Reproducing Razouk and Deal 1979: interface state density against oxidation temperature, orientation and the end of the 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/razouk_deal_1979.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

R. R. Razouk and B. E. Deal, “Dependence of Interface State Density on Silicon Thermal Oxidation Process Variables”, J. Electrochem. Soc. 126, 1573–1581 (1979).

Fairchild's own measurement of midgap interface state density against oxidation temperature, orientation and the way an oxidation ends, from the laboratory whose fixed-charge work (Deal 1967, Deal and Razouk 1980) our charge program is tested on. The trap-density program was fitted on Vitkavage 1990 only, so every number here is a test in another laboratory. The project's earlier analysis (scripts/analyse_razouk.py, scripts/analyse_lab_gap.py, evaluations/razouk_analysis.json, evaluations/lab_gap_analysis.json) found that on the same nominal recipe (dry oxygen, fast pull in oxygen, no anneal) Razouk's (100) values are 3.0 times Vitkavage's at 900 °C and 6.0 times at 1000 °C: laboratories differ 3 to 7 times for reasons the papers do not record. This page shows what that means for a simulation.

How well can this study be reproduced?

Low. Gas, temperature, pull and hydrogen anneal are stated, but the oxidation time is stated only for the inert-anneal experiment (360 min at 1000 °C, 60 min at 1200 °C). For the temperature series it has to be inferred from a thickness range given for the whole paper. The pull's end and the wafer's cooling in the quartz “elephant” are not stated. Every value is on a figure; n- and p-type are averaged in some figures and not in others.

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, 6 approximated, 4 not in ours.

The timing of the history

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

(100), 900 °C, fast pull in oxygen, as oxidized

Simulated time in this history: 17 h 30 min 03 s.

Across the samples

Timing the paper does not give

• Oxidation time for the temperature series (Figures 8, 13) and for Figures 2–5 and 9: “oxidized for the specified time”, never specified. Ours is inferred from the thickness range, which itself is given only at 800 and 1200 °C.
• How long the wafer stays in the quartz elephant after the pull, in what gas, and how fast it cools.
• The end temperature of the 2 min inert pull/cool.
• Load temperature, push rate and gas before oxygen.
• Ramp and cool-down of the 500 °C hydrogen anneal; time between oxidation, metallization and anneal.
• Figure 13's caption says “cooled in dry O2” without a pull time; we assume the fast pull of Figure 8, because the unannealed n-type points agree.

What the second reading changed

• There is no dataset in data/derived for this paper and no stored recipe: the project's analyses read figures_agent_read_UNVERIFIED.csv directly, with the oxidation times 360 and 60 min for Figure 7 only and no history for Figures 8 and 13.
• The two readings of the figures (ours earlier, and the second reading) agree within 5% on 41 of the 44 values both hold. They disagree on three: Figure 13 after hydrogen at 1200 °C (0.60 earlier, 0.52 in the second reading, 13%), Figure 7 (100) at 1200 °C, 10 min in nitrogen, unannealed (3.2 against 3.0, 6%) and the same in argon for 60 min after hydrogen (0.123 against 0.13, 6%). The values compared on this page are the earlier reading's, which the project's analyses use. The second reading also gives what the first did not: Figure 13 before hydrogen and after a 450 °C, 25% H2 anneal, and the fixed charge of Figures 7 and 9.
• The earlier reading records only Figures 7, 8 and 13. Figure 9 (oxidation ambient at 1000 °C) puts the (111) oxygen-cooled value at about 16 × 10^11, against 26.5 on Figure 8 at the same temperature; the pull speed of Figure 9 is not stated, so the two cannot be reconciled.
• The project's analyses treat Figure 8 values as wafers pulled “in under 3 s”; the paper also says pull rates “were varied from 1-3 sec to 10 min”, and Figure 13's oxygen-cooled wafers have no stated pull time.
• evaluations/razouk_analysis.json compares each inert-held wafer with the oxygen-cooled wafer of Figure 8 at the same temperature. Those were oxidized for different (unstated) times and pulled in a different gas and at a different speed (3 s in oxygen against 2 min in nitrogen), as its own note says.

Their terms and ours

The simulation in our language

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

(100), 900 °C, fast pull in oxygen, as oxidized

# (100), 900 °C, fast pull in oxygen, as oxidized
SAMPLE F8_100_900 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 63000 TEMP 900->900 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 48000..87600
    RUN Pull DURATION 3 TEMP 900->400 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING bound VARY duration 1..3
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    EVENT NoAnneal KIND other TIMING assumed                     # The “as oxidized” half: no hydrogen anneal
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(100), 1000 °C, fast pull in oxygen, as oxidized

# (100), 1000 °C, fast pull in oxygen, as oxidized
SAMPLE F8_100_1000 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 19800 TEMP 1000->1000 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 12000..25200
    RUN Pull DURATION 3 TEMP 1000->400 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING bound VARY duration 1..3
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    EVENT NoAnneal KIND other TIMING assumed                     # The “as oxidized” half: no hydrogen anneal
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(100), 1100 °C, fast pull in oxygen, as oxidized

# (100), 1100 °C, fast pull in oxygen, as oxidized
SAMPLE F8_100_1100 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 8100 TEMP 1100->1100 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 3900..9300
    RUN Pull DURATION 3 TEMP 1100->400 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING bound VARY duration 1..3
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    EVENT NoAnneal KIND other TIMING assumed                     # The “as oxidized” half: no hydrogen anneal
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(100), 1200 °C, fast pull in oxygen, as oxidized

# (100), 1200 °C, fast pull in oxygen, as oxidized
SAMPLE F8_100_1200 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 3900 TEMP 1200->1200 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 1560..4200
    RUN Pull DURATION 3 TEMP 1200->400 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING bound VARY duration 1..3
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    EVENT NoAnneal KIND other TIMING assumed                     # The “as oxidized” half: no hydrogen anneal
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(111), 900 °C, fast pull in oxygen, as oxidized

# (111), 900 °C, fast pull in oxygen, as oxidized
SAMPLE F8_111_900 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 63000 TEMP 900->900 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 48000..87600
    RUN Pull DURATION 3 TEMP 900->400 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING bound VARY duration 1..3
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    EVENT NoAnneal KIND other TIMING assumed                     # The “as oxidized” half: no hydrogen anneal
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(111), 1000 °C, fast pull in oxygen, as oxidized

# (111), 1000 °C, fast pull in oxygen, as oxidized
SAMPLE F8_111_1000 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 19800 TEMP 1000->1000 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 12000..25200
    RUN Pull DURATION 3 TEMP 1000->400 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING bound VARY duration 1..3
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    EVENT NoAnneal KIND other TIMING assumed                     # The “as oxidized” half: no hydrogen anneal
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(111), 1100 °C, fast pull in oxygen, as oxidized

# (111), 1100 °C, fast pull in oxygen, as oxidized
SAMPLE F8_111_1100 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 8100 TEMP 1100->1100 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 3900..9300
    RUN Pull DURATION 3 TEMP 1100->400 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING bound VARY duration 1..3
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    EVENT NoAnneal KIND other TIMING assumed                     # The “as oxidized” half: no hydrogen anneal
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(111), 1200 °C, fast pull in oxygen, as oxidized

# (111), 1200 °C, fast pull in oxygen, as oxidized
SAMPLE F8_111_1200 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 3900 TEMP 1200->1200 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 1560..4200
    RUN Pull DURATION 3 TEMP 1200->400 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING bound VARY duration 1..3
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    EVENT NoAnneal KIND other TIMING assumed                     # The “as oxidized” half: no hydrogen anneal
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(100), 900 °C, fast pull in oxygen, n-type, after the hydrogen anneal

# (100), 900 °C, fast pull in oxygen, n-type, after the hydrogen anneal
SAMPLE F13_100_900 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_type_phosphorus
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 63000 TEMP 900->900 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 48000..87600
    RUN Pull DURATION 3 TEMP 900->400 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING bound VARY duration 1..3
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    RUN PMA DURATION 600 TEMP 500->500 AMBIENT mix:H2=0.1,N2=0.9 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(100), 1000 °C, fast pull in oxygen, n-type, after the hydrogen anneal

# (100), 1000 °C, fast pull in oxygen, n-type, after the hydrogen anneal
SAMPLE F13_100_1000 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_type_phosphorus
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 19800 TEMP 1000->1000 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 12000..25200
    RUN Pull DURATION 3 TEMP 1000->400 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING bound VARY duration 1..3
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    RUN PMA DURATION 600 TEMP 500->500 AMBIENT mix:H2=0.1,N2=0.9 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(100), 1100 °C, fast pull in oxygen, n-type, after the hydrogen anneal

# (100), 1100 °C, fast pull in oxygen, n-type, after the hydrogen anneal
SAMPLE F13_100_1100 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_type_phosphorus
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 8100 TEMP 1100->1100 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 3900..9300
    RUN Pull DURATION 3 TEMP 1100->400 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING bound VARY duration 1..3
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    RUN PMA DURATION 600 TEMP 500->500 AMBIENT mix:H2=0.1,N2=0.9 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(100), 1200 °C, fast pull in oxygen, n-type, after the hydrogen anneal

# (100), 1200 °C, fast pull in oxygen, n-type, after the hydrogen anneal
SAMPLE F13_100_1200 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_type_phosphorus
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 3900 TEMP 1200->1200 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 1560..4200
    RUN Pull DURATION 3 TEMP 1200->400 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING bound VARY duration 1..3
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    RUN PMA DURATION 600 TEMP 500->500 AMBIENT mix:H2=0.1,N2=0.9 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(100), 1000 °C, 360 min, then 60 min in nitrogen, as oxidized

# (100), 1000 °C, 360 min, then 60 min in nitrogen, as oxidized
SAMPLE F7_100_1000_N2_noH2 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 21600 TEMP 1000->1000 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING stated
    RUN InertAnneal DURATION 3600 TEMP 1000->1000 AMBIENT inert_N2 TIMING stated
    RUN Pull DURATION 120 TEMP 1000->400 AMBIENT inert_N2 TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    EVENT NoAnneal KIND other TIMING assumed                     # The “as oxidized” half: no hydrogen anneal
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(100), 1200 °C, 60 min, then 60 min in nitrogen, as oxidized

# (100), 1200 °C, 60 min, then 60 min in nitrogen, as oxidized
SAMPLE F7_100_1200_N2_noH2 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 3600 TEMP 1200->1200 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING stated
    RUN InertAnneal DURATION 3600 TEMP 1200->1200 AMBIENT inert_N2 TIMING stated
    RUN Pull DURATION 120 TEMP 1200->400 AMBIENT inert_N2 TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    EVENT NoAnneal KIND other TIMING assumed                     # The “as oxidized” half: no hydrogen anneal
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(111), 1000 °C, 360 min, then 60 min in nitrogen, as oxidized

# (111), 1000 °C, 360 min, then 60 min in nitrogen, as oxidized
SAMPLE F7_111_1000_N2_noH2 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 21600 TEMP 1000->1000 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING stated
    RUN InertAnneal DURATION 3600 TEMP 1000->1000 AMBIENT inert_N2 TIMING stated
    RUN Pull DURATION 120 TEMP 1000->400 AMBIENT inert_N2 TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    EVENT NoAnneal KIND other TIMING assumed                     # The “as oxidized” half: no hydrogen anneal
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(111), 1200 °C, 60 min, then 60 min in nitrogen, as oxidized

# (111), 1200 °C, 60 min, then 60 min in nitrogen, as oxidized
SAMPLE F7_111_1200_N2_noH2 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 3600 TEMP 1200->1200 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING stated
    RUN InertAnneal DURATION 3600 TEMP 1200->1200 AMBIENT inert_N2 TIMING stated
    RUN Pull DURATION 120 TEMP 1200->400 AMBIENT inert_N2 TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    EVENT NoAnneal KIND other TIMING assumed                     # The “as oxidized” half: no hydrogen anneal
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(100), 1000 °C, 360 min, then 60 min in nitrogen, after the hydrogen anneal

# (100), 1000 °C, 360 min, then 60 min in nitrogen, after the hydrogen anneal
SAMPLE F7_100_1000_N2_H2 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 21600 TEMP 1000->1000 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING stated
    RUN InertAnneal DURATION 3600 TEMP 1000->1000 AMBIENT inert_N2 TIMING stated
    RUN Pull DURATION 120 TEMP 1000->400 AMBIENT inert_N2 TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    RUN PMA DURATION 600 TEMP 500->500 AMBIENT mix:H2=0.1,N2=0.9 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(100), 1200 °C, 60 min, then 60 min in nitrogen, after the hydrogen anneal

# (100), 1200 °C, 60 min, then 60 min in nitrogen, after the hydrogen anneal
SAMPLE F7_100_1200_N2_H2 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 3600 TEMP 1200->1200 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING stated
    RUN InertAnneal DURATION 3600 TEMP 1200->1200 AMBIENT inert_N2 TIMING stated
    RUN Pull DURATION 120 TEMP 1200->400 AMBIENT inert_N2 TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    RUN PMA DURATION 600 TEMP 500->500 AMBIENT mix:H2=0.1,N2=0.9 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(111), 1000 °C, 360 min, then 60 min in nitrogen, after the hydrogen anneal

# (111), 1000 °C, 360 min, then 60 min in nitrogen, after the hydrogen anneal
SAMPLE F7_111_1000_N2_H2 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 21600 TEMP 1000->1000 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING stated
    RUN InertAnneal DURATION 3600 TEMP 1000->1000 AMBIENT inert_N2 TIMING stated
    RUN Pull DURATION 120 TEMP 1000->400 AMBIENT inert_N2 TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    RUN PMA DURATION 600 TEMP 500->500 AMBIENT mix:H2=0.1,N2=0.9 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(111), 1200 °C, 60 min, then 60 min in nitrogen, after the hydrogen anneal

# (111), 1200 °C, 60 min, then 60 min in nitrogen, after the hydrogen anneal
SAMPLE F7_111_1200_N2_H2 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 3600 TEMP 1200->1200 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING stated
    RUN InertAnneal DURATION 3600 TEMP 1200->1200 AMBIENT inert_N2 TIMING stated
    RUN Pull DURATION 120 TEMP 1200->400 AMBIENT inert_N2 TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    RUN PMA DURATION 600 TEMP 500->500 AMBIENT mix:H2=0.1,N2=0.9 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(100), 1200 °C, 60 min, then 60 min in argon, after the hydrogen anneal

# (100), 1200 °C, 60 min, then 60 min in argon, after the hydrogen anneal
SAMPLE F7_100_1200_Ar_H2 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 3600 TEMP 1200->1200 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING stated
    RUN InertAnneal DURATION 3600 TEMP 1200->1200 AMBIENT inert_Ar TIMING stated
    RUN Pull DURATION 120 TEMP 1200->400 AMBIENT inert_Ar TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    RUN PMA DURATION 600 TEMP 500->500 AMBIENT mix:H2=0.1,N2=0.9 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

(111), 1200 °C, 60 min, then 60 min in argon, after the hydrogen anneal

# (111), 1200 °C, 60 min, then 60 min in argon, after the hydrogen anneal
SAMPLE F7_111_1200_Ar_H2 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: sulfuric_aqua_regia_HF
    DOPING: n_and_p_averaged
    GROWTH: Cz
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Acid clean, HF, isopropanol vapour
    EVENT Load KIND load TIMING assumed                          # Loaded “in the appropriate ambient”
    RUN Oxidation DURATION 3600 TEMP 1200->1200 AMBIENT mix:O2=0.999998,H2O=2.0e-6 TIMING stated
    RUN InertAnneal DURATION 3600 TEMP 1200->1200 AMBIENT inert_Ar TIMING stated
    RUN Pull DURATION 120 TEMP 1200->400 AMBIENT inert_Ar TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Aluminium dots, flash evaporated at 25 °C
    RUN PMA DURATION 600 TEMP 500->500 AMBIENT mix:H2=0.1,N2=0.9 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # Quasi-static and high-frequency C-V; midgap density
}

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/vitkavage_dit/oxide_growth.isl.template, as it is written. Every equation the simulation uses is in this text; the runtime holds no physics.

# ==============================================================================
# ISL MODEL: DRY THERMAL OXIDATION OF SILICON (growth sector)
#
# Linear-parabolic (Deal-Grove) growth written as one ISL operator. Nothing is
# fitted to the test data: every parameter keeps the value declared here.
#
# Provenance of the constants: the rate constants are an Arrhenius fit to Table II of
# Deal and Grove (1965), which is for (111) silicon; see scripts/derive_deal_grove_constants.py.
# The orientation factor for other faces is not in that paper and remains a hypothesis.
# Fields in {{braces}} are filled by scripts/run_vitkavage_growth.py.
# ==============================================================================
SAMPLE {sample_id} {{
    FAMILY: Si_Planar
    ORIENTATION: Si{orientation}
}}
# Oxide thickness. The initial value is Deal and Grove's effective starting thickness
# for dry oxygen, which stands in for the fast initial regime their model does not describe.
STATE x_ox {{
    UNIT: cm
    INITIAL: x_i
    MIN: 0
    MAX: 1.0e-3
}}
CONTROL T {{ UNIT: K }}
CONTROL p_O2 {{ UNIT: atm }}
# Parabolic rate constant B = B0 * exp(-E_B / kT).
PARAMETER B0 {{ VALUE: 3.6053e-09; UNIT: cm^2 s^-1; STATUS: sourced; SOURCE: Deal and Grove, J. Appl. Phys. 36, 3770 (1965), Table II, dry oxygen on (111), Arrhenius least-squares fit, table agent-read }}
PARAMETER E_B {{ VALUE: 1.2860; UNIT: eV; STATUS: sourced; SOURCE: Deal and Grove, J. Appl. Phys. 36, 3770 (1965), Table II, dry oxygen on (111), Arrhenius least-squares fit, table agent-read }}
# Linear rate constant B/A on (111) = BA0 * exp(-E_BA / kT).
PARAMETER BA0 {{ VALUE: 2.4265e-01; UNIT: cm s^-1; STATUS: sourced; SOURCE: Deal and Grove, J. Appl. Phys. 36, 3770 (1965), Table II, dry oxygen on (111), Arrhenius least-squares fit, table agent-read }}
PARAMETER E_BA {{ VALUE: 2.0303; UNIT: eV; STATUS: sourced; SOURCE: Deal and Grove, J. Appl. Phys. 36, 3770 (1965), Table II, dry oxygen on (111), Arrhenius least-squares fit, table agent-read }}
# Orientation factor on the linear rate, relative to (111).
PARAMETER r_or {{ VALUE: {r_or}; UNIT: 1; STATUS: hypothesis }}
# Effective initial thickness for dry oxygen.
PARAMETER x_i {{ VALUE: 2.3e-6; UNIT: cm; STATUS: sourced; SOURCE: Deal and Grove, J. Appl. Phys. 36, 3770 (1965), stated intercept 230 +/- 30 angstrom for dry oxygen, agent-read }}
# Both rate constants are proportional to oxidant pressure; the constants above are for 1 atm.
PARAMETER p_ref {{ VALUE: 1.0; UNIT: atm; STATUS: constant }}
PARAMETER k_B {{ VALUE: 8.617333262e-5; UNIT: eV K^-1; STATUS: constant }}
CONTROL_TRAJECTORY {trajectory_id} {{
    RUN Oxidation DURATION {duration_s} TEMP {T_C}->{T_C} AMBIENT dry_O2
}}
# dx/dt = B / (2x + A), with A = B / (B/A).
OPERATOR F_LinearParabolicGrowth : OxideGrowth {{
    EQUATION: d(x_ox)/dt = (p_O2 / p_ref) * B0 * exp(-E_B / (k_B * T)) / (2 * x_ox + B0 * exp(-E_B / (k_B * T)) / (r_or * BA0 * exp(-E_BA / (k_B * T))))
}}
OBSERVATION_MODEL Obs_Oxide_Thickness {{
    TARGET: Thickness
    UNIT: cm
    EQUATION: Thickness = x_ox
}}
# Silicon consumed by the oxide grown in this recipe: 0.44 of its thickness, by the ratio of molar volumes.
OBSERVATION_MODEL Obs_Consumed_Silicon {{
    TARGET: Consumed_substrate
    UNIT: cm
    EQUATION: Consumed_substrate = 0.44 * (x_ox - x_i)
}}
EVALUATION_CONTRACT {contract_id} {{
    FROZEN: true
    DATASET: data/derived/vitkavage_1990_thickness.csv
    DATASET_DIGEST: sha256:{dataset_sha256}
    SPLIT: test
    TARGET: Thickness = {target} +/- {tolerance} rel
}}

Our simulation against the paper

5 within, 27 off of 32 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 F8_100_1000, F8_100_1100, F8_100_1200, F8_100_900, F8_111_1000, F8_111_1100, F8_111_1200, F8_111_900 only; every other number is a test they played no part in.

Together: Oxidation duration 48000 s (was 63000); Pull duration 3 s (was 3); Oxidation duration 12000 s (was 19800); Pull duration 3 s (was 3); Oxidation duration 3900 s (was 8100); Pull duration 3 s (was 3); Oxidation duration 1560 s (was 3900); Pull duration 3 s (was 3).

As reproduced: 6 of 32 within tolerance, median error 64.8%. Aligned: 6 of 32 within tolerance, median error 63.7%. On the held-out samples only: 6 of 24 within tolerance, median error 50.5% as reproduced, 6 of 24 within tolerance, median error 45.5% aligned.

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

The unknowns are the oxidation time of each temperature run of Figures 8 and 13 (both orientations and the n-type hydrogen halves share one run per temperature) and the fast pull's duration. They were chosen on the eight unannealed values of Figure 8 and tested on the four hydrogen-annealed halves of Figure 13, which come from the same runs; the Figure 7 wafers have stated times and no unknowns, so their rows are unchanged.

Nothing the paper leaves open closes the gap. On Figure 8 the program is 4 to 7 times below the paper on (100) (2.4 against 12.1 × 10^11 cm^-2 eV^-1 at 900 °C) and 35 to 48 times below on (111), and 0 of 8 are within tolerance at every setting searched. The search pushes every oxidation time to the short end of its range (800, 200, 65 and 26 min at 900 to 1200 °C), because a younger oxide carries more traps in the program; that is the thinnest oxide the paper's 120–220 nm allows, and it is chosen for direction, not for agreement. The fast pull (1 to 3 s) changes nothing in the trap program.

Held out. On the Figure 13 hydrogen halves the shorter times raise the simulation toward the paper (at 1000 °C 3.7 to 5.3 against 10 × 10^10), but all four stay outside tolerance: 6 of 24 test numbers within tolerance before and after, median error 51% before and 46% after. The variant with Figure 13 pulled slowly over 10 min in oxygen changes no trap number: the program does not read the pull.

What does pass is not the trap density: the oxide thickness of the 1200 °C, 60 min wafers (193 and 206 nm against 200 and 220 nm, nothing chosen), and the fixed charge of the (111) wafer held 60 min in nitrogen at 1000 °C (1.66 against 1.73 × 10^11 cm^-2), with the midgap density of that wafer's hydrogen half (3.9 against 3.8 × 10^10).

6 within, 2 near, 16 off of 24 numbers with the aligned settings (the samples used to choose the unknowns are left out).

What alignment cannot fix. Unannealed, the program sits a factor of 4 to 7 below Razouk on (100), the factor the project's earlier analysis found between Razouk and Vitkavage on one nominal recipe (evaluations/lab_gap_analysis.json: 3.0 at 900 °C, 6.0 at 1000 °C). The temperature dependence is close: from 900 to 1200 °C the paper falls 3.4 times on (100), the program 2.9 times. So the program carries the laboratory it was fitted in as a level, and the laboratory is not a variable any history can set. On (111) without hydrogen the program has no fitted value at midgap (no such wafer could be measured in Vitkavage's set), and it puts (111) below (100), against the paper's 3:1 the other way.

After hydrogen the error changes sign with the history: oxygen-cooled (100) wafers are 1.9 to 2.7 times higher in the paper than in the program, inert-held (100) wafers 2 to 2.6 times lower. The paper's central finding, that inert-annealed oxides are the worst as oxidized and the best after hydrogen, is not in the program at all: an hour in nitrogen or argon at temperature moves its midgap density by under 2%, and nitrogen and argon are the same gas to it. The fixed charge of the inert-held (111) wafers at 1200 °C is half the paper's (1.22 against 2.2–2.5 × 10^11), the same shortfall the program shows on the 1980 Fairchild wafers.

What our language and ontology cannot yet say

• A laboratory as a property of the sample. The largest single error here (4 to 7 times) is the laboratory. The ontology has the process factor laboratory but no sample or history field that records where a wafer was made and measured, so no program can carry a laboratory level, and the dataset cannot say which numbers share one.
• An unknown that is a measured quantity. The oxidation time here should be inferred from a thickness the paper states. VARY lets us search the time, but the range had to be computed by hand from the 1965 law; a statement INFER duration FROM Thickness 120..220 nm would let the language derive it and record that it was derived.
• Halves of one wafer. Every value here comes in pairs: one half annealed in hydrogen, one not. Two separate SAMPLEs lose that they share an oxidation; a CLEAVE that forks one history into two would carry it.
• Cooling in an end-piece. “Pulled … in less than 3 sec into a quartz elephant” is a fast withdrawal followed by an unknown dwell in a closed, still oxygen-filled quartz piece. A RUN with PROFILE exponential can hold the cooling but the language has no word for where the wafer is.
• Mixtures with HCl and pyrogenic steam. Figure 9's 5% and 10% HCl in oxygen cannot be written (the mixture gases are O2, N2, H2, H2O, Ar), so that figure is left off this page.
• Doping read by a program. Figure 8's n- and p-type (100) differ by 40% at 1100 and 1200 °C; DOPING is recorded on every sample and read by nothing.
• The predictor: the trap program does not respond to the gas of a step or to a pull, and labels (111) without hydrogen “outside the tested scope” while still reporting a number 35 to 48 times low. A refusal would be more honest than a number.

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. Would Fairchild in 1979 have oxidized (100) and (111) together in one run at each temperature, with one time chosen for a target thickness?
2. What happens to a wafer in a quartz “elephant” after a 3 s pull: how long does it stay, and is the elephant still full of oxygen?
3. The paper's unannealed (100) values are 3 to 6 times Vitkavage's for the same nominal recipe. Is a factor like that ordinary between laboratories in that period, and what would you suspect first: the clean, the metal, the C-V method or the furnace?
4. Figure 9's (111) oxygen-cooled value at 1000 °C is about 60% of Figure 8's. Is Figure 9 likely a slow pull?