The prospects for an improved absorption correction in electron probe microanalysis

Abstract

It is shown that the absorption correction f(χ) is dependent on two parameters: the mean depth which essentially determines the correction for f(χ)>0·8 and which accounts for variations with incident beam energy, and a shape function that is a function of overvoltage ratio and the mean atomic number of the specimen. The commonly used modified Philibert correction represents the mean depth reasonably well but has a very inadequate shape function. The general effect of the shape function can be demonstrated conveniently by the behaviour of the ratio f(χ)/f sq(χ) where f sq(χ) is the absorption correction predicted by a square model for the depth distribution of ionization. For many practical purposes the overvoltage variation of the shape function can be neglected, but there is always a substantial atomic number dependence in the range 0·05<f(χ)<0·5. Although there are not sufficient consistent experimental data available on which to base an accurate absorption correction covering the full range of f(χ), possible forms for such a correction procedure are discussed. A simple expression for use in the case of high absorption, f(χ)<0·2, is proposed.

Quantitative electron probe microanalysis of nitrogen

“…The problems began, however, as soon as we touched on nitrides like ZrN, HfN and TaN. In the case of ZrN we actually measured a variatien of k-ratio for Ni trogen wi th voltage that was completely opposite to the predictions of our matrix correction program: instead of showing a decrease between 4 and 15 kV, followed by a slight increase again between 20 and 30 kV we measured (with air jet) an increase between 4 and 15 kV, followed by a decrease with increasing voltage. Throughout the complete voltage range the k-ratios were dramatically too low, but especially at the lowest voltages: at 4 kV by a factor of 5 too low!…”

“…In these cases combined N+O contertts were repoi::"ted which were Contradietory to the (sometimes scàrce) information on phase diagrams. The maximum limit of the homogeneity region was 22 exceeded by 5 (in the case of TiN) up to as much as 20 % relative (HfN). This seems to point to severe systematic errors in the chemica!…”

“…Their first matrix correction program, which was also based on a typical "ZAF" approach in the sense that the Z and A factors were calculated separately, contained an atomie number correction of their own 19 and an absorption correction based on 20 .…”

“…Therefore, we were forced to perferm the vast majority of the intensity measurements in a completely integral fashion, which took 1 night per nitride for each accelerating voltage. The measurements themsel ves were carried out at 4,6,8,10,12,15,20,25 and 30 kV. So, almest 2 weeks per nitride specimen were necessary to complete one series on only one compound.…”

Optimal algorithm to improve the calculation accuracy of energy deposition for betavoltaic MEMS batteries design

“…Bishop raised that subdividing for 25 times can reach sufficient accuracy for gold (heavy atoms) [9 ] to calculate energy deposition; G. Love divided total path length into 100 segments to calculate energy deposition [ 9 ] ; Mao et al [ 1 5 ] The stopping power of electrons obtained according to Bethe formula can be found in authoritative database [1 4 ] . The uncertainty of the data is 1-2% for electrons above 100keV, 2-3% for low-Z materials, 5-10% for high-Z materials [1 4 ] .. …”