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[06_プラハ_2006-1_cor.pdf](https://mdr.nims.go.jp/filesets/aea4bbc1-1c21-4e6d-943e-a629b15ae021/download)

## Creator

[Tanuma，S](https://orcid.org/0000-0003-2628-9941), Okamoto, N, Azuma, Y, Kimura, T, Goto, K

## Rights

[Creative Commons BY-NC Attribution-NonCommercial 4.0 International](https://creativecommons.org/licenses/by-nc/4.0/)

## Other metadata

[Determination of Inelastic Mean Free Paths  in Elemental Solids in the 200 to 5000 eV Energy Range by Absolute Elastic Peak Electron Spectroscopy](https://mdr.nims.go.jp/datasets/4a1e664c-dfbb-4631-9e02-2eb365d34d7f)

## Fulltext

06_プラハ_2006-1_cor  -  互換モード1Determination of Inelastic Mean Free Paths  in Elemental Solids in the 200 to 5000 eV Energy Range by Absolute Elastic Peak Electron SpectroscopyS. Tanuma, N. Okamoto, Y. Azuma, T. Kimura and K. Goto• Introduction• Measurement of EPI - Comparison of measured and calculated EPI• IMFP determination- Comparison of measured and calculated IMFPs( TPP-2M and from ELFs)• Analysis of IMFPs determined from EPIs by Fano Plots- comparison of EPES with Ni-std method• Summary2- Knowledge of the values of inelastic mean free paths (IMFPs) for low-energy electrons in solids is important for quantitative surface analysis by AES, XPS, and EELS.: We have determined IMFPs for Ag, Au, Cr, Cu, Fe, Ga, C (Graphite) , Mo,Ni, Pt, Si, Ta, W and Zn in the 50 - 5000 eV energy range from Absolute backscattered elastic-peak intensities and compared with the corresponding calculated IMFPs ( optical and TPP-2M ) in order to check their reliability.1. Introduction3Measurements of EPIsCMA DE/E = 0.25% Accuracy± 0.01% (primary beam energy)± 0.5% (Auger spectra)Measurement of  Elastic Peak IntensityEnergy range : 1 - 5,000 eV   ( 50 - 5,000 eV )Instrument: Absolute Auger Spectrometer-detection angle (42.3± 6°)Primary beam: 1 µADetector: Faraday cup 4Measured elastic peak intensity as a function of electron energy -15Measured elastic peak intensity as a function of electron energy -2!!! =  $" × $# × &$' ()*)+,%!/.!exp(-+3, )S   6Calculation of EPIs with MC methodSurface excitation factorTotal path length distributionIMFPGt : transmission efficiency of CMAI0 : incident electron currentN0: number of input elctrons:Elastic scattering cross sectionDHF potential: Pseudo random number generatorMersenne TwisterGw : correction for window in CMA7Measurement of transmission efficiency Gt8Simulation of Gt9Gt : Measured transmission efficiency of CMA10Comparison of measured and calculated EPIs for Au in the 50 - 5000 eVMeasured intensity- solid circles: EP current /incidentCalculated intensities from MC method (without fs correction)- solid line ( optical IMFPs)- dotted line ( TPP-2M)200eV >      : good agreement200 eV<      : large diffirence11Comparison of measured and calculated EPIs of Ag, Si and Cu in the 50 - 5000 eV12Determination of IMFPs from Absolute EPIs- solve above eq. for parameter lx (IMFP): Measured EPI  : Calculated EPI with MC  (parameter lx (IMFP)): IMFP determination13Calculation of IMFPs from optical data(Optical IMFPs)• Flow of calculationExperimental optical data: optical constants: atomic  scattering    factorIm[-1/e(DE)](ELF)- check with Sum RulesIMFPs- function of E- energy dependence : energy loss function- q dependence :  Lindhard model dielectric  function (RPA)single pole approximation ( E>300 eV)Penn algorithm14TPP-2M(A)M: atomic weightr: densityNv: number of valence electronsEg: band-gap energy15IMFPs determined from Absolute EPI16IMFPs determined from absolute EPI17IMFPs determined from absolute EPI18IMFPs determined from absolute EPI19Analysis of IMFPs with Fano Plot- We have analyzed experimentally determined IMFPs using Fano Plots which were constructed by plotting values of E/l versus ln E. solid symbols :experimentally determined IMFPsred solid line: fit to the energy/IMFP values with the Bethe equationdotted line: calculated from Bethe equation (experimental IMFP value: EPES-Ni-std ) Simple Bethe equation20Dotted line: IMFPs from EPIs using Ni-std: Determination of IMFPs  using Ni-std- solve for parameter lx (IMFP)- Calculation of EPI ratio to Ni-reference- assume that  surface excitation  effect is negligible for Ni-reference method.;  remove GtSimple Bethe equation: Parameters were determined from curve fits- dotted line : calculated from  these parameters21Analysis of IMFPs with Fano Plot(1)22Analysis of IMFPs with Fano Plot (2)23Analysis of IMFPs with Fano Plot(3)24Analysis of IMFPs with Fano Plot (4)25Results of Bethe eq. fits to measured IMFPs in the 100 - 5,000 eV range•Average RMS deviationBethe fit:- present work (from absolute EPI): 8.7 %-EPI- Ni-ref method : 9.1%W-comparison of Bethe fit results: absolute EPI (present work)and  Ni-ref EPI  : 5.0 %26Comparison of resulting IMFPs from the Bethe fit with optical IMFPs , TPP-2M, EPES-Ni-std (Si, W)27rms(%) difference of IMFPs determined present work from  IMFPs of the Penn algorithm (optical IMFPs) and the TPP-2M Average RMS(%): 100 - 5000 eV  : 9.1 %(optical), 10.8 %(TPP-2M) average RMS(%): 100 - 5000 eV : 11.0%(optical), 10.7%(TPP-2M)28Summary- We have carried out the experimental determinations of IMFPs for 14 elemental solids (Ag, Au,Cr, Cu, Fe, Ga, graphite,(glassy carbon,) Mo, Pt, Si, Ta, W and Zn) in the 50-5000 eV energy range from absolute backscattered elastic-peak intensities taken by a novel CMA with Monte Carlo (MC) calculations and also compared with IMFPs of the elemental solids with the Penn algorithm. -The IMFPs determined from EPES could be fit by asimple Bethe formula in the 100 – 5000 eV energy rangeusing Fano plot (average RMS deviation : 9%)29-The EPES-IMFPs of Ag, Au,Cu, Cr, glassy carbon,Ni, Pt,Si, Ta and W are in excellent agreement (RMS deviationsis less than 10%; average:7% ) with those calculatedfrom the Penn algorithm in the 100-5000 eV energyrange. The average RMS deviation for 15 elementalsolids is about 10%. However, the RMS deviations forMo and graphite were large;16 and 28 % , respectively.- Differences between the present EPES-IMFPs andIMFPs from EPES-Ni-ref method are also small (averageRMS differences was 5.0 %) in the 100-5000 eV energyrange.-We may conclude that the accuracy of IMFP values for elemental solids calculated from measured ELFs are about 10% in the 100 - 5000 eV energy range.- Surface-electronic excitation ?