Inelastic mean free path of swift electrons and stopping power in Ta 2 O 5

Energy Loss Function (ELF) of 2 5 Ta O derived from optical limitand extended to the total part of momentum and their energyexcitation region ELF plays an important function in calculatingenergy loss of electron in materials. The parameter Inelastic MeanFree Path (IMFP) is most important in quantitative surface sensitiveelectron spectroscopies, defined as the average distance that anelectron with a given energy travels between successive inelasticcollisions. The stopping cross section and single differential crosssectionSDCS are also calculated and gives good agreement withprevious work.


Introduction
The excitation spectrum of Ta 2 O 5 has been studied theoretically and calculated by Reflection Electron Energy Loss Spectroscopy (REELS), which only covers a small region is improved and extended to the all of excitation region out of a suitable theoretical analysis that requires the investigation of physically motivated sum rules given in [1] and includes the contribution of intermediate and inner shell excitations.
Energy Loss Function (ELF) derive from several ways are based on experimental measurements, theoretical considerations, but the information provided by the former rarely covers the whole momentum and electronic excitation energy region, but the theoretical calculations many times lack of a direct experimental assessment [1].The dielectric formalism used the resulting of ELF as input to evaluate the energy loss magnitudes to distinguish the passage of swift ions through matter.
These calculations are compared with the stopping cross section of Ta 2 O 5 films for electron beams by means of Rutherford backscattering spectrometry.
ELF can be used as input function in the main formula which defined Stopping Cross Section (SCS) of swift ions through matter.
In solid state physics and electron spectroscopy there is an important material parameter known as (IMFP) Inelastic Mean Free Path of electrons.There are many number of papers published on the subject of IMFP evaluation.Only paper summarizes this problem [2].
In general, three experimental ways are applied to calculate the values of IMFP: 1-The method that can be confined to 1-2 peaks, where energy values are characteristic of the elements called x-ray photoelectron spectroscopy [3].2-In this method the over layer must be perfectly regular in thickness and evident to electrons.Away from experimental difficulties in preparing thin layers, this method rather supplies the value of IMFP affected by multiple electron scattering.This way known as the over layer method [2].3-Elastic peak electron spectroscopy (EPES) method [4,5] a study of the development of EPES was given [6].This method shows a possibility to calculate the value of IMFP for all solid surfaces.
Consider ELF given in the following equation [1]: where and are the intensity, position, width and threshold, respectively of Drude-ELF peaks, ( ) represents the Heaviside step function [7] and the extend from of Eq. ( 1) is [1].
) with a=10 eV, b=6eV, c=1.2 and d=0. 4 The parameters of dielectric for Ta 2 O 5 are shown in Table 1.There are spectraphotometric and transmittance measurements in a wavelength range that only permit obtaining the absorptive and refractive index for energies that less than 6 eV.In the present work, we make use of an approximation which limits the IMFP calculation to electron energies greater than about 200 eV.
The dielectric formalism for non relativistic electron with kinetic energy T gives by Eq.( 1) with its parameters given in Eq.( 2) and Table 1, the stopping power e S is given as follows [1]: where The maximum energy transferred where  is the incident electron velocity.Dielectric formalism gives also the inverse mean free path  in terms of kinetic energy for the interact of electron with solids [1], Finally according to the dielectric function, the macroscopic single differential cross section (SDCS) to ejection of an electron with kinetic energy from the electronic i-shell of the target by the electron of kinetic energy T, i B is the binding energy of i-shell.
Stopping power represents the mean energy loss per unit distance traveled by an energetic electron where IMFP indicates the average distance traveled by an energetic electron between two successive energy-loss events, there are many domains of research and applications such as, surface test with charged particles, micro dosimetry, and radiotherapy based on inelastic mean free paths, Inelastic interactions of energetic electron with condensed matter and stopping power describing the inelastic interactions of energetic electrons with condensed matter [8].
Energy loss function derived from reflection electron energy loss measurements only accounts for contributions of outer-shell electrons to the target ( ω ≤ 80 eV) to optical (i.e., k = 0) excitations.Used the Mermin Energy Loss Function−Generalized Oscillator Strength (MELF-GOS) this method to obtain an ELF that covers the all momentum and energy transfers region.This procedure supported by its effective application to describe the electron excitation spectra of elemental and compound targets. and energy functions.ELF of Ta 2 O 5 has five peaks which agree with previous work presented in [1].

Results and discussion
Fig. 2 shows the stopping power with incident electron energy e T in eV calculated from the results of ELF given in Eqs.(1)(2)(3)(4), and its solution given in Eq. ( 5) for interact of electron with Ta 2 O 5 .ELF applied to obtain the inelastic mean free path of electrons and the stopping power of in Ta 2 O 5 which is consider relevant for description and modification of solid media by means of electron beam techniques like as electron microscopy-ray photoelectron, auger electron spectroscopy and other techniques.The variation of electron stopping power agree very well with previous work [1].The range of incident electron energy between ((10-10000)eV) the maximum stopping power, ( ⁄ ) (i.e Bragg peak) is at energy 700 eV which is agree with [1].Fig. 3 shows the IMFP 1 for the interaction of electrons with

Conclusions
In this work a theoretical study performed to calculate ELF energy loss function of Ta 2 O 5 which magnitude that enters as a main ingredient in numerous areas of materials science, outer shell electron of the target excitations contribution to the ELF was derived from reflection electron energy loss spectroscopy measurements, phase and chemical effects have been taken into account to derive a realistic ELF for Ta 2 O 5 , for all momentum and energy transfer measurements.
The inelastic mean free path and the stopping cross section of swift electron in Ta 2 O 5 was calculated, both has relevance in more studies of this material in the microelectronics industry.According to Fig. 4 (i) The most ejected electron are generated in the low energy region.(ii) The number of ejected electrons increases with incident proton energies decreases.
(iii) The influence of target energy loss function in the ionization of secondary differential cross section is larger for lower proton energies.
Quantitative surface sensitive electron spectroscopies the parameter Inelastic Mean Free Path IMFP is most important that defined as the average distance that an electron with the transportation energy between successive inelastic collisions.The stopping cross section is calculated and gives good agreement with previous work given in [1].
At intermediate and high electron energies we need these two parameter in order to elucidate the discrepancy between ELF models of the target electron excitations.

Fig. 1
the 3D of Im[ ( ) ] as a function of the transferred momentum 