Determination of Inelastic Mean Free Path by Electron Energy-Loss Spectroscopy in TEM: A Model Study using Si and Ge
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0982-KK07-13
Determination of Inelastic Mean Free Path by Electron Energy-Loss Spectroscopy in TEM: A Model Study using Si and Ge Chongmin Wang1 and Bret D. Cannon2 1 Pacific Northwest National Laboratory, 3335 Q Ave, MSIN:K8-93, Richland, WA, 99352 2 Pacific Northwest National Laboratory, Richland, WA, 99352
ABSTRACT Although the inelastic mean free path for Si and Ge have been measured previously, reported experimental values for silicon range from 121 nm to 160 nm for 200 keV and a large collection angle. A key factor responsible for this uncertainty is the lack of an accurate measurement of the specimen thickness at the point at which the EELS spectra are obtained. In this research, we have evaluated a systematic methodology for determination of the specimen thickness. In the thickness measurement based on converging beam electron diffraction, CBED, instead of the classic “trial and error” straight-line-fitting method to either the maxima or minima, a non-linear least square fitting of the theoretical diffraction profile to the energy filtered two-beam CBED is used. The low-loss EELS spectrum is also obtained from the same location. The inelastic mean free path was determined using the measured thickness and EELS data. INTRODUCTION A key process in the energy cascade that underlies the operation of radiation detectors is excitation of plasmons, where plasmons are a collective motion of the valence electrons in a solid, which decay into electron-hole pairs and heat. The plasmon excitation cross section can be determined by measuring the electron mean free path corresponding to the plasmon scattering, Λp. The probability Pn(t) for transmission of an electron with energy loss ∆E = n∆Ep through a thin foil specimen with thickness t can be described by the joint probability that the electron is transmitted, detected, and produces n plasmon excitations. The first two factors are independent of n while the later probability distribution is given by the Poisson distribution, Pn(t) = (t/Λp)n exp(-t/Λp)/n!, where n = 0 corresponds to elastic scattering and n = 1, 2, … , corresponds to the 1st , 2nd , etc. plasmon losses. The area of a specific plasmon loss peak normalized by the overall low loss peak area gives Pn(t) and hence the ratio t/Λp. Measurement of this ratio for various specimen thickness will allow the determination of plasmon loss mean free path and mean cross section for plasmon excitation. Critical for this determination of Λp is accurate measurement of the specimen thicknesses at the points at which the energy loss spectra were acquired. The inelastic mean free path (IMFP) of a fast electron in a material is the characteristic distance between the inelastic collisions by which a fast electron loses energy. IMFP values are needed for thickness measurements by the log-ratio technique in a transmission electron microscope (TEM).1,2 For primary electron energies below about 2 keV, IMFP information is needed for quantitative interpretation of surface analysis measurements by techniques such as Auger and x-ray
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