Electron deposition in a resist on Si

10 keV electrons at normal incidence on a 100 nm resist layer over Si. The input is examples/electron/e_10keV_resist_on_si.toml:

# 10 keV electrons into a 100 nm resist layer on Si: energy deposition in a
# layered target (an electron run).
#
# Run:   lindhard run examples/electron/e_10keV_resist_on_si.toml --out out/e_10keV_resist_on_si
# Check: lindhard check examples/electron/e_10keV_resist_on_si.toml
#
# Schema: docs/cli.md, "Electron runs". Energies are in eV, lengths in nm,
# angles in degrees.
#
# SYNTHETIC DATA, as in e_10keV_si.toml. "Resist" is an illustrative organic
# compound (the composition C5H8O2 and the density 1.19 g/cm^3 of a
# PMMA-class polymer), but its electron data are not that polymer's, and not
# Si's either: both materials use the same synthetic Drude-Lorentz plasmon
# ELF (synthetic_plasmon_elf.toml) and round-number band parameters. No
# optical or band data of real materials is committed
# (docs/data-provenance.md; the PMMA ELF is a recorded gap). The output shows
# the layered-target mechanics of a run (a layer over a substrate, deposition
# per layer), not what a real resist stack does.

[electron.beam]
energy_ev = 10000.0
tilt_deg = 0.0

[electron.transport]
cutoff_ev = 1.0
cutoff_reference = "vacuum-level"
secondaries = "kieft-bosch"
boundary = "step-barrier"

[electron.elastic]
model = "mott"
# The only potential that runs today is a stand-in (docs/data-provenance.md).
potential = "thomas-fermi-yukawa"
exchange = false

[electron.inelastic]
model = "penn-single-pole"

[electron.tables]
# A coarse grid keeps the example quick.
min_energy_ev = 10.0
points_per_decade = 8.0

[electron.materials.Resist]
optical_elf = "synthetic_plasmon_elf.toml"
band = { kind = "insulator", valence_band_width_ev = 10.0, band_gap_ev = 4.0, affinity_ev = 1.0, provenance = "SYNTHETIC round numbers for the gallery example (examples/electron/e_10keV_resist_on_si.toml), not band parameters of any resist" }

[electron.materials.Si]
optical_elf = "synthetic_plasmon_elf.toml"
band = { kind = "insulator", valence_band_width_ev = 10.0, band_gap_ev = 2.0, affinity_ev = 3.0, provenance = "SYNTHETIC round numbers for the gallery example (examples/electron/e_10keV_resist_on_si.toml), not band parameters of Si" }

[electron.tally]
escape_energy_bins = 100
escape_polar_bins = 18

# Deposited energy: 20 radial bins of 50 nm and 30 depth bins of 50 nm, so the
# resist (the first two bins) and the Si below it are separate rows.
[electron.tally.cylindrical]
r = { lo_nm = 0.0, hi_nm = 1000.0, bins = 20 }
depth = { lo_nm = 0.0, hi_nm = 1500.0, bins = 30 }

[materials.Resist]
density_g_cm3 = 1.19
elements = [
  { symbol = "C", atom_fraction = 5.0 },
  { symbol = "H", atom_fraction = 8.0 },
  { symbol = "O", atom_fraction = 2.0 },
]

[target]
substrate = "Si"

[[target.layers]]
material = "Resist"
thickness_nm = 100.0

[run]
histories = 1000
seed = 1

It uses the [electron] table of an electron run (TOML input reference) with a layered [target]: a [[target.layers]] entry in front of the substrate, and an [electron.materials.<name>] table (optical ELF and band) for each of the two materials. Resist is defined in [materials] by the composition and the density of a PMMA-class polymer. Run and check it with

lindhard check examples/electron/e_10keV_resist_on_si.toml
lindhard run examples/electron/e_10keV_resist_on_si.toml --out out/e_10keV_resist_on_si

A run takes about ten seconds, mostly building the cross-section tables.

Synthetic data: read this first

The electron data of this example are not those of a resist or of Si. Both materials use the same synthetic Drude-Lorentz plasmon as their optical energy-loss function (examples/electron/synthetic_plasmon_elf.toml), the band parameters are round numbers, and the elastic potential is the Thomas-Fermi stand-in. No optical data of PMMA or any other resist is in the repository: the source could not be opened (docs/data-provenance.md, the PMMA rows), and this example adds no dataset. The figure below shows what an electron run reports for a layered target, not how a resist stack behaves.

Result

1000 histories, seed 1. The figure sums electron_deposition_cylindrical.csv over the radial bins, in 50 nm depth bins, and divides by the total energy deposited. The shaded band is the resist layer.

The library measures deposited energy from the band bottom of each layer, so the total deposited includes the Fermi-sea energy of the conduction electrons that secondaries liberate and exceeds the beam energy. This is why the figure is a share of the total and the table lists the balance incident - escaped = deposited - Fermi-sea energy (checked here: electron_summary.json, results.budget; see Output files and docs/cli.md). With the synthetic 12 eV conduction-band bottom of the Si the Fermi-sea term is large.

What is validated, and what is an illustration

• Validated: only the energy bookkeeping of the run: the relative imbalance in the table is at the level of rounding. The transport comparisons in docs/validation.md use their own cited data, not the synthetic data here, and say what they do and do not establish.
• Illustration only: every number in the figure and table. There is no validated resist point-spread function: the comparison with a measured one is a recorded gap (docs/validation.md, “Resist PSF vs a published measurement”). The grid is coarse (50 nm bins), the histories few, and the layer thickness, composition and density are illustrative.