X-Ray analysis and EDX service   

   General information to the microanalysis
EPMA     Info1    Info2     Info3     Info4     Info5     Info6     Info7     Info8      Micro-XRF    Info1                           

Basics of the x-ray excitation by electrons

Bremsstrahlung (Background)   
Detection limits   

In the energy region of the primary electrons from 5 to 50 keV the following interaction processes between electrons and target (specimen) are important, from the view of Electron Probe Microanalysis (EPMA):


A         elastic interaction effects of the electrons
                -> backscattering electrons
                -> expansion of the focused electron beam

B         stopping radiation of charged particles in the electrical Coloumb field of nucleous
                -> Bremsstrahlung (x-rays with continuous spectrum)

C         ionization by pulling out electrons from the internal levels of the electron shell of atoms
                - > characteristic x-rays (discrete characteristic energies)

The three interaciton effect processes lead to the model of the "ionization pear" in the EPMA:

ionization pear in the EPMA       Pattern of the "ionization pear"

The characteristic radiation results from suggestions in the atomic shell. An electron is pulling out from an internal level. A so-called vacancy develops. Since the excited atomic shell aims at the equilibrium of the smallest internal energy due to generally accepted principles, this vacancy fills up itself by an electron of a higher energy level. According to the potential model exists a difference between both energy levels of the electron shell. This energy difference is lost, but in form of a radiation quantum is delivered.

generation of characteristic radiation (X-Rays)

There exists a competitive process, the delivery of the energy difference via emitting an Auger electron.

The energy of a x-ray line (energetic position of the line in the spectrum) is the indicator for it, which element it concerns (Mosely's law). The ' strength ' of the line depends on the concentration of the element within the sample.


The middle penetration depth of the electrons Zm and with this the lateral resolution of the EPMA can be calculated from the middle loss of energy of the electrons within the sample:

Zm = 0.033 ( Eo2 - Ec2) / dens                         (Eo und Ec in keV; dens in g/cm3)

Eo ...primary electron energy
Ec ...energy of the excited electron shell
dens ... density of the sample


Detection of Fe (iron, Ec = 7,12 keV) in a sample with dens = 8 g/cm3:

Eo        15 keV        20 keV        30 keV
Zm        0.7 um        1.5 um         3.5 um

For real samples and excitation conditions values in the order of magnitude of microns result.

ColorSEM image ColorSEM image

Element picture (map) of a chip structure at the border of resolution of x-rays with 15 kV high voltage -
right picture with electron image overlays (red = Si / yellow = Al)

The optimum for the ionization of the regarded shell (thus the characteristic x-ray) is attached:

Uo = Eo / Ec = 3

Thereby an optimal excitation of all lines of the examined sample is never given, there a spectrum of all x-ray quanta with only unique primary electron energy (high voltage of Scanning Electron Microscope - SEM) is measured. The ionization cross-section has its maximum with a "overvoltage" Uo (quotient from primary electron energy Eo and critical excitation energy of the regarded shell Ec) with approximately 3 and falls at larger values however again only slowly. At smaller values, thus if the energy of the electron comes into the region of the critical energy, the ionisation cross-section drops rapidly.

excitation of X-Rays       Plot of the ionization cross-section over U

That is a substantial difference to the ionization by x-ray quanta (- > x-ray fluorescence), since there exists the suggestion by x-ray 'resonance' with the electron shell and because of that a maximum of the ionization cross-section exactly. A too large overvoltage is less critical thereby than a too small.

With the primary electron energy and the choice, which line series of an element is to be analyzed, also a different surface sensitivity and a lateral resolution of the EDX analysis are selected:

interaction with specimen, depth distribution of electron based X-ray excitation
green: Pb-L / red: Pb-M

The analyst always stands before the problem of the optimization of the analysis conditions. A larger accelerating voltage improves the excitation, increased however the penetration depth of the electrons and with this the absorption of the x-ray quanta produced in the sample, too. The excitation should be so large that for all elements in the sample a overvoltage Uo of at least 2 exists.

Due to the absorption effects, which can make a quantitative evaluation more difficult of the spectra substantially, the choice of primary electron energy should be anough but not higher than necessary. Naturally also lateral resolution and resolution in depth worsen with a higher primary electron energy.


In the sample in a depth of typically a micrometer produced x-ray quanta have to penetrate the specimen layers above to fly finally to the x-ray detector (energy dispersive x-ray detector, EDX). In this way it is weakened within the sample (self absorption) and within the x-ray entrance windows of the detector (absorption of x-rays -> efficiency of the x-ray detector).

absorption of X-Rays     

The absorption of x-ray is described with the exponential mass attenuation (or mass absorption) law and depends on the energy of the x-ray quanta and the kind and thickness of the material which can be penetrated:

mass absorption coefficients Mass absorption coefficient for Zr

The mass absorption coefficient is a complicated function of the atomic number of the absorption layer and the energy of the x-ray. Every time the energy of the radiation can excite a further shell of the atoms of the attenuation layer, a jump of the function (absorption edges) takes place.

Further information for self-absorption in the sample: Info4 

Bremsstrahlung, the background in the EPMA:

Every time charged particles are accelerated or braked, they produce electromagnetic radiation. This principle is used in an antenna, in which electrons are back and forth moved. With the radio or the TV home receiver this electromagnetic radiation will receive.

Since the electrons in the scanning electron microscope have however a very high speed (a 10 keV electron has a speed of approx. 20% of the speed of light!), with the deflection and/or braking of the electrons in the electrical field of the atomic nuclei in the examined sample an electromagnetic radiation in the x-ray energy region is emitted.

generation of Bremsstrahlung

Since all possible deflections and decelerations can take place in the electrical fields of the atomic nuclei, a continuous energetic spectrum of x-ray quanta (the Bremsstrahlung) develops . The maximally possible energy develops if an electron, which was not affected yet and so that still have the entire primary electron energy, completely is braked. The continuous Bremsstrahlung spectrum ends exactly with the primary electron energy Eo.

The measured spectra in energy dispersive EPMA consists thus of two basic components, the "peaks" of the characteristic radiation and the Bremsstrahlung background:

EDX spectrum       Overlay: char. Radiation, Bremsstrahlung and absorption

Detection limits (EPMA):

Since for the detection limit of an element then the measuring signal/background (signal / noise) relationship is substantial, the Bremsstrahlung is responsible for the fact that the relative detection limit cmin with approximately 0,1 % mass fraction of an element. In the comparison to trace element analytics it is very modestly.

In connection with the local resolution of the electron microscope it results however that the analyzed substance volume is in the order of magnitude from typically a cube micron. Thus the absolutely detectable substance quantities of mmin of the energy dispersive EPMA are in the order of magnitude of 0.1 pg (see diagram) and almost unbeatable by other methods of instrumental analytics:

detection limits of EPMA / X-ray microanalysis
Detection limits of the energy dispersive EPMA with an EDX spectrometer
(full image )

The detection limits depend slightly on the middle atomic number of the examined sample volume and the excitation conditions (selected high voltage SEM). The delimitation of the detection limits on approx. 0,1% arises as a result of the always parallel produced bremsstrahlung background and is method dependent.

Only if the resolution of energy (semiconductor detectors with typically 140 eV) can be improved around an order of magnitude, also the detection limits are reduced to approx. 0,01% (WDX spectrometer, micro calorimeter)

  X-Ray analysis and EDX service   


  Menü        Info2