Volume 107, Number 6, November–December 2002Journal of Research of the National Institute of Standards and Technology[J. Res. Natl. Inst. Stand. Technol. 107, 555–566 (2002)]The Analysis of Particles at Low AcceleratingVoltages (ⱕ 10 kV) With Energy DispersiveX-Ray Spectroscopy (EDS)Volume 107 Number 6 November–December 2002J. A. SmallNational Institute of Standards andTechnology,Gaithersburg, MD [email protected] recent years, there have been a series ofadvancements in electron beam instru-ments and x-ray detectors which may makeit possible to improve significantly thequality of results from the quantitative elec-tron-probe analysis of individual parti-cles. These advances include: (1) field-emission gun electron beam instrumentssuch as scanning electron microscopes(FEG-SEMs) that have high brightnesselectron guns with excellent performance atlow beam energies, E0ⱕ 10 keV and (2)high-resolution energy-dispersive x-rayspectrometers, like the microcalorimeterdetector, that provide high-resolution (< 10eV) parallel x-ray collection. Thesedevices make it possible to separate lowenergy (< 4 keV) x-ray lines includingthe K lines of carbon, nitrogen and oxygenand the L and M lines for elements withatomic numbers in the range of 25 to 83.In light of these advances, this paper in-vestigates the possibility of using accelerat-ing voltages ⱕ 10 kV, as a method toimprove the accuracy of elemental analysisfor micrometer-sized particles.Key words: electron probe analysis; lowvoltage analysis; particle analysis; scanningelectron microscopy; x-ray microanalysis.Accepted: August 27, 2002Available online: http://www.nist.gov/jres1. IntroductionIn classical electron probe analysis schemes employ-ing either a ZAF, bulk-sample␾(␳z), or Bence-Albeeapproach, both sample and standard are assumed to beinfinitely thick with respect to the penetration of theelectron beam and have flat polished surfaces. For sucha semi-infinite plate, the corrections for the interactionof the electron beam with the sample and the subsequentx-ray emission can be calculated from simple geometricrelationships. In the quantitative analysis of particles, thesize and shape of the particle often cannot be controlledor accurately measured which results in two first-orderparticle effects that influence the generation and mea-surement of x rays from these samples. The first particleeffect is the result of the finite size (mass) of the parti-cle. The mass effect is related to the elastic scattering ofthe electrons and is strongly affected by the averageatomic number of the particle. The mass effect is impor-tant when the particle size is smaller than the range ofthe primary electron beam so that a significant fractionof the beam escapes the particle before exciting x rays.The second particle effect is the result of x-ray absorp-tion, which is dependant on the shape of the analyzedparticle. In the analysis of most particles, the x-rayemergence angle and therefore the absorption pathlength cannot be determined as it can for polished spec-imens. The magnitude of this effect is largest whenthere is high absorption as is t ypically the case for “soft”x rays from elements like Al or Si that have energies lessthan about 2 keV [1,2]. (A third particle effect due tosecondary fluorescence is considered at most a secondorder effect and is not covered in this paper.)Over the years, several researchers have developedcorrection procedures to minimize the particle effectsand reduce the uncertainties associated with particle555Volume 107, Number 6, November–December 2002Journal of Research of the National Institute of Standards and Technologyanalysis. These procedures range from simple nor mal-ization of the elemental weight fractions obtained withconventional bulk-sample analysis procedures [3] toelaborate correction procedures based on modeling par-ticle size and shape [4]. Although these correction pro-cedures significantly reduce the effects of particle ge-ometry, elemental concentrations determined from thequantitative analysis of particles by EDS are often char-acterized by relative uncertainties on the order of⫾ 0.10 to ⫾ 0.20. This compares to relative uncertain-ties of ⫾ 0.02 to ⫾ 0.05 for the EDS analysis of bulkpolished samples as shown in Fig. 1 for the analysis ofglass particles and bulk glass samples where RD refersto the relative differences between the experimentallydetermined concentrations and the known concentra-tions (see Sec. 1.3.1) [5].Fig. 1. Relative error distributions for the analysis of glass particlesand bulk glass samples.1.1 Particle Analysis at Lower Electron BeamEnergiesIn conventional electron probe microanalysis the ac-celerating voltage is generally in the range of 15 kV to25 kV, which provides the necessary overvoltage andsufficient current from the thermionic source to exciteefficiently the K and L x-ray lines for elements withatomic numbers as high as Z = 83. In general, this samecriterion has been applied to the analysis of particles andthe development of the methods used to analyze them.The FEG-SEM in conjunction with a high resolutionenergy-dispersive x-ray detector such as the mi-crocalorimeter detector will make it possible to use ac-celerating voltages in the range of 1 kV to 10 kV de-pending on the specific elements to be measured, toexcite lower-energy characteristic x-ray lines with ener-gies less than about 4 keV. Employing the L and M x-raylines (energies from 0.640 keV to 2.42 keV) for theelements with atomic numbers in the range 25 to 83,rather than the K and L x-ray lines of these elements(energies 5.85 keV to 10.83 keV) should reduce signifi-cantly the magnitude of both the particle mass and ab-sorption corrections.The advantage of reducing the electron beam energywhen analyzing particles is that the electron beam inter-action volume within the particle is reduced and there-fore the x-ray generation volume for the particle will besimilar to that from a bulk material, despite the particlegeometry. This is illustrated in Figs. 2 and 3 which areMonte Carlo plots from the Electron Flight Simulatorprogram version 3.1E (Small World Inc.1) based on theMonte Carlo model of Joy [6]. Figure 2 shows the elec-tron trajectories (Fig. 2a) and the Mg K␣ x-ray genera-tion locations (Fig. 2b) for a 20 kV analysis of a 3 ␮mK-411 glass microspheres [7]. At 20 kV, the electronsinteract throughout most of the particle volume with asignificant fraction scattering out of