Reproducing Akinwande, Ho and Plummer 1981: fixed charge against growth and anneal temperature, the earlier Stanford report

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/stanford_1981.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

T. Akinwande, C. Ho and J. Plummer, “Si/SiO2 Interface Charges”, section 7 of J. D. Plummer et al., Computer-Aided Design of Integrated Circuit Fabrication Processes for VLSI Devices, final report for 15 February 1981 to 31 March 1982, Stanford Integrated Circuits Laboratory TR-DXG501-82, July 1982, DTIC AD-A121414, printed pages 230 to 241 (PDF pages 238 to 249).

This is the earlier report the 1983 Stanford report (reproduced as stanford-1982) summarizes in its Figures 1 to 3. It holds the experiments that first showed the argon-annealed charge is not flat in temperature and cycles reversibly, which the fixed-charge program's second equilibrium (in a gas without oxygen) is built on. New to the project here: the (100) half of the 900/1100 °C cycling (the 1983 redrawing keeps only (111)), all trap densities (Figures 7.5 and 7.8), the 1200 °C argon values as the authors explain them, and the proposed rate law Nf − Nfe = K1 (dx/dt)^n exp(EA/kT). The as-grown and argon-annealed charges against temperature were already in the project as the 1983 redrawings; here they are run as histories through the predictor for the first time.

How well can this study be reproduced?

Low. The section states the orientation and doping type (n-type (111) and (100)), the anneal gas (argon), the anneal and growth temperatures (as figure abscissas), and that the as-grown wafers were “fast pulled”. It states nothing else: no clean, no oxidation gas, time or thickness, no anneal time, no pull time, no electrode, no measurement method. The 1983 report, which redraws three of these figures, adds the oxidation of the cycling wafers (1000 °C, 75 min, dry O2), the argon's water (< 2 ppm) and that the anneal times were chosen to reach equilibrium.

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, 2 approximated, 3 assumed, 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.

(111) grown at 750 °C, fast pulled

Simulated time in this history: 1 h 15 min 02 s.

Across the samples

Timing the paper does not give

• The oxidation of every wafer: gas, time, thickness (only the growth temperature of the as-grown series is given).
• The pull after oxidation: only “fast pulled”; no time, end temperature or gas.
• The argon anneal time at each temperature in Figures 7.4 and 7.5; the 1983 report says only that it was chosen to reach equilibrium.
• How the anneal wafers went into and out of the argon furnace, and whether the anneal followed the oxidation in the same tube.
• The time of each 900 °C and 1100 °C step of the cycling, and whether the wafers were measured (and so metallized) between steps.
• Electrode, metallization and any anneal after it for the fixed-charge values.

What the second reading changed

• No stored recipe or dataset holds this report: ontology/library.json lists the source as “held … Not yet read”. Its as-grown and argon-annealed charges are in the project as the 1983 report's redrawings (data/primary_sources/stanford_suprem_report_ada130105/figures_1_2_6_7_agent_read_UNVERIFIED.csv, Figures 1 and 2), read there from a lower-resolution scan.
• The two readings agree. As grown, the 1983 redrawing's (111) values are within 5% of ours at every temperature (e.g. 3.5 against 3.4 × 10^11 at 750 °C, 1.53 against 1.55 at 1200 °C); (100) within 10% except 1100 °C (4.5 against 4.65 × 10^10). Argon-annealed: within 5% for (111); (100) 5.0 against 5.05 at 900 °C, 2.8 against 3.5 × 10^10 at 1100 °C (the two symbols there are 1.5 and 5.5, so the mean depends on the reading).
• The 1983 report's Figure 3 (cycling between 900 and 1100 °C) shows only the (111) wafers. Figure 7.6 here also has (100): 1.64 × 10^11 as grown, then 0.69, 0.76, 0.69 and 0.75 × 10^11: a 58% drop at the first 900 °C step and nothing after. That half is new to the project.
• The 1983 report attributes the cycling to “(111) Si wafers oxidized in dry O2 at 1000° C for 75 minutes … annealed in argon (< 2 ppm H2O)”. This report states neither the oxidation nor the water. We use the 1983 statement for all cycling wafers, both orientations.
• The 1983 report's caption to its Figure 2 adds “The times were adjusted at each temperature to reach an equilibrium value”; this report's Figure 7.4 says nothing about time.
• The stanford-1982 page tests the as-grown value only at 1000 °C (three wafers). Here the as-grown series runs from 750 to 1200 °C (20 conditions) and the fixed-charge program's starting line (Deal 1967) is tested over that range through the predictor.
• This report's text calls the cycling figure “Fig. 7.5” (PDF p. 241); it is Figure 7.6. The lowest decade label of Figure 7.4 is printed 10^12 and must be 10^10.

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>.

(111) grown at 750 °C, fast pulled

# (111) grown at 750 °C, fast pulled
SAMPLE Wafer_asgrown_111_750 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 750->750 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 750->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) grown at 800 °C, fast pulled

# (111) grown at 800 °C, fast pulled
SAMPLE Wafer_asgrown_111_800 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 800->800 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 800->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) grown at 850 °C, fast pulled

# (111) grown at 850 °C, fast pulled
SAMPLE Wafer_asgrown_111_850 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 850->850 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 850->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) grown at 900 °C, fast pulled

# (111) grown at 900 °C, fast pulled
SAMPLE Wafer_asgrown_111_900 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 900->900 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 900->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) grown at 950 °C, fast pulled

# (111) grown at 950 °C, fast pulled
SAMPLE Wafer_asgrown_111_950 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 950->950 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 950->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) grown at 1000 °C, fast pulled

# (111) grown at 1000 °C, fast pulled
SAMPLE Wafer_asgrown_111_1000 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) grown at 1050 °C, fast pulled

# (111) grown at 1050 °C, fast pulled
SAMPLE Wafer_asgrown_111_1050 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1050->1050 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1050->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) grown at 1100 °C, fast pulled

# (111) grown at 1100 °C, fast pulled
SAMPLE Wafer_asgrown_111_1100 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1100->1100 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1100->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) grown at 1150 °C, fast pulled

# (111) grown at 1150 °C, fast pulled
SAMPLE Wafer_asgrown_111_1150 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1150->1150 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1150->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) grown at 1200 °C, fast pulled

# (111) grown at 1200 °C, fast pulled
SAMPLE Wafer_asgrown_111_1200 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1200->1200 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1200->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) grown at 750 °C, fast pulled

# (100) grown at 750 °C, fast pulled
SAMPLE Wafer_asgrown_100_750 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 750->750 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 750->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) grown at 800 °C, fast pulled

# (100) grown at 800 °C, fast pulled
SAMPLE Wafer_asgrown_100_800 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 800->800 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 800->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) grown at 850 °C, fast pulled

# (100) grown at 850 °C, fast pulled
SAMPLE Wafer_asgrown_100_850 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 850->850 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 850->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) grown at 900 °C, fast pulled

# (100) grown at 900 °C, fast pulled
SAMPLE Wafer_asgrown_100_900 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 900->900 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 900->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) grown at 950 °C, fast pulled

# (100) grown at 950 °C, fast pulled
SAMPLE Wafer_asgrown_100_950 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 950->950 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 950->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) grown at 1000 °C, fast pulled

# (100) grown at 1000 °C, fast pulled
SAMPLE Wafer_asgrown_100_1000 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) grown at 1050 °C, fast pulled

# (100) grown at 1050 °C, fast pulled
SAMPLE Wafer_asgrown_100_1050 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1050->1050 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1050->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) grown at 1100 °C, fast pulled

# (100) grown at 1100 °C, fast pulled
SAMPLE Wafer_asgrown_100_1100 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1100->1100 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1100->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) grown at 1150 °C, fast pulled

# (100) grown at 1150 °C, fast pulled
SAMPLE Wafer_asgrown_100_1150 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1150->1150 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1150->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) grown at 1200 °C, fast pulled

# (100) grown at 1200 °C, fast pulled
SAMPLE Wafer_asgrown_100_1200 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1200->1200 AMBIENT dry_O2 TIMING bound VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1200->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) argon anneal at 700 °C

# (111) argon anneal at 700 °C
SAMPLE Wafer_argon_111_700 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Transfer KIND transfer TIMING assumed                  # From the oxidation furnace to the argon anneal
    RUN Ar700Push DURATION 30 TEMP 400->700 AMBIENT inert_Ar TIMING assumed VARY duration 5..600
    RUN Ar700 DURATION 172800 TEMP 700->700 AMBIENT inert_Ar TIMING bound VARY duration 34560..864000
    RUN Ar700Pull DURATION 30 TEMP 700->400 AMBIENT inert_Ar TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

The symbols at 700 °C sit on the left axis of Figure 7.4; they may be an as-grown reference rather than a 700 °C anneal.

(111) argon anneal at 800 °C

# (111) argon anneal at 800 °C
SAMPLE Wafer_argon_111_800 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Transfer KIND transfer TIMING assumed                  # From the oxidation furnace to the argon anneal
    RUN Ar800Push DURATION 30 TEMP 400->800 AMBIENT inert_Ar TIMING assumed VARY duration 5..600
    RUN Ar800 DURATION 90000 TEMP 800->800 AMBIENT inert_Ar TIMING bound VARY duration 18000..450000
    RUN Ar800Pull DURATION 30 TEMP 800->400 AMBIENT inert_Ar TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) argon anneal at 900 °C

# (111) argon anneal at 900 °C
SAMPLE Wafer_argon_111_900 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Transfer KIND transfer TIMING assumed                  # From the oxidation furnace to the argon anneal
    RUN Ar900Push DURATION 30 TEMP 400->900 AMBIENT inert_Ar TIMING assumed VARY duration 5..600
    RUN Ar900 DURATION 14400 TEMP 900->900 AMBIENT inert_Ar TIMING bound VARY duration 2880..72000
    RUN Ar900Pull DURATION 30 TEMP 900->400 AMBIENT inert_Ar TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) argon anneal at 1000 °C

# (111) argon anneal at 1000 °C
SAMPLE Wafer_argon_111_1000 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Transfer KIND transfer TIMING assumed                  # From the oxidation furnace to the argon anneal
    RUN Ar1000Push DURATION 30 TEMP 400->1000 AMBIENT inert_Ar TIMING assumed VARY duration 5..600
    RUN Ar1000 DURATION 3600 TEMP 1000->1000 AMBIENT inert_Ar TIMING bound VARY duration 720..18000
    RUN Ar1000Pull DURATION 30 TEMP 1000->400 AMBIENT inert_Ar TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) argon anneal at 1100 °C

# (111) argon anneal at 1100 °C
SAMPLE Wafer_argon_111_1100 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Transfer KIND transfer TIMING assumed                  # From the oxidation furnace to the argon anneal
    RUN Ar1100Push DURATION 30 TEMP 400->1100 AMBIENT inert_Ar TIMING assumed VARY duration 5..600
    RUN Ar1100 DURATION 1800 TEMP 1100->1100 AMBIENT inert_Ar TIMING bound VARY duration 360..9000
    RUN Ar1100Pull DURATION 30 TEMP 1100->400 AMBIENT inert_Ar TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) argon anneal at 1200 °C

# (111) argon anneal at 1200 °C
SAMPLE Wafer_argon_111_1200 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Transfer KIND transfer TIMING assumed                  # From the oxidation furnace to the argon anneal
    RUN Ar1200Push DURATION 30 TEMP 400->1200 AMBIENT inert_Ar TIMING assumed VARY duration 5..600
    RUN Ar1200 DURATION 900 TEMP 1200->1200 AMBIENT inert_Ar TIMING bound VARY duration 180..4500
    RUN Ar1200Pull DURATION 30 TEMP 1200->400 AMBIENT inert_Ar TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) argon anneal at 700 °C

# (100) argon anneal at 700 °C
SAMPLE Wafer_argon_100_700 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Transfer KIND transfer TIMING assumed                  # From the oxidation furnace to the argon anneal
    RUN Ar700Push DURATION 30 TEMP 400->700 AMBIENT inert_Ar TIMING assumed VARY duration 5..600
    RUN Ar700 DURATION 172800 TEMP 700->700 AMBIENT inert_Ar TIMING bound VARY duration 34560..864000
    RUN Ar700Pull DURATION 30 TEMP 700->400 AMBIENT inert_Ar TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

The symbols at 700 °C sit on the left axis of Figure 7.4; they may be an as-grown reference rather than a 700 °C anneal.

(100) argon anneal at 800 °C

# (100) argon anneal at 800 °C
SAMPLE Wafer_argon_100_800 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Transfer KIND transfer TIMING assumed                  # From the oxidation furnace to the argon anneal
    RUN Ar800Push DURATION 30 TEMP 400->800 AMBIENT inert_Ar TIMING assumed VARY duration 5..600
    RUN Ar800 DURATION 90000 TEMP 800->800 AMBIENT inert_Ar TIMING bound VARY duration 18000..450000
    RUN Ar800Pull DURATION 30 TEMP 800->400 AMBIENT inert_Ar TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) argon anneal at 900 °C

# (100) argon anneal at 900 °C
SAMPLE Wafer_argon_100_900 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Transfer KIND transfer TIMING assumed                  # From the oxidation furnace to the argon anneal
    RUN Ar900Push DURATION 30 TEMP 400->900 AMBIENT inert_Ar TIMING assumed VARY duration 5..600
    RUN Ar900 DURATION 14400 TEMP 900->900 AMBIENT inert_Ar TIMING bound VARY duration 2880..72000
    RUN Ar900Pull DURATION 30 TEMP 900->400 AMBIENT inert_Ar TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) argon anneal at 1000 °C

# (100) argon anneal at 1000 °C
SAMPLE Wafer_argon_100_1000 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Transfer KIND transfer TIMING assumed                  # From the oxidation furnace to the argon anneal
    RUN Ar1000Push DURATION 30 TEMP 400->1000 AMBIENT inert_Ar TIMING assumed VARY duration 5..600
    RUN Ar1000 DURATION 3600 TEMP 1000->1000 AMBIENT inert_Ar TIMING bound VARY duration 720..18000
    RUN Ar1000Pull DURATION 30 TEMP 1000->400 AMBIENT inert_Ar TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) argon anneal at 1100 °C

# (100) argon anneal at 1100 °C
SAMPLE Wafer_argon_100_1100 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Transfer KIND transfer TIMING assumed                  # From the oxidation furnace to the argon anneal
    RUN Ar1100Push DURATION 30 TEMP 400->1100 AMBIENT inert_Ar TIMING assumed VARY duration 5..600
    RUN Ar1100 DURATION 1800 TEMP 1100->1100 AMBIENT inert_Ar TIMING bound VARY duration 360..9000
    RUN Ar1100Pull DURATION 30 TEMP 1100->400 AMBIENT inert_Ar TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) argon anneal at 1200 °C

# (100) argon anneal at 1200 °C
SAMPLE Wafer_argon_100_1200 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Transfer KIND transfer TIMING assumed                  # From the oxidation furnace to the argon anneal
    RUN Ar1200Push DURATION 30 TEMP 400->1200 AMBIENT inert_Ar TIMING assumed VARY duration 5..600
    RUN Ar1200 DURATION 900 TEMP 1200->1200 AMBIENT inert_Ar TIMING bound VARY duration 180..4500
    RUN Ar1200Pull DURATION 30 TEMP 1200->400 AMBIENT inert_Ar TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) cycling, as grown

# (111) cycling, as grown
SAMPLE Wafer_cycle_111_0 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) cycling, after step 1 (900 °C)

# (111) cycling, after step 1 (900 °C)
SAMPLE Wafer_cycle_111_1 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    RUN Cycle900Push DURATION 30 TEMP 400->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle900 DURATION 7200 TEMP 900->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 600..86400
    RUN Cycle900Pull DURATION 30 TEMP 900->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) cycling, after step 2 (1100 °C)

# (111) cycling, after step 2 (1100 °C)
SAMPLE Wafer_cycle_111_2 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    RUN Cycle900Push DURATION 30 TEMP 400->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle900 DURATION 7200 TEMP 900->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 600..86400
    RUN Cycle900Pull DURATION 30 TEMP 900->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    RUN Cycle1100Push DURATION 30 TEMP 400->1100 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle1100 DURATION 1198.8 TEMP 1100->1100 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 199.8..7192.8
    RUN Cycle1100Pull DURATION 30 TEMP 1100->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) cycling, after step 3 (900 °C)

# (111) cycling, after step 3 (900 °C)
SAMPLE Wafer_cycle_111_3 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    RUN Cycle900Push DURATION 30 TEMP 400->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle900 DURATION 7200 TEMP 900->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 600..86400
    RUN Cycle900Pull DURATION 30 TEMP 900->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    RUN Cycle1100Push DURATION 30 TEMP 400->1100 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle1100 DURATION 1198.8 TEMP 1100->1100 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 199.8..7192.8
    RUN Cycle1100Pull DURATION 30 TEMP 1100->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    RUN Cycle900Push DURATION 30 TEMP 400->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle900 DURATION 7200 TEMP 900->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 600..86400
    RUN Cycle900Pull DURATION 30 TEMP 900->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(111) cycling, after step 4 (1100 °C)

# (111) cycling, after step 4 (1100 °C)
SAMPLE Wafer_cycle_111_4 {
    FAMILY: Si_Planar
    ORIENTATION: Si111
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    RUN Cycle900Push DURATION 30 TEMP 400->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle900 DURATION 7200 TEMP 900->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 600..86400
    RUN Cycle900Pull DURATION 30 TEMP 900->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    RUN Cycle1100Push DURATION 30 TEMP 400->1100 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle1100 DURATION 1198.8 TEMP 1100->1100 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 199.8..7192.8
    RUN Cycle1100Pull DURATION 30 TEMP 1100->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    RUN Cycle900Push DURATION 30 TEMP 400->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle900 DURATION 7200 TEMP 900->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 600..86400
    RUN Cycle900Pull DURATION 30 TEMP 900->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    RUN Cycle1100Push DURATION 30 TEMP 400->1100 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle1100 DURATION 1198.8 TEMP 1100->1100 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 199.8..7192.8
    RUN Cycle1100Pull DURATION 30 TEMP 1100->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) cycling, as grown

# (100) cycling, as grown
SAMPLE Wafer_cycle_100_0 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) cycling, after step 1 (900 °C)

# (100) cycling, after step 1 (900 °C)
SAMPLE Wafer_cycle_100_1 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    RUN Cycle900Push DURATION 30 TEMP 400->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle900 DURATION 7200 TEMP 900->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 600..86400
    RUN Cycle900Pull DURATION 30 TEMP 900->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) cycling, after step 2 (1100 °C)

# (100) cycling, after step 2 (1100 °C)
SAMPLE Wafer_cycle_100_2 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    RUN Cycle900Push DURATION 30 TEMP 400->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle900 DURATION 7200 TEMP 900->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 600..86400
    RUN Cycle900Pull DURATION 30 TEMP 900->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    RUN Cycle1100Push DURATION 30 TEMP 400->1100 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle1100 DURATION 1198.8 TEMP 1100->1100 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 199.8..7192.8
    RUN Cycle1100Pull DURATION 30 TEMP 1100->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) cycling, after step 3 (900 °C)

# (100) cycling, after step 3 (900 °C)
SAMPLE Wafer_cycle_100_3 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    RUN Cycle900Push DURATION 30 TEMP 400->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle900 DURATION 7200 TEMP 900->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 600..86400
    RUN Cycle900Pull DURATION 30 TEMP 900->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    RUN Cycle1100Push DURATION 30 TEMP 400->1100 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle1100 DURATION 1198.8 TEMP 1100->1100 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 199.8..7192.8
    RUN Cycle1100Pull DURATION 30 TEMP 1100->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    RUN Cycle900Push DURATION 30 TEMP 400->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle900 DURATION 7200 TEMP 900->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 600..86400
    RUN Cycle900Pull DURATION 30 TEMP 900->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

(100) cycling, after step 4 (1100 °C)

# (100) cycling, after step 4 (1100 °C)
SAMPLE Wafer_cycle_100_4 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type
}
CONTROL_TRAJECTORY History {
    EVENT Load KIND load TIMING assumed                          # Clean and load into the oxidation furnace
    RUN Oxidation DURATION 4500 TEMP 1000->1000 AMBIENT dry_O2 TIMING assumed VARY duration 600..36000
    RUN Pull DURATION 2 TEMP 1000->400 AMBIENT dry_O2 TIMING bound VARY duration 1..10 VARY T_end 200..700
    RUN Cycle900Push DURATION 30 TEMP 400->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle900 DURATION 7200 TEMP 900->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 600..86400
    RUN Cycle900Pull DURATION 30 TEMP 900->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    RUN Cycle1100Push DURATION 30 TEMP 400->1100 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle1100 DURATION 1198.8 TEMP 1100->1100 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 199.8..7192.8
    RUN Cycle1100Pull DURATION 30 TEMP 1100->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    RUN Cycle900Push DURATION 30 TEMP 400->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle900 DURATION 7200 TEMP 900->900 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 600..86400
    RUN Cycle900Pull DURATION 30 TEMP 900->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    RUN Cycle1100Push DURATION 30 TEMP 400->1100 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 5..600
    RUN Cycle1100 DURATION 1198.8 TEMP 1100->1100 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING bound VARY duration 199.8..7192.8
    RUN Cycle1100Pull DURATION 30 TEMP 1100->400 AMBIENT mix:Ar=0.999998,H2O=2.0e-6 TIMING assumed VARY duration 2..600
    EVENT Metal KIND metallization TIMING assumed                # Gate electrode and C-V capacitor
    EVENT CV KIND measurement TIMING assumed                     # C-V: fixed charge and midgap trap density
}

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

4 within, 6 near, 58 off of 68 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 argon_100_1000, argon_100_800, argon_111_1000, argon_111_800, asgrown_100_1000, asgrown_111_1000 only; every other number is a test they played no part in.

Together: Oxidation duration 2349 s (was 4500); Pull duration 1 s (was 2); Pull T end 700 °C (was 400); Ar800Push duration 30 s (was 30); Ar800 duration 18000 s (was 90000); Ar800Pull duration 600 s (was 30); Ar1000Push duration 30 s (was 30); Ar1000 duration 3600 s (was 3600); Ar1000Pull duration 30 s (was 30).

As reproduced: 4 of 68 within tolerance, median error 59.4%. Aligned: 5 of 68 within tolerance, median error 58.7%. On the held-out samples only: 3 of 57 within tolerance, median error 64.0% as reproduced, 3 of 57 within tolerance, median error 60.6% aligned.

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

Read this section knowing what was fitted where. The fixed-charge program was fitted to the 1983 report's argon time series at 800 and 1000 °C ((100)) and its (111) cycling between 800 and 1100 °C; nothing on this page was used. The unknowns of the history were chosen on six numbers at the temperatures of that fit (the argon anneals at 800 and 1000 °C, both orientations, and the as-grown wafers at 1000 °C) and tested on the other 57: the as-grown series from 750 to 1200 °C, the argon anneals at 700, 900, 1100 and 1200 °C, the 900/1100 °C cycling and every trap density. The anneal times at 700, 900, 1100 and 1200 °C and the cycling steps carry no chosen sample, so they kept the values written here (18 unknowns not searched).

As reproduced: 4 of 68 within tolerance, median error 59.4%. Aligned (history only): 5 of 68, 58.7%. On the 57 held-out numbers: 3 of 57 before and after, median error 64.0% and 60.6%.

The history does not matter for the fixed charge. Every scan of a pull, a push or an anneal time is flat on the fixed charges. The argon anneals are long enough at every temperature that the program sits at its argon equilibrium; the program starts the as-grown wafers at Deal's 1967 steady value for the growth temperature, which no history step before the pull can change. The one scan that moves is the oxidation time (from 2 numbers within at 10 to 20 min to 1 at 75 min and more), through the trap-density program, which reads it; the combined search settled on 39 min. With one or two numbers deciding, that is not evidence about Stanford's oxidation time.

As grown, 750 to 1200 °C: Deal's line is too high and too flat for Stanford. Fast-pulled (2 s to 400 °C in oxygen), the program gives 1.25 to 2.0 times the report on (111) and 1.4 to 2.65 times on (100), the ratio growing with temperature on (100): the report's (100) charge falls elevenfold from 750 to 1200 °C (1.63 to 0.14 × 10^11 cm⁻²), the program's sevenfold (2.68 to 0.38). This is the authors' own point that (100) falls faster than (111). No break near 950 °C appears, since the program's starting value is a straight line in temperature.

Cooling after the pull tests the freeze-out hypothesis, and it fails here. With every pull written as a cool to 25 °C in the gas the wafer left (PROFILE exponential, TAU 30 s, 5 min), the as-grown charge becomes almost independent of growth temperature: (111) 8.1 × 10^11 at 750 °C and 6.8 at 1200 °C, (100) 3.4 and 2.75, against 3.4 to 1.55 and 1.63 to 0.14 measured. The program's oxygen rate (activation energy 0.05 eV) relaxes the charge toward Deal's line extrapolated down to the 350 °C freeze point during the 10 to 20 s the wafer spends hot, so the growth temperature is forgotten. The same happens with the owner's cooling scenarios after a straight 2 s pull to 400 °C (section below): (100) grown at 1000 °C goes from 1.40 to 2.07 × 10^11 (fast cooling) and 3.64 (slow). Run outside this page with T_freeze raised to 450 °C, those scenarios move the as-grown values by under 2%; with it at 400 °C, by 3 to 36% (fast cooling) and up to 2.7 times (slow cooling, (100) grown at 1200 °C). So this report's as-grown series asks for a freeze-out at or above about 450 °C, consistent with the Deal and Razouk alignment's 530 °C.

Cooling in nitrogen (the 1983 report's flushed furnace mouth; no oxygen exchange after the wafer leaves the hot zone) is the best variant: 7 of 68, median error 54.8%, because each as-grown wafer then keeps Deal's value for its growth temperature; (111) at 1150 and 1200 °C and (100) at 1200 °C come within tolerance. Below 1100 °C Deal's line is still 1.3 to 2.0 times high. Neither report states the cooling gas.

Argon equilibrium against temperature (Figure 7.4). The program's argon equilibrium falls with temperature with nearly the same energy on both orientations (0.41 eV (111), 0.38 eV (100)). The report's (111) values fall more gently (about 0.3 eV from 700 to 1000 °C: 3.05 to 1.30 × 10^11 against 5.1 to 1.6 simulated) and its (100) values more steeply (about 0.6 eV: 1.9 to 0.36 against 0.83 to 0.28). Above 1000 °C the report is flat on (111) and (100) and rises again at 1200 °C (3.05 × 10^11 (111), 0.48 (100)), where the program keeps falling (1.04, 0.19). Within tolerance: (111) at 1100 °C and (100) at 1000 °C only.

Cycling between 900 and 1100 °C (Figure 7.6), fully held out. (111): the program reproduces the shape (down, down, up, down) with 2.22 × 10^11 at 900 °C against 1.58 and 1.50, and 1.26 at 1100 °C against 1.13 and 1.22 (one within, one near). (100), new to the project: the report falls from 1.64 to 0.69 × 10^11 at the first 900 °C anneal and then stays between 0.69 and 0.76 whatever the temperature; the program alternates between 0.38 and 0.22, 45 to 71% low. The 1983 report's (100) cycling between 800 and 1100 °C did alternate (8.3, 1.7, 9.7, 2.0 × 10^10). One laboratory, two batches: one alternates by a factor 5, the other not at all.

Trap density without hydrogen. (100): within 10% after argon at 900 °C, near at 950 °C as grown and 1200 °C as grown; otherwise 0.45 to 0.8 of the report as grown, and after argon the program's fall with anneal temperature is too shallow (2.1 to 1.5 × 10^11 from 800 to 1200 °C against 2.7 to 0.69). (111): the program gives 0.5 to 3 × 10^11 against 1.2 to 7.4 × 10^12 measured, 15 to 50 times low. The program itself says it has no fitted value for the second population on unannealed (111), because Vitkavage could not measure one at midgap; Figures 7.5 and 7.8 are such measurements.

Heating and cooling transitions (section below). The four scenarios leave 4 of 68 within tolerance but raise the median error from 61% to 85% (hot push) and 95% (slow cooling). The numbers that move (22 to 32 of 68) are the as-grown and cycling-start charges, through the oxygen cooling described above; argon-annealed wafers and trap densities move by under 2%.

Oxidized at the anneal temperature (Deal's in-situ reading of Figure 7.4) changes nothing on the argon wafers (3 of 68 alone): the program forgets the oxidation once the argon anneal reaches equilibrium. The data cannot tell the two readings apart.

3 within, 8 near, 46 off of 57 numbers with the aligned settings (the samples used to choose the unknowns are left out).

What alignment cannot fix. The program's as-grown value is Deal's 1967 line for each orientation, a laboratory property, and Stanford's wafers sit 1.25 to 2.65 times lower and fall more steeply on (100). The authors' own proposal, Nf − Nfe = K1 (dx/dt)^n exp(EA/kT), ties the as-grown charge to the oxidation rate, which the program does not see; on (100) the faster fall with temperature is what such a term would have to supply.

The argon equilibrium has the wrong temperature dependence per orientation (too steep on (111), too shallow on (100)) and no minimum: above 1000 °C the report's values are flat and rise at 1200 °C, which the authors attribute to SiO formation or cooling transients. Neither mechanism is in any program; the argon pull here moves the charge by under 1%, because the program's argon clock (1.8 eV) is slow on cooling.

The (100) cycling between 900 and 1100 °C does not alternate in the report, while the program's equilibrium does by a factor 1.7. A reversible equilibrium per temperature cannot give a value that stays put after the first anneal; the authors read (100) as within noise. That Stanford's 1983 (100) wafers alternated by a factor 5 between 800 and 1100 °C makes this batch to batch, not a model test that can be passed.

The trap-density program cannot be tested on unannealed (111): it has no fitted second population for it. This report's Figures 7.5 and 7.8 are the measurement the program lacks.

What our language and ontology cannot yet say

• A freezing point that is stated and testable. The as-grown series is the cleanest test of where the oxygen exchange stops: ten growth temperatures, one pull. With the stated hypothesis at 350 °C a realistic cool erases the growth temperature; at 450 °C it does not. The ontology could carry the freeze-out temperature of each operator as a declared hypothesis with its own test set (this series and Deal and Razouk's pulls), so that raising it is a recorded decision, not a template edit.
• The gas a wafer cools in. A fast pull leaves the oxidation gas for a flushed mouth and then room air. The best variant here (cooling in nitrogen) is a Python edit; a PROFILE or WITHDRAW statement that names the gas after withdrawal would make it a declared unknown (VARY ambient).
• A starting charge from the laboratory. The program's as-grown value is Deal's Fairchild line. INITIAL Q_f FROM <laboratory line> would let Stanford's own as-grown line (this report's Figure 7.7) be the start for Stanford's wafers, and make the Fairchild line one stated choice.
• A target observed on a fixed time grid, not a history. The argon anneal times were “adjusted at each temperature to reach an equilibrium value” (1983 report). The language can only write a guessed duration. RUN … UNTIL steady (an anneal that lasts until the state stops moving) would state what the authors did and make the anneal time a program output instead of an assumption.
• One wafer measured between anneals. The cycling is one sequence with a C-V after each step; it is written as five histories. A MEASURE event inside one history whose readings are the scored values would say it once, and would show that metal must come off between steps.
• Oxidation rate as a sample-history quantity. Eq. 7.1 makes the as-grown charge a function of dx/dt at the end of growth. The growth programs compute it; the charge program cannot read another program's output. A cross-program QUANTITY (the oxidation rate at the pull) would let a rate-dependent charge law be written and tested on Figure 7.7.

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. Figure 7.4 has symbols on the left axis at 700 °C. Would a 1981 plot put a 700 °C anneal there, or is it an as-grown reference?
2. The (100) argon values at 1100 and 1200 °C spread by a factor 4 to 5 between two symbols. Is that measurement noise at a few 10^10 cm⁻², or two kinds of wafer?
3. The authors offer SiO formation or cooling transients for the high 1200 °C argon values. Would a 1200 °C argon anneal followed by a normal pull be expected to raise the charge on cooling?
4. Were the as-grown wafers of Figure 7.7 grown in dry oxygen to a fixed time or to a fixed thickness? The 1983 report later shows the as-grown charge depends on thickness below about 1000 Å.