helsinki, june 28 - july 2, 2004 cosires 2004: 7th international conference on computer simulation...

Helsinki, June 28 - July 2, 2004

COSIRES 2004: 7th International Conference on Computer Simulation of

Radiation Effects in Solids

Monte Carlo simulation of electron depth distribution and backscattering for

carbon films deposited on aluminium as a function of incidence

angle and primary energy

Maurizio Dapor

Istituto per la Ricerca Scientifica e Tecnologica (IRST)

I-38050 Povo, Trento, Italy

[email protected]




Abstract

The few keV electron depth distribution and backscattering coefficient for the special case of film of carbon deposited on aluminium are investigated, by a Monte Carlo simulation, as a function of the incidence angle and primary electron energy. The simulated results can be used as a way to measure the carbon film thickness by a set of measures of the backscattering coefficient.




Contents Introduction Motivation The Monte Carlo code The differential elastic scattering cross-section The stopping power Results and discussion Conclusion




When an electron-beam impinges on a solid target, each individual electron loses energy and changes its direction of motion due to atomic electron excitation, plasmon emission and interactions with the nuclei of the medium.

The travel of the electron in the solid may be described by means of the inelastic scattering processes due to the interaction between the incident electrons and the atomic electrons, and the elastic scattering processes due to the collisions between the incident electrons and the nuclei.

Introduction




Once calculated the electron inelastic and elastic scattering cross sections, it is possible to deal with the problem of the interaction of an electron-beam with a solid by using the Monte Carlo method, a statistical tool able to solve mathematical problems.

This work is focused on the simulation of the interaction of an electron-beam with solid targets constituted by thin films of carbon deposited on aluminium substrates.

Introduction




Carbon films are deposited on various substrates (polymers, polyester fabrics, polyester yarns, metal alloys) both for experimental and technological motivations. There are a lot of technological uses of the films of carbon, as carbon characteristics are very useful in many fields.

Carbon films deposited on polymeric substrates can be used to replace the metallic coatings on plastic materials used for food package. Carbon-based coatings allow plastics to be recycled and today several researchers are looking for carbon films for food package impermeable to atmospheric gases, transparent to visible light, and mechanically stable.

Carbon films are also widely employed in medical devices. Biomedical investigators have demonstrated that permanent thin films of pure carbon show an excellent haemo/biocompatibility: they are used, in particular, as coating for the stainless steel stents to be implanted in coronary arteries.

Motivation




Spherical coordinates: ,,r

The Monte Carlo code

The path-length distribution is assumed to follow a Poisson-type law: 11ln rndl

A stream of mono-energetic electrons irradiates a solid target in the direction +z

Here l is the step-length, l the total elastic mean free path calculated by the differentialelastic scattering cross-section and rnd1 is a random number uniformly distributed in the range [0,1].

The differential elastic scattering cross-section has been calculated using the Quantum Relativistic Partial Wave Expansion Method (QRPWEM).




The Monte Carlo code

The inelastic scattering can be quantified by using the stopping power, a quantity related to the probability of energy loss per unit distance travelled by the electron within the solid.

An electron can lose a large fraction of its energy in a single collision: nevertheless the continuous energy loss slowing down approximation is often accepted.

In this approximation, the electron is assumed to continuously dissipate its energy whilst travelling within the solid.




The differential elastic scattering cross-sectionThe phase shifts necessary to compute the differential elastic scattering cross-section can be calculated by numerically solving the Dirac equation for a central electrostatic field up to a large radius in which the atomic potential is negligible.

The atomic potential used here is that of Hartree-Fock (for atomic number smaller than 19) and that of Dirac-Hartree-Fock-Slater (for atomic numbers greater than 18).




The differential elastic scattering cross-section

Differential elastic scattering cross-section of 400 eV electrons scattered by Ar as a function of the scattering angle.Solid line: RPWEM calculations(Dapor, 2003)●: Experimental data(Iga et al., 1987)





Differential elastic scattering cross-section of 300 eV electrons scattered by Hg as a function of the scattering angle.Solid line: RPWEM calculations(Dapor, 2003)●: Experimental data(Bromberg, 1969)○: Experimental data(Holtkamp et al., 1987)





Differential elastic scattering cross-section of 1 100 eV electrons scattered by Au as a function of the scattering angle.Solid line: RPWEM calculations(Dapor, 2003)●: Experimental data(Reichert, 1963)





Differential elastic scattering cross-section of electrons scattered by Al as a function of the electron kinetic energy.

RPWEM calculations:

+: Salvat and Mayol, 1993

○: Dapor and Miotello, 1997




The differential elastic scattering cross-section Transport elastic scattering cross-section of positrons scattered by C as a function of the positron kinetic energy.

RPWEM calculations:●: Liljequist, Ismail, Salvat, Mayol and Martínez, 1990

□: Dapor and Miotello, 1998




The stopping power

ldldEE /

The energy loss E along the segment of trajectory l is approximated by:

where E/l is the Ashley's electron stopping power (Ashley, 1988, 1990).




Results and DiscussionThe knowledge of the initial depth distribution of the electrons and positrons absorbed in a solid target is important for many reasons: it is an essential requisite for the solution of the diffusion equation.

We present, in the following figures, the depth distribution of 2 keV electron-beams penetrating in a target constituted by a 400 Å film of carbon deposited on an aluminium substrate, for different angles of incidence.

We observe the superimposition of two stopping profiles, reflecting the presence of the layer of carbon on the aluminium substrate.



Radiation Effects in SolidsDepth profile of electrons penetrating into a thin film of C deposited on an Al substrate.

Film thickness400 Å

Primary energy 2 000 eV

Incidence angle (respect to the normal to the surface)0 deg






Incidence angle (respect to the normal to the surface)30 deg





Primary energy 2 000 eV Incidence angle (respect to the normal to the surface)60 deg




Results and Discussion

The shape of the depth profile depends on , the incidence angle with respect to the normal to the surface: as the angle increases, the maximum of the profile corresponding to the carbon film, starting with values lower than that of the aluminium substrate, becomes, for =60 deg, higher than the values of the maximum of the aluminium profile.

On the other hand the area under the curve, which represents the total fraction of

absorbed electrons, decreases as the angle with respect to the normal to the surface increases, while the backscattering coefficient increases (see the next two figures).



Radiation Effects in SolidsDepth profiles of electrons penetrating into thin films of C deposited on an Al substrates.



Incidence angle (respect to the normal to the surface)□ : 0 deg○ : 30 deg∆ : 60 deg



Radiation Effects in SolidsBackscattering coefficient for electrons penetrating into a thin film of carbon deposited on an aluminium substrate as a function of the incidence angle .






Results and Discussion As the energy decreases from 10 keV to 250 eV, our simulations show that the backscattering coefficient of low atomic number elements increases.

In the next figure we show the trend of the backscattering coefficient as a function of the electron beam primary energy for electrons impinging on bulk targets of C and Al as calculated by our Monte Carlo code.

For both the examined elements, the backscattering coefficient increases as the energy becomes lower than ~2000-3000 eV and decreases towards 250 eV.



Radiation Effects in SolidsBackscattering coefficient for electrons penetrating into a bulk of C (◦) and into a bulk of Al (•) as a function of the primary energy.

+: Bishop experimental data for C◊: Bishop experimental data for Alx: Hunger and Kükler experimental data for C

Incidence angle 0 deg





The effect of a few layers of carbon contamination on backscattering coefficients for aluminium has not been completely clarified experimentally.

Therefore, two sets of measurements on aluminium surfaces contaminated with 25 and 50 Å thick carbon films have been simulated.



Radiation Effects in SolidsBackscattering coefficient for electrons impinging on samples of aluminum with a surface film of carbon contamination as a function of the primary energy.

Film thickness25 Å (◊) 50 Å (x)





Results and Discussion If one is interested in measuring the backscattering coefficient for primary energies lower than 2-3 keV, it is evident—from our simulation results—that it becomes necessary to take into account the carbon contamination. An accurate measurement of the backscattering coefficient for low energy electrons requires an accurate cleaning of the surface, obtained in vacuum by sputtering—or by some other in situ cleaning procedure—in order to obtain the correct values. Indeed the carbon contamination decreases the value of the low energy backscattering coefficient in aluminium: and it is reasonable to suppose that this phenomenon is present for any material with mean atomic number higher than the carbon atomic number.





Note that, typically, the thickness of the carbon contamination is not known. Furthermore there are not reasons to believe that the film of carbon contamination is constant in thickness.

The values we have used in our simulation may be, in some cases, rather high. Actually the characteristics of the contamination strongly depend on the cleanness of the surface sample.




Results and Discussion Carbon films are not only present on the samples as surface contamination. They are, in many cases, deliberately deposited for experimental or technological motivations. There are indeed a lot of technological uses of the films of carbon, because their characteristics are very useful in many fields.

Films of carbon can be deposited on heat-sensitive substrates (polymers, polyester fabrics, polyester yarns, metal alloys). Carbon films deposited on polymeric substrates can be used to replace the metallic coatings on plastic materials used for food package. Carbon films are also widely employed in medical devices.





Investigating the behaviour of the backscattering coefficient as a function of the primary energy for various film thicknesses, we have found an interesting property, i.e. the appearance, for carbon film thicknesses higher than ~100 Å on aluminium, of relative maxima of absorption (and relative minima of backscattering).



Radiation Effects in SolidsBackscattering coefficient for electrons penetrating into a thin film of C deposited on an Al substrate as a function of the primary energy.

Film thickness400 Å (◊)




Radiation Effects in SolidsBackscattering coefficient for electrons penetrating into a thin film of C deposited on an Al substrate as a function of the primary energy.

Film thickness800 Å (◊)






The backscattering coefficient reaches a relative minimum and then it increases up to the aluminium backscattering coefficient. Then it follows the decreasing trend typical of the backscattering coefficient of aluminium.

An interesting characteristic of the relative minima is that their position shifts towards higher energies as the film thickness increases.




Results and Discussion So, as the film thickness increases, the positions of the relative minima shift towards higher energies while the peaks are broadening.

If experimentally confirmed and quantitatively better defined, the qualitative trends presented—here obtained by a Monte Carlo simulation—can be used as a way to measure the carbon film thickness by a set of measures of the backscattering coefficient.




Conclusion The study of carbon film is important for many applications. Carbon films deposited on polymeric substrates can be used to replace the metallic coatings on plastic materials used for food package. Carbon films are also widely employed in medical devices.

We have reported the results of a Monte Carlo simulation of the depth distribution and backscattering coefficient of low-medium energy electron beams of carbon films of various thicknesses deposited on aluminium substrates.

The behaviour of the backscattering coefficient as a function of the beam primary energy can be used to calculate the carbon film thickness.

helsinki, june 28 - july 2, 2004 cosires 2004: 7th international conference on computer simulation...

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