5.12. [ Track Structure ] section

By performing track-structure simulation for electrons or positrons of low energy below 1 keV, deceleration processes caused by many collision events for ionization, excitation, and molecular vibration and rotation can be calculated precisely. [1] Because track-structure simulation takes a very long time, it is not recommended to activate this mode in conventional-scale particle transport simulations on the cm scale due to the large production of low-energy electrons around 10 eV.

In this section, you can specify the cells where track-structure simulation is performed. mID is the track-structure model specifier explained below.

Table 5.12.1 Track structure model specification by mID

mID	Model	Electron, Positron	Proton 0-300 MeV, Carbon 0-10 MeV/n	The other proton and ion
-1	Track structure mode for arbitrary materials	chem=H2O: ETS, chem=Si: ETS for Si, others: ETSART	ITSART	ITSART
0	No track structure calculation	– (EGS etc.)	– (ATIMA etc.)	– (ATIMA etc.)
1	Track structure mode for liquid water	ETS	KURBUC	ITSART

• –: no track structure mode, and the model used instead of track structure is switched by negs or ndedx

• ETS: electron-positron track structure mode dedicated to liquid water target

• KURBUC: track structure mode for protons and carbon ions dedicated to liquid water target [2] [3] [4] [5]

• ITSART: generalized track structure mode for arbitrary materials and ions

• ETSART: electron-positron track structure mode for arbitrary targets

• ETS for Si: electron-positron track structure mode dedicated to semiconductor silicon target [6]

When ETS or KURBUC is applied to materials other than liquid water, mean free paths of particles in target materials are derived by scaling the cross section of liquid water by the electron density of the target material. The track structure mode for specific materials, activated by mID=1, is applicable only to liquid water, but it simulates each reaction channel such as excitation and ionization accurately. In contrast, ITSART, the track structure model for arbitrary radiation and targets invoked by mID=-1, has the following advantages.

1. It is applicable to arbitrary target materials.

2. It considers atomic recoil by Rutherford scattering.

This is at the cost of some accuracy, such as the implicit treatment of target excitation. If the target material is included in the following list, the accuracy of the track structure mode for arbitrary materials can be improved by specifying the chemical form in the [material] section using the chem parameter. H2O, CO2, NH2, NH3, SF6, TeF6, CH4, CH3, C2H2, C2H4, C2H6, C6H6, and (CH3)2NH.

Listing 5.12.1 [ Track Structure ] section example (1)

[track structure]
reg  mID
  1    1
  2    0

You can use the format ( { 2 - 5 } 89 ). However, a value must be enclosed by ( ) if it is not a single numeric value. You cannot use the lattice and universe style ( 6 < 10[100] < u=3 ). If you want to replace the order of region number (reg) and index of the cross section database (mID), set it as mID reg. You can use the skip operator non.

The following are important parameters for this mode. The parameters etsmax and etsmin in the [parameters] section are the maximum and minimum energies of particles simulated by track-structure mode. When using the track structure mode, emin(12) and emin(13) should be set concurrently to 1.0e-3, and EGS5 should be activated by negs=1 or 2.

Listing 5.12.2 [ Parameters ] section example for track structure

[ Parameters ]
emin(12) = 1.E-03
emin(13) = 1.E-03
negs     = 1
etsmax   = 1.E-2
etsmin   = 1.E-6

The parameter etsmax with default value 1e-3 MeV/n needs to be defined in the [parameters] section. etsmax defines the maximum energies of protons and ions when track structure mode is used. The energy lower bounds of track structure modes can be adjusted by emin(1) and emin(19) with default value 1e-3 MeV/n for protons and ions, respectively. If mID is 1 and etsmax is higher than the maximum energies of the track-structure cross section libraries, that is, 300 MeV for protons and 10 MeV/n for carbon ions, PHITS performs track structure simulation of protons and carbon ions by KURBUC up to these maximum energies. Above these energies, and for ions other than carbon and protons, PHITS uses ITSART.

Listing 5.12.3 [ Track Structure ] section example (2)

[ Track structure ]
reg     mID     ebg     wvl
1       -1
2       -1      2.8     6.5

ETSART and Si-ETS are available from version 3.34. ETSART is activated by setting mID=-1. ETSART can simulate excitation reactions in semiconductor materials by entering the bandgap energy. The [track structure] section defines the bandgap energy as ebg [eV]. When ebg is undefined, ebg=0 by default, and excitation reactions are ignored. The energy required to produce one electron-hole pair in a material, the w-value, can be defined as wvl [eV] in [track structure]. When electrons reach the cutoff energy etsmin, the number of generated electrons is calculated by dividing etsmin by the w-value and tallied in [t-interact]. This function allows efficient calculation of the number of electrons produced by relatively high-energy radiation by setting etsmin to a high value. In the [material] section, if chem is specified and mID=-1, electron track structure analysis can be performed for that material. Currently, ETS can be performed with chem=H2O and Si-ETS with chem=Si.

[1]

20. Kai et al., “Thermal equilibrium and prehydration processes of electrons injected into liquid water calculated by dynamic Monte Carlo method,” Radiat. Phys. Chem., 115, 1-5 (2015).

[2]

Uehara S, Nikjoo H, Goodhead DT, 1993, “Cross sections for water vapour for Monte Carlo electron Track structure from 10 eV to 10 MeV region.” Phys. Med. Biol. 38, 1841-1858.

[3]

Hooshang Nikjoo, Shuzo Uehara, Dimitris Emfietzoglou, Interaction of Radiation with Matter, CRC Press, Published June 11, 2012.

[4]

Liamsuwan T, Uehara S, Emfietzoglou D and Nikjoo H, 2011, “Physical and biophysical properties of proton tracks of energies 1 keV to 300 MeV in water,” Int. J. Radiat. Biol. 87, 141-160.

[5]

Liamsuwan T and Nikjoo H, 2013, “A Monte Carlo track structure simulation code for the full-slowing-down carbon projectiles of energies 1 keV u^-1 - 10 MeV u^-1 in water,” Phys. Med. Biol. 58, 673-701.

[6]

Yuho Hirata, Takeshi Kai, Tatsuhiko Ogawa, Yusuke Matsuya and Tatsuhiko Sato, 2022, “Implementation of the electron track-structure mode for silicon into PHITS for investigating the radiation effects in semiconductor devices,” Japanese Journal of Applied Physics, 61, 106004.