X-RAY SPECTROMETRY, VOL. 21, 229-238 (1992) Accurate Description of Surface Ionization in Electron Probe Microanalysis: an Improved Formulation Claude Merlet Universitk de Montpellier zyxwvutsrq 11, Sciences et Techniques du Languedoc, Centre Geologique et GCophysique UPR 0361 CNRS, Case 060, Place E. Bataillon, 34095 Montpellier Cedex 5, France A new analytical expression of the surface ionization zyxwvu Q(0) is derived in terms of atomic number and overvoltage. This expression is obtained by means of an analytical description of the energy distribution of backscattered electrons. The Q(0) data for Pt, W, Sb, InSb, Ni, Co and Mg have zyxwv been measured using the tracer technique. The Q(0) values obtained by using the new expression compare more favourably with experimental results, Monte Carlo simulation and backscattering data from the literature than those obtained with the previous analytical models. INTRODUCTION zyxwvutsrq ~__ ~ zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Correction factors for quantitative electron probe microanalysis require an accurate knowledge of x-ray distribution with depth in the target. This distribution is usually represented by the zyxwvutsr +(pz) curve, where 4 rep- resents the ionization and pz the mass depth in the sample. Then the x-ray intensity generated in the speci- men is given by zyxwvuts pw d(P4 Some equations have been used to approximate the 4(pz) curves. The simplest assumes constant intensity down to some depth chosen to represent the total inten- sity generated in the specimen. Philibert' used an expo- nential expression, Packwood and Brown2 a Gaussian centring at the surface and modifying its shape close to the 4(pz) axis, Tanuma and Nagashima3 a Gaussian profile with its centre displaced along the &pz) axis, Pouchou and Pichoir4 a double parabolic shape and Sewell zyxwvutsrqp et aL5 a simple quadrilateral shape. An important parameter of these models is zyxwvuts 4(0), which represents the surface value of &pz). Some empirical or semi-empirical models of 4(0) have been established by Reuter,6 Love et ~l.,~ Packwood and Brown,' Ichimura et ~l.,~ Pouchou and Pichoir: Tirira Saa and Riveros,' Rehbach and Karduck" and Cazaux. The aim of this study was to establish a new analyti- cal expression for 4(0) and to compare the values obtained by this model with experimental data deter- mined by Castaing and Descamps," Castaing and Henoc,13 Shimizu et al.,I4 Brown," Vignes and Dez,I6 Packwood and Brown' and Sewell et di7 and with new measurements obtained for this study. 4(0) can be considered to be composed of two terms: ionization of the incident electron through the surface layer and the contribution to the ionization by the 0049-8246/92/050229- 10 $10.00 GI 1992 by John Wiley & Sons, Ltd. backscattered electrons that leave the specimen. Thus, in order to develop an exact analytical expression for 4(0), several experimental data [direct experimental, z 4(0) measurements, experimental backscattering and Monte Carlo data] have been used. This combined approach is necessary because it is impossible to produce by the tracer technique a sufficient amount of data to cover the wide range of electron energies and materials. Moreover a few publications'8-'2 provide an energetic distribution of backscattered electrons and the accuracy of the Monte Carlo method may be doubtful at low electron energies and for high atomic number elements. EXPERIMENTAL As the published data for 4(0) are generally given within error ranges larger than lo%, the tracer methodi2 was first used to increase the reference experimental data- base. The principle of this method is to compare the x-ray intensities of a film simultaneously deposited on a 600 8, Bioden film (self-supporting film) or a 300 8, carbon film (the backscattering coefficient of the 300 8, carbon film is 0.006 at 20 keV, and therefore has a neg- ligible effect on the result) and on a thick substrate with similar electron scattering characteristics. The measurements were made on platinum, tungsten, antimony, InSb, nickel, cobalt and magnesium, with an electron microprobe CAMEBAX DATANIM. The fol- lowing tracers were used for the b(0) determinations : gold (La) for the 4(0) of platinum at 15, 20, 25, 30, 35 and 40 keV; gold (Ma) for the 4(0) of tungsten at 15, 20, 25, 30 and 35 keV; tellurium (La) for the &O) of anti- mony and InSb at 5, 7.6, 10, 12.5, 15, 20, 25, 30, 35, 40 and 45 keV; copper (Ka and La) for the $(O) of nickel and cobalt at 5, 10, 15, 20, 25, 30, 35, 40 and 45 keV; and aluminium (Ka) for the 4(0) of magnesium at 10, 15,20, 25, 30 and 35 keV. At the maximum these tracer Received 13 May 1991 Accepted (revised) 10 February 1992