Mean Escape Depth Research Articles

Secondary electron emission and photoelectric emission with account of excited electrons’ moving backward emission surface

From existing old photoelectric emission PEE and secondary electron emission SEE models and the process that 50 % excited electrons are treated as as those moving backward emission surface, this study develops new SEE model for negative electron affinity semiconductor NEAS with large lSEE and new PEE model, respectively; lSEE denotes mean escape depth of secondary electrons. From our investigations of PEE from metals and NEAS with large lPEE and SEE from NEAS with large lSEE, it can be concluded that the new SEE model for NEAS with large lSEE and new PEE model developed here are correct; lPEE denotes mean escape depth of photo-emitted electrons. The theories of SEE from insulators with 120 Å≤ lSEE ≤ 1.0 × 104 Å are also developed and discussed.

Expressions of electron escape probability and photo-emission from metals

The expressions of electron escape probability of several kinds of metal emitters are determined and proved correct here, respectively. From the determined expression of electron escape probability, existing formulas, characteristics of photo-emission PE and experimental data, the formulas for several parameters of PE from metals near threshold frequency γ0 and farther away γ0 were deduced and proved correct, respectively. The Cγ calculated here were analyzed, it concludes that the calculated Cγ are correct, Cγ is the probability that one electron of the conduction band of a given metal absorbs one given frequency photon. Based on the universal formula for λ of photo-emitted electrons undergoing PE from metals near γ0 and corresponding parameters, several special formulas for λ of photo-emitted electrons undergoing PE from Au and Ni near γ0 were obtained, respectively; λ is the mean escape depth of photo-emitted electrons from metals.

Inelastic mean-free path and mean escape depth of 10-140 eV electrons in SiO2 nanoparticles determined by Si 2p photoelectron yields.

We report on photoelectron spectra of SiO2 nanoparticles (d = 157 ± 6 nm) above the Si 2p threshold in the photon energy range 118-248 eV with electron kinetic energy 10-140 eV and analyze the photoelectron yield as a function of photon energy. Comparison of the experimental results with Monte-Carlo simulations on electron transport allows us to quantify the inelastic mean-free path and mean escape depth of photoelectrons in the nanoparticle samples. The influence of the nanoparticle geometry and electron elastic scattering on photoelectron yields is highlighted. The results show that the previously proposed direct proportionality of the photoelectron signal to the inelastic mean-free path or the mean escape depth does not hold for photoelectron kinetic energies below 30 eV due to the strong influence of electron elastic scattering. The present results deviate for photoelectron kinetic energies below 30 eV from the previously proposed direct proportionality of the photoelectron signal to the inelastic mean-free path or the mean escape depth, which is the result of a strong influence of electron elastic scattering. The presented inelastic mean-free paths and mean escape depths appear to be useful for the quantitative interpretation of photoemission experiments on nanoparticles and for modeling of the experimental results.

Secondary electron emission and photoemission from a negative electron affinity semiconductor with large mean escape depth of excited electrons

The formulae for parameters of a negative electron affinity semiconductor (NEAS) with large mean escape depth of secondary electrons λ (NEASLD) are deduced. The methods for obtaining parameters such as λ, B, E pom and the maximum δ and δ at 100.0 keV ≥ E po ≥ 1.0 keV of a NEASLD with the deduced formulae are presented (B is the probability that an internal secondary electron escapes into the vacuum upon reaching the emission surface of the emitter, δ is the secondary electron yield, E po is the incident energy of primary electrons and E pom is the E po corresponding to the maximum δ). The parameters obtained here are analyzed, and it can be concluded that several parameters of NEASLDs obtained by the methods presented here agree with those obtained by other authors. The relation between the secondary electron emission and photoemission from a NEAS with large mean escape depth of excited electrons is investigated, and it is concluded that the presented method of obtaining λ is more accurate than that of obtaining the corresponding parameter for a NEAS with large λ ph (λ ph being the mean escape depth of photoelectrons), and that the presented method of calculating B at E po > 10.0 keV is more widely applicable for obtaining the corresponding parameters for a NEAS with large λ ph.

Secondary Electron Emission and Photoemission from Negative Electron Affinity Semiconductor with Large Mean Escape Depth of Excited Electrons

Secondary Electron Emission and Photoemission from Negative Electron Affinity Semiconductor with Large Mean Escape Depth of Excited Electrons

Analytical formalism for calculations of parameters needed for quantitative analysis by X-ray photoelectron spectroscopy

Analytical formalism for calculations of parameters needed for quantitative analysis by X-ray photoelectron spectroscopy

Electron-insulator interaction and secondary electron yield at any Kelvin temperature

The universal formulae for λ(χreal, Eg, T) and λ(χreal, Eg, T)p of insulator having less impurities are experimentally proved, where λ(χreal, Eg, T) is the mean escape depth at Kelvin temperature T of secondary electrons emitted from insulators with band gap Eg and efficient electron affinity χreal, λ(χreal, Eg, T)p is the λ(χreal, Eg, T) due to electron-lattice interaction. Based on the mechanism of electron-insulator interaction, experimental data, existing formulae, ESTAR program and formulae for λ(χreal, Eg, T) and λ(χreal, Eg, T)p of insulator having less impurities, the methods of obtaining λ(χreal, Eg, T)e-e, λ(χreal, Eg, T)e-defect and λ(χreal, Eg, T)i are presented, where λ(χreal, Eg, T)e-e is the λ(χreal, Eg, T) due to electron–electron interaction, λ(χreal, Eg, T)e-defect is the λ(χreal, Eg, T) due to electron–defect interaction, λ(χreal, Eg, T)i is the λ(χreal, Eg, T) due to electron-impurity interaction. The λ(χreal, Eg, T)p, λ(χreal, Eg, T)e-e, λ(χreal, Eg, T)e-defect and λ(χreal, Eg, T)i can provide corresponding information regarding electron-insulator interaction. Thus, it can be concluded that the method of investigating electron-insulator interaction by secondary electron emission SEE is successfully presented in this work. According to experimental data, formula for λ(χreal, Eg, T), ESTAR program, calculated parameters of primary range and existing formulae for SEE, the method of calculating the ẟ at different T and in the range of 1.0 keV ≤ Epo ≤ 100.0 keV from insulator having less impurities is successfully presented, where ẟ is secondary electron yield, Epo is incident energy of primary electron.

Secondary Electron Emission and Photoemission from Negative Electron Affinity Semiconductor With Large Mean Escape Depth of Excited Electrons

Secondary Electron Emission and Photoemission from Negative Electron Affinity Semiconductor With Large Mean Escape Depth of Excited Electrons

Secondary Electron Emission and Photoemission from Negative Electronaffinity Semiconductor with Large Mean Escape Depth of Excited Electrons

Secondary Electron Emission and Photoemission from Negative Electronaffinity Semiconductor with Large Mean Escape Depth of Excited Electrons

Secondary electron emission from insulators and negative electron affinity semiconductors

Based on expression of primary range R and the R at Epo ≥ 10.0 keV and L at Epo ≥ 1.0 keV calculated by ESTAR program [1], the method of obtaining formula for R at Epo ≥ 1.0 keV is presented; where Epo is incident energy of primary electron, and L is the energy loss of primary electron per unit path length at the incident surface of the materials. Based on the obtained formula for R, experimental δ, relationships among parameters of δ and the processes and characteristics of secondary electron emission SEE, the universal formula for δ is deduced and the method of calculating δ at Epo ≥ 1.0 keV of insulators and negative electron affinity NEA semiconductors is presented and experimentally proved, where δ is secondary electron yield. The methods of calculating mean escape depth of secondary electrons 1/α and B of insulators and NEA semiconductors are presented, respectively; where B is the probability that an internal secondary electron escapes into vacuum upon reaching the surface of emitter. From the relationships among parameters of SEE and the comparison between the values of 1/α and B obtained in this study and those obtained in former work, it concludes that the methods of calculating 1/α and B are correct.

Electron-lattice and electron–electron interactions and Debye temperature studied by temperature dependence of secondary electron emission from insulators

The formulas for temperature dependence of λ(χreal, Eg, T), λ(χreal, Eg, T)p, ẟ and σ of insulators with less impurities were deduced and proved to be true; λ(χreal, Eg, T) is the mean escape depth of secondary electrons emitted from insulators with efficient electron affinity χreal and band gap Eg at Kelvin temperature T, λ(χreal, Eg, T)p is the λ(χreal, Eg, T) due to electron-lattice scatterring in insulators, ẟ is secondary electron yield, σ is total ẟ. Analyses of data and the deduced formulas indicate that the temperature dependence of ẟ and σ of insulators with less impurities increase with the increasing [λ(χreal, Eg, T)/λ(χreal, Eg, T)p], and that λ(χreal, Eg, T), λ(χreal, Eg, T)p, ẟ and σ of insulators with less impurities decrease nearly linearly with increasing T in the range T > ΘD but decrease nonlinearly with increasing T in the range mΘD < T < ΘD, ΘD is Debye temperature, m of a given insulator is a constant which is < 0.4. The method of obtaining λ(χreal, Eg, T)Mee and corresponding χreal by secondary electron emission (SEE) was presented, λ(χreal, Eg, T)Mee is the λ(χreal, Eg, T) due to electron–electron scatterring in insulator. It concludes that the method presented here to obtain special formula for λ(χreal, Eg, T)p and corresponding χreal is a good method to research electron-lattice interaction by SEE, and that the method presented here to obtain values of λ(χreal, Eg)Mee and corresponding χreal is a good method to research electron–electron interaction by SEE. According to the values of ΘD, experimental σ, characteristics of temperature dependence of ẟ and σ and deduced formulas, it concludes that the method presented here to determine ΘD by SEE is a better method to determine ΘD of insulator with less impurities.

Theoretical calculations of the mean escape depth of secondary electron emission from compound semiconductor materials

We have performed a systematic Monte Carlo simulation of primary and secondary electron trajectories to predicate the mean escape depth of secondary electron emission for six compound semiconductors, i.e., TiN, VN, GaAs, InAs, InSb, and PbS. Mott's cross section is used for the description of electron elastic scattering in the simulation model, and the full-Penn's dielectric function approach is adopted for the modeling of electron inelastic scattering, where the energy loss function obtained with the optical data is contributed from phonon excitation, interband transition of the loosely bound valance electrons, and inner-shell electron excitations. We have calculated the excitation depth distribution function, emission depth distribution function, and their combining effect in probability depth distribution function at different primary energies for the excited and emitted secondary electrons in these materials. The calculation leads to the primary energy dependence of mean escape depth whose values are found in the range of 0.4–1.4 nm for these materials.

Practical guide for inelastic mean free paths, effective attenuation lengths, mean escape depths, and information depths in x-ray photoelectron spectroscopy

Information is provided on four terms that are used for different purposes in x-ray photoelectron spectroscopy (XPS): the inelastic mean free path (IMFP), the effective attenuation length (EAL), the mean escape depth (MED), and the information depth (ID). While the IMFP is a parameter that depends on both the material and electron energy, the other three terms depend on the IMFP, the instrumental configuration, and the magnitude of elastic-scattering effects in the sample material. In addition, different EALs can be defined for different XPS applications, and the numerical values for each application can differ. Guidance is given on sources of IMFP and EAL data and on predictive equations for IMFPs, EALs, MEDs, and IDs. This guide is one of a series intended to highlight best practices in the use of XPS.

Study of secondary electron emission from semiconductors induced by electrons from 20 eV to 800 eV and surface state of semiconductors

Based on processes and characteristics of secondary electron emission (SEE), experimental data and the relations among parameters of secondary electron yield from semiconductors δ, the formula for δ in the range of 20 eV ≤ Epo ≤ 800 eV of semiconductors with Epom ≤ 800 eV as a function of Epo, Epom, atomic number Z and maximum δ (δm) was deduced and proved experimentally, where Epo and Epom are incident energy of primary electron and the Epo of δm, respectively. From the existing formula and the relation among Z, mean escape depth of secondary electrons emitted from semiconductors and primary range R at Epom deduced in this study, the formula for R in the range of 150 eV ≤ Epo ≤ 800 eV in monocrystalline semiconductors with Epom ≤ 800 eV, χ ≥ 0.6 eV and Eg ≥ 0.6 eV was successfully deduced, where χ is original electron affinity, Eg is the width of forbidden band. The method of calculating B(χreal, Eg) of semiconductor with Epom ≤ 800 eV, χreal ≥ 0.5 eV and Eg ≥ 0.6 eV and that of calculating B of semiconductor with Epom ≤ 800 eV were presented, respectively; Where B is the probability that an internal secondary electron escapes into vacuum upon reaching the surface of semiconductor, and the B(χreal, Eg) is the B relative to semiconductor with Eg and real electron affinity χreal. It can be concluded that the two methods are correct. From the analysis of calculated B, experimental Epom and relations among parameters of SEE, it can be concluded that this paper can research the surface state of semiconductor with Epom ≤ 800 eV by SEE.

THEORETICAL RESEARCH OF SECONDARY ELECTRON EMISSION FROM NEGATIVE ELECTRON AFFINITY SEMICONDUCTORS

Based on primary range [Formula: see text], relationships among parameters of secondary electron yield [Formula: see text] and the processes and characteristics of secondary electron emission (SEE) from negative electron affinity (NEA) semiconductors, the universal formulas for [Formula: see text] at [Formula: see text] and at [Formula: see text] for NEA semiconductors were deduced, respectively; where [Formula: see text] is incident energy of primary electron. According to the characteristics of SEE from NEA semiconductors with [Formula: see text], [Formula: see text], deduced universal formulas for [Formula: see text] at [Formula: see text] and at [Formula: see text] for NEA semiconductors and experimental data, special formulas for [Formula: see text] at 0.5[Formula: see text] of several NEA semiconductors with [Formula: see text] were deduced and proved to be true experimentally, respectively; where [Formula: see text] is the [Formula: see text] at which [Formula: see text] reaches maximum secondary electron yield. It can be concluded that the formula for [Formula: see text] of NEA semiconductors with [Formula: see text] was deduced and could be used to calculate [Formula: see text], and that the method of calculating the 1/[Formula: see text] of NEA semiconductors with [Formula: see text] is plausible; where [Formula: see text] is the probability that an internal secondary electron escapes into vacuum upon reaching the surface of emitter, and 1/[Formula: see text] is mean escape depth of secondary electron.

A study of secondary electron emission from semiconductors and insulators

No rude approximations were made in the course of deducing formula for B(χ, Eg) as a function of parameters of secondary electron emission SEE; where B(χ, Eg) is the probability that an internal secondary electron escapes into vacuum upon reaching the surface of semiconductors and insulators SI with width of forbidden band Eg and original electron affinity χ. It can be concluded that the formula for B(χ, Eg) as a function of parameters of SEE can be used to calculate B(χ, Eg). The B(χ, Eg) calculated with the formula for B(χ, Eg) as a function of parameters of SEE and characteristics of B(χ, Eg) and SEE from SI were studied, the formula for B(χ, Eg) of SI with Eg≥0.6 eV and χ≥0.5 eV as a function of χ and Eg was determined. It concludes that the determined formula can be used to calculate B(χ, Eg) of SI with Eg≥0.6 eV and χ≥0.5 eV. The processes and characteristics of SEE from SI, energy loss of primary electron and parameters of SEE were studied, the formulae for δm(Epom, χreal, Eg) in the general case and 1/α(χreal, Eg) of SI with Eg≥0.6 eV and χ≥0.5 eV were deduced and experimentally proved, respectively; where δm(Epom, χreal, Eg) is the maximum secondary electron yield δm of SI with Eg and χreal, Epom is primary incident energy corresponding to δm, χreal is real electron affinity,1/α(χreal, Eg) is mean escape depth of secondary electrons emitted from SI with Eg and χreal.

The Chandrasekhar function for modeling photoelectron transport in solids

The objective of this study was to design an algorithm for calculating the Chandrasekhar function (H-function) dedicated for theoretical models of photoelectron transport in condensed matter. It has been shown that only the H-function values for non-conservative isotropic scattering are needed with the largest albedo, ω, values reaching 0.85. Different algorithms for calculating the H-function were analyzed to identify values of arguments for which an accuracy of 14 decimals is reached. It turned out that the most universal approach was an algorithm implementing the double-exponential rule which provided accurate values of the H-function for arguments varying over 10 orders of magnitude. However, the execution time was found to be shorter for algorithms implementing approximate analytical expressions in the region of small argument values, and the Stibbs and Weir algorithm (Stibbs and Weir, 1959) in the region of largest albedo values considered here. Based on these results, a mixed algorithm was created, and tested in calculations of integrals with integrands containing the H-function that are needed in the formalism for photoelectron transport. The execution time of calculations of the photoelectron current emitted from a solid or the photoelectron mean escape depth usually was very short, well below 1 s despite the fact that several such integrals were calculated, and the desired and attained accuracy was 13 decimals or better. Program summaryProgram title: H_FUNProgram Files doi: http://dx.doi.org/10.17632/xf4k25cnpk.1Licensing provisions: GNU General Public License 3 (GPL)Programming language: Fortran 90Nature of problem: Analytical formalism of photoelectron transport requires access to a program providing accurate values of the Chandrasekhar H-function within a possibly short execution time. However, the theory is based on non-conservative scattering; thus the albedo values associated with photoelectron transport vary in a limited range of values, not exceeding ω=0.85. Furthermore, the H-function in the range of small arguments is expressed by analytical formulas that can be implemented in programs providing the H-function with high speed and high accuracy. It would be of interest to develop an algorithm for calculating the H-function with the following features: (i) optimized with respect to execution time, (ii) providing the results with accuracy of 14 decimals, and (iii) taking into account the limited range of albedo values.Solution method: It has been proved that the H-function for both arguments smaller than about 10−5–10−4 are obtained with the desired accuracy from analytical formulas. In the remaining region of arguments, algorithms involving the integral representation need to be used. In recent reports, the integration method based on the double-exponential rule was recommended as an accurate and fast approach. Similarly, an algorithm implementing the Stibbs and Weir theory was also recently indicated as a very effective source of the H-function. In the present work, the execution times for the above algorithms were compared for different pairs of arguments. Finally, separate domains were ascribed to tested algorithms in such a way that the execution times were always the shortest. Based on these results, a program HFUNELE dedicated to calculations of photoelectron transport was developed.Additional comments:(i) Restrictions: The program HFUNELE optimized with respect to speed can be used for the directional variable, μ, varying in the range from zero to unity, while the allowed albedo, ω, range is from zero to 0.85, i.e., the range needed for applications in photoelectron transport theory.(ii) Unusual features: The enclosed test program demonstrates the fact that the typical integrals over the integrands containing the H-function reach or even exceed an accuracy of 13 decimals. Furthermore, application of the program HFUNELE is illustrated in exemplary calculations related to photoelectron transport theory (determination of the photoelectron signal intensity or the photoelectron mean escape depth). To facilitate the performance of the test program, several databases of parameters needed for the calculations are implemented using the DATA statement (electron inelastic mean free paths, albedo values for elements, atomic weights and densities), or included as accompanying text files: BAND_MG.TXT and BAND_AL.TXT (atomic subshells, subshell photoionization cross sections, electron binding energies, and asymmetry parameters).

Calculation of CsI photocathode spectral response in 10-100 keV X-ray energy region

CsI photocathode is widely applied to high energy X-ray detection. And the spectral response is an important character of CsI photocathode. In this paper, the interaction process of high energy X-ray with CsI is analyzed and the spectral response of CsI photocathode is calculated in a 10-100 keV range. The influences of Compton scattering, X-ray fluorescence radiation and Auger emission on the spectral response are analyzed in accordance with the physical process of high energy X-ray interaction with CsI photocathode. These influences prove to be negligible in comparison with photo-ionization influence. Thus only the photoelectric transition is taken into account in calculation. According to the analyses of the processes of the photoelectron creation, transition and escaping, the formula for CsI spectral response is deduced as a function of secondary electron mean escape depth and photocathode thickness. The formula of secondary electron mean escape depth is then deduced as a function of X-ray energy. These formulae indicate that the mean escape depth of the secondary electrons increases markedly with the rise of X-ray energy and has a remarkable influence on the CsI spectral response. The spectral responses for different CsI thickness values are then calculated in a range of 10-100 keV. The results show that 1000 nm CsI has the best response under 20 keV, while 10000 nm CsI has a higher response over 60 keV. Then the calculation data are compared with experimental data of Hara's and Khan's hard X-ray streak camera measurements. These data agree well with each other and prove that our calculation of CsI spectral response for high energy X-ray is reliable. The spectral responses to CsI thickness for 17.5 keV and 60 keV are also calculated and shown in figures. These calculation data match experimental data of Frumkin and Monte-Carlo simulation data of Gibrekhterman. The measurement error of Frumkin's experiment and the uncertainty of the secondary electron mean escape depth are considered to be the reasons for the deviations of calculation and experimental data. The figures of spectral responses to CsI thickness also reveal the optimal thickness values of CsI for different X-ray photon energies. It is shown that 1 m is the optimal thickness for 17.5 keV X-ray detection, and 10 m is optimal for 60 keV. Finally the spectral response of CsI photocathode in a 10-100 keV range is calculated and the formulae prove to be reliable. According to these formulae and calculations, the optimal thickness of CsI photocathode can thus be given for designing and optimizing the high energy X-ray imaging detectors.

Modeling and parameterization of photoelectrons emitted in condensed matter by linearly polarized synchrotron radiation

Growing availability of synchrotron facilities stimulates an interest in quantitative applications of hard X-ray photoemission spectroscopy (HAXPES) using linearly polarized radiation. An advantage of this approach is the possibility of continuous variation of radiation energy that makes it possible to control the sampling depth for a measurement. Quantitative applications are based on accurate and reliable theory relating the measured spectral features to needed characteristics of the surface region of solids. A major complication in the case of polarized radiation is an involved structure of the photoemission cross-section for hard X-rays. In the present work, details of the relevant formalism are described and algorithms implementing this formalism for different experimental configurations are proposed. The photoelectron signal intensity may be considerably affected by variation in the positioning of the polarization vector with respect to the surface plane. This information is critical for any quantitative application of HAXPES by polarized X-rays. Different quantitative applications based on photoelectrons with energies up to 10 keV are considered here: (i) determination of surface composition, (ii) estimation of sampling depth, and (iii) measurements of an overlayer thickness. Parameters facilitating these applications (mean escape depths, information depths, effective attenuation lengths) were calculated for a number of photoelectron lines in four elemental solids (Si, Cu, Ag and Au) in different experimental configurations and locations of the polarization vector. One of the considered configurations, with polarization vector located in a plane perpendicular to the surface, was recommended for quantitative applications of HAXPES. In this configurations, it was found that the considered parameters vary weakly in the range of photoelectron emission angles from normal emission to about 50° with respect to the surface normal. The averaged values of the mean escape depth and effective attenuation length were approximated with accurate predictive formulas. The predicted effective attenuation lengths were compared with published values; major discrepancies observed can be ascribed to a possibility of discontinuous structure of the deposited overlayer.

Formulae for maximum yield and mean escape depth of secondary electrons emitted from metals

Based on the characteristics of secondary electron emission, the former formulae for the maximum yield of metals [Formula: see text] and primary range in the energy range of [Formula: see text] eV, relation [Formula: see text] among secondary electron escape probability [Formula: see text], average energy required to produce an internal secondary electron [Formula: see text], [Formula: see text], primary energy of [Formula: see text] ([Formula: see text] and parameter [Formula: see text] was deduced. On the basis of [Formula: see text] and the former formula for [Formula: see text], relation [Formula: see text] among mean escape depth of secondary electrons emitted from metals [Formula: see text], atomic number [Formula: see text], back-scattering coefficient [Formula: see text], material density [Formula: see text], [Formula: see text], atomic weight [Formula: see text] and [Formula: see text] was deduced. According to the deduced [Formula: see text], the formula for the ratio of [Formula: see text] to [Formula: see text] and experimental ratio of [Formula: see text] to [Formula: see text], relation [Formula: see text] among [Formula: see text], original work function [Formula: see text] and [Formula: see text] were empirically obtained. According to the characteristics of metal surface, [Formula: see text], [Formula: see text] and [Formula: see text], the formula for [Formula: see text] as a function of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] and that for [Formula: see text] as a function of [Formula: see text], [Formula: see text] and [Formula: see text] were deduced, respectively. The influences of surface change on [Formula: see text] and [Formula: see text] were analyzed. Calculated [Formula: see text] and [Formula: see text] were compared with the corresponding experimental ones. It was concluded that the deduced formulae for [Formula: see text] and [Formula: see text] can be used to estimate [Formula: see text] and [Formula: see text], respectively.