intensities of X-ray peaks for elements of low atomic number are smaller compared to those with a higher fluorescence yield.
Not all of the X-rays that are generated in the sample by the primary electron beam are emitted from the sample. This is particularly true in the SEM where X-rays are generated within the interaction volume at a depth of many microns. X-rays may be absorbed by other elements in the sample due to the photo-electric effect (see Photo-electric animation). If the energy of an X-ray photon is equal to the critical ionization energy of an electron in another element in the sample then there is a high probability that the X-ray will be absorbed and a photo-electron produced.
While the absorption of X-rays depends on the other elements present in the sample, it is also true that low-energy X-rays are more likely to be absorbed than those with higher energies, and elements with higher atomic numbers tend to be strong absorbers of lower energy X-rays.
The length of the path that the X-ray travels through the sample will also influence absorption. The longer the path length, the more likely it is that the X-ray will be absorbed. Again, low-energy X-rays are more likely to be affected by longer path lengths than higher energy X-rays.