Reproducing Reed 1989: how fast hydrogen anneals interface traps

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/reed_1989.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

M. L. Reed, “Models of Si-SiO2 interface reactions”, Semicond. Sci. Technol. 4, 980-985 (1989).

The trap-density program caps dangling bonds in any step with hydrogen at a rate k_H·p_H2, with k_H fitted on one anneal (Vitkavage 1990, 400 °C, 30 min). Until commit 7f1ec87 nothing in the project held how that rate depends on temperature; the program now takes Brower's activation energy (1.66 eV, rate linear in p_H2) and Brower's release of capped sites (1.2×10^12 s⁻¹, 2.56 eV) from the literature, keeping the 400 °C rate fitted. This review tests that change: Burte and Matthies' decay curves at 450 and 570 °C, and Reed and Plummer's 340 °C curves for (100) and (111). It also bears on the Quantum ESPRESSO bound, which says how far capping could go at equilibrium.

How well can this study be reproduced?

Low. A review. It reports no experiment of its own; it re-plots three anneal series from other papers (Brower; Burte and Matthies; Reed and Plummer) with their anneal temperature, time and, for two, ambient. None of them states the oxidation that made the traps, the oxide thickness, the metallisation, or the forming-gas composition, so every starting density here rests on an oxidation we invented. What it does give, and what the predictor can be tested on, is how the anneal depends on temperature and time: activation energies of 1.66 and 1.57 eV, a plateau, and dissociation above about 420 to 550 °C.

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.

RUN Oxidation DURATION 3600 TEMP 1000->1000 AMBIENT dry_O2

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, 2 approximated, 3 assumed, 2 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.

Burte and Matthies, (100), Al gate, before the anneal

Simulated time in this history: 1 h 00 min.

Across the samples

Timing the paper does not give

• The oxidation that made the traps, for all three data sets: temperature, time, gas, cooling.
• Burte and Matthies: the three metallisations (each partly anneals), the forming-gas composition, the furnace push and pull for anneals of 6 and 12 s.
• Reed and Plummer: the RTA ambient, ramp-up and cool-down; whether one capacitor was annealed repeatedly or each time is a fresh one.
• Brower: how the Pb centres were depassivated before the H2 anneal.

What the second reading changed

• The project had no dataset, script or stored recipe from this paper (library status “skimmed”); SOURCE.md says only the first page was read. Everything here is new.
• A 6 s or 12 s furnace anneal cannot reach 450 or 570 °C in the wafer; the review writes them as anneal times without saying how the wafer was heated. Ours holds the wafer at temperature for the stated time.

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>.

Burte and Matthies, (100), Al gate, before the anneal

# Burte and Matthies, (100), Al gate, before the anneal
SAMPLE Reed_burte_before {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    GATE: Al
}
CONTROL_TRAJECTORY History {
    RUN Oxidation DURATION 3600 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..14400 VARY T_hold 800..1100
    EVENT Metal KIND metallization TIMING assumed                # Three separate aluminium metallisations, each able to anneal traps partly
    EVENT CV KIND measurement TIMING assumed                     # Midgap Dit by C-V before any forming gas
}

Burte and Matthies, (100), Al gate, forming gas at 450 °C

# Burte and Matthies, (100), Al gate, forming gas at 450 °C
SAMPLE Reed_burte_450 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    GATE: Al
}
CONTROL_TRAJECTORY History {
    RUN Oxidation DURATION 3600 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..14400 VARY T_hold 800..1100
    EVENT Metal KIND metallization TIMING assumed                # Three separate aluminium metallisations, each able to anneal traps partly
    RUN FormingGas DURATION 7200 TEMP 450->450 AMBIENT forming_gas_H2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # Midgap Dit by C-V after each anneal
}

Burte and Matthies, (100), Al gate, forming gas at 570 °C

# Burte and Matthies, (100), Al gate, forming gas at 570 °C
SAMPLE Reed_burte_570 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    GATE: Al
}
CONTROL_TRAJECTORY History {
    RUN Oxidation DURATION 3600 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..14400 VARY T_hold 800..1100
    EVENT Metal KIND metallization TIMING assumed                # Three separate aluminium metallisations, each able to anneal traps partly
    RUN FormingGas DURATION 900 TEMP 570->570 AMBIENT forming_gas_H2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # Midgap Dit by C-V after each anneal
}

Reed and Plummer, (100), Al gate, rapid thermal anneal at 340 °C

# Reed and Plummer, (100), Al gate, rapid thermal anneal at 340 °C
SAMPLE Reed_reed_100 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    GATE: Al
}
CONTROL_TRAJECTORY History {
    RUN OxidationRP DURATION 3600 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..14400 VARY T_hold 800..1100
    EVENT Metal KIND metallization TIMING assumed                # Aluminium gate
    RUN RTA DURATION 600 TEMP 340->340 AMBIENT inert_N2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # C-V after each anneal
}

Figure 3 plots an integrated density in cm⁻²; the program's midgap Dit is its site count times c_mid = 1 eV⁻¹ (a hypothesis of the program), so the two numbers are compared through that hypothesis only.

Reed and Plummer, (111), Al gate, rapid thermal anneal at 340 °C

# Reed and Plummer, (111), Al gate, rapid thermal anneal at 340 °C
SAMPLE Reed_reed_111 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    GATE: Al
}
CONTROL_TRAJECTORY History {
    RUN OxidationRP DURATION 3600 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..14400 VARY T_hold 800..1100
    EVENT Metal KIND metallization TIMING assumed                # Aluminium gate
    RUN RTA DURATION 600 TEMP 340->340 AMBIENT inert_N2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # C-V after each anneal
}

Figure 3 plots an integrated density in cm⁻²; the program's midgap Dit is its site count times c_mid = 1 eV⁻¹ (a hypothesis of the program), so the two numbers are compared through that hypothesis only.

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

1 within, 32 off of 33 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 burte_450, burte_before only; every other number is a test they played no part in.

Together: Oxidation duration 14400 s (was 3600); Oxidation T hold 1100 °C (was 1000).

As reproduced: 1 of 33 within tolerance, median error 314.4%. Aligned: 4 of 33 within tolerance, median error 200.8%. On the held-out samples only: 0 of 24 within tolerance, median error 504.1% as reproduced, 1 of 24 within tolerance, median error 504.1% aligned.

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

Two unknowns were declared, both on the oxidation that made the traps, which the review never states: its duration (10 min to 4 h) and temperature (800 to 1100 °C). Burte and Matthies' oxidation and Reed and Plummer's are separate unknowns. They were chosen on Burte's sample before the anneal and the 450 °C curve; the 570 °C curve and both 340 °C curves are the test. Reed and Plummer's oxidation is carried by no sample the search chose on, so it keeps its assumed value (1000 °C, 1 h). As reproduced: 1 of 33 within tolerance (median error 314%). Aligned: 4 of 33 (median 201%). On the 24 held-out numbers: 0 before and 1 after (median 504% both). These are the numbers with the trap-density program of commit 7f1ec87 (Brower's activation energy and release); before it, 1 of 33 (749%) as reproduced and 1 of 33 (270%) aligned.

The search can only lower the starting density, and it goes to the edge of its range. The program's density before any hydrogen is set by the oxidation: 2.61×10^11 after 1 h at 1000 °C, 1.03×10^11 after the chosen 4 h at 1100 °C (the corner of the range), against Burte's 8.4×10^10. Lower is not reachable inside the range, and Burte's value is itself after three metallisations that the review says partly annealed it. The chosen oxidation is therefore not a finding about the experiment; it is the program asking for a lower start.

At 450 °C the first seconds now match; the plateau does not. With the aligned start, 10% forming gas at 450 °C takes the program from 1.03×10^11 to 4.18×10^10 after 6 s, 4.02×10^10 after 12 s, 1.65×10^10 after 5 min, 6.5×10^9 after 10 min, 1.8×10^8 after 30 min and 2.3×10^7 after 2 h. Burte measures 4.3, 3.6, 1.0, 1.0, 0.8 and 1.0×10^10: the 6 s, 12 s and 10 min points are within tolerance; the fourth number within after alignment is 570 °C at 6 s (1.84×10^10 against 1.8×10^10), held out of the search. The fast first fall is the program's second population N_B, whose capping rate (k_HB = 1 atm⁻¹ s⁻¹ at 400 °C, a hypothesis, times Brower's factor of 7.2 at 450 °C) clears it in about 1.4 s in 10% H2; the dangling bonds N_Pb then cap with k_H·p_H2 = 4.3×10^-3 × 7.2 × 0.1 s⁻¹, a time constant of 5.4 min (39 min before Brower's factor). Burte's density is flat from 5 min on; the program's keeps falling for another half hour. Run after 1 h at 1000 °C, forming gas for 6 s, 60 s, 5 min, 30 min and 2 h gives 2.57, 2.30, 1.77, 1.55 and 1.34×10^11 at 340 °C, 1.60, 1.35, 0.64, 0.0071 and 0.00091×10^11 at 450 °C, and 0.71, 0.0075, 0.0071, 0.0071 and 0.0071×10^11 at 570 °C (scratch script rd.py, not stored). Brower's 1.66 eV makes the rate at 570 °C 2.4×10^6 times the rate at 240 °C, at 450 °C 5.4×10^4 times, and at 450 °C 119 times the rate at 340 °C; the program now carries those ratios because it took the energy from Brower.

The rate's level, not its slope, is now what is off. In pure H2 at 240 °C, Brower's Pb0 intensity falls by a factor 0.77 in 89 min and 0.34 in 389 min (a first-order rate of 2.7×10^-3 per min). The program's dangling-bond rate in 1 atm H2 at 240 °C is now 3.4×10^-5 per min, 80 times slower (before the change it was 0.26 per min, 95 times faster). Its midgap density falls by 0.80 and 0.63 in the same times, close to Brower's first point, but that fall is the second population, not the dangling bonds Brower counts. Burte's decay at 450 °C, over within about 12 s, asks for a dangling-bond rate at least 25 times the program's. Brower's 240 °C rate carried to 450 °C with his own 1.66 eV gives a time constant of about 4 s in 10% H2, consistent with Burte; so the two data sets agree with each other and both put the program's rate, anchored on Vitkavage's 400 °C anneal, 25 to 80 times low.

A plateau, but far too low; and a reverse reaction. Capping and release now balance where k_d = k_H·p_H2 times the ratio of uncapped to capped sites: after 1 h at 1000 °C the program settles at 9.1×10^7 at 450 °C (reached after about 1 h) and 7.05×10^8 at 570 °C (within 5 min). Burte's density stops at about 1×10^10 at both temperatures, 110 and 18 times higher. Brower's release rate is 1.7×10^-6 s⁻¹ at 450 °C and 6.0×10^-4 s⁻¹ at 570 °C, so with hydrogen present capping always wins and the density never rises, while Reed reports that above 420 °C a long anneal raises it. Without hydrogen it does rise: after 30 min of forming gas at 450 °C (7.5×10^8), vacuum at 550 °C gives 2.4×10^10 after 10 min, 6.0×10^10 after 30 min and 1.4×10^11 after 2 h, Brower's dissociation near 550 °C. A plateau at 1×10^10 needs something the program does not have: a population hydrogen does not cap (Reed's “annealed Pb1 not detected electrically”), or a spread of capping barriers.

Reed and Plummer's anneals do nothing in the program. Written as stated (ambient not given, nitrogen ours), the RTA carries no hydrogen, so the program holds 2.61×10^11 for (100) and 1.86×10^11 for (111) through 600 s, while the paper's density falls from 3.7×10^10 to 3.4×10^9 (100) and from 1.2×10^11 to 2.5×10^10 (111). The variant that writes the RTA as forming gas changes the score by nothing (1 of 33 alone, 4 of 33 with the aligned oxidation, as without it): at 340 °C Brower's factor makes the dangling-bond time constant 10.7 h in 10% H2, and in 600 s the (100) density falls only from 2.61 to 1.62×10^11, mostly the second population; (111) moves by under 1%. Writing Burte's anneals in pure H2 instead of 10% forming gas now lowers the score (0 of 33 alone, 2 of 33 with the aligned oxidation, against 1 and 4 in forming gas); before the change it raised it.

With Quantum ESPRESSO switched on. The computed bound on the density hydrogen could reach at equilibrium is 7.0×10^6 cm⁻² eV⁻¹ at 450 °C and 1.4×10^8 at 570 °C in 10% forming gas (and 1.4×10^3, 1.6×10^5 and 1.5×10^6 at 240, 340 and 400 °C). Burte's plateaus (1.0×10^10 and about 1.3×10^10) are 1400 and 90 times above it, and Reed's (100) density after 600 s at 340 °C (3.4×10^9) is 2×10^4 times above the 340 °C bound. So the plateau is not set by the thermodynamics of the Si–H bond computed on the cluster: either the anneal stops short of equilibrium, or the plateau is traps that hydrogen does not cap (Reed's “annealed Pb1 not detected electrically”, a second kind of site). The bound rises 10^5 times between 240 and 570 °C, the direction Thanh and Balk report for their temperature-only steady state, but it is 2 to 4 orders too low to be that steady state.

With heating and cooling transitions. A hot push (1 to 5 min heat-up) before the assumed oxidation, ramps around the anneals and a cool-down at the end move 7 of 33 numbers by more than 2% and lower the median error from 314% to 293%, and keep 1 of 33 within tolerance (as reproduced, that one is 450 °C after 15 min, which the program reaches only by decaying through it). A cold-furnace ramp of 60 to 120 min in nitrogen before the oxidation moves all 33 (the program's first population relaxes for longer, lowering every start): median 280% with fast or slow cooling, and 0 of 33. The ramps in forming gas around the anneals are at most 450 or 570 °C, where release is too slow to matter; they cannot raise the plateau.

1 within, 23 off of 24 numbers with the aligned settings (the samples used to choose the unknowns are left out).

What alignment cannot fix: the program's hydrogen step now has Brower's temperature dependence and release, but its dangling-bond rate is anchored on one 400 °C anneal and is 25 to 80 times below what Burte's 450 °C and Brower's 240 °C curves ask for; its steady state is 18 to 110 times below the plateau near 1×10^10 cm⁻² eV⁻¹ that both of Burte's curves end on; and it needs H2 in the gas. No choice of the unstated oxidation changes any of that; it only moves the starting value, and the starting value it would need (8.4×10^10) is below what any oxidation in the searched range gives.

Still missing from the program: atomic hydrogen, which anneals bare oxides much faster than H2; a gate that supplies hydrogen (Reed's Al); a population or a spread of barriers that leaves a plateau; any difference between (100) and (111) beyond the starting density; and a hydrogen inventory, so that released hydrogen can cap again. These matter for every page that has a forming-gas anneal: the program is anchored where its rate was fitted (400 °C, 30 min) and is used from 340 to 570 °C and from seconds to hours.

The review cannot be reproduced as a set of experiments: none of its three data sets states the oxidation, the gate process or the gas composition, and Figure 3's unit (cm⁻²) is matched to the program's midgap density only through the program's own hypothesis c_mid = 1 eV⁻¹.

What our language and ontology cannot yet say

• A gate that supplies hydrogen. Reed's Al-gate capacitors anneal at the same rate in any ambient because aluminium reacting with hydroxyl at the Al–SiO2 interface releases atomic hydrogen. The language can record GATE: Al on a sample, but no statement says the gate is a hydrogen source during every later heat; an RTA in nitrogen therefore anneals nothing. A sample layer with a declared reservoir (LAYER Al { SOURCE: H }) or a SOURCE H clause on a RUN would let the Al-gate curves be simulated at all.
• Atomic against molecular hydrogen. Bare oxides anneal much faster in atomic hydrogen than in H2 (PDF p. 3); the language's gases are Ar, H2, H2O, N2 and O2. An H species in mix: (and a program that reads it) is needed before corona, plasma or post-metal anneals can be written.
• A measured starting state. Every case here starts from an oxidation we invented because the program cannot be told “the sample has 8.4×10^10 cm⁻² eV⁻¹ of traps at t = 0”. A sample field such as STARTING_DIT: 8.4e10 (as STARTING_OXIDE_NM does for thickness) would let an anneal series be tested on its kinetics alone, without an unknown oxidation in front of it.
• One sample measured along an anneal. Each point of a decay curve is written as a separate history ending at that time. Whether the paper annealed one capacitor repeatedly (with cooling and a measurement between anneals) or a fresh one each time is not stated, and the language cannot say which. A REPEAT of anneal-and-measure on one sample, with the cooling between, would make the difference explicit.
• A plateau in the trap-density program (a predictor change). Commit 7f1ec87 added Brower's Arrhenius capping (1.66 eV) and dissociation of Si–H (2.56 eV); the steady state they give is 18 to 110 times below Burte's plateau. Still missing: a floor of sites hydrogen does not cap, or a spread of capping barriers, and a rate level set by data at more than one temperature.

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. Burte and Matthies' decay is complete within 6 to 12 s at 450 °C. Can a wafer in a furnace reach 450 °C in 6 s, or is most of that anneal happening during the push and pull?
2. Is Brower's 1.66 eV the right activation energy for the capping rate in a forming-gas anneal of a gate oxide, or only for a bare oxide in pure H2?
3. Should a trap-density model carry a plateau after hydrogen (Burte about 1×10^10, Thanh and Balk a temperature-dependent steady state), and is that plateau the same population as the program's second population?
4. Reed's Al-gate anneals do not depend on the ambient. Should a sample with an Al gate be treated as carrying its own hydrogen source in every anneal?