Hee Seo, Chan-Hyeung Kim, Lorenzo Moneta, Maria Grazia Pia

Hanyang Univ. (Korea), INFN Genova (Italy), CERN (Switzerland)

18 October 2010

Design, development and validation of electron ionisation models for nano-scale simulation

SNA + MC 2010Joint International Conference on

Supercomputing in Nuclear Applications + Monte Carlo 2010

Outline

Experimental and software context

Electron ionisation cross section models

Software development and verification

Experimental validation

Conclusions and outlook

Experimental requirements

Nano-scale simulation is required in various exper-imental applications:– Nanotechnology-based radiation detectors– Radiation effects on semiconductor devices– Gaseous tracking detectors– Plasma physics including material processes– Biological effects of radiation– etc.

HEP detector R&D

LHC and beyond

Radiation protection

Monte Carlo codes

• General-purpose Monte Carlo simulation codes– Geant4, MCNP, EGS etc.– based on condensed history technique– cutoff energy / secondary production threshold: 1 keV

• Penelope, Geant4 low energy models– < 1 keV, but scarce quantitative evidence of modeling accuracy be-

low 1 keV– Conventional particle transport scheme and physics models are ad-

equate for macroscopic observables; however, they are NOT appro-priate for nano-scale simulation

• “Track structure codes”– Developed ad hoc for nano-scale simulation– Limited applicability: usually specific to one or a few materials– Limited public availability– Long term maintenance is often an issue

Vision

For the first time, endow a general purpose Monte Carlo codewith the capability of nano-scale simulation for any material

Further advancement:

multi-scale simulation in the same software environmentseamless transition between particle transport schemes

1st development cycle: focused on electron impact ionisation

the very heart of the problem!

Cross sectionsthis talk

Final state generatorin progress

Major investment in the experimental validation of the new physics models

Also: for the first time, validation of EEDL below 1 keV

Development strategy

• Cross section models for electron impact ionization at energies down to the ionization potential (a few eV) for any target atom:– implemented (based on existing design)

– verified, – validated

• Cross section models:– Binary-Encounter-Bethe (BEB)– Deutsch-Märk (DM)– EEDL

Ionisation cross sections: BEB model

• Binary-Encounter-Bethe (BEB) model– Proposed by Kim and Rudd in 19941

– Simplified version of BED (Binary Encounter Dipole) model– Modified form of Mott theory for close collision– Dipole interaction of Bethe theory for distant collision

• Total ionization cross section

– In the present study, orbital parameters (Bk, Uk, Nk) in EADL2 were used

( )2

ln 1 1 ln( ) 1 1

( 1) / 2 1k

ik

S t tT

t u m t t t

2 20

2

4 , , k K

k k k

πa N R UTwhere S t u

B B B

1. Y. Kim and M. Rudd, Phys. Rev. A 50(5):3954–3966 (1994).2. S. T. Perkins et al., UCRL-50400, vol.30 (1991).

B=binding energyU=<kinetic energy>N=occupation number

of shell

Ionisation cross sections: DM model

• Deutsch-Märk (DM)1 model– Originated from Thomson2 and Gryzinski3

– Some parameters are derived from fits to experimental data– Values of these fitted parameters are reported in original

author’s publications– The up-to-date formula is

1. H. Deutsch, T. D. Märk, Int. J. Mass Spectrom. Ion Processes, 79:R1–R8 (1987).2. J. J. Thomson, Philos. Mag., 23:449–457 (1912).3. M. Gryzinski, Phys. Rev. A, 138:305–321 (1965).

2 ( )

,

ln( )( )q nl

DM nl nl nl nln l

c ug r b u

u

( ) 1 22

3

where ( )1 ( / )

qnl p

A Ab u A

u A

Ionisation cross sections: EEDL

• Evaluated Electron Data Library (EEDL)1

– Lawrence Livermore National Laboratory (LLNL)– Z=1–100 and E=10 eV–100 GeV– Elastic scattering, Bremsstrahlung, excitation and impact

ionization cross sections– Ionization cross sections for each shell (i.e., K, L, M, …)– Based on Seltzer’s modifications on

• Möller binary collision cross section for close collisions• Weizsacker-Williams method for distant collisions

1. S. T. Perkins et al., UCRL-50400, vol.31 (1991)

Cross sections of the three models

Large differences for some elements

Similar valuesfor some elements

Software design

• Policy-based class design– See: M.G. Pia et al., Design and performance evaluations of

generic programming techniques in a R&D prototype of Geant4 physics , CHEP 2009

• Main advantages: – fine-grained configuration of particle interaction

processes with a variety of physics models– computational performance– ease of test (verification and validation)

• Prototype design– Subject to further refinement based on concrete

experience and experiments’ feedback

Implementation

• The implementation was based on the most recent for-mulations and associated parameters of the BEB and DM models

• The atomic parameters needed by the models’ formula-tion were taken from the same sources as the original authors’ ones whenever practically possible

• If not available, they were taken from EADL or NIST– Side project: validation of some atomic parameters used by

major Monte Carlo systems (paper in preparation)

• Based on this implementation, the electron ionization cross section can be calculated for Z=1-100 and ener-gies from the ionization potential up to10 keV

Verification

• Verification was done by comparing calculated val-ues to published data by original authors– 48 atoms for DM model, 8 atoms for BEB model

• In most cases, they show good agreement– differences associated with different atomic parameters

BEB model for boron (Z=5) atom DM model for oxygen (Z=8) atom

Validation

• Experimental data used in the validation process– 181 experimental data sets for 57 atoms

Elements for which experimental data are available

Validation: sometimes it is easy…

H (Z=1)

He (Z=2)

Ne (Z=10)

Ar (Z=18) Kr (Z=36)

Several independent measurements, mostly compatible among them

Validation: who is right?

Na (Z=11) Mg (Z=12)

Ga (Z=31)

Cs (Z=55)

Eu (Z=63)

Several independent measurements, mostly incompatible among them

Validation: shall we trust a single measurement?

C (Z=6) Si (Z=14) Cl (Z=17)

Ti (Z=22)

Cd (Z=48)

Au (Z=79)

Limited availability of experimental data (some not documenting errors)

Validation method

• Validation process exploited rigorous statistical analysis to quantitatively estimate the compatibility with experimental data for the two theoretical models as well as EEDL

• Validation process divided into two parts:– Goodness-of-fit tests to evaluate the hypothesis of compatibility

between calculated values and experimental data

– Categorical analysis exploiting contingency tables using Fisher’s exact test, χ2 test with Yates correction, and Pearson χ2 test

• Validation tests were performed in various energy ranges<20 eV, 20–50 eV, 50–100 eV, 100–250 eV, 250 eV–1 keV, >1 keV

• Possible sources of systematic effects evaluated– Single vs. total ionisation, absolute vs. relative measurement

Validation results

<20 20-50 50-100 100-250

250-1000

>10000

10

20

30

40

50

60

70

80

90

100

BEB DM EEDL

Electron energy range (eV)

Com

pati

bilit

y w

ith

ele

men

tal exp

eri

men

tal

data

(%

)

Percentage of elements for which a model is compatible with experimental data at 95% CL

DM modelbest overall accuracy

EEDLdegradedaccuracy below 250 eV

GoF tests• c2

• Kolmogorov-Smirnov

• Anderson-Darling• Cramer-von Mises

Detailed resultsPercentage of test cases in which cross section models are compatible with experimental data

Preliminary

Significance of DM-BEB differences

Contingency tables related to DM and BEB cross section compatibility with experimental data

Preliminary

Significance of DM-EEDL differences

Contingency tables related to DM and EEDL cross section compatibility with experimental data

Preliminary

Conclusions• Electron ionization cross section models suitable for nano-scale

simulation are available for use with general purpose Geant4– Capability for the first time available in a Monte Carlo system

• Rigorous validation w.r.t. extensive collection of independent exper-imental measurements

• We demonstrated that– DM model shows the best agreement with experiment– BEB model’s accuracy is comparable to DM model’s for E

up to 50 eV and above 250 eV, worse for 50 < E < 250 eV– EEDL shows lower accuracy below 250 eV

• Outlook– New cross section models will be proposed for release in the Geant4 toolkit– Cross section data will be distributed as a data library (RSICC at ORNL)– Final state generator development in progress– Generic host ionization process is already available– Extensions to molecules and other refinements are foreseen

Paper with full set of results in

progress