Reproducing Raider and Flitsch 1978: width and composition of the silicon-to-oxide transition region

One of the [studies we reproduced](/writing/interface-studies-reproduced) for [Questions we need Emily to answer](/writing/questions-for-emily-testing-a-theory-of-the-interface), the companion to [the essay](/writing/testing-a-theory-of-the-interface-with-an-ontology). Generated by `scripts/reproduce_studies.py` from `reproductions/raider_flitsch_1978.py`. Every value from the paper was read by an AI agent and has not been checked by a person; the sample and history were re-read from the PDF alone by a second agent that had not seen our earlier transcription.

The study and why we depend on it

S. I. Raider and R. Flitsch, “X-Ray Photoelectron Spectroscopy of SiO2-Si Interfacial Regions: Ultrathin Oxide Films”, IBM J. Res. Develop. 22(3), 294-303 (1978), doi:10.1147/rd.223.0294.

This is the challenge's composition-profile target for planar silicon (system 1): the only paper in the library that measures how wide the silicon-to-oxide transition is and how it changes with processing. The library had it as skimmed, with no dataset and no stored recipe. The predictor reports “composition profile” as not modelled for every planar-silicon history. This page writes the paper's sample groups as histories, sets the printed widths and compositions beside them (the rows say “no program”), scores the one number a program does report (the thinnest oxide at 850 °C), and compares the printed values with an unvalidated candidate model of the silicon-to-oxide gradient that another session is building.

How well can this study be reproduced?

Low. The paper's result is one transition-region width and composition per orientation, fitted to a cloud of films (Figure 5) grown at 23 to 850 °C in six oxidants, with and without an anneal. No film has its own recipe: temperatures between 100 and 700 °C are given only as a range, the 850 °C and room-temperature times are not given, the O2/N2 ratio is not given, and which films were annealed is not said. The result is stated to be independent of all of these, so the missing recipes matter less for the width than they would for a growth rate, but no single film can be followed from history to number.

The grade is ours and is about the paper as a source for simulation, not about the quality of the experiment: high means the sample, every step and its timing are stated well enough that a simulation needs no choices of ours; moderate that some choices are ours and are listed; low that the result depends on choices the paper does not constrain.

The sample and its history, played back

The sample is drawn from the simulation: layer heights and the read-outs are what the ISL programs compute at each moment of the history. Steps the language cannot state (a clean, a metallization, a measurement) are on the clock and marked as recorded, not simulated.

Does our sample and history match the paper's?

Left: the paper's own words, with the page of the PDF. Right: what we simulate. 5 same, 4 approximated, 5 assumed, 4 not in ours.

The timing of the history

Time is counted from the start of the first simulated step. A step the language cannot state takes no simulated time; where the paper gives its duration, the duration is in the last column. Stated means the paper gives the duration; partly stated that it gives a bound or a range; not stated; assumed that the duration in our history is ours.

(100), 23 °C in air

Simulated time in this history: 1 h 00 min.

Across the samples

Timing the paper does not give

• Duration of the 1050 °C sacrificial oxidation (set by its 200 nm target), the HF etch, the rinse and drying, and the time before reoxidation.
• Room-temperature oxidation in air or water: duration not stated (the paper refers to its ref. 18).
• 100-700 °C in dry O2: “generally for about half an hour”, varied in some cases; the temperature of each film is not given.
• (111) at 600 °C and every 850 °C oxidation: no time stated; only the 1.1 nm minimum thickness at 850 °C.
• N2 anneal: 10 to 30 min, and which films had it, not stated.
• No heat-up, push, pull or cooling stated for any heated film.
• Time in air between oxidation, ellipsometry and XPS: “rapidly” for ellipsometry; not stated for XPS.

What the second reading changed

• The project had no dataset, no stored recipe and no transcription for this paper; the library marks it “skimmed”. Every number on this page is from the second reading.
• SOURCE.md and the library note say the region “depends on orientation, not on other process parameters”, which is the paper's summary. The second reading adds what that rests on: one fitted width per orientation in 0.25 nm steps, from a cloud of films whose recipes are not individually given.
• SOURCE.md calls it a candidate for system 1's composition target. The paper prints no Si+1/Si+2/Si+3 fractions and says its spectra cannot be resolved into suboxide lines, so the comparable quantities are width, first-layer composition and Si-Si bond count, not suboxide fractions.

Their terms and ours

The simulation in our language

Each sample is one history file: a SAMPLE and a CONTROL_TRAJECTORY. This is the whole input; run it with PYTHONPATH=. python -m isl_harness.predict <file>.

(100), 23 °C in air

# (100), 23 °C in air
SAMPLE RF_100_rt_air {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_or_p_1_to_2_ohm_cm
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Chemically cleaned and etched (recipe not stated)
    EVENT SacrificialOxide KIND other TIMING assumed             # Dry oxidation at 1050 °C to 200 nm
    EVENT Strip KIND etch TIMING assumed                         # Oxide removed in HF, rinsed in deionized water, dried
    EVENT Store KIND storage TIMING assumed                      # Time between drying and reoxidation
    RUN AirExposure DURATION 3600 TEMP 23->23 AMBIENT mix:O2=0.21,N2=0.79 TIMING assumed VARY duration 600..604800
    EVENT Unload KIND other TIMING assumed                       # End of exposure
    EVENT Ellipsometry KIND measurement TIMING assumed           # Ellipsometry at 546.1 nm, n = 1.46 assumed, measured rapidly
    EVENT XPS KIND measurement TIMING assumed                    # XPS, Mg Kα, AEI ES-100: Si(2p) shift δ, intensity ratio R, linewidths, O(1s)/Si(2p)
}

(100), dry O2 at 100 to 700 °C, about 30 min

# (100), dry O2 at 100 to 700 °C, about 30 min
SAMPLE RF_100_dry_o2_100_700 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_or_p_1_to_2_ohm_cm
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Chemically cleaned and etched (recipe not stated)
    EVENT SacrificialOxide KIND other TIMING assumed             # Dry oxidation at 1050 °C to 200 nm
    EVENT Strip KIND etch TIMING assumed                         # Oxide removed in HF, rinsed in deionized water, dried
    EVENT Store KIND storage TIMING assumed                      # Time between drying and reoxidation
    RUN Oxidation DURATION 1800 TEMP 400->400 AMBIENT dry_O2 TIMING bound VARY duration 900..3600 VARY T_hold 100..700
    EVENT Unload KIND other TIMING assumed                       # Removal from the furnace and cooling
    EVENT Ellipsometry KIND measurement TIMING assumed           # Ellipsometry at 546.1 nm, n = 1.46 assumed, measured rapidly
    EVENT XPS KIND measurement TIMING assumed                    # XPS, Mg Kα, AEI ES-100: Si(2p) shift δ, intensity ratio R, linewidths, O(1s)/Si(2p)
}

(100), boiling H2O, HNO3 or H2O2 (30%), 1 h

# (100), boiling H2O, HNO3 or H2O2 (30%), 1 h
SAMPLE RF_100_boiling {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_or_p_1_to_2_ohm_cm
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Chemically cleaned and etched (recipe not stated)
    EVENT SacrificialOxide KIND other TIMING assumed             # Dry oxidation at 1050 °C to 200 nm
    EVENT Strip KIND etch TIMING assumed                         # Oxide removed in HF, rinsed in deionized water, dried
    EVENT Store KIND storage TIMING assumed                      # Time between drying and reoxidation
    RUN ChemicalOxidation DURATION 3600 TEMP 100->100 AMBIENT steam TIMING stated
    EVENT Unload KIND other TIMING assumed                       # End of exposure
    EVENT Ellipsometry KIND measurement TIMING assumed           # Ellipsometry at 546.1 nm, n = 1.46 assumed, measured rapidly
    EVENT XPS KIND measurement TIMING assumed                    # XPS, Mg Kα, AEI ES-100: Si(2p) shift δ, intensity ratio R, linewidths, O(1s)/Si(2p)
}

Boiling nitric acid and hydrogen peroxide give the same XPS data as boiling water (PDF p. 5); our history can carry only the water.

(100), dry O2 at 850 °C, thinnest film (about 1.1 nm)

# (100), dry O2 at 850 °C, thinnest film (about 1.1 nm)
SAMPLE RF_100_850_thinnest {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_or_p_1_to_2_ohm_cm
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Chemically cleaned and etched (recipe not stated)
    EVENT SacrificialOxide KIND other TIMING assumed             # Dry oxidation at 1050 °C to 200 nm
    EVENT Strip KIND etch TIMING assumed                         # Oxide removed in HF, rinsed in deionized water, dried
    EVENT Store KIND storage TIMING assumed                      # Time between drying and reoxidation
    RUN Oxidation850 DURATION 60 TEMP 850->850 AMBIENT dry_O2 TIMING assumed VARY duration 10..1800
    EVENT Unload KIND other TIMING assumed                       # Removal from the furnace and cooling
    EVENT Ellipsometry KIND measurement TIMING assumed           # Ellipsometry at 546.1 nm, n = 1.46 assumed, measured rapidly
    EVENT XPS KIND measurement TIMING assumed                    # XPS, Mg Kα, AEI ES-100: Si(2p) shift δ, intensity ratio R, linewidths, O(1s)/Si(2p)
}

(100), O2/N2 at 850 °C, then N2 at 850 °C for 10 to 30 min

# (100), O2/N2 at 850 °C, then N2 at 850 °C for 10 to 30 min
SAMPLE RF_100_850_o2n2_annealed {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_or_p_1_to_2_ohm_cm
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Chemically cleaned and etched (recipe not stated)
    EVENT SacrificialOxide KIND other TIMING assumed             # Dry oxidation at 1050 °C to 200 nm
    EVENT Strip KIND etch TIMING assumed                         # Oxide removed in HF, rinsed in deionized water, dried
    EVENT Store KIND storage TIMING assumed                      # Time between drying and reoxidation
    RUN OxidationMix DURATION 300 TEMP 850->850 AMBIENT mix:O2=0.2,N2=0.8 TIMING assumed VARY duration 30..1800
    RUN Anneal DURATION 1200 TEMP 850->850 AMBIENT inert_N2 TIMING range VARY duration 600..1800
    EVENT Unload KIND other TIMING assumed                       # Removal from the furnace and cooling
    EVENT Ellipsometry KIND measurement TIMING assumed           # Ellipsometry at 546.1 nm, n = 1.46 assumed, measured rapidly
    EVENT XPS KIND measurement TIMING assumed                    # XPS, Mg Kα, AEI ES-100: Si(2p) shift δ, intensity ratio R, linewidths, O(1s)/Si(2p)
}

(111), 23 °C in air

# (111), 23 °C in air
SAMPLE RF_111_rt_air {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_or_p_1_to_2_ohm_cm
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Chemically cleaned and etched (recipe not stated)
    EVENT SacrificialOxide KIND other TIMING assumed             # Dry oxidation at 1050 °C to 200 nm
    EVENT Strip KIND etch TIMING assumed                         # Oxide removed in HF, rinsed in deionized water, dried
    EVENT Store KIND storage TIMING assumed                      # Time between drying and reoxidation
    RUN AirExposure DURATION 3600 TEMP 23->23 AMBIENT mix:O2=0.21,N2=0.79 TIMING assumed VARY duration 600..604800
    EVENT Unload KIND other TIMING assumed                       # End of exposure
    EVENT Ellipsometry KIND measurement TIMING assumed           # Ellipsometry at 546.1 nm, n = 1.46 assumed, measured rapidly
    EVENT XPS KIND measurement TIMING assumed                    # XPS, Mg Kα, AEI ES-100: Si(2p) shift δ, intensity ratio R, linewidths, O(1s)/Si(2p)
}

(111), dry O2 at 600 °C

# (111), dry O2 at 600 °C
SAMPLE RF_111_600_dry_o2 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_or_p_1_to_2_ohm_cm
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Chemically cleaned and etched (recipe not stated)
    EVENT SacrificialOxide KIND other TIMING assumed             # Dry oxidation at 1050 °C to 200 nm
    EVENT Strip KIND etch TIMING assumed                         # Oxide removed in HF, rinsed in deionized water, dried
    EVENT Store KIND storage TIMING assumed                      # Time between drying and reoxidation
    RUN Oxidation600 DURATION 1800 TEMP 600->600 AMBIENT dry_O2 TIMING assumed VARY duration 300..7200
    EVENT Unload KIND other TIMING assumed                       # Removal from the furnace and cooling
    EVENT Ellipsometry KIND measurement TIMING assumed           # Ellipsometry at 546.1 nm, n = 1.46 assumed, measured rapidly
    EVENT XPS KIND measurement TIMING assumed                    # XPS, Mg Kα, AEI ES-100: Si(2p) shift δ, intensity ratio R, linewidths, O(1s)/Si(2p)
}

(111), O2 at 850 °C

# (111), O2 at 850 °C
SAMPLE RF_111_850_dry_o2 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_or_p_1_to_2_ohm_cm
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Chemically cleaned and etched (recipe not stated)
    EVENT SacrificialOxide KIND other TIMING assumed             # Dry oxidation at 1050 °C to 200 nm
    EVENT Strip KIND etch TIMING assumed                         # Oxide removed in HF, rinsed in deionized water, dried
    EVENT Store KIND storage TIMING assumed                      # Time between drying and reoxidation
    RUN Oxidation850b DURATION 60 TEMP 850->850 AMBIENT dry_O2 TIMING assumed VARY duration 10..1800
    EVENT Unload KIND other TIMING assumed                       # Removal from the furnace and cooling
    EVENT Ellipsometry KIND measurement TIMING assumed           # Ellipsometry at 546.1 nm, n = 1.46 assumed, measured rapidly
    EVENT XPS KIND measurement TIMING assumed                    # XPS, Mg Kα, AEI ES-100: Si(2p) shift δ, intensity ratio R, linewidths, O(1s)/Si(2p)
}

The programs the predictor ran on these histories: experiments/deal_qss/two_equilibria.isl.template, experiments/vitkavage_dit/oxide_growth.isl.template, scripts/search_growth.py (structure generated from the grammar), scripts/search_trap_density.py (structure generated from the grammar).

The model itself, experiments/si_oxide_gradient/reaction_diffusion.isl.template, as it is written. Every equation the simulation uses is in this text; the runtime holds no physics.

# Exploratory Si -> SiOx -> SiO2 composition gradient on a fixed one-dimensional slab.
# All transport and reaction coefficients below are HYPOTHESES, not fitted or computed.
# Motivation for resolving Si(0)...Si(IV): Himpsel et al., PRB 38, 6084 (1988),
# doi:10.1103/PhysRevB.38.6084. That paper does not supply these kinetic coefficients.
#
# S0...S4 are fractions of silicon sites in each formal oxidation state.
# M is mobile O2 molecules per silicon site; B is bound oxygen in O2 equivalents
# per silicon site. Each oxidation-state increment binds 1/4 O2 per Si, assuming
# bridging oxygen. Thus O/Si = (S1 + 2 S2 + 3 S3 + 4 S4)/2 = 2 B.
# B is a redundant oxygen ledger, checked against the oxidation-state fields.
# Gas_ledger + integral(M) + integral(B) is conserved; negative Gas_ledger means
# oxygen entered from the atmosphere. Silicon sites are conserved separately.
# The coordinate is fixed: volume expansion, strain, orientation, charge states,
# reverse reactions, hydrogen chemistry and atomistic structure are not represented.
SAMPLE Gradient {{ FAMILY: Si_Planar }}
GRID z {{ UNIT: cm; FROM: 0; TO: {length_cm}; CELLS: {cells} }}
FIELD S0 {{ UNIT: 1; GRID: z; INITIAL: {initial_si}; MIN: 0; MAX: 1 }}
FIELD S1 {{ UNIT: 1; GRID: z; INITIAL: 0; MIN: 0; MAX: 1 }}
FIELD S2 {{ UNIT: 1; GRID: z; INITIAL: 0; MIN: 0; MAX: 1 }}
FIELD S3 {{ UNIT: 1; GRID: z; INITIAL: 0; MIN: 0; MAX: 1 }}
FIELD S4 {{ UNIT: 1; GRID: z; INITIAL: {initial_oxide}; MIN: 0; MAX: 1 }}
FIELD M {{ UNIT: 1; GRID: z; INITIAL: 0; MIN: 0; MAX: 1 }}
FIELD B {{ UNIT: 1; GRID: z; INITIAL: {initial_oxide}; MIN: 0; MAX: 1 }}
STATE Gas_ledger {{ UNIT: cm; INITIAL: 0; MIN: -1; MAX: 1 }}
CONTROL T {{ UNIT: K }}
CONTROL p_O2 {{ UNIT: atm }}
PARAMETER k_B {{ VALUE: 8.617333262e-5; UNIT: eV K^-1; STATUS: constant }}
PARAMETER T_ref {{ VALUE: 1273.15; UNIT: K; STATUS: constant }}
PARAMETER p_ref {{ VALUE: 1; UNIT: atm; STATUS: constant }}
PARAMETER initial_front {{ VALUE: {initial_front_cm}; UNIT: cm; STATUS: hypothesis }}
PARAMETER seed_width {{ VALUE: 1.0e-12; UNIT: cm; STATUS: hypothesis }}
PARAMETER D_si {{ VALUE: 1.0e-14; UNIT: cm^2 s^-1; STATUS: hypothesis }}
PARAMETER D_oxide {{ VALUE: 1.0e-11; UNIT: cm^2 s^-1; STATUS: hypothesis }}
PARAMETER E_D {{ VALUE: 1.2; UNIT: eV; STATUS: hypothesis }}
PARAMETER k0 {{ VALUE: 80; UNIT: s^-1; STATUS: hypothesis }}
PARAMETER k1 {{ VALUE: 60; UNIT: s^-1; STATUS: hypothesis }}
PARAMETER k2 {{ VALUE: 40; UNIT: s^-1; STATUS: hypothesis }}
PARAMETER k3 {{ VALUE: 20; UNIT: s^-1; STATUS: hypothesis }}
PARAMETER E_reaction {{ VALUE: 1.2; UNIT: eV; STATUS: hypothesis }}
PARAMETER surface_speed {{ VALUE: 1.0e-3; UNIT: cm s^-1; STATUS: hypothesis }}
PARAMETER mobile_at_1atm {{ VALUE: 1.0e-5; UNIT: 1; STATUS: hypothesis }}
PARAMETER N_sites {{ VALUE: 5.0e22; UNIT: cm^-3; STATUS: hypothesis }}
QUANTITY thermal_D {{ UNIT: 1; EQUATION: thermal_D = exp(E_D / k_B * (1 / T_ref - 1 / T)) }}
QUANTITY thermal_k {{ UNIT: 1; EQUATION: thermal_k = exp(E_reaction / k_B * (1 / T_ref - 1 / T)) }}
QUANTITY gas_flux {{ UNIT: cm s^-1; EQUATION: gas_flux = surface_speed * (mobile_at_1atm * p_O2 / p_ref - left(M)) }}
CONTROL_TRAJECTORY History {{
{runs}
}}
OPERATOR OxygenTransport : Transport {{
    FLUX: J(M) = -(D_si + (D_oxide - D_si) * S4) * thermal_D * grad(M)
    BOUNDARY: M AT left FLUX = gas_flux
    EQUATION: d(Gas_ledger)/dt = -gas_flux
    CONSERVATION: Gas_ledger + integral(M) = const
}}
# These sequential steps are a coarse-grained kinetic hypothesis, not elementary
# reactions or charges measured on individual atoms.
OPERATOR SequentialOxidation : OxideGrowth {{
    EQUATION: d(S0)/dt = -thermal_k * k0 * M * S0
    EQUATION: d(S1)/dt = thermal_k * M * (k0 * S0 - k1 * S1)
    EQUATION: d(S2)/dt = thermal_k * M * (k1 * S1 - k2 * S2)
    EQUATION: d(S3)/dt = thermal_k * M * (k2 * S2 - k3 * S3)
    EQUATION: d(S4)/dt = thermal_k * k3 * M * S3
    EQUATION: d(B)/dt = 0.25 * thermal_k * M * (k0 * S0 + k1 * S1 + k2 * S2 + k3 * S3)
    EQUATION: d(M)/dt = -0.25 * thermal_k * M * (k0 * S0 + k1 * S1 + k2 * S2 + k3 * S3)
    CONSERVATION: integral(S0) + integral(S1) + integral(S2) + integral(S3) + integral(S4) = const
    CONSERVATION: integral(M) + integral(B) = const
}}
OBSERVATION_MODEL BoundO {{ TARGET: Bound_oxygen; UNIT: cm^-2; EQUATION: Bound_oxygen = 2 * N_sites * integral(B) }}
OBSERVATION_MODEL MobileO {{ TARGET: Mobile_oxygen; UNIT: cm^-2; EQUATION: Mobile_oxygen = 2 * N_sites * integral(M) }}
OBSERVATION_MODEL GasO {{ TARGET: Oxygen_from_gas; UNIT: cm^-2; EQUATION: Oxygen_from_gas = -2 * N_sites * Gas_ledger }}
OBSERVATION_MODEL Suboxides {{ TARGET: Suboxide_sites; UNIT: cm^-2; EQUATION: Suboxide_sites = N_sites * (integral(S1) + integral(S2) + integral(S3)) }}

Our simulation against the paper

1 off, 18 not modelled of 19 numbers. Tolerance is stated per row; nothing was fitted for this page.

Aligning the simulation: what the unstated things would have to be

Every step whose timing or temperature the paper leaves open carries a range in the history above (VARY). scripts/align_study.py searched those ranges against the paper's numbers through the same predictor, first one unknown at a time, then all together. No parameter a program declares fitted was touched. There are no held-out samples here: the unknowns were chosen on the same numbers they are scored on, so the aligned score is an upper bound, not a test.

Together: AirExposure duration 3600 s (was 3600); Oxidation duration 1800 s (was 1800); Oxidation T hold 400 °C (was 400); Oxidation850 duration 10 s (was 60); OxidationMix duration 300 s (was 300); Anneal duration 1200 s (was 1200); Oxidation600 duration 1800 s (was 1800); Oxidation850b duration 60 s (was 60).

As reproduced: 0 of 19 within tolerance, median error 80.6%. Aligned: 0 of 19 within tolerance, median error 60.0%.

What the search could test. The VARY ranges are the room-temperature exposure (10 min to 7 days), the 100-700 °C group's time and temperature, the 850 °C oxidation times and the anneal time. Only one number on the page has a program behind it: the thinnest oxide at 850 °C, about 1.1 nm. Every transition-region row is “no program”, so the search has one number to choose from, chooses and scores on it, and the result is an upper bound, not a test. Every other unknown is flat: no row it touches has a program. As reproduced (1 min at 850 °C) the thin-oxide program gives 1.99 nm against 1.1 nm (+81%); the search takes the shortest time it allows, 10 s, which gives 1.76 nm (+60%). 0 of 19 numbers are within tolerance before and after.

The thin-oxide program cannot make a 1.1 nm film at 850 °C. It returns 1.99 nm after one minute, 1.76 nm after 10 s and 1.72 nm after 1 s (its fitted start stands in for fast initial growth, and the 23 °C and 100 °C histories also return 1.71 nm, against the paper's < 1.3 nm). No oxidation time in the range searched brings it within 10% of 1.1 nm. The paper's thinnest 850 °C film is about 0.6 nm thinner than the program's floor; whether that floor is an ellipsometry convention (n = 1.46 overstates thin films, PDF p. 9) or a real difference is open.

The candidate gradient model, an unvalidated hypothesis. isl_harness/si_oxide_gradient.py with experiments/si_oxide_gradient/reaction_diffusion.isl.template resolves Si(0) to Si(IV) site fractions in a fixed slab. It was run read-only on histories for these samples (160 cells over 4 nm, bare HF-etched start, and the template's 1.0 nm start for comparison), first with the template's values: k0..k3 = 80, 60, 40, 20 s⁻¹; mobile_at_1atm 1e-5; D_oxide 1e-11 cm²/s; D_si 1e-14 cm²/s; E_D = E_reaction = 1.2 eV, then with parameter values replaced in the program text in memory. Nothing in its files was changed and nothing below is fitted into it. Width is measured on the bound O/Si profile; suboxide sites and Si-Si bonds are integrals of its S1 to S3 fields (definitions in the study file).

With its own parameters the model does not match. It barely oxidizes: 0.0065 nm of SiO2-equivalent in 10 min at 850 °C from a bare surface, where the paper's films are at least 1.1 nm. Its oxygen dissolves deep into the silicon instead of reacting at a front, so 98% of its suboxide is Si+1 spread thinly over nanometres, with 1.9 × 10^14 Si-Si bonds cm⁻² against 0.8 × 10^15. Started from its default sharp 1.0 nm oxide, its 10-90% width is the grid spacing (0.02 nm). It does nothing at 23 to 300 °C, and it gives (111) exactly what it gives (100).

What its parameters would need to be (found by hand, not fitted into the model). Reaction rates about 100 times faster (k0 to k2 of 4000 to 8000 s⁻¹), a surface oxygen solubility 1000 times higher (1e-2 per site) with oxide diffusivity 1000 times lower (1e-14 cm²/s at 1000 °C), and a last step Si(III) → Si(IV) about 100 times slower than the others (k3 = 40 s⁻¹, against the template's 20 with k2 = 40). With those (the “(100) set”) it grows 0.5 nm in 1 min and 1.7 nm in 10 min at 850 °C, makes 8.1 × 10^14 Si-Si bonds cm⁻² (the paper's (100) value is 0.8 × 10^15), puts 82% of its suboxide in Si+3, and has a mean O/Si of 1.35 to 1.46 between its 10% and 90% points (the paper's first layer is SiO1.4). Its width is 0.28 nm (10-90%) or 0.47 nm (2-98%), narrower than the paper's 0.75 nm. Making it wider (slower reactions, or slower k3) raises its Si-Si bonds in step: at 0.86 nm (2-98%) it has 1.36 × 10^15. In this model, width and Si-Si count cannot be set separately to the paper's (100) pair. They can to the (111) pair: the “(111) set”, with k3 four times slower, gives 0.86 nm and 1.36 × 10^15 against the paper's 1.0 nm and 1.4 × 10^15. So the orientation effect would need an orientation-dependent last oxidation step; the template has no orientation term.

Processing invariance is a consequence of one assumption. With the rescaled parameters the width is the same at 600 and 850 °C, after 1 or 30 min, in 10% or pure O2 and after 30 min in N2 (all within 0.01 nm), which is the paper's central finding. That holds because the template gives diffusion and reaction the same activation energy (1.2 eV): with E_D = 1.8 eV the 2-98% width moves from 0.15 nm at 600 °C to 0.33 nm at 850 °C. The paper's invariance from 23 to 850 °C is evidence for equal activation energies in this model, but it cannot reach 23 °C at all: with 1.2 eV referenced to 1000 °C it adds 0.002 nm in 30 min at 300 °C and nothing at 23 °C, while the paper has films up to 1.3 nm at room temperature with the same transition region.

Boiling water and acids. The gradient model refuses steam (it has no water chemistry), so the boiling-solution case has no gradient number.

Heating and cooling transitions (section below): in all four scenarios 0 of 19 numbers are within tolerance and none moves by more than 2%; the median error goes from 80.6% to 80.8% (fast cooling) or 81.6% (slow cooling), because extra time hot only thickens the 850 °C film. The transition-region rows stay “no program”. In the gradient model with the rescaled parameters, extra time at temperature does not change the width either (the 1 and 30 min rows of the table).

1 off, 18 not modelled of 19 numbers with the aligned settings.

What alignment cannot fix: no program in the predictor reports a transition-region width, a layer composition or a Si-Si bond count (category (c) of the brief). A program for this paper would need: Si oxidation-state populations against depth (the gradient model has these); an orientation term (the paper's one effect); a mechanism for oxidation at room temperature and in liquid water and acids; and an XPS observation model (escape depths 2.5 and 2.3 nm, Gaussian lines of 1.3 and 1.8 eV, δ = 2.2x eV) so that the program's profile can be turned into the δ-against-R curves of Figures 5 to 7, which are what was measured. Without the last, a model's 10-90% width and the paper's layer-count width are different quantities, and any comparison carries a definition error of about one 0.25 nm layer.

The candidate gradient model, as written, misses on every count (oxide grown, Si-Si bonds, suboxide distribution, orientation, room temperature). Hand-chosen values bring the (100) Si-Si bonds and first-layer composition, and the (111) width and bonds, into line, at the cost of a (100) width about 40% narrower than printed. Those values are a statement of what the model would need, not a calibration: they were chosen by looking at the paper's numbers, and nothing was held out.

The thin-oxide program's fitted start (about 1.7 nm) is above the paper's thinnest 850 °C film (1.1 nm) and its room-temperature films (< 1.3 nm).

What our language and ontology cannot yet say

• An XPS observation statement. The paper measures Si(2p) shifts, intensity ratios and linewidths, not a profile. An OBSERVE XPS LINE Si2p TAKEOFF <deg> LAMBDA_OXIDE 2.5 nm LAMBDA_SI 2.3 nm that turns a simulated profile into δ and R would let a model be scored on the measured Figures 5 to 7 rather than on the authors' 0.25 nm-layer fit.
• Liquid and chemical-oxidant ambients. Room-temperature water, boiling water, concentrated HNO3 and 30% H2O2 are half of the paper's oxidants. AMBIENT liquid:H2O or liquid:HNO3 (with temperature) would let them be written; today boiling water is approximated as steam and the acids cannot be written at all.
• An etch that removes a layer. The 200 nm sacrificial oxide is grown and stripped in HF before every film. It had to be an EVENT because the language cannot take the oxide off again; a STRIP oxide or ETCH TO 0 nm would let the whole history be simulated, including what the first oxidation does to the silicon surface.
• A group of samples with one pooled result. The width is fitted to all (100) films together and stated to be the same for each. A result attached to a group of histories (RESULT width 0.75 nm OVER SAMPLES 100_*), rather than repeated on each, would say what was measured.
• Ranges of temperature as an unknown of the sample group. “100 to 700 °C” is a spread of samples, not an uncertainty about one; VARY T_hold 100..700 searches it as if it were one unknown value. A way to say “one history per value in this range” would match what was done.
• Adsorbed contamination. A carbon layer of 0.2-0.6 nm on every surface (PDF p. 2) changes the XPS intensities; a sample field for an adsorbate layer would let an observation model account for it.

With heating and cooling transitions

No paper we hold states how its wafers heated up or cooled down. The project owner specified scenarios for one Vitkavage wafer (isl_harness/vitkavage_transitions.py); isl_harness/thermal_transitions.py applies the same numbers to every sample here: a heat-up in nitrogen before the first furnace step (a hot push of 1 to 5 min, or a cold-furnace ramp of 60 to 120 min), the owner's radiative cooling knots after the last furnace step or after the paper's own pull (fast, or every time multiplied by 5), and ramps around an anneal at 300 to 500 °C. The paper's own steps are kept as written. All transitions are assumptions, written in the history with TIMING assumed.

The paper's own conclusions

What we would like Emily to check

1. The paper's width is the number of 0.25 nm non-stoichiometric layers in its fit. Is it fair to compare it with a model's 10-90% (or 2-98%) width of O/Si, or does a comparison need the XPS forward model (escape depth, linewidths)?
2. The 0.8 and 1.4 × 10^15 Si-Si bonds cm⁻²: would you count them as (4 - n)/2 per Si in each layer, as we did for the model, or do they include the bonds to the substrate's last plane?
3. Later high-resolution work (Himpsel et al. 1988) resolved Si+1, Si+2 and Si+3 at this interface. Should this page be paired with such a paper for the suboxide fractions, since Raider and Flitsch print none?
4. Room-temperature films in air and water (< 1.3 nm) are said to have the same transition region as 850 °C films. Is that plausible, given that native oxide grows by a different mechanism?
5. The thinnest film at 850 °C is about 1.1 nm by ellipsometry with n = 1.46. The paper's own Figure 11 says n is higher in thin films, so is 1.1 nm an overestimate, and by how much?