Reproducing O'Sullivan et al. 2001: dangling bonds exposed by rapid thermal processing

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/osullivan_2001.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

B. J. O'Sullivan, P. K. Hurley, C. Leveugle and J. H. Das, “Si(100)–SiO2 interface properties following rapid thermal processing”, J. Appl. Phys. 89, 3811–3820 (2001).

The paper that says why dangling-bond states are seen after some thermal steps and not after others: an inert anneal above about 500 °C takes the hydrogen off the Pb centres, and whether they are passivated again depends on the cooling rate and on hydrogen or moisture in the cooling ambient. That is a statement about the hydrogen step of the trap-density program run backwards, and about the history around it: a 10 s RTA in nitrogen at 925 to 1050 °C, the last step, raises the midgap density two- to three-fold, and a 60 min alloy in 5% H2 at 440 °C removes it. It is the test of whether our language can carry the hydrogen a history brings (silane, POCl3, moisture during a slow pull) and whether the predictor has a reverse of the capping reaction.

How well can this study be reproduced?

Moderate. Oxidation temperatures, anneals, the RTA (10 s in nitrogen) and the RTO conditions are stated, with the forming-gas alloy's gas, temperature and time. Not stated: any oxidation time for the furnace oxides, the polysilicon deposition and POCl3 doping conditions for process 1 (and the POCl3 for process 2), the RTA ramps, the withdrawals after the 850 and 900 °C anneals, and how long each sample waited before measurement. The midgap densities exist only on log-axis figures; the printed numbers are band-edge peaks after a background is subtracted.

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. 7 same, 4 approximated, 4 assumed, 6 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.

Process 1, p-Si, 120 Å, no RTA (control)

Simulated time in this history: 4 h 26 min 40 s.

Across the samples

Timing the paper does not give

• Oxidation time at 850 °C (120 Å) and at 950 °C (260 Å).
• Process 1: the gas during the 3 °C/min ramp, the boat travel during the 8 cm/min pull from 600 °C, and so how long the wafer spends between 600 °C and room temperature.
• Process 1: polysilicon deposition temperature and time; POCl3 temperature and time (both processes).
• The withdrawal after the 900 °C (process 1) and 950 °C (process 2) nitrogen anneals.
• RTA heat-up and cool-down rates for processes 1 and 2 (only “10^1–10^2 °C/s” cooling in general).
• RTO: start temperature of the heat-up and its gas; the temperature at which the RTP cycle ends.
• Ramps into and out of the 440 °C alloy.
• Time between the last step and measurement (the RTA samples are said to be stable for six years).

What the second reading changed

• No dataset and no script uses this paper; SOURCE.md says the figures and Table I were not digitized. The midgap values here are new graph readings and Table I is transcribed here for the first time.
• ontology/library.json gives the source's conditions as “pull: rapid thermal, 10 to 100 C/s” and “metal: mercury probe, no gate”. That describes processes 3–5 only. Processes 1 and 2 are polysilicon-gate capacitors whose oxides were furnace grown and pulled slowly (3 °C/min to 600 °C, then 8 cm/min, for process 1); only their last step is rapid.
• SOURCE.md says the note added in proof cites evidence that vacuum anneals create additional centres. The note says post-oxidation vacuum annealing (600–1100 °C) can generate additional Pb1 while Pb0 stays constant, and that this matters only if Pb1 is electrically active; the authors keep their conclusion that RTA creates no more states than a furnace anneal.
• SOURCE.md quotes peak densities 3e12 to 1.7e13; these are after subtracting a hydrogen-passivated background, not total densities.

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>.

Process 1, p-Si, 120 Å, no RTA (control)

# Process 1, p-Si, 120 Å, no RTA (control)
SAMPLE Wafer_P1_control {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: p_type_boron_1e15
    GATE: n_poly_POCl3
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Pre-oxidation clean
    RUN Oxidation850 DURATION 4400 TEMP 850->850 AMBIENT dry_O2 TIMING assumed VARY duration 3000..6000
    RUN Anneal850 DURATION 3600 TEMP 850->850 AMBIENT inert_N2 TIMING stated
    RUN RampDown DURATION 5000 TEMP 850->600 AMBIENT inert_N2 TIMING stated
    RUN Pull600 DURATION 600 TEMP 600->200 AMBIENT inert_N2 TIMING bound VARY duration 120..1800 VARY T_end 25..400
    EVENT Poly KIND deposition TIMING assumed                    # Polysilicon, 3000 Å, chemical vapour deposition
    EVENT POCl3 KIND deposition TIMING assumed                   # Backside strip; phosphorus doping of the polysilicon from POCl3
    EVENT Etch KIND etch TIMING assumed                          # Dry etch of the polysilicon; resist strip
    RUN Anneal900 DURATION 1800 TEMP 900->900 AMBIENT inert_N2 TIMING stated
    RUN Pull900 DURATION 600 TEMP 900->200 AMBIENT inert_N2 TIMING assumed VARY duration 120..1800
    EVENT NoRTA KIND other TIMING assumed                        # No RTA (control)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz HFCV and quasi-static CV at room temperature; no forming gas
}

Process 1, p-Si, 120 Å, RTA 925 °C 10 s

# Process 1, p-Si, 120 Å, RTA 925 °C 10 s
SAMPLE Wafer_P1_RTA925 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: p_type_boron_1e15
    GATE: n_poly_POCl3
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Pre-oxidation clean
    RUN Oxidation850 DURATION 4400 TEMP 850->850 AMBIENT dry_O2 TIMING assumed VARY duration 3000..6000
    RUN Anneal850 DURATION 3600 TEMP 850->850 AMBIENT inert_N2 TIMING stated
    RUN RampDown DURATION 5000 TEMP 850->600 AMBIENT inert_N2 TIMING stated
    RUN Pull600 DURATION 600 TEMP 600->200 AMBIENT inert_N2 TIMING bound VARY duration 120..1800 VARY T_end 25..400
    EVENT Poly KIND deposition TIMING assumed                    # Polysilicon, 3000 Å, chemical vapour deposition
    EVENT POCl3 KIND deposition TIMING assumed                   # Backside strip; phosphorus doping of the polysilicon from POCl3
    EVENT Etch KIND etch TIMING assumed                          # Dry etch of the polysilicon; resist strip
    RUN Anneal900 DURATION 1800 TEMP 900->900 AMBIENT inert_N2 TIMING stated
    RUN Pull900 DURATION 600 TEMP 900->200 AMBIENT inert_N2 TIMING assumed VARY duration 120..1800
    RUN RTAUp DURATION 15 TEMP 25->925 AMBIENT inert_N2 TIMING assumed VARY duration 5..60
    RUN RTA DURATION 10 TEMP 925->925 AMBIENT inert_N2 TIMING stated
    RUN RTADown DURATION 22.5 TEMP 925->25 AMBIENT inert_N2 TIMING bound VARY duration 10..100
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz HFCV and quasi-static CV at room temperature; no forming gas
}

Process 1, p-Si, 120 Å, RTA 1050 °C 10 s

# Process 1, p-Si, 120 Å, RTA 1050 °C 10 s
SAMPLE Wafer_P1_RTA1050 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: p_type_boron_1e15
    GATE: n_poly_POCl3
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Pre-oxidation clean
    RUN Oxidation850 DURATION 4400 TEMP 850->850 AMBIENT dry_O2 TIMING assumed VARY duration 3000..6000
    RUN Anneal850 DURATION 3600 TEMP 850->850 AMBIENT inert_N2 TIMING stated
    RUN RampDown DURATION 5000 TEMP 850->600 AMBIENT inert_N2 TIMING stated
    RUN Pull600 DURATION 600 TEMP 600->200 AMBIENT inert_N2 TIMING bound VARY duration 120..1800 VARY T_end 25..400
    EVENT Poly KIND deposition TIMING assumed                    # Polysilicon, 3000 Å, chemical vapour deposition
    EVENT POCl3 KIND deposition TIMING assumed                   # Backside strip; phosphorus doping of the polysilicon from POCl3
    EVENT Etch KIND etch TIMING assumed                          # Dry etch of the polysilicon; resist strip
    RUN Anneal900 DURATION 1800 TEMP 900->900 AMBIENT inert_N2 TIMING stated
    RUN Pull900 DURATION 600 TEMP 900->200 AMBIENT inert_N2 TIMING assumed VARY duration 120..1800
    RUN RTAUp DURATION 17.0833 TEMP 25->1050 AMBIENT inert_N2 TIMING assumed VARY duration 5..60
    RUN RTA DURATION 10 TEMP 1050->1050 AMBIENT inert_N2 TIMING stated
    RUN RTADown DURATION 25.625 TEMP 1050->25 AMBIENT inert_N2 TIMING bound VARY duration 10..100
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz HFCV and quasi-static CV at room temperature; no forming gas
}

Process 2, n-Si, 260 Å, RTA 1050 °C 10 s

# Process 2, n-Si, 260 Å, RTA 1050 °C 10 s
SAMPLE Wafer_P2_RTA {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type_phosphorus_1e15
    GATE: n_poly_POCl3
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Pre-oxidation clean
    RUN Oxidation950 DURATION 2700 TEMP 950->950 AMBIENT dry_O2 TIMING assumed VARY duration 1800..4500
    RUN Anneal950 DURATION 1200 TEMP 950->950 AMBIENT inert_N2 TIMING stated
    RUN Pull950 DURATION 600 TEMP 950->200 AMBIENT inert_N2 TIMING assumed VARY duration 120..1800
    EVENT Poly KIND deposition TIMING assumed                    # Polysilicon, 4500 Å, chemical vapour deposition at 620 °C
    EVENT POCl3 KIND deposition TIMING assumed                   # Backside strip; phosphorus doping from POCl3
    EVENT Etch KIND etch TIMING assumed                          # Wet etch of the polysilicon
    RUN RTAUp DURATION 17.0833 TEMP 25->1050 AMBIENT inert_N2 TIMING assumed VARY duration 5..60
    RUN RTA DURATION 10 TEMP 1050->1050 AMBIENT inert_N2 TIMING stated
    RUN RTADown DURATION 25.625 TEMP 1050->25 AMBIENT inert_N2 TIMING bound VARY duration 10..100
    EVENT CV KIND measurement TIMING assumed                     # 8 kHz HFCV at room temperature
}

Process 2, n-Si, 260 Å, RTA 1050 °C 10 s + alloy 440 °C 60 min

# Process 2, n-Si, 260 Å, RTA 1050 °C 10 s + alloy 440 °C 60 min
SAMPLE Wafer_P2_RTA_alloy {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type_phosphorus_1e15
    GATE: n_poly_POCl3
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Pre-oxidation clean
    RUN Oxidation950 DURATION 2700 TEMP 950->950 AMBIENT dry_O2 TIMING assumed VARY duration 1800..4500
    RUN Anneal950 DURATION 1200 TEMP 950->950 AMBIENT inert_N2 TIMING stated
    RUN Pull950 DURATION 600 TEMP 950->200 AMBIENT inert_N2 TIMING assumed VARY duration 120..1800
    EVENT Poly KIND deposition TIMING assumed                    # Polysilicon, 4500 Å, chemical vapour deposition at 620 °C
    EVENT POCl3 KIND deposition TIMING assumed                   # Backside strip; phosphorus doping from POCl3
    EVENT Etch KIND etch TIMING assumed                          # Wet etch of the polysilicon
    RUN RTAUp DURATION 17.0833 TEMP 25->1050 AMBIENT inert_N2 TIMING assumed VARY duration 5..60
    RUN RTA DURATION 10 TEMP 1050->1050 AMBIENT inert_N2 TIMING stated
    RUN RTADown DURATION 25.625 TEMP 1050->25 AMBIENT inert_N2 TIMING bound VARY duration 10..100
    RUN Alloy DURATION 3600 TEMP 440->440 AMBIENT mix:H2=0.05,N2=0.95 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # 8 kHz HFCV at room temperature
}

Process 3, p-Si, dry RTO, 1100 °C, 30 s, Hg probe

# Process 3, p-Si, dry RTO, 1100 °C, 30 s, Hg probe
SAMPLE Wafer_P3_dry_RTO_1100 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: p_type_5e14
    GATE: mercury_probe
}
CONTROL_TRAJECTORY History {
    EVENT HFDip KIND clean TIMING assumed                        # Pre-oxidation HF dip
    RUN RTOUp DURATION 17.9167 TEMP 25->1100 AMBIENT inert_N2 TIMING bound VARY duration 10..30
    RUN RTO DURATION 30 TEMP 1100->1100 AMBIENT dry_O2 TIMING stated
    RUN RTODown DURATION 26.875 TEMP 1100->25 AMBIENT inert_N2 TIMING bound VARY duration 15..100
    EVENT HgCV KIND measurement TIMING assumed                   # Mercury-probe QSCV straight after the RTO
}

Process 4, p-Si, dry RTO, 1000 °C, 8 s, Hg probe

# Process 4, p-Si, dry RTO, 1000 °C, 8 s, Hg probe
SAMPLE Wafer_P4_dry_RTO_1000 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: p_type_boron_8e14
    GATE: mercury_probe
}
CONTROL_TRAJECTORY History {
    RUN RTOUp DURATION 16.25 TEMP 25->1000 AMBIENT inert_N2 TIMING bound VARY duration 10..30
    RUN RTO DURATION 8 TEMP 1000->1000 AMBIENT dry_O2 TIMING stated
    RUN RTODown DURATION 24.375 TEMP 1000->25 AMBIENT inert_N2 TIMING bound VARY duration 15..100
    EVENT HgCV KIND measurement TIMING assumed                   # Mercury-probe QSCV straight after the RTO
}

Process 5, p-Si, steam RTO, 1015 °C, 33 s, Hg probe

# Process 5, p-Si, steam RTO, 1015 °C, 33 s, Hg probe
SAMPLE Wafer_P5_steam_RTO_1015 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: p_type_boron_8e14
    GATE: mercury_probe
}
CONTROL_TRAJECTORY History {
    RUN RTOUp DURATION 16.5 TEMP 25->1015 AMBIENT inert_N2 TIMING bound VARY duration 10..30
    RUN RTO DURATION 33 TEMP 1015->1015 AMBIENT mix:H2O=0.45,N2=0.55 TIMING stated
    RUN RTODown DURATION 24.75 TEMP 1015->25 AMBIENT inert_N2 TIMING bound VARY duration 15..100
    EVENT HgCV KIND measurement TIMING assumed                   # Mercury-probe QSCV straight after the RTO
}

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

6 within, 2 near, 5 off, 11 not modelled of 24 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 P1_RTA1050, P1_RTA925, P1_control only; every other number is a test they played no part in.

Together: Oxidation850 duration 4500 s (was 4400); Pull600 duration 600 s (was 600); Pull600 T end 200 °C (was 200); Pull900 duration 1800 s (was 600); RTAUp duration 1× (was 1); RTADown duration 1× (was 1).

As reproduced: 6 of 24 within tolerance, median error 17.2%. Aligned: 6 of 24 within tolerance, median error 17.2%. On the held-out samples only: 2 of 14 within tolerance, median error 46.1% as reproduced, 2 of 14 within tolerance, median error 46.1% aligned.

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

Six unknowns were declared: the 850 °C oxidation time, the duration and end temperature of the pull from 600 °C, the withdrawal after the 900 °C anneal, and the RTA heat-up and cool-down (as factors on the assumed 60 and 40 °C/s). They were chosen on the three process 1 capacitors (control, 925 °C and 1050 °C RTA) and tested on processes 2 to 5. As reproduced: 6 of 24 numbers within tolerance (median error 17.2%; 11 of the 24 have no program). Aligned: 6 of 24. On the held-out processes: 2 of 14 before and after (median error 46.1%).

Only the oxidation time is seen by the data, and only through thickness. 4000 to 4500 s at 850 °C give 12 nm within 10%; 3000 s gives 1 of 10 within tolerance. The search moved it from 4400 to 4500 s. The midgap density moves by under 1% over the whole range.

The pulls and the RTA ramps change nothing. Every value of the 600 °C pull (2 to 30 min, ending at 25 to 400 °C), of the 900 °C withdrawal and of the RTA ramp factors scores the same (4 of 10, median 3.8%), so the values printed for them are not findings. The search moved the 900 °C withdrawal to 1800 s on a tie. Cooling the RTA and RTO at 10 °C/s instead of 40 °C/s (the declared variant) also scores the same, 6 of 24. In this predictor no cooling before the alloy can matter to the trap density: its capping operator needs hydrogen in the gas, no step of these histories before the alloy has any, and so its release operator has nothing to release.

The control fits and the RTA does not move. Without any hydrogen step the program gives 4.68 × 10^11 cm⁻² eV⁻¹ at midgap for the control (measured 4.4 × 10^11, +6%). After a 10 s RTA in nitrogen at 925 or 1050 °C it gives 4.68 and 4.67 × 10^11; the paper measures 9 × 10^11 and 1.0 × 10^12, a two-fold rise. On process 2 the program gives 3.37 × 10^11 after the RTA (measured 7.4 × 10^11, -54%) and 4.68 × 10^9 after the alloy in 5% H2 (measured 1.7 × 10^11, -97%). The program is low after every RTA and gets the direction of the alloy right, but now overshoots it: see the capping rate below.

With Quantum ESPRESSO switched on, the computed equilibrium bound after the 440 °C alloy in 5% H2 is 9.6 × 10^6 cm⁻² eV⁻¹. The measured 1.7 × 10^11 is 1.8 × 10^4 times the bound, and the fitted program's 4.68 × 10^9 is 490 times it. What remains after this alloy is not limited by the thermodynamics of the Si–H bond: the alloy is far from equilibrium (a polysilicon gate slows hydrogen, as the paper notes for lightly doped gates), or the states left are not ones hydrogen caps. The bound is only computed for hydrogen steps; the same reaction, run backwards in nitrogen at 1050 °C, is the paper's mechanism and is not computed.

With heating and cooling transitions (a hot push or a cold-furnace ramp before the first furnace step, fast or slow radiative cooling after it, ramps around the alloy), every scenario keeps 6 of 24 within tolerance and a median error of 17.2%. The cold-furnace scenarios move one number of 24 by more than 2%: the alloy on process 2, 4.68 to 3.67 × 10^9 (-21%), almost all from the 30 min heat-up and 60 min cool-down in forming gas around the 440 °C alloy, which with Brower's 1.66 eV count as about 5 min at 440 °C. The hot push moves it 1%. The page's result does not depend on how the wafers heated or cooled: before the alloy no step has hydrogen to cap or to release.

2 within, 1 near, 4 off, 7 not modelled of 14 numbers with the aligned settings (the samples used to choose the unknowns are left out).

What alignment cannot fix. The reverse of hydrogen capping has nothing to act on. The paper's central result is that an inert anneal above about 500 °C takes hydrogen off Pb centres that earlier steps passivated, and fast cooling in a hydrogen-free gas leaves them bare. Since 11 November the trap-density program has the reverse, F_HydrogenRelease: N_SiH returns to N_Pb at 1.2 × 10^12 exp(-2.56 eV/kT) s⁻¹ (Brower, as quoted by Stesmans and Afanas'ev 1996; the paper cites Stesmans 1996 for dissociation above 500 °C). In a 10 s RTA that releases 2% of the capped sites at 600 °C and all of them at 925 and 1050 °C. But N_SiH is zero when every RTA here starts, because no earlier step can be written with hydrogen (next paragraph), so the RTA still only lowers the density, by relaxation (4.68 to 4.67 × 10^11 at 1050 °C). The release is first order and does not use the computed Si–H energy (-1.28 eV per ½H2), and the program's second population has no release.

No hydrogen before the alloy. For the RTA to expose states, earlier steps must have passivated them: silane during the polysilicon deposition at 620 °C, POCl3 doping, and moisture during the slow pull at 600 °C. None of these can be written, so the predictor's control is an unpassivated interface that happens to match the measured 4.4 × 10^11.

The capping rate's temperature dependence is Brower's, applied to a polysilicon gate. The rate is fitted at 400 °C on Vitkavage's aluminium-gate wafers; Brower's E_f = 1.66 eV makes it 5.0 times faster at 440 °C (1.3 × 10⁻⁴ of it at 240 °C, 320 times it at 570 °C), so the 60 min alloy in 5% H2 caps as much as 2.5 h in 10% H2 at 400 °C would. The program now gives 4.68 × 10^9 after the alloy against 1.7 × 10^11 measured (-97%); before the 11 November change, with no temperature in the rate, it gave 9.65 × 10^10 (-43%). The paper says a lightly doped polysilicon gate needs a longer alloy; nothing in the program slows hydrogen through a gate.

No wet oxidation and no thin RTO. The trap-density program returns nothing for the steam RTO (it needs a dry-oxygen RUN) and does not read water. The dry RTO at 1000 °C, 8 s, is predicted at 3.7 × 10^11 against 2.5 × 10^12 measured (-85%): the program's second population is set by temperature alone, and its time scale is an hour. The thin-oxide program grows 2.2 nm in 8 s at 1000 °C against 4.0 nm printed and 6.2 nm in 30 s at 1100 °C against 7.5 nm, outside its fitted 800 to 1000 °C and its fitted times.

Peaks and energies. Nine printed numbers are band-edge peak densities after subtracting a hydrogen-passivated background. No program gives a distribution over energy without hydrogen, and no observation statement says that a measured value is the difference between two samples.

What our language and ontology cannot yet say

• Hydrogen release tied to what the history put there (predictor). The program now releases hydrogen (Si–H → Si• + H at Brower's rate), but a release can only raise the density where an earlier step capped sites, and on this page none can. It also has no release for the second population and does not use the computed Si–H energy against the gas's p_H2. Until the hydrogen sources below can be written, an RTA, a vacuum anneal and a rapid pull still look the same as no step.
• Hydrogen brought by a step that is not a gas anneal. Polysilicon from silane at 620 °C, POCl3 doping, plasma steps and moisture during a slow pull passivate the interface (the paper, PDF p. 9-10). The language records them as EVENTs that do nothing. A SOURCE hydrogen clause on a deposition EVENT, or an AMBIENT for a deposition (mix:SiH4=…), and a stated moisture on pulls, would let a program see them. The vocabulary of gases is Ar, H2, H2O, N2, O2; silane, POCl3, NH3 and N2O are refused.
• Which step is the oxidation. The RTO heat-up had to be written in nitrogen: the trap-density program takes the oxidation's temperature and time from the first dry-oxygen RUN, so a heat-up in oxygen from 25 °C would be read as an oxidation at 25 °C. A ROLE oxidation|anneal|ramp|pull on each RUN (as Hung's page asked) would remove the trap.
• A gate on the sample. Polysilicon, aluminium and a mercury probe behave differently under hydrogen (the paper: lightly doped polysilicon needs a longer alloy). GATE is recorded here as a sample field no program reads. A gate field in the ontology, read by the hydrogen operator as a barrier or a source, would let processes 1-2 and 3-5 differ.
• A pull as a speed. “a pull from the furnace at 600 °C at 8 cm/min” is a speed, not a duration or a cooling rate; the boat travel is unknown. A PULL SPEED 8 cm/min FROM 600 statement with a furnace profile would turn it into a temperature against time.
• A measurement that is a difference. Table I's peaks are densities after subtracting a background measured on another (hydrogen-passivated) sample. An observation statement naming the reference sample would let such numbers be compared with a difference of two simulations.
• An HF dip as a clean. CLEAN accepts named cleans only; a bare pre-oxidation HF dip (process 3) had to be written not_stated.

With Quantum ESPRESSO switched on

This page was simulated with parameters from atomic calculations switched on (ISL_USE_COMPUTED=1). They come from Quantum ESPRESSO (the discovered-materials dm_qe build), run locally on CPU and on an H100 on RunPod, recorded in evaluations/atomistic/ with the code version, inputs, pseudopotential checksums and convergence, and carried into ISL as STATUS: computed. They never replace a fitted or sourced number: the rows scored above are the same with the switch off. Each computed row sits beside the measurement it bears on.

What is computed so far is one reaction: Si• + ½H₂ → Si–H for a silicon dangling bond with three silicon back-bonds (the local structure of a Pb centre), on a 14-atom cluster. With the free energy of hydrogen gas it bounds the share of dangling bonds that a hydrogen step could leave uncapped if it reached equilibrium, and so the lowest interface state density that step could reach. A measurement far above the bound means what remains after the hydrogen step is not limited by the strength of the Si–H bond: the anneal is far from equilibrium, or the traps that remain are not dangling bonds hydrogen can cap.

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. For process 1, what would the polysilicon deposition (silane, about 600 to 650 °C) and the POCl3 doping (about 900 °C) do to the interface? The paper names deposition as a hydrogen source; is the control's 4×10^11 at midgap a partly passivated interface?
2. How long would a 150 mm boat pulled at 8 cm/min from a 600 °C zone take to bring the wafers below 300 °C, and is a furnace's nitrogen moist enough to passivate Pb in that time?
3. Is a 10 s RTA at 600 °C enough to take hydrogen off Pb centres, as the distorted QSCV at 600 °C suggests? Brower's release rate, now in the trap-density program (1.2×10^12 exp(-2.56 eV/kT)), gives 2×10⁻³ s⁻¹ at 600 °C: 2% of the capped sites in 10 s.
4. Are the midgap values read from Figures 4, 7 and 12 meaningful as midgap Dit, given that Figure 7 is from 8 kHz HFCV and Figure 12 from 40 Å oxides with a mercury probe?
5. Is the steam RTO's lower midgap density (about 1.5 against 2.5×10^12) the hydrogen passivation the authors describe, or the difference in oxide charge (Vfb about -1.2 V)?