Reproducing Hung 1987: fixed charge and trap density of thin oxides

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/hung_1987.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

Hung Kwok Kwong, “Electrical Characterization of Si-SiO2 Interface for Thin Oxides”, PhD thesis, University of Hong Kong (1987), chapters 4 and 5 and Appendix A.

A thesis on oxides 8 to 43 nm thick, the thinnest planar oxides in the graph. The project holds 26 fixed charges (chapter 4's tables and the anneal series of Figure 5.9) and 34 midgap trap densities (Figures 5.4 and 5.9) from it. It is the second laboratory for the trap-density program, which was found on Vitkavage's wafers, and a laboratory the fixed-charge program never saw. Here both chapters are written out with the Appendix's furnace recipe, which the stored recipes leave out: the boat-in, the boat-out or fast pull, and the anneal after metallization.

How well can this study be reproduced?

Moderate. Oxidation temperature, gas, time and the nitrogen anneal are printed per wafer, and the Appendix gives a recipe with boat-in, anneal and boat-out times. What a simulation still has to supply: whether the printed oxidation times include the 3 min boat-in, the furnace's ramp from 900 to 1050 °C for chapter 4's second batch, how the anneal series was withdrawn, and the wafer's cooling after every withdrawal. The trap densities of chapter 5 exist only as points on two figures.

The grade is ours and is about the paper as a source for simulation, not about the quality of the experiment: high means the sample, every step and its timing are stated well enough that a simulation needs no choices of ours; moderate that some choices are ours and are listed; low that the result depends on choices the paper does not constrain.

The sample and its history, played back

The sample is drawn from the simulation: layer heights and the read-outs are what the ISL programs compute at each moment of the history. Steps the language cannot state (a clean, a metallization, a measurement) are on the clock and marked as recorded, not simulated.

Does our sample and history match the paper's?

Left: the paper's own words, with the page of the PDF. Right: what we simulate. 7 same, 2 approximated, 1 assumed, 1 differs, 16 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.

M1: 1050 °C, 20% O2 in N2, 8 min, 101 Å, N2 anneal

Simulated time in this history: 1 h 44 min.

Across the samples

Timing the paper does not give

• Whether the oxidation times of Tables 4.1 and 5.1 include the 3 min boat-in. For B1 (1.5 min in oxygen at 1050 °C) the boat-in is twice the printed time.
• Boat-in and boat-out for chapter 4's 900 °C batch: the Appendix gives them for the 1050 °C, 20% O2 recipe only.
• How the furnace went from 900 °C (oxidation) to 1050 °C (anneal) for batches K and J: time, gas, and whether the wafers stayed inside.
• Where the wafer cools after a boat-out or a fast pull, and how fast.
• How the anneal series P and Q were withdrawn after the nitrogen anneal: fast pull or 3 min boat-out, in nitrogen or oxygen; and whether the 0 min wafers had a gas switch at all.
• The forming-gas anneal: 30 min (chapter 4), 10 min (chapter 5), “10-30 min” (Appendix), with 15 min of nitrogen at 400 °C before and after in the Appendix.
• Time between steps: storage “in a dry environment throughout the course of experiments” for the capacitor wafers.

What the second reading changed

• The stored recipes have one or two RUNs: the oxidation and, in chapter 4 and the anneal series, the nitrogen anneal. The thesis's Appendix adds a 3 min boat-in in the oxidation gas, a 3 min boat-out in nitrogen (chapter 4), a fast pull in the oxidation gas (chapter 5), and in chapter 4 a 30 min forming-gas anneal with 15 min of nitrogen before and after. None of these is in the stored recipes.
• The anneal series P (1050 °C, 20% O2) is stored with 27 min of oxidation, “inferred from the thickness”; Table 5.1b prints 20 min. The datasets were built before Table 5.1b was read.
• Batches K and J are stored as 900 °C oxidation followed at once by 30 min at 1050 °C; the ramp between them is not described in the thesis and is not in the stored recipe.
• The library records the pull as “under 3 s in the oxidation ambient” for the whole source. That is chapter 5's; chapter 4's wafers had a 30 min nitrogen anneal and a 3 min boat-out in nitrogen.
• The time_law_dit dataset has no 0 min rows for the anneal series; two_population_dit has them (5.48 and 1.42 × 10^11). The 0 min wafers of Figure 5.9 are separate wafers from those of Figure 5.4.
• Figure 5.9's fixed charge comes from the half of each wafer that had forming gas, its trap density from the other half. One stored recipe stands for both.

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>.

M1: 1050 °C, 20% O2 in N2, 8 min, 101 Å, N2 anneal

# M1: 1050 °C, 20% O2 in N2, 8 min, 101 Å, N2 anneal
SAMPLE Wafer_M1 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT SourceDrain KIND other TIMING stated                   # Phosphorus source and drain: predeposition at 1000 °C, drive-in 60 min at 1050 °C in O2
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh4 DURATION 180 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 480 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated
    RUN NitrogenAnneal DURATION 1800 TEMP 1050->1050 AMBIENT inert_N2 TIMING stated
    RUN BoatOut DURATION 180 TEMP 1050->400 AMBIENT inert_N2 TIMING stated VARY T_end 200..900
    EVENT ContactWindows KIND etch TIMING assumed                # Source and drain contact windows opened
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament
    RUN PMAFlushIn DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    RUN PostMetalAnneal DURATION 1800 TEMP 400->400 AMBIENT forming_gas_H2 TIMING stated VARY duration 600..1800
    RUN PMAFlushOut DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT Package KIND other TIMING assumed                      # Lapped to 150 µm, scribed, bonded, sealed in TO-5
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V; thickness from the 10 Hz accumulation capacitance
}

M2: 1050 °C, 20% O2 in N2, 22 min, 157 Å, N2 anneal

# M2: 1050 °C, 20% O2 in N2, 22 min, 157 Å, N2 anneal
SAMPLE Wafer_M2 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT SourceDrain KIND other TIMING stated                   # Phosphorus source and drain: predeposition at 1000 °C, drive-in 60 min at 1050 °C in O2
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh4 DURATION 180 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 1320 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated
    RUN NitrogenAnneal DURATION 1800 TEMP 1050->1050 AMBIENT inert_N2 TIMING stated
    RUN BoatOut DURATION 180 TEMP 1050->400 AMBIENT inert_N2 TIMING stated VARY T_end 200..900
    EVENT ContactWindows KIND etch TIMING assumed                # Source and drain contact windows opened
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament
    RUN PMAFlushIn DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    RUN PostMetalAnneal DURATION 1800 TEMP 400->400 AMBIENT forming_gas_H2 TIMING stated VARY duration 600..1800
    RUN PMAFlushOut DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT Package KIND other TIMING assumed                      # Lapped to 150 µm, scribed, bonded, sealed in TO-5
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V; thickness from the 10 Hz accumulation capacitance
}

M3: 1050 °C, 20% O2 in N2, 55 min, 265 Å, N2 anneal

# M3: 1050 °C, 20% O2 in N2, 55 min, 265 Å, N2 anneal
SAMPLE Wafer_M3 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT SourceDrain KIND other TIMING stated                   # Phosphorus source and drain: predeposition at 1000 °C, drive-in 60 min at 1050 °C in O2
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh4 DURATION 180 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 3300 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated
    RUN NitrogenAnneal DURATION 1800 TEMP 1050->1050 AMBIENT inert_N2 TIMING stated
    RUN BoatOut DURATION 180 TEMP 1050->400 AMBIENT inert_N2 TIMING stated VARY T_end 200..900
    EVENT ContactWindows KIND etch TIMING assumed                # Source and drain contact windows opened
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament
    RUN PMAFlushIn DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    RUN PostMetalAnneal DURATION 1800 TEMP 400->400 AMBIENT forming_gas_H2 TIMING stated VARY duration 600..1800
    RUN PMAFlushOut DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT Package KIND other TIMING assumed                      # Lapped to 150 µm, scribed, bonded, sealed in TO-5
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V; thickness from the 10 Hz accumulation capacitance
}

M4: 1050 °C, 20% O2 in N2, 110 min, 392 Å, N2 anneal

# M4: 1050 °C, 20% O2 in N2, 110 min, 392 Å, N2 anneal
SAMPLE Wafer_M4 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT SourceDrain KIND other TIMING stated                   # Phosphorus source and drain: predeposition at 1000 °C, drive-in 60 min at 1050 °C in O2
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh4 DURATION 180 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 6600 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated
    RUN NitrogenAnneal DURATION 1800 TEMP 1050->1050 AMBIENT inert_N2 TIMING stated
    RUN BoatOut DURATION 180 TEMP 1050->400 AMBIENT inert_N2 TIMING stated VARY T_end 200..900
    EVENT ContactWindows KIND etch TIMING assumed                # Source and drain contact windows opened
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament
    RUN PMAFlushIn DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    RUN PostMetalAnneal DURATION 1800 TEMP 400->400 AMBIENT forming_gas_H2 TIMING stated VARY duration 600..1800
    RUN PMAFlushOut DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT Package KIND other TIMING assumed                      # Lapped to 150 µm, scribed, bonded, sealed in TO-5
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V; thickness from the 10 Hz accumulation capacitance
}

N1: 1050 °C, 20% O2 in N2, 110 min, etched back to 145 Å, N2 anneal

# N1: 1050 °C, 20% O2 in N2, 110 min, etched back to 145 Å, N2 anneal
SAMPLE Wafer_N1 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT SourceDrain KIND other TIMING stated                   # Phosphorus source and drain: predeposition at 1000 °C, drive-in 60 min at 1050 °C in O2
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh4 DURATION 180 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 6600 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated
    RUN NitrogenAnneal DURATION 1800 TEMP 1050->1050 AMBIENT inert_N2 TIMING stated
    RUN BoatOut DURATION 180 TEMP 1050->400 AMBIENT inert_N2 TIMING stated VARY T_end 200..900
    EVENT EtchBack KIND etch TIMING stated                       # Etched back in 2.5% HF for 210 s, to 145 Å
    EVENT ContactWindows KIND etch TIMING assumed                # Source and drain contact windows opened
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament
    RUN PMAFlushIn DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    RUN PostMetalAnneal DURATION 1800 TEMP 400->400 AMBIENT forming_gas_H2 TIMING stated VARY duration 600..1800
    RUN PMAFlushOut DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT Package KIND other TIMING assumed                      # Lapped to 150 µm, scribed, bonded, sealed in TO-5
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V; thickness from the 10 Hz accumulation capacitance
}

Etched back after the anneal. Its fixed charge is the 40 nm oxide's; the simulation does not thin the oxide, so its thickness is not compared.

K1: 900 °C, dry O2, 27 min, 103 Å, N2 anneal

# K1: 900 °C, dry O2, 27 min, 103 Å, N2 anneal
SAMPLE Wafer_K1 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT SourceDrain KIND other TIMING stated                   # Phosphorus source and drain: predeposition at 1000 °C, drive-in 60 min at 1050 °C in O2
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh4 DURATION 180 TEMP 900->900 AMBIENT dry_O2 TIMING assumed VARY duration 1..180
    RUN Oxidation DURATION 1620 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Ramp DURATION 1200 TEMP 900->1050 AMBIENT inert_N2 TIMING assumed VARY duration 300..3600
    RUN NitrogenAnneal DURATION 1800 TEMP 1050->1050 AMBIENT inert_N2 TIMING stated
    RUN BoatOut DURATION 180 TEMP 1050->400 AMBIENT inert_N2 TIMING assumed VARY T_end 200..900
    EVENT ContactWindows KIND etch TIMING assumed                # Source and drain contact windows opened
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament
    RUN PMAFlushIn DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    RUN PostMetalAnneal DURATION 1800 TEMP 400->400 AMBIENT forming_gas_H2 TIMING stated VARY duration 600..1800
    RUN PMAFlushOut DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT Package KIND other TIMING assumed                      # Lapped to 150 µm, scribed, bonded, sealed in TO-5
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V; thickness from the 10 Hz accumulation capacitance
}

K2: 900 °C, dry O2, 48 min, 150 Å, N2 anneal

# K2: 900 °C, dry O2, 48 min, 150 Å, N2 anneal
SAMPLE Wafer_K2 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT SourceDrain KIND other TIMING stated                   # Phosphorus source and drain: predeposition at 1000 °C, drive-in 60 min at 1050 °C in O2
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh4 DURATION 180 TEMP 900->900 AMBIENT dry_O2 TIMING assumed VARY duration 1..180
    RUN Oxidation DURATION 2880 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Ramp DURATION 1200 TEMP 900->1050 AMBIENT inert_N2 TIMING assumed VARY duration 300..3600
    RUN NitrogenAnneal DURATION 1800 TEMP 1050->1050 AMBIENT inert_N2 TIMING stated
    RUN BoatOut DURATION 180 TEMP 1050->400 AMBIENT inert_N2 TIMING assumed VARY T_end 200..900
    EVENT ContactWindows KIND etch TIMING assumed                # Source and drain contact windows opened
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament
    RUN PMAFlushIn DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    RUN PostMetalAnneal DURATION 1800 TEMP 400->400 AMBIENT forming_gas_H2 TIMING stated VARY duration 600..1800
    RUN PMAFlushOut DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT Package KIND other TIMING assumed                      # Lapped to 150 µm, scribed, bonded, sealed in TO-5
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V; thickness from the 10 Hz accumulation capacitance
}

K3: 900 °C, dry O2, 93 min, 230 Å, N2 anneal

# K3: 900 °C, dry O2, 93 min, 230 Å, N2 anneal
SAMPLE Wafer_K3 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT SourceDrain KIND other TIMING stated                   # Phosphorus source and drain: predeposition at 1000 °C, drive-in 60 min at 1050 °C in O2
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh4 DURATION 180 TEMP 900->900 AMBIENT dry_O2 TIMING assumed VARY duration 1..180
    RUN Oxidation DURATION 5580 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Ramp DURATION 1200 TEMP 900->1050 AMBIENT inert_N2 TIMING assumed VARY duration 300..3600
    RUN NitrogenAnneal DURATION 1800 TEMP 1050->1050 AMBIENT inert_N2 TIMING stated
    RUN BoatOut DURATION 180 TEMP 1050->400 AMBIENT inert_N2 TIMING assumed VARY T_end 200..900
    EVENT ContactWindows KIND etch TIMING assumed                # Source and drain contact windows opened
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament
    RUN PMAFlushIn DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    RUN PostMetalAnneal DURATION 1800 TEMP 400->400 AMBIENT forming_gas_H2 TIMING stated VARY duration 600..1800
    RUN PMAFlushOut DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT Package KIND other TIMING assumed                      # Lapped to 150 µm, scribed, bonded, sealed in TO-5
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V; thickness from the 10 Hz accumulation capacitance
}

K4: 900 °C, dry O2, 151 min, 318 Å, N2 anneal

# K4: 900 °C, dry O2, 151 min, 318 Å, N2 anneal
SAMPLE Wafer_K4 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT SourceDrain KIND other TIMING stated                   # Phosphorus source and drain: predeposition at 1000 °C, drive-in 60 min at 1050 °C in O2
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh4 DURATION 180 TEMP 900->900 AMBIENT dry_O2 TIMING assumed VARY duration 1..180
    RUN Oxidation DURATION 9060 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Ramp DURATION 1200 TEMP 900->1050 AMBIENT inert_N2 TIMING assumed VARY duration 300..3600
    RUN NitrogenAnneal DURATION 1800 TEMP 1050->1050 AMBIENT inert_N2 TIMING stated
    RUN BoatOut DURATION 180 TEMP 1050->400 AMBIENT inert_N2 TIMING assumed VARY T_end 200..900
    EVENT ContactWindows KIND etch TIMING assumed                # Source and drain contact windows opened
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament
    RUN PMAFlushIn DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    RUN PostMetalAnneal DURATION 1800 TEMP 400->400 AMBIENT forming_gas_H2 TIMING stated VARY duration 600..1800
    RUN PMAFlushOut DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT Package KIND other TIMING assumed                      # Lapped to 150 µm, scribed, bonded, sealed in TO-5
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V; thickness from the 10 Hz accumulation capacitance
}

J1: 900 °C, dry O2, 151 min, etched back to 140 Å, N2 anneal

# J1: 900 °C, dry O2, 151 min, etched back to 140 Å, N2 anneal
SAMPLE Wafer_J1 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT SourceDrain KIND other TIMING stated                   # Phosphorus source and drain: predeposition at 1000 °C, drive-in 60 min at 1050 °C in O2
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh4 DURATION 180 TEMP 900->900 AMBIENT dry_O2 TIMING assumed VARY duration 1..180
    RUN Oxidation DURATION 9060 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Ramp DURATION 1200 TEMP 900->1050 AMBIENT inert_N2 TIMING assumed VARY duration 300..3600
    RUN NitrogenAnneal DURATION 1800 TEMP 1050->1050 AMBIENT inert_N2 TIMING stated
    RUN BoatOut DURATION 180 TEMP 1050->400 AMBIENT inert_N2 TIMING assumed VARY T_end 200..900
    EVENT EtchBack KIND etch TIMING stated                       # Etched back in 2.5% HF for 145 s, to 140 Å
    EVENT ContactWindows KIND etch TIMING assumed                # Source and drain contact windows opened
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament
    RUN PMAFlushIn DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    RUN PostMetalAnneal DURATION 1800 TEMP 400->400 AMBIENT forming_gas_H2 TIMING stated VARY duration 600..1800
    RUN PMAFlushOut DURATION 900 TEMP 400->400 AMBIENT inert_N2 TIMING stated
    EVENT Package KIND other TIMING assumed                      # Lapped to 150 µm, scribed, bonded, sealed in TO-5
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V; thickness from the 10 Hz accumulation capacitance
}

Etched back after the anneal. Its fixed charge is the 40 nm oxide's; the simulation does not thin the oxide, so its thickness is not compared.

U1: 1050 °C, 20% O2 in N2, 8 min, as oxidized

# U1: 1050 °C, 20% O2 in N2, 8 min, as oxidized
SAMPLE Wafer_U1 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 480 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated
    RUN Pull DURATION 3 TEMP 1050->400 AMBIENT mix:O2=0.2,N2=0.8 TIMING bound VARY duration 1..3 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

U4: 1050 °C, 20% O2 in N2, 110 min, as oxidized

# U4: 1050 °C, 20% O2 in N2, 110 min, as oxidized
SAMPLE Wafer_U4 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 6600 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated
    RUN Pull DURATION 3 TEMP 1050->400 AMBIENT mix:O2=0.2,N2=0.8 TIMING bound VARY duration 1..3 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

B1: 1050 °C, dry O2, 1.5 min, as oxidized

# B1: 1050 °C, dry O2, 1.5 min, as oxidized
SAMPLE Wafer_B1 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 1050->1050 AMBIENT dry_O2 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 90 TEMP 1050->1050 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 3 TEMP 1050->400 AMBIENT dry_O2 TIMING bound VARY duration 1..3 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

B4: 1050 °C, dry O2, 22 min, as oxidized

# B4: 1050 °C, dry O2, 22 min, as oxidized
SAMPLE Wafer_B4 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 1050->1050 AMBIENT dry_O2 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 1320 TEMP 1050->1050 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 3 TEMP 1050->400 AMBIENT dry_O2 TIMING bound VARY duration 1..3 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

Y1: 975 °C, 50% O2 in N2, 12 min, as oxidized

# Y1: 975 °C, 50% O2 in N2, 12 min, as oxidized
SAMPLE Wafer_Y1 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 975->975 AMBIENT mix:O2=0.5,N2=0.5 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 720 TEMP 975->975 AMBIENT mix:O2=0.5,N2=0.5 TIMING stated
    RUN Pull DURATION 3 TEMP 975->400 AMBIENT mix:O2=0.5,N2=0.5 TIMING bound VARY duration 1..3 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

C1: 975 °C, dry O2, 6 min, as oxidized

# C1: 975 °C, dry O2, 6 min, as oxidized
SAMPLE Wafer_C1 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 975->975 AMBIENT dry_O2 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 360 TEMP 975->975 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 3 TEMP 975->400 AMBIENT dry_O2 TIMING bound VARY duration 1..3 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

D1: 900 °C, dry O2, 27 min, as oxidized

# D1: 900 °C, dry O2, 27 min, as oxidized
SAMPLE Wafer_D1 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 900->900 AMBIENT dry_O2 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 1620 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 3 TEMP 900->400 AMBIENT dry_O2 TIMING bound VARY duration 1..3 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

D2: 900 °C, dry O2, 48 min, as oxidized

# D2: 900 °C, dry O2, 48 min, as oxidized
SAMPLE Wafer_D2 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 900->900 AMBIENT dry_O2 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 2880 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 3 TEMP 900->400 AMBIENT dry_O2 TIMING bound VARY duration 1..3 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

D4: 900 °C, dry O2, 151 min, as oxidized

# D4: 900 °C, dry O2, 151 min, as oxidized
SAMPLE Wafer_D4 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 900->900 AMBIENT dry_O2 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 9060 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 3 TEMP 900->400 AMBIENT dry_O2 TIMING bound VARY duration 1..3 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

P: 1050 °C, 20% O2 in N2, 20 min, then 0 min in N2

# P: 1050 °C, 20% O2 in N2, 20 min, then 0 min in N2
SAMPLE Wafer_P0 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 1200 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated
    RUN PullAfterAnneal DURATION 180 TEMP 1050->400 AMBIENT inert_N2 TIMING assumed VARY duration 3..180 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

P: 1050 °C, 20% O2 in N2, 20 min, then 10 min in N2

# P: 1050 °C, 20% O2 in N2, 20 min, then 10 min in N2
SAMPLE Wafer_P10 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 1200 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated
    RUN NitrogenAnneal DURATION 600 TEMP 1050->1050 AMBIENT inert_N2 TIMING stated
    RUN PullAfterAnneal DURATION 180 TEMP 1050->400 AMBIENT inert_N2 TIMING assumed VARY duration 3..180 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

P: 1050 °C, 20% O2 in N2, 20 min, then 20 min in N2

# P: 1050 °C, 20% O2 in N2, 20 min, then 20 min in N2
SAMPLE Wafer_P20 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 1200 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated
    RUN NitrogenAnneal DURATION 1200 TEMP 1050->1050 AMBIENT inert_N2 TIMING stated
    RUN PullAfterAnneal DURATION 180 TEMP 1050->400 AMBIENT inert_N2 TIMING assumed VARY duration 3..180 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

P: 1050 °C, 20% O2 in N2, 20 min, then 30 min in N2

# P: 1050 °C, 20% O2 in N2, 20 min, then 30 min in N2
SAMPLE Wafer_P30 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 1200 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated
    RUN NitrogenAnneal DURATION 1800 TEMP 1050->1050 AMBIENT inert_N2 TIMING stated
    RUN PullAfterAnneal DURATION 180 TEMP 1050->400 AMBIENT inert_N2 TIMING assumed VARY duration 3..180 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

P: 1050 °C, 20% O2 in N2, 20 min, then 40 min in N2

# P: 1050 °C, 20% O2 in N2, 20 min, then 40 min in N2
SAMPLE Wafer_P40 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 1200 TEMP 1050->1050 AMBIENT mix:O2=0.2,N2=0.8 TIMING stated
    RUN NitrogenAnneal DURATION 2400 TEMP 1050->1050 AMBIENT inert_N2 TIMING stated
    RUN PullAfterAnneal DURATION 180 TEMP 1050->400 AMBIENT inert_N2 TIMING assumed VARY duration 3..180 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

Q: 900 °C, dry O2, 48 min, then 0 min in N2

# Q: 900 °C, dry O2, 48 min, then 0 min in N2
SAMPLE Wafer_Q0 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 900->900 AMBIENT dry_O2 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 2880 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN PullAfterAnneal DURATION 180 TEMP 900->400 AMBIENT inert_N2 TIMING assumed VARY duration 3..180 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

Q: 900 °C, dry O2, 48 min, then 10 min in N2

# Q: 900 °C, dry O2, 48 min, then 10 min in N2
SAMPLE Wafer_Q10 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 900->900 AMBIENT dry_O2 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 2880 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN NitrogenAnneal DURATION 600 TEMP 900->900 AMBIENT inert_N2 TIMING stated
    RUN PullAfterAnneal DURATION 180 TEMP 900->400 AMBIENT inert_N2 TIMING assumed VARY duration 3..180 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

Q: 900 °C, dry O2, 48 min, then 20 min in N2

# Q: 900 °C, dry O2, 48 min, then 20 min in N2
SAMPLE Wafer_Q20 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 900->900 AMBIENT dry_O2 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 2880 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN NitrogenAnneal DURATION 1200 TEMP 900->900 AMBIENT inert_N2 TIMING stated
    RUN PullAfterAnneal DURATION 180 TEMP 900->400 AMBIENT inert_N2 TIMING assumed VARY duration 3..180 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

Q: 900 °C, dry O2, 48 min, then 30 min in N2

# Q: 900 °C, dry O2, 48 min, then 30 min in N2
SAMPLE Wafer_Q30 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 900->900 AMBIENT dry_O2 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 2880 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN NitrogenAnneal DURATION 1800 TEMP 900->900 AMBIENT inert_N2 TIMING stated
    RUN PullAfterAnneal DURATION 180 TEMP 900->400 AMBIENT inert_N2 TIMING assumed VARY duration 3..180 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

Q: 900 °C, dry O2, 48 min, then 40 min in N2

# Q: 900 °C, dry O2, 48 min, then 40 min in N2
SAMPLE Wafer_Q40 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: peroxide_HF
    DOPING: p_type_boron
}
CONTROL_TRAJECTORY History {
    EVENT FieldOxide KIND other TIMING stated                    # Field oxide, 8000 Å, dry-wet-dry at 1050 °C
    EVENT GateWindow KIND etch TIMING bound                      # Gate windows opened in buffered HF
    EVENT Clean KIND clean TIMING stated                         # RCA clean ending in 10 s of 5% HF
    RUN BoatInCh5 DURATION 180 TEMP 900->900 AMBIENT dry_O2 TIMING stated VARY duration 1..180
    RUN Oxidation DURATION 2880 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN NitrogenAnneal DURATION 2400 TEMP 900->900 AMBIENT inert_N2 TIMING stated
    RUN PullAfterAnneal DURATION 180 TEMP 900->400 AMBIENT inert_N2 TIMING assumed VARY duration 3..180 VARY T_end 200..700
    EVENT Metal KIND metallization TIMING assumed                # Pure aluminium, 1 µm, from a tungsten filament, onto unheated wafers
    EVENT BackContact KIND deposition TIMING assumed             # Back oxide swabbed off in dilute HF, thick aluminium on the back, not sintered
    EVENT Cleave KIND cleave TIMING stated                       # Wafer split in two; one half to forming gas, 400 °C, 10 min
    EVENT NoAnneal KIND other TIMING assumed                     # No post-metallization anneal (this half)
    EVENT CV KIND measurement TIMING assumed                     # 1 MHz and quasi-static C-V on the probe station, in dry nitrogen
}

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/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

16 within, 14 near, 46 off of 76 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 B1, B4, M1, M2, M3, M4, N1, P0, P10, P20, P30, P40, U1, U4 only; every other number is a test they played no part in.

Together: BoatInCh4 duration 1 s (was 180); BoatOut T end 400 °C (was 400); PostMetalAnneal duration 1800 s (was 1800); BoatInCh5 duration 75.75 s (was 180); Pull duration 3 s (was 3); Pull T end 400 °C (was 400); PullAfterAnneal duration 3 s (was 180); PullAfterAnneal T end 400 °C (was 400).

As reproduced: 16 of 76 within tolerance, median error 28.9%. Aligned: 21 of 76 within tolerance, median error 25.1%. On the held-out samples only: 10 of 39 within tolerance, median error 24.8% as reproduced, 13 of 39 within tolerance, median error 23.2% aligned.

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

Nine unknowns were declared: the two boat-ins (chapter 4 and chapter 5), chapter 4's boat-out end temperature, its forming-gas time (10 to 30 min, the Appendix's range), the 900 to 1050 °C ramp of batches K and J, the fast pull's time and end temperature, and the anneal series' withdrawal time and end temperature. They were chosen on every wafer oxidized at 1050 °C (batches M and N, series U, B and P) and tested on the 900 and 975 °C wafers (K, J, D, C, Y, Q). As reproduced: 5 of 76 numbers within tolerance (median error 85.3%). Aligned: 6 of 76 (89.0%). On the held-out wafers: 3 of 39 before and after; the median error there rose from 47.2% to 84.7%.

The data do not constrain most of the unknowns. Eight of the nine scans cannot raise the count within tolerance on the 1050 °C wafers (2 of 37 at every value, or fewer); only the chapter 5 boat-in does, from 2 to 3 at 76 s. Where scores tie, the search keeps the first grid value that reached them, so the aligned values printed for those eight (ramp 300 s, pull 1 s to 200 °C, forming gas 800 s, and so on) are not findings. The reason is the size of the model errors: fixed charge is 80 to 96% low on every wafer and no history step moves it by more than 25%.

The forming-gas time was a tie and it made the test worse. On the 1050 °C wafers 800 s and the stated 1800 s score the same; 800 s puts M1 instead of M2 on the printed “~5×10^10”, which is one rounded value for the whole group. On the 900 °C batch 800 s doubles the simulated value (8.7 to 10.4 × 10^10 against 5 × 10^10, from 5.2 to 6.2 before), and the four K and J trap densities that were within twice the tolerance no longer are. That is the held-out loss. Chapter 4 states 30 min; nothing here argues against it.

The boat-in is pinned by thickness, not by charge or traps. Scanned on its own, thickness of the pure-oxygen wafers decides it. B1 (1.5 min printed, 11.1 nm) is 8.05 nm with no boat-in, 10.8 nm with 60 s of boat-in at 1050 °C, 12.1 nm with 90 s and 15.6 nm with the full 180 s. C1 (6 min at 975 °C) is within 10% only with 30 s or less. So the full 3 min at furnace temperature added to the printed time is too much; about one minute at temperature, the end of a 3 min push, fits B1, and the printed times are best read as starting once the boat is in. The trap density moves by under 5% over the whole range, and fixed charge not at all.

Variants. Storing the P series with 27 min of oxidation (as the datasets do) instead of the printed 20 min adds one number within tolerance (a trap density) and makes the thickness worse (52.6 against 18 nm). Thickness from the 1965 law instead of the thin-oxide program loses 2 numbers; that law starts every oxide at 23 nm, above most of these oxides. Ramping K and J in oxygen instead of nitrogen changes nothing: the 30 min in nitrogen at 1050 °C that follows erases it in both programs.

13 within, 3 near, 23 off of 39 numbers with the aligned settings (the samples used to choose the unknowns are left out).

What alignment cannot fix. Fixed charge: after 30 min of nitrogen at 1050 °C the program sits at its equilibrium without oxygen, 2.7 × 10^10 cm⁻², for every chapter 4 wafer. Hung measures 3.8 to 6.0 × 10^11, rising as the as-grown oxide gets thinner and flat for the etched-back oxides. The program has no thickness and no memory of the growth once the anneal is over, so the thesis's central result (as-grown against etched-back) cannot appear in it. In the anneal series the program falls in both series (Q: 1.74 to 0.39 × 10^11; P: 0.47 to 0.27 × 10^11) where Hung's 900 °C series falls by 22% and the 1050 °C series rises from 2.2 to 4.8 × 10^11 after 10 min.

Trap density without hydrogen: on the as-oxidized wafers the program is 28 to 86% high at 1050 °C and 10 to 34% low at 900 and 975 °C, so Hung's temperature dependence is steeper (D1 over B1: 2.5 measured, 1.3 simulated), and so is the fall with oxidation time (D1 to D4: -34% measured, -11% simulated). The program has no oxygen-pressure term, which Hung finds at 975 °C (Y against C). In nitrogen at 900 °C Hung's density falls by 71% in 40 min and the program's by 4%; at 1050 °C Hung's dips and then rises and the program's falls. Every one of these histories is outside the range the program was fitted on (Vitkavage: 750 to 1000 °C, one hour or more).

Thickness: the thin-oxide program does not read the oxygen pressure (8 min in 20% oxygen and in pure oxygen both give 22.4 nm) and keeps growing oxide in nitrogen, so every 20% and 50% oxide is two to three times too thick and every oxide that had a nitrogen anneal is 2 to 6 times too thick (M1: 64 against 10.1 nm). On the pure-oxygen wafers without an anneal it does well: B4 +8%, D4 -4%, D2 +12%, Q0 +10% as reproduced.

How to read the aligned numbers: the unknowns were chosen on the 1050 °C wafers only, so the rows shown (900 and 975 °C) are a test. The ramp is the one unknown the 1050 °C wafers cannot inform at all; it kept its first grid value.

What our language and ontology cannot yet say

• Which step is the oxidation. The fixed-charge and trap-density programs take the oxidation temperature from the first oxygen-bearing RUN. A boat-in written as a heating ramp (TEMP 25->1050 PROFILE exponential) would then be read as an oxidation at 25 °C, so the boat-in here had to be written as a hold at furnace temperature. A ROLE oxidation|anneal|load|pull on each RUN would let programs find the step by what it is, and let a push-in be written as the heating it is.
• An unknown that is an offset, not a duration. “Does the printed time include the 3 min boat-in?” is one question for all 24 wafers whose oxidation times run from 1.5 to 151 min. VARY duration on the boat-in stands in for it; VARY offset -180..0 on the oxidation, shared across samples, would say it directly.
• A choice of gas as an unknown. The ramp from 900 to 1050 °C and the withdrawal after the anneal series have unknown gases. The language varies numbers only; the gas had to become a Python variant. VARY ambient inert_N2|dry_O2 would make it a declared unknown.
• A wafer split in two. In chapter 5 each wafer was cleaved and only one half had forming gas; Figure 5.9's trap density is from one half and its fixed charge from the other. EVENT Cleave records it, but one history cannot carry two halves. A SPLIT that forks the trajectory into named halves, with each observation bound to its half, would let both values be compared on the right history.
• An etch that removes oxide. The etched-back oxides are Hung's control: same growth, different final thickness. EVENT EtchBack KIND etch takes nothing off the simulated oxide. A statement that sets or removes thickness (ETCH REMOVE 25 nm or ETCH TO 14.5 nm) is needed before any program with a thickness term can be tested against this control.
• How a charge was extracted. Hung's Qf uses φMS = -0.715 V from the etched-back intercept. At 10 nm, 0.1 V of φMS is 2.1 × 10^11 cm⁻² of charge; at 40 nm it is 0.5 × 10^11. An observation statement carrying the φMS, the frequency and whether the half had forming gas would let charge from different laboratories be compared on one basis.
• Gas by pressure in every program. Writing mix:O2=0.2,N2=0.8 now reaches the programs, but the thin-oxide growth program ignores the oxygen pressure and grows oxide in nitrogen. That is a predictor change, not a language one, and it decides every 20% and 50% thickness on this page.
• Rounded and typical values. Table 4.2 gives “~5×10^10” for a group of four, and chapter 5 reports “only typical or representative results”. A result's tolerance should be able to say it is a rounding of a group value, so that a search does not fit one wafer to it, as happened with the forming-gas time here.

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. In a 1980s furnace recipe written “Boat-in 3 min, Oxidation variable”, would the printed oxidation time start after the boat-in? For B1 (1.5 min printed) it decides most of the oxide.
2. For batch K, oxidized at 900 °C and annealed in situ at 1050 °C: how long would such a furnace take to climb 150 °C, and would the tube be in nitrogen during the climb?
3. Fixed charge of 3.9 to 6 × 10^11 cm⁻² after 30 min of nitrogen at 1050 °C is higher than Deal's values for the same anneal (about 1.5 to 2 × 10^11). Is this the thin oxides, the φMS of -0.715 V, or the laboratory?
4. The P series (20 min in 20% O2 at 1050 °C) is about 180 Å where U2 on the same nominal recipe is 153 Å. Is a 15% run-to-run difference in thickness usual for such a furnace?
5. The trap density rises again after 10 min of nitrogen at 1050 °C but not at 900 °C. Is that a known effect (nitrogen at the interface, as the author suggests), or could the withdrawal after the anneal differ between the two series?