Reproducing Deal and Razouk 1980: four ways to end an oxidation

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/deal_razouk_1980.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. E. Deal and R. R. Razouk, Fairchild report on the process-variable dependence of oxide charges and trapping (1980), DTIC ADA091299, Section 4, Tables 4-1 and 4-2.

Twenty-four (111) wafers, each oxidation ended four ways: pulled fast in oxygen, pulled slowly in oxygen, or annealed ten minutes in nitrogen or argon and pulled in that gas. It is the cleanest test we hold of the fixed-charge program, because that program was fitted to Stanford's anneals and has never been adjusted to these wafers: 12 of 16 within tolerance, and 2 of 16 with the inert step switched off.

How well can this study be reproduced?

High. Every wafer has its own row: oxidation temperature and time, anneal gas and time, pull gas and time, oxide thickness and charge. The oxide was held near one thickness at three temperatures, which removes a confound the other studies have. A simulation needs one choice of ours, the temperature path of a pull.

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, 2 approximated, 3 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.

TR-5: n-type, 1000 °C, fast pull in oxygen

Simulated time in this history: 1 h 34 min 03 s.

Across the samples

Timing the paper does not give

• The design is confounded in time: the oxygen slow pull is 10 min, the inert slow pull is 2 min and always follows a 10 min anneal. There is no 2 min pull in oxygen and no inert pull without an anneal.
• The temperature of the in-situ anneal is never stated.
• The fast pull is “<3 sec” in the tables, “1-3 sec” in the text and 0 in the time column.
• What the wafer's temperature does during a pull, and where it cools afterwards.
• Load gas, push rate and any ramp.

What the second reading changed

• The stored recipes begin after the oxidation. Written out in full, each history is the oxidation (300, 84 or 28 min), the anneal if any, the pull, and ten minutes at 400 °C after metallization.
• The argon runs (TR-4, 8, 12, 16, 20, 24) are stored as nitrogen anneals. The paper treats the two gases as one curve, so the numbers are not affected; the record is wrong.
• Every wafer was split and annealed at 400 °C for 10 min after metallization, one half in nitrogen and one in 10% hydrogen. The stored recipe has neither; the dataset holds both values.
• n-type wafers are 2-inch and p-type 3-inch, so a difference between the two types is also a difference between wafer sizes and furnace loads.

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>.

TR-5: n-type, 1000 °C, fast pull in oxygen

# TR-5: n-type, 1000 °C, fast pull in oxygen
SAMPLE TR_5 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, propanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 5040 TEMP 1000->1000 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 3 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY T_end 200..700 VARY duration 1..3
    EVENT Metal KIND metallization TIMING assumed                # Al-Cu-Si by cold flash evaporation
    RUN PostMetalAnneal DURATION 600 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V, before any injection
}

TR-6: n-type, 1000 °C, slow pull in oxygen

# TR-6: n-type, 1000 °C, slow pull in oxygen
SAMPLE TR_6 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, propanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 5040 TEMP 1000->1000 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 600 TEMP 1000->400 AMBIENT dry_O2 TIMING stated VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Al-Cu-Si by cold flash evaporation
    RUN PostMetalAnneal DURATION 600 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V, before any injection
}

TR-7: n-type, 1000 °C, nitrogen anneal, slow pull in nitrogen

# TR-7: n-type, 1000 °C, nitrogen anneal, slow pull in nitrogen
SAMPLE TR_7 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, propanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 5040 TEMP 1000->1000 AMBIENT dry_O2 TIMING stated
    RUN InertAnneal DURATION 600 TEMP 1000->1000 AMBIENT inert_N2 TIMING stated VARY T_hold 900..1000
    RUN Pull DURATION 120 TEMP 1000->400 AMBIENT inert_N2 TIMING stated VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Al-Cu-Si by cold flash evaporation
    RUN PostMetalAnneal DURATION 600 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V, before any injection
}

TR-8: n-type, 1000 °C, argon anneal, slow pull in argon

# TR-8: n-type, 1000 °C, argon anneal, slow pull in argon
SAMPLE TR_8 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, propanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 5040 TEMP 1000->1000 AMBIENT dry_O2 TIMING stated
    RUN InertAnneal DURATION 600 TEMP 1000->1000 AMBIENT inert_Ar TIMING stated VARY T_hold 900..1000
    RUN Pull DURATION 120 TEMP 1000->400 AMBIENT inert_Ar TIMING stated VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Al-Cu-Si by cold flash evaporation
    RUN PostMetalAnneal DURATION 600 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V, before any injection
}

TR-1: n-type, 900 °C, fast pull in oxygen

# TR-1: n-type, 900 °C, fast pull in oxygen
SAMPLE TR_1 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, propanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 18000 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 3 TEMP 900->400 AMBIENT dry_O2 TIMING bound VARY T_end 200..700 VARY duration 1..3
    EVENT Metal KIND metallization TIMING assumed                # Al-Cu-Si by cold flash evaporation
    RUN PostMetalAnneal DURATION 600 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V, before any injection
}

TR-2: n-type, 900 °C, slow pull in oxygen

# TR-2: n-type, 900 °C, slow pull in oxygen
SAMPLE TR_2 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, propanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 18000 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 600 TEMP 900->400 AMBIENT dry_O2 TIMING stated VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Al-Cu-Si by cold flash evaporation
    RUN PostMetalAnneal DURATION 600 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V, before any injection
}

TR-3: n-type, 900 °C, nitrogen anneal, slow pull in nitrogen

# TR-3: n-type, 900 °C, nitrogen anneal, slow pull in nitrogen
SAMPLE TR_3 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, propanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 18000 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN InertAnneal DURATION 600 TEMP 900->900 AMBIENT inert_N2 TIMING stated VARY T_hold 800..900
    RUN Pull DURATION 120 TEMP 900->400 AMBIENT inert_N2 TIMING stated VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Al-Cu-Si by cold flash evaporation
    RUN PostMetalAnneal DURATION 600 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V, before any injection
}

TR-9: n-type, 1100 °C, fast pull in oxygen

# TR-9: n-type, 1100 °C, fast pull in oxygen
SAMPLE TR_9 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, propanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 1680 TEMP 1100->1100 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 3 TEMP 1100->400 AMBIENT dry_O2 TIMING bound VARY T_end 200..700 VARY duration 1..3
    EVENT Metal KIND metallization TIMING assumed                # Al-Cu-Si by cold flash evaporation
    RUN PostMetalAnneal DURATION 600 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V, before any injection
}

TR-10: n-type, 1100 °C, slow pull in oxygen

# TR-10: n-type, 1100 °C, slow pull in oxygen
SAMPLE TR_10 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, propanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 1680 TEMP 1100->1100 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 600 TEMP 1100->400 AMBIENT dry_O2 TIMING stated VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Al-Cu-Si by cold flash evaporation
    RUN PostMetalAnneal DURATION 600 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V, before any injection
}

TR-11: n-type, 1100 °C, nitrogen anneal, slow pull in nitrogen

# TR-11: n-type, 1100 °C, nitrogen anneal, slow pull in nitrogen
SAMPLE TR_11 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, propanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 1680 TEMP 1100->1100 AMBIENT dry_O2 TIMING stated
    RUN InertAnneal DURATION 600 TEMP 1100->1100 AMBIENT inert_N2 TIMING stated VARY T_hold 1000..1100
    RUN Pull DURATION 120 TEMP 1100->400 AMBIENT inert_N2 TIMING stated VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Al-Cu-Si by cold flash evaporation
    RUN PostMetalAnneal DURATION 600 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V, before any injection
}

TR-17: p-type, 1000 °C, fast pull in oxygen

# TR-17: p-type, 1000 °C, fast pull in oxygen
SAMPLE TR_17 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: p_type
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, propanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 5040 TEMP 1000->1000 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 3 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY T_end 200..700 VARY duration 1..3
    EVENT Metal KIND metallization TIMING assumed                # Al-Cu-Si by cold flash evaporation
    RUN PostMetalAnneal DURATION 600 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V, before any injection
}

TR-19: p-type, 1000 °C, nitrogen anneal, slow pull in nitrogen

# TR-19: p-type, 1000 °C, nitrogen anneal, slow pull in nitrogen
SAMPLE TR_19 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: p_type
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, propanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 5040 TEMP 1000->1000 AMBIENT dry_O2 TIMING stated
    RUN InertAnneal DURATION 600 TEMP 1000->1000 AMBIENT inert_N2 TIMING stated VARY T_hold 900..1000
    RUN Pull DURATION 120 TEMP 1000->400 AMBIENT inert_N2 TIMING stated VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Al-Cu-Si by cold flash evaporation
    RUN PostMetalAnneal DURATION 600 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V, before any injection
}

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

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

# ==============================================================================
# ISL MODEL: FIXED CHARGE WITH AN EQUILIBRIUM IN EACH GAS
#
# In oxygen the charge moves toward a steady value that falls with temperature (the
# line of Deal et al. 1967, unchanged, with the oxygen kinetics fitted there).
# In a gas without oxygen it moves toward a lower equilibrium that also falls with
# temperature, Qi_ref * exp(E_q / k_B * (1/T - 1/T_iref)), at a rate of its own.
#
# The inert clock and the (100) inert equilibrium are fitted to the argon time series
# of Akinwande, Ho and Plummer (1982). The (111) inert equilibrium is fitted to their
# cycling experiment, with the clock carried over from (100). The model is then
# tested, unchanged, on the Fairchild wafers of 1967 and 1980.
# Fields in {{braces}} are filled by scripts/run_fixed_charge_two_lines.py.
# ==============================================================================
SAMPLE Wafer_{tag} {{
    FAMILY: Si_Planar
    ORIENTATION: Si{orientation}
}}
# The wafer starts at the steady value for its oxidation temperature.
STATE Q_f {{ UNIT: cm^-2; INITIAL: Q_hot + slope * (T_hot - T_ox); MIN: 0; MAX: 1.0e14 }}
CONTROL T {{ UNIT: K }}
CONTROL p_O2 {{ UNIT: atm }}
PARAMETER Q_hot {{ VALUE: {Q_hot}; UNIT: cm^-2; STATUS: sourced; SOURCE: Deal et al. 1967 Table II, steady value after dry oxidation at 1200 C }}
PARAMETER slope {{ VALUE: {slope}; UNIT: cm^-2 K^-1; STATUS: sourced; SOURCE: Deal et al. 1967 Table II, line through the 1200 C and 920 C steady values }}
PARAMETER T_hot {{ VALUE: 1473.15; UNIT: K; STATUS: constant }}
PARAMETER T_ox {{ VALUE: {T_ox_K}; UNIT: K; STATUS: constant }}
# ---- fitted to the pull-rate series ------------------------------------------------
PARAMETER k0 {{ VALUE: 1.0e3; UNIT: s^-1; STATUS: fitted }}
PARAMETER E_a {{ VALUE: 1.0; UNIT: eV; STATUS: fitted }}
# ---- fitted to the argon anneals of Akinwande, Ho and Plummer (1982) -----------------
PARAMETER k_i0 {{ VALUE: 1.0e1; UNIT: s^-1; STATUS: fitted }}
PARAMETER E_i {{ VALUE: 0.9; UNIT: eV; STATUS: fitted }}
PARAMETER Qi_ref {{ VALUE: 2.5e10; UNIT: cm^-2; STATUS: fitted }}
PARAMETER E_q {{ VALUE: 0.4; UNIT: eV; STATUS: fitted }}
PARAMETER T_iref {{ VALUE: 1273.15; 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 }}
# ---- where the exchange with oxygen stops as the wafer cools (hypothesis, added 10 November 2026) ----------------------
# The oxygen rate above was fitted with an activation energy at its lower bound (0.05 eV), so on its own it keeps moving
# charge at room temperature. Every history it was fitted and tested on ended its pull at 400 C, a cut-off that stood in for
# this. Reproducing Stanford 1982, Deal 1967 and Deal and Razouk 1980 with a wafer cooling to room temperature made the charge
# 3 to 5 times too high. The cut-off is now stated: the exchange is switched off over about 20 K around T_freeze. At 400 C it
# is 99% on, so every fitted and tested history is unchanged; how high the true freezing point is, is an open question
# (the Deal and Razouk alignment prefers pulls ending near 530 C).
PARAMETER T_freeze {{ VALUE: 623.15; UNIT: K; STATUS: hypothesis }}
PARAMETER w_freeze {{ VALUE: 10.0; UNIT: K; STATUS: hypothesis }}
QUANTITY rate {{ UNIT: s^-1; EQUATION: rate = k0 * exp(-E_a / (k_B * T)) / (1 + exp(-(T - T_freeze) / w_freeze)) }}
QUANTITY rate_inert {{ UNIT: s^-1; EQUATION: rate_inert = k_i0 * exp(-E_i / (k_B * T)) }}
QUANTITY Q_inert {{ UNIT: cm^-2; EQUATION: Q_inert = Qi_ref * exp((E_q / k_B) * (1 / T - 1 / T_iref)) }}
QUANTITY oxidizing {{ UNIT: 1; EQUATION: oxidizing = p_O2 / p_ref }}
QUANTITY Q_steady {{ UNIT: cm^-2; EQUATION: Q_steady = Q_hot + slope * (T_hot - T) }}
CONTROL_TRAJECTORY History_{tag} {{
{runs}
}}
# In oxygen the charge follows the temperature-dependent steady value.
OPERATOR F_OxidizingEquilibration : Relaxation {{
    EQUATION: d(Q_f)/dt = -rate * oxidizing * (Q_f - Q_steady)
}}
# Without oxygen it relaxes, at its own rate, toward an equilibrium of its own that falls as temperature rises.
# Akinwande, Ho and Plummer (1982) show the annealed charge cycling reversibly with temperature in argon.
OPERATOR F_InertRelaxation : Relaxation {{
    EQUATION: d(Q_f)/dt = -rate_inert * (1 - oxidizing) * (Q_f - Q_inert)
}}
OBSERVATION_MODEL Obs_Fixed_Charge {{ TARGET: Qss; UNIT: cm^-2; EQUATION: Qss = Q_f }}
EVALUATION_CONTRACT Contract_{tag} {{
    FROZEN: true
    DATASET: data/derived/deal_1967_qss.csv
    DATASET_DIGEST: sha256:{dataset_sha256}
    SPLIT: {split}
    TARGET: Qss = {target} +/- {tolerance} abs
}}

Our simulation against the paper

19 within, 4 near, 1 off 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 TR-5, TR-6, TR-7, TR-8 only; every other number is a test they played no part in.

Together: Pull T end 533.3 °C (was 400); Pull duration 3 s (was 3); InertAnneal T hold -66.67 °C shift (was 0).

As reproduced: 19 of 24 within tolerance, median error 5.0%. Aligned: 20 of 24 within tolerance, median error 4.4%. On the held-out samples only: 12 of 16 within tolerance, median error 5.0% as reproduced, 13 of 16 within tolerance, median error 4.4% aligned.

The unknowns were chosen on the four n-type wafers oxidized at 1000 °C, one per ending, and tested on the eight other wafers on this page (900 and 1100 °C, and the p-type wafers at 1000 °C). On the four 1000 °C wafers every setting passes 6 or 7 of 8, so the choice rests on the median error, which is weak evidence.

The end of a pull. The stored recipe ends every pull at 400 °C, a value chosen in 1967 against Deal's Table I. Here a pull that ends near 530 °C does better: the 10 minute pull in oxygen at 900 °C falls from 10.0 to 8.7 × 10^11 cm^-2 against 8.9 measured. Read physically, charge stops following the oxygen equilibrium at a higher temperature than our cut-off says during a slow pull. That is a statement about cooling, which a straight line to a fixed end temperature cannot carry; see below.

The temperature of the in-situ anneal. The report never states it. Moving it below the oxidation temperature improves the 1000 °C p-type wafer (1.67 to 2.12 against 2.22) and the 1100 °C wafer, and spoils the 900 °C wafer (2.80 to 4.01 against 2.96). No single shift serves all three, so this is not evidence that the anneal ran cooler. It is evidence that the program's level without oxygen, fitted to Stanford's argon anneals, does not have the temperature dependence these nitrogen anneals show.

The fast pull's duration (1 to 3 s) moves nothing: at these temperatures three seconds is too short for the program to change the charge.

13 within, 2 near, 1 off of 16 numbers with the aligned settings (the samples used to choose the unknowns are left out).

What alignment cannot fix. The slow pull in oxygen at 1100 °C stays 20% high (8.6 against 7.2) under every setting, and n-type and p-type wafers on one recipe differ by up to 2.5 × 10^11 cm^-2 in the report while the program gives them one value: doping is not an input to any program. The thickness rows pass throughout and were never in question.

What our language and ontology cannot yet say

• Cooling with a freezing point. With PROFILE exponential the language can now cool a wafer realistically, but the charge program then keeps moving charge down to room temperature, because its oxygen rate was fitted with an activation energy of 0.05 eV. A program needs a rate that vanishes as the wafer cools, fitted against pulls written as real cooling curves; then the pull's end temperature stops being a free number.
• Doping as an input. DOPING is recorded on each sample and read by nothing. The report's n-type and p-type wafers differ by more than the tolerance.
• The anneal's gas as a separate level. Nitrogen and argon are one curve in the report and one level in the program; if they differ (the 1100 °C rows hint that they might), the program needs a level per inert gas.

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. Is it right to read “in situ” as “at the oxidation temperature” for the ten-minute anneal?
2. The n-type and p-type wafers on one recipe differ by up to 2.5 × 10^11 cm^-2. Is that doping, wafer size, or run-to-run scatter?
3. Should the charge we compare be the nitrogen half or the hydrogen half of each wafer?