Reproducing Stesmans and Afanas'ev 1996: Pb defects released from hydrogen and created by vacuum anneals

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/stesmans_1996.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

A. Stesmans and V. V. Afanas'ev, “Creation of Pb interface defects in thermal Si/SiO2 through annealing”, J. Phys.: Condens. Matter 8, L505-L509 (1996).

The paper the Quantum ESPRESSO calculation bears on most directly. It measures the Pb centre itself (the dangling bond with three silicon back-bonds that the 14-atom cluster models) after a full hydrogen passivation and after anneals that drive the hydrogen off, and it quotes the measured barriers for both directions: passivation in H2 with 1.66 eV and dissociation of PbH with 2.56 eV (Brower). It is also the source of the project's finding that vacuum anneals above about 640 °C create dangling bonds (ontology/findings.json, bonds-created). Nothing was scored against it before this page.

How well can this study be reproduced?

Moderate. The anneal series is stated precisely: a fresh, fully hydrogen-passivated sample for each temperature, 62 min in a diffusion-pumped vacuum (≤4×10⁻⁷ Torr), temperature to 0.3%. The oxidation is stated by temperature, pressure and thickness only (about 970 °C, 1.1 atm O2, about 42 nm), the passivation as about 40 min at 405 °C in 1.1 atm H2. Not stated: oxidation time, cooling, the clean, and any heat-up or cool-down of the anneals. The results exist as one figure; three values are printed in the text (N0 = 4.7×10¹², 12.3×10¹² after 968 °C, Nc = 7.6×10¹² at 960 °C) and the fitted kinetic parameters are given.

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. 3 same, 4 approximated, 5 assumed, 1 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.

Fresh sample, H2 405 °C, vacuum 520 °C 62 min

Simulated time in this history: 2 h 23 min 40 s.

Across the samples

Timing the paper does not give

• Oxidation time: not stated (about 42 nm at about 970 °C).
• Cooling after oxidation and after the passivation: gas, rate, end temperature not stated.
• Passivation: “∼40 min”; heat-up and cool-down not stated; for the cycled sample, the repassivation time is not stated at all.
• Vacuum anneals: 62 min hold stated; heat-up and cool-down of the slices not stated (in a diffusion-pumped vacuum a small slice heats by radiation).
• Time between passivation, anneal and ESR not stated.

What the second reading changed

• The project had no stored recipe and no dataset for this paper; SOURCE.md summarises the text and says Figure 1 was not digitized. The values in SOURCE.md agree with this reading.
• SOURCE.md says “Up to about 640 C the density recovers to the as-oxidized pool, 4.7e12”. The 4.7×10¹² is the authors' fit (N0) under the HPb-dissociation model, and the paper calls it “the natural Pb bath … found in the as-oxidized state” (p. L508); no as-oxidized measurement before passivation is shown.
• evaluations/atomistic/si_dangling_bond_hydrogen.json names this paper as giving the measured passivation and dissociation barriers. It quotes them (1.66 and 2.56 eV) from Brower 1988-1990, which the project does not hold; the paper's own fits are 2.63 eV with a 0.105 eV spread (fresh oxide) and 2.71 eV (cycled sample), both with Brower's prefactor 1.2×10¹² s⁻¹ adopted, not fitted.
• ontology/findings.json (bonds-created) scopes the creation to “(111), vacuum, 62 min above about 640 C”. The paper puts the onset of creation at about 640-660 °C and says the same happens in N2 and Ar.

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>.

Fresh sample, H2 405 °C, vacuum 520 °C 62 min

# Fresh sample, H2 405 °C, vacuum 520 °C 62 min
SAMPLE Stesmans_F520 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: p_type_10_ohm_cm_float_zone
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # “Appropriate cleaning” (not described)
    RUN Oxidation DURATION 1900 TEMP 970->970 AMBIENT dry_O2 TIMING assumed VARY duration 900..3600
    RUN Cool DURATION 600 TEMP 970->25 AMBIENT dry_O2 TIMING assumed VARY duration 60..3600
    RUN Passivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING bound
    RUN VacuumAnneal DURATION 3720 TEMP 520->520 AMBIENT vacuum TIMING stated
    EVENT ESR KIND measurement TIMING assumed                    # K-band ESR (20.6 GHz) at 4.3 K, B ∥ [111], against a Si:P standard
}

Fresh sample, H2 405 °C, vacuum 550 °C 62 min

# Fresh sample, H2 405 °C, vacuum 550 °C 62 min
SAMPLE Stesmans_F550 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: p_type_10_ohm_cm_float_zone
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # “Appropriate cleaning” (not described)
    RUN Oxidation DURATION 1900 TEMP 970->970 AMBIENT dry_O2 TIMING assumed VARY duration 900..3600
    RUN Cool DURATION 600 TEMP 970->25 AMBIENT dry_O2 TIMING assumed VARY duration 60..3600
    RUN Passivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING bound
    RUN VacuumAnneal DURATION 3720 TEMP 550->550 AMBIENT vacuum TIMING stated
    EVENT ESR KIND measurement TIMING assumed                    # K-band ESR (20.6 GHz) at 4.3 K, B ∥ [111], against a Si:P standard
}

Fresh sample, H2 405 °C, vacuum 575 °C 62 min

# Fresh sample, H2 405 °C, vacuum 575 °C 62 min
SAMPLE Stesmans_F575 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: p_type_10_ohm_cm_float_zone
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # “Appropriate cleaning” (not described)
    RUN Oxidation DURATION 1900 TEMP 970->970 AMBIENT dry_O2 TIMING assumed VARY duration 900..3600
    RUN Cool DURATION 600 TEMP 970->25 AMBIENT dry_O2 TIMING assumed VARY duration 60..3600
    RUN Passivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING bound
    RUN VacuumAnneal DURATION 3720 TEMP 575->575 AMBIENT vacuum TIMING stated
    EVENT ESR KIND measurement TIMING assumed                    # K-band ESR (20.6 GHz) at 4.3 K, B ∥ [111], against a Si:P standard
}

Fresh sample, H2 405 °C, vacuum 590 °C 62 min

# Fresh sample, H2 405 °C, vacuum 590 °C 62 min
SAMPLE Stesmans_F590 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: p_type_10_ohm_cm_float_zone
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # “Appropriate cleaning” (not described)
    RUN Oxidation DURATION 1900 TEMP 970->970 AMBIENT dry_O2 TIMING assumed VARY duration 900..3600
    RUN Cool DURATION 600 TEMP 970->25 AMBIENT dry_O2 TIMING assumed VARY duration 60..3600
    RUN Passivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING bound
    RUN VacuumAnneal DURATION 3720 TEMP 590->590 AMBIENT vacuum TIMING stated
    EVENT ESR KIND measurement TIMING assumed                    # K-band ESR (20.6 GHz) at 4.3 K, B ∥ [111], against a Si:P standard
}

Fresh sample, H2 405 °C, vacuum 620 °C 62 min

# Fresh sample, H2 405 °C, vacuum 620 °C 62 min
SAMPLE Stesmans_F620 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: p_type_10_ohm_cm_float_zone
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # “Appropriate cleaning” (not described)
    RUN Oxidation DURATION 1900 TEMP 970->970 AMBIENT dry_O2 TIMING assumed VARY duration 900..3600
    RUN Cool DURATION 600 TEMP 970->25 AMBIENT dry_O2 TIMING assumed VARY duration 60..3600
    RUN Passivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING bound
    RUN VacuumAnneal DURATION 3720 TEMP 620->620 AMBIENT vacuum TIMING stated
    EVENT ESR KIND measurement TIMING assumed                    # K-band ESR (20.6 GHz) at 4.3 K, B ∥ [111], against a Si:P standard
}

Fresh sample, H2 405 °C, vacuum 645 °C 62 min

# Fresh sample, H2 405 °C, vacuum 645 °C 62 min
SAMPLE Stesmans_F645 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: p_type_10_ohm_cm_float_zone
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # “Appropriate cleaning” (not described)
    RUN Oxidation DURATION 1900 TEMP 970->970 AMBIENT dry_O2 TIMING assumed VARY duration 900..3600
    RUN Cool DURATION 600 TEMP 970->25 AMBIENT dry_O2 TIMING assumed VARY duration 60..3600
    RUN Passivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING bound
    RUN VacuumAnneal DURATION 3720 TEMP 645->645 AMBIENT vacuum TIMING stated
    EVENT ESR KIND measurement TIMING assumed                    # K-band ESR (20.6 GHz) at 4.3 K, B ∥ [111], against a Si:P standard
}

Fresh sample, H2 405 °C, vacuum 665 °C 62 min

# Fresh sample, H2 405 °C, vacuum 665 °C 62 min
SAMPLE Stesmans_F665 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: p_type_10_ohm_cm_float_zone
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # “Appropriate cleaning” (not described)
    RUN Oxidation DURATION 1900 TEMP 970->970 AMBIENT dry_O2 TIMING assumed VARY duration 900..3600
    RUN Cool DURATION 600 TEMP 970->25 AMBIENT dry_O2 TIMING assumed VARY duration 60..3600
    RUN Passivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING bound
    RUN VacuumAnneal DURATION 3720 TEMP 665->665 AMBIENT vacuum TIMING stated
    EVENT ESR KIND measurement TIMING assumed                    # K-band ESR (20.6 GHz) at 4.3 K, B ∥ [111], against a Si:P standard
}

Above about 660 °C the paper finds new Pb created; a share above 1 is outside what any program can give.

Fresh sample, H2 405 °C, vacuum 750 °C 62 min

# Fresh sample, H2 405 °C, vacuum 750 °C 62 min
SAMPLE Stesmans_F750 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: p_type_10_ohm_cm_float_zone
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # “Appropriate cleaning” (not described)
    RUN Oxidation DURATION 1900 TEMP 970->970 AMBIENT dry_O2 TIMING assumed VARY duration 900..3600
    RUN Cool DURATION 600 TEMP 970->25 AMBIENT dry_O2 TIMING assumed VARY duration 60..3600
    RUN Passivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING bound
    RUN VacuumAnneal DURATION 3720 TEMP 750->750 AMBIENT vacuum TIMING stated
    EVENT ESR KIND measurement TIMING assumed                    # K-band ESR (20.6 GHz) at 4.3 K, B ∥ [111], against a Si:P standard
}

Above about 660 °C the paper finds new Pb created; a share above 1 is outside what any program can give.

Fresh sample, H2 405 °C, vacuum 900 °C 62 min

# Fresh sample, H2 405 °C, vacuum 900 °C 62 min
SAMPLE Stesmans_F900 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: p_type_10_ohm_cm_float_zone
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # “Appropriate cleaning” (not described)
    RUN Oxidation DURATION 1900 TEMP 970->970 AMBIENT dry_O2 TIMING assumed VARY duration 900..3600
    RUN Cool DURATION 600 TEMP 970->25 AMBIENT dry_O2 TIMING assumed VARY duration 60..3600
    RUN Passivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING bound
    RUN VacuumAnneal DURATION 3720 TEMP 900->900 AMBIENT vacuum TIMING stated
    EVENT ESR KIND measurement TIMING assumed                    # K-band ESR (20.6 GHz) at 4.3 K, B ∥ [111], against a Si:P standard
}

Above about 660 °C the paper finds new Pb created; a share above 1 is outside what any program can give.

Fresh sample, H2 405 °C, vacuum 968 °C 62 min

# Fresh sample, H2 405 °C, vacuum 968 °C 62 min
SAMPLE Stesmans_F968 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: p_type_10_ohm_cm_float_zone
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # “Appropriate cleaning” (not described)
    RUN Oxidation DURATION 1900 TEMP 970->970 AMBIENT dry_O2 TIMING assumed VARY duration 900..3600
    RUN Cool DURATION 600 TEMP 970->25 AMBIENT dry_O2 TIMING assumed VARY duration 60..3600
    RUN Passivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING bound
    RUN VacuumAnneal DURATION 3720 TEMP 968->968 AMBIENT vacuum TIMING stated
    EVENT ESR KIND measurement TIMING assumed                    # K-band ESR (20.6 GHz) at 4.3 K, B ∥ [111], against a Si:P standard
}

Above about 660 °C the paper finds new Pb created; a share above 1 is outside what any program can give.

Fresh sample, H2 405 °C, vacuum 1125 °C 62 min

# Fresh sample, H2 405 °C, vacuum 1125 °C 62 min
SAMPLE Stesmans_F1125 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: p_type_10_ohm_cm_float_zone
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # “Appropriate cleaning” (not described)
    RUN Oxidation DURATION 1900 TEMP 970->970 AMBIENT dry_O2 TIMING assumed VARY duration 900..3600
    RUN Cool DURATION 600 TEMP 970->25 AMBIENT dry_O2 TIMING assumed VARY duration 60..3600
    RUN Passivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING bound
    RUN VacuumAnneal DURATION 3720 TEMP 1125->1125 AMBIENT vacuum TIMING stated
    EVENT ESR KIND measurement TIMING assumed                    # K-band ESR (20.6 GHz) at 4.3 K, B ∥ [111], against a Si:P standard
}

Above about 660 °C the paper finds new Pb created; a share above 1 is outside what any program can give.

Cycled sample (968 °C 1 h first), H2 405 °C, vacuum 555 °C 62 min

# Cycled sample (968 °C 1 h first), H2 405 °C, vacuum 555 °C 62 min
SAMPLE Stesmans_C555 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: p_type_10_ohm_cm_float_zone
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # “Appropriate cleaning” (not described)
    RUN Oxidation DURATION 1900 TEMP 970->970 AMBIENT dry_O2 TIMING assumed VARY duration 900..3600
    RUN Cool DURATION 600 TEMP 970->25 AMBIENT dry_O2 TIMING assumed VARY duration 60..3600
    RUN Passivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING bound
    RUN Creation DURATION 3600 TEMP 968->968 AMBIENT vacuum TIMING stated
    RUN Repassivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING assumed
    RUN VacuumAnneal DURATION 3720 TEMP 555->555 AMBIENT vacuum TIMING stated
    EVENT ESR KIND measurement TIMING assumed                    # K-band ESR (20.6 GHz) at 4.3 K, B ∥ [111], against a Si:P standard
}

Cycled sample (968 °C 1 h first), H2 405 °C, vacuum 585 °C 62 min

# Cycled sample (968 °C 1 h first), H2 405 °C, vacuum 585 °C 62 min
SAMPLE Stesmans_C585 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: p_type_10_ohm_cm_float_zone
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # “Appropriate cleaning” (not described)
    RUN Oxidation DURATION 1900 TEMP 970->970 AMBIENT dry_O2 TIMING assumed VARY duration 900..3600
    RUN Cool DURATION 600 TEMP 970->25 AMBIENT dry_O2 TIMING assumed VARY duration 60..3600
    RUN Passivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING bound
    RUN Creation DURATION 3600 TEMP 968->968 AMBIENT vacuum TIMING stated
    RUN Repassivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING assumed
    RUN VacuumAnneal DURATION 3720 TEMP 585->585 AMBIENT vacuum TIMING stated
    EVENT ESR KIND measurement TIMING assumed                    # K-band ESR (20.6 GHz) at 4.3 K, B ∥ [111], against a Si:P standard
}

Cycled sample (968 °C 1 h first), H2 405 °C, vacuum 620 °C 62 min

# Cycled sample (968 °C 1 h first), H2 405 °C, vacuum 620 °C 62 min
SAMPLE Stesmans_C620 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: p_type_10_ohm_cm_float_zone
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # “Appropriate cleaning” (not described)
    RUN Oxidation DURATION 1900 TEMP 970->970 AMBIENT dry_O2 TIMING assumed VARY duration 900..3600
    RUN Cool DURATION 600 TEMP 970->25 AMBIENT dry_O2 TIMING assumed VARY duration 60..3600
    RUN Passivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING bound
    RUN Creation DURATION 3600 TEMP 968->968 AMBIENT vacuum TIMING stated
    RUN Repassivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING assumed
    RUN VacuumAnneal DURATION 3720 TEMP 620->620 AMBIENT vacuum TIMING stated
    EVENT ESR KIND measurement TIMING assumed                    # K-band ESR (20.6 GHz) at 4.3 K, B ∥ [111], against a Si:P standard
}

Cycled sample (968 °C 1 h first), H2 405 °C, vacuum 700 °C 62 min

# Cycled sample (968 °C 1 h first), H2 405 °C, vacuum 700 °C 62 min
SAMPLE Stesmans_C700 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: p_type_10_ohm_cm_float_zone
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # “Appropriate cleaning” (not described)
    RUN Oxidation DURATION 1900 TEMP 970->970 AMBIENT dry_O2 TIMING assumed VARY duration 900..3600
    RUN Cool DURATION 600 TEMP 970->25 AMBIENT dry_O2 TIMING assumed VARY duration 60..3600
    RUN Passivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING bound
    RUN Creation DURATION 3600 TEMP 968->968 AMBIENT vacuum TIMING stated
    RUN Repassivation DURATION 2400 TEMP 405->405 AMBIENT pure_H2 TIMING assumed
    RUN VacuumAnneal DURATION 3720 TEMP 700->700 AMBIENT vacuum TIMING stated
    EVENT ESR KIND measurement TIMING assumed                    # K-band ESR (20.6 GHz) at 4.3 K, B ∥ [111], against a Si:P standard
}

The programs the predictor ran on these histories: experiments/atomistic/hydrogen_passivation_equilibrium.isl.template, 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/atomistic/hydrogen_passivation_equilibrium.isl.template, as it is written. Every equation the simulation uses is in this text; the runtime holds no physics.

# ==============================================================================
# ISL MODEL: HOW FAR HYDROGEN CAN CAP SILICON DANGLING BONDS AT EQUILIBRIUM
#
# Si* + 1/2 H2 <-> Si-H. The energy of the reaction is a COMPUTED parameter: a Quantum ESPRESSO
# calculation on a small cluster (atomistic/calcs/si_dangling_bond_hydrogen.json), not a measurement
# and not a fit. With the free energy of hydrogen gas it gives the equilibrium constant, and so the
# share of dangling bonds that hydrogen at a given temperature and pressure would leave uncapped if
# the anneal were long enough to reach equilibrium.
#
# What this is for: a bound. The trap-density program has a fitted share of sites that the
# hydrogen anneal does not remove. If equilibrium already leaves that share, the residue is
# thermodynamic; if equilibrium leaves far less, the residue is kinetic or is another defect.
# What it is not: a rate. How fast equilibrium is approached is the hypothesis k_eq below.
#
# Used by isl_harness/predict.py only when computed parameters are switched on (ISL_USE_COMPUTED=1
# or --computed). Fields in {{braces}} are filled from evaluations/atomistic/<id>.json.
# ==============================================================================
SAMPLE {sample_id} {{
    FAMILY: Si_Planar
}}
# Fractions of the sites: uncapped (electrically active) and capped by hydrogen.
STATE N_free {{ UNIT: 1; INITIAL: 1; MIN: 0; MAX: 1.000001 }}
STATE N_capped {{ UNIT: 1; INITIAL: 0; MIN: 0; MAX: 1.000001 }}
CONTROL T {{ UNIT: K }}
CONTROL p_H2 {{ UNIT: atm }}
PARAMETER dE_cap {{ VALUE: {dE_cap}; UNIT: eV; STATUS: computed; SOURCE: {source} }}
# Zero-point energy of the Si-H bond (one stretch, two bends) less half that of H2. Recalled from vibrational frequencies
# (about 2100 and 630 cm^-1 for Si-H, 4400 cm^-1 for H2), not from a source in the library and not yet computed (ph.x can).
PARAMETER dZPE {{ VALUE: 0.07; UNIT: eV; STATUS: hypothesis }}
# Hydrogen gas as an ideal diatomic: standard entropy 130.7 J/mol/K at 298.15 K and 1 atm, heat capacity 3.5 k_B.
# Textbook values, recalled, not from a source in the library.
PARAMETER S_ref {{ VALUE: 1.3546e-3; UNIT: eV K^-1; STATUS: hypothesis }}
PARAMETER c_p {{ VALUE: 3.0161e-4; UNIT: eV K^-1; STATUS: hypothesis }}
PARAMETER T_ref {{ VALUE: 298.15; UNIT: K; STATUS: constant }}
PARAMETER p_ref {{ VALUE: 1.0; UNIT: atm; STATUS: constant }}
PARAMETER k_B {{ VALUE: 8.617333262e-5; UNIT: eV K^-1; STATUS: constant }}
# How fast equilibrium is approached: assumed fast against any anneal. The answer is the equilibrium, not the path.
PARAMETER k_eq {{ VALUE: 1.0; UNIT: s^-1; STATUS: hypothesis }}
# Free energy of one H2 molecule at 1 atm above its energy at rest: enthalpy 3.5 k_B T less T times the entropy.
QUANTITY mu_H2 {{ UNIT: eV; EQUATION: mu_H2 = c_p * T - T * (S_ref + c_p * log(T / T_ref)) }}
QUANTITY dG {{ UNIT: eV; EQUATION: dG = dE_cap + dZPE - 0.5 * mu_H2 }}
QUANTITY K_eq {{ UNIT: 1; EQUATION: K_eq = exp(-dG / (k_B * T)) }}
CONTROL_TRAJECTORY {trajectory_id} {{
    RUN PostMetalAnneal DURATION 1800 TEMP 400->400 AMBIENT forming_gas_H2
}}
# Capping at a rate proportional to the square root of the hydrogen pressure; uncapping at the rate detailed balance requires.
OPERATOR F_HydrogenCapping : Passivation {{
    EQUATION: d(N_free)/dt = -k_eq * (sqrt(p_H2 / p_ref) * N_free - N_capped / K_eq)
    EQUATION: d(N_capped)/dt = k_eq * (sqrt(p_H2 / p_ref) * N_free - N_capped / K_eq)
    CONSERVATION: N_free + N_capped = const
}}
OBSERVATION_MODEL Obs_Uncapped {{
    TARGET: Normalized_Pb
    UNIT: 1
    EQUATION: Normalized_Pb = N_free
}}

Our simulation against the paper

8 within, 1 near, 7 off of 16 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. The unknowns were chosen on F520, F550, F575, F590, F620, F645 only; every other number is a test they played no part in.

Together: Oxidation duration 1900 s (was 1900); Cool duration 600 s (was 600).

As reproduced: 8 of 16 within tolerance, median error 12.2%. Aligned: 8 of 16 within tolerance, median error 12.2%. On the held-out samples only: 2 of 9 within tolerance, median error 47.2% as reproduced, 2 of 9 within tolerance, median error 47.2% aligned.

Choices of program or material property, each scored on its own and on top of the aligned history:

Two unknowns were declared: the oxidation time (not stated; 42 nm at about 970 °C) and the cool after oxidation. They were chosen on the six fresh samples annealed at 520 to 645 °C, where the paper attributes the Pb to dissociation of hydrogen; the fresh samples at 665 to 1125 °C (creation) and the four cycled points are the test. Two variants add a heat-up and a cool-down in vacuum around every vacuum anneal (1 and 10 min each), which the paper does not state.

As reproduced: 8 of 16 within tolerance (median error 12.2%). Aligned: 8 of 16 (12.2%). On the held-out rows: 2 of 9 before and after (47.2%).

The history unknowns do not matter here. The oxidation time sets the thickness (42.5 nm at the assumed 1900 s, within 1%) and nothing else on the page: the share of uncapped bonds is reset by the hydrogen anneal, and the vacuum anneal decides it. The cool after oxidation is flat. Ramps of 1 or 10 min around each vacuum anneal move the shares by at most 0.01 (10 min ramps: 8 of 16, median 12.8%). The anneals were 62 min at a temperature known to 0.3%; nothing the paper leaves open competes with that.

Rows chosen on are not fitted. No parameter of the program that produces the shares is fitted to anything, and the alignment had nothing to tune that reaches them, so the six dissociation rows are as much a test as the others: 5 of 6 within 10%, the 590 °C point 15% low (0.63 against 0.745). For comparison, outside the predictor: the paper's own fit (Ed 2.63 eV, σ 0.105 eV, 1.2×10¹² s⁻¹) gives 0.17, 0.39, 0.62, 0.74, 0.91, 0.98 at 520 to 645 °C. Inside it, the trap-density program carries Brower's 2.56 eV without a spread and gives 0.21, 0.61, 0.94, 0.99, 1.00, 1.00, too steep, which is why the paper introduced the spread.

What the tests show. Above 660 °C the program stays at 1 and the paper climbs to 3.5 times N0 at 1125 °C: creation, 33 to 72% off. The cycled sample is held to its own plateau (12.3×10¹²) and rises later and more steeply than the fresh ones (Ed 2.71 eV in the paper): the program gives it the fresh curve, 70% high at 555 °C and 28% high at 585 °C, within 10% at 620 and 700 °C. The program's apparent 1.33 eV is too shallow for this sample, which no spread of barriers flattens.

Heating and cooling transitions (section below). None of the four assumed heat-up and cooling scenarios moves any of the 16 numbers by more than 2%: the transitions are applied around the oxidation and in nitrogen, and the hydrogen anneal resets the share before the vacuum anneal that decides it.

2 within, 7 off of 9 numbers with the aligned settings (the samples used to choose the unknowns are left out).

What alignment cannot fix. One release barrier where the paper needs a spread. The trap-density program, which is the predictor's model for interface states, now gives hydrogen back at Brower's single barrier (2.56 eV, 1.2×10¹² s⁻¹): its Pb share starts at the right temperature (0.21 against 0.17 at 520 °C) and rises too steeply (0.61 against 0.34 at 550 °C, 0.94 against 0.55 at 575 °C). The paper fits the same data with a Gaussian spread of release barriers, σ = 0.105 eV about 2.63 eV; the program has one barrier and no state distributed over a parameter that could carry σ. The equilibrium program, which is scored here, gives the bonds back at a rate set by a placeholder (k_eq = 1 s⁻¹) that was written to say “fast” and is not a measured or computed rate.

No program creates dangling bonds. Above about 660 °C in vacuum (and, the paper says, in N₂ or Ar) new Pb appears, 7.6×10¹² cm⁻² at 960 °C, and only reoxidation removes it. The trap program's relaxation moves the density toward a fitted floor of 4.8×10¹⁰ cm⁻², two orders of magnitude below; the equilibrium program works on shares of a fixed population. A creation operator (irreversible, oxygen-free, thermally activated, with reoxidation as its only reverse) is needed; Hung 1987's rise in trap density during nitrogen at 1050 °C may be the same effect.

Spin density is not an observable. The page compares Pb/N0, using the authors' fitted N0. A spin-density target in cm⁻² from either program would let the paper's 4.7×10¹² be compared directly with the trap program's own population (about 2.6×10¹¹ cm⁻² before the hydrogen anneal in these histories), a factor of 18 below.

What our language and ontology cannot yet say

• A kinetic hydrogen program: what it still needs. The trap-density program now has both forward rates with Brower's numbers: passivation Pb + H₂ → HPb + H (its fitted 400 °C rate times exp(−(Ef/k)(1/T − 1/T_H)), Ef 1.66 eV) and release HPb → Pb + H (kd = kd0·exp(−Ed/kT), Ed 2.56 eV, kd0 1.2×10¹² s⁻¹). Still missing: a state for the released hydrogen (in the oxide, at the interface, or recombined to H₂) so that the reverse rates follow from detailed balance with the computed reaction energies instead of a placeholder; a Gaussian spread of Ed (σ 0.105 eV), which needs a STATE distributed over a parameter (e.g. STATE N_HPb { DISTRIBUTED: Ed GAUSSIAN(2.63, 0.105) }) since one exponential cannot give the measured breadth with the measured barrier; and a creation term above about 650 °C in oxygen-free gas. With the barriers written PARAMETER Ed { STATUS: computed; SOURCE: evaluations/atomistic/<neb record> } instead of sourced from Brower, the measured values from Brower and this paper would be the test, not the input.
• Which barriers Quantum ESPRESSO can compute on the H100, and how. The cluster already relaxed (Si₄H₉/Si₄H₁₀, PBEsol, 40/320 Ry, spin-polarized) is the starting point; neb.x (climbing image, 7 to 9 images) does the rest. (1) Passivation, Pb + H₂ → HPb + H, on the cluster: H₂ approaching the dangling bond, final state HPb with a free H; this is small (15 to 16 atoms) and runs in hours, and gives a first number to set beside 1.66 eV. (2) Dissociation into a bound site: on the bare cluster HPb → Pb + H has no barrier beyond its 3.54 eV endothermicity, so the hydrogen needs somewhere to go. That needs an interface model: a (111) Si slab with a thin oxide (for example 4 to 6 Si bilayers under 1 to 1.5 nm of SiO₂ built from tridymite or a relaxed amorphous cell, about 150 to 250 atoms) with one Pb pointing into an oxide void, and final states at a back-bond centre, an oxide interstitial, and HPb + H → Pb + H₂ with a second H nearby. On one H100 an SCF of that size takes minutes; a 9-image NEB of 50 to 100 iterations is one to three days per path. (3) Prefactors: ph.x at the initial state and the saddle (harmonic transition state theory, Vineyard) gives kd0 to compare with 1.2×10¹² s⁻¹, and the same with deuterium masses gives the isotope effect Johnson 1981 needs. (4) The spread: the same path at several Pb sites of an amorphous interface gives a distribution of Ed to compare with σ = 0.105 eV. Each result enters the program as STATUS: computed and is scored against this page's 16 rows.
• Partial pressures above 1 atm. The paper oxidizes and passivates in 1.1 atm; the runtime refuses any partial pressure above 1 (mix:H2=1.1 is rejected). Allowing it would let the stated pressure through; in the equilibrium program it moves the uncapped share by a factor 1/√1.1.
• A vacuum with a pressure. “Diffusion-pumped vacuum (⩽4×10⁻⁷ Torr)” is written as vacuum. Johnson 1981's vacuum, which removes Pb where this one restores it, has no pressure at all. AMBIENT vacuum PRESSURE 4e-7 Torr and a residual-gas composition would let the two be told apart; no program reads either yet.
• One sample annealed in a series. The cycled sample is one slice taken through passivation and anneal at rising temperatures with ESR in between. Each history here is cut to its last cycle. A REPEAT … FOR T IN … with an observation after each pass would state the sequence and let a program with memory (created Pb) be tested on it.
• An observable named for what it is. The program's target is called the share left uncapped “at equilibrium”, and after a vacuum anneal it is not: it is the rate hypothesis. The predictor should report the equilibrium share (1 in vacuum, the bound in hydrogen) separately from the share at the end of the history, so a page cannot read one as the other.

With Quantum ESPRESSO switched on

This page was simulated with the computed parameters switched on (ISL_USE_COMPUTED=1): the energy of Si• + ½H₂ → Si–H, −1.284 eV, and its zero-point correction, +0.079 eV, both from Quantum ESPRESSO (PBEsol) on a 14-atom cluster, Si₄H₉ with the dangling bond and Si₄H₁₀ capped (evaluations/atomistic/si_dangling_bond_hydrogen.json, si_dangling_bond_hydrogen_vibrations.json). The same calculation gives the energy to pull the hydrogen off into vacuum, D(Si–H) = 3.54 eV, and the H₂ binding energy, 4.52 eV. No barrier was computed. Every Pb share scored above comes from the program these numbers feed, experiments/atomistic/hydrogen_passivation_equilibrium.isl.template.

Reaction energies against the measured barriers. The paper quotes two measured activation energies (Brower): passivation Pb + H₂ → HPb + H, 1.66 eV, and dissociation HPb → Pb + H, 2.56 eV; it fits 2.63 eV with a 0.105 eV spread on its own fresh oxides and 2.71 eV on the cycled sample, all with Brower's prefactor 1.2×10¹² s⁻¹. A barrier cannot be below the energy the reaction must climb. From the calculation, passivation by H₂ climbs D(H₂) − D(Si–H) = 0.98 eV if the second H is left free: 1.66 eV is above that, consistent. Dissociation to a free H atom climbs 3.54 eV, a full eV above the measured 2.56-2.71 eV; dissociation to half an H₂ molecule climbs 1.28 eV (1.21 eV with the zero-point correction), below it. So the measured barrier is consistent with the cluster only if the hydrogen that leaves is caught at once, bound by at least 1 eV relative to a free atom (in the oxide or at the interface, or by a second H forming H₂), or if a real Pb holds its hydrogen about 1 eV less strongly than the cluster. Johnson 1981's SIMS, deuterium held at the interface to above 500 °C, is direct evidence for such bound sites. The two measured barriers together (1.66 + 2.56 = 4.22 eV, the cycle H₂ → 2H) are 0.3 eV short of the computed 4.52 eV, which says the same thing.

Two calculations since, run on an H100 (11 November). (1) The passivation path on the cluster, Pb + H₂ → HPb + H, by nudged elastic band (7 images, climbing image; evaluations/atomistic/pb_passivation_barrier.json): the energy rises the whole way to the end state, 1.05 eV, and finds no saddle, so the cluster gives the reaction energy, a lower bound, not the 1.66 eV barrier. (2) The Pb site in a lattice: a Si(111) 3×3 slab of three bilayers (80 atoms) with one Pb dangling bond along [111], its eight neighbours capped by hydroxyl (oxygen above each, as on the oxide side) and, as a control, by hydrogen (evaluations/atomistic/pb_interface_slab.json). The HPb bond to a free H atom is 3.44 eV with hydroxyl neighbours, 3.42 eV with hydrogen ones and 3.54 eV on the cluster; capping by ½H₂ is −1.18 eV against −1.28 eV; passivation by H₂ climbs 1.08 eV. The lattice moves the bond by 0.1 eV and the neighbours' oxygen by 0.01 eV. So the eV between the bond (3.44) and the measured release (2.56-2.71) is not the Pb's surroundings: it is where the hydrogen goes. Released hydrogen must end bound by at least about 0.9 eV against a free atom, and the reverse of passivation (H + HPb → Pb + H₂) has about 1.66 − 1.08 = 0.6 eV. These numbers do not enter a program: the trap-density program takes Brower's measured barriers as sourced, which no calculation here has bettered.

The equilibrium bound after the hydrogen anneal. At 405 °C in 1 atm of H₂ equilibrium leaves 2.1×10⁻⁶ of the dangling bonds uncapped (2.0×10⁻⁶ at the paper's 1.1 atm), about 10⁷ cm⁻² of the 4.7×10¹² bath. The paper says the bath was “fully passivated … as affirmed by ESR”: consistent, and the bound is far below anything ESR resolves, so the measurement cannot test it. The 40 min anneal reaching full passivation also says that at 405 °C the passivation rate is not the limit, which a 1.66 eV barrier allows.

After the dissociating anneals the bound says nothing. In vacuum there is no hydrogen gas, so equilibrium is all bonds uncapped, a share of 1. Up to 645 °C the measured share stays below 1 (0.17 to 0.94), which is consistent and uninformative: how far the bonds get is set by the dissociation barrier and the 62 min. Above 660 °C the measured share exceeds 1 (1.5 to 3.5): Pb is created, and a share of a fixed population cannot express that. The paper's statement that the same happens in N₂ and Ar fits the same picture: no hydrogen, equilibrium fully uncapped, kinetics decide.

What the program reports after a vacuum anneal is not a bound. Its capping operator also uncaps, at the rate k_eq/K_eq that detailed balance requires, with k_eq = 1 s⁻¹ a hypothesis (“assumed fast against any anneal”). In vacuum that rate is the whole answer. From 480 to 650 °C it behaves as an Arrhenius law with 1.33 eV and 1.6×10⁴ s⁻¹; the measured law is 2.6 eV and 1.2×10¹² s⁻¹. The two cross near 515 °C and stay within a factor of 3 from 480 to 560 °C; above that both are fast enough to saturate in 62 min. That is why five of six fresh-oxide points fall within 10%. Outside this window they part: at 400 °C the program's rate is 22 times Brower's, at 700 °C a thirtieth of it. The match is not evidence for the program; it shows that one isochronal series cannot separate an activation energy from a prefactor, and that a spread of barriers (the paper's σ = 0.105 eV) and a lower single barrier broaden the curve alike.

The table above. “Our fitted program” is the trap-density program after the full history. The hydrogen anneal takes it to 6.4×10⁶ cm⁻² eV⁻¹ (2.5×10⁻⁵ of the 2.61×10¹¹ it has without that anneal); its release, Brower's 2.56 eV and 1.2×10¹² s⁻¹, then gives back 0.21, 0.61, 0.94 and 0.99 of it after 62 min at 520, 550, 575 and 590 °C, and all of it from 620 °C. Scored as Pb shares against the paper that is 2 of 15 within tolerance (645 °C fresh and 700 °C cycled), median error 47%: the onset is right and the rise too steep. Above 750 °C its density falls (1.9×10¹¹ at 968 °C, 5.2×10¹⁰ at 1125 °C), because its relaxation pulls the population toward its fitted floor (4.8×10¹⁰ cm⁻²), where the paper creates Pb. “Computed equilibrium bound” is the predictor's product of the trap program without the hydrogen step and the share at the end of the history; after a vacuum anneal that share is the hypothesis rate above, so the column is not a bound on this page. There is no interface-state density in this paper to set beside 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 adopts Brower's prefactor 1.2×10¹² s⁻¹ and fits only Ed and a spread. On one isochronal series a prefactor and an activation energy trade against each other; is there an isothermal series (Brower 1990, 500-590 °C) we should hold to separate them?
2. Brower's dissociation energy, 2.56 eV, is about 1 eV below the computed energy to pull H off the cluster into vacuum (3.54 eV). Is the accepted picture that the released H is bound elsewhere in the oxide or interface (so the barrier is below the free-atom limit), or that the dissociation is assisted (HPb + H → Pb + H2)?
3. Is 4.7×10¹² cm⁻² the usual natural Pb density for dry (111) oxides near 970 °C? Johnson 1981 reports about 6×10¹¹ as oxidized on (111) at 1000 °C.