Reproducing Kar and Narasimhan 1987: interface states across the gap of thin unannealed 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/kar_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

S. Kar and R. L. Narasimhan, “Characteristics of the Si-SiO2 interface states in thin (70-230 Å) oxide structures”, J. Appl. Phys. 61, 5353 (1987).

The challenge asks for Dit(E), the interface state density across the band gap. This paper measures it on unannealed (100) oxides 79 to 227 Å thick, from both band edges (n- and p-type), and finds two peaks over a U-shaped background, one 0.23 to 0.44 eV above the valence band and one 0.85 to 0.93 eV above it, whose height first falls and then rises with thickness (minimum near 110 Å, maximum near 155 Å). The project read it and set it aside as “not comparable with midgap values” (SOURCE.md). Figure 3 does reach midgap for two devices, and Figure 1 is a thickness-against-time series at 900 °C that the project has not used. This page runs both through the predictor and sets the measured distributions beside what the predictor's spectrum rows can and cannot say.

How well can this study be reproduced?

Moderate. The process is short and mostly stated: a sacrificial 1100 °C oxide stripped in HF, dry oxidation at 900 °C and 1 atm, a 6 s pull, cooling in the tube in oxygen, no anneal of any kind. What a simulation must supply: the push and warm-up, the cooling time, and which oxidation time made which measured device (only Figure 1 links time to thickness). The measured quantity is the whole distribution over the gap, which no program in the predictor computes without a hydrogen anneal.

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. 5 same, 5 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.

900 °C, 20 min (Figure 1)

Simulated time in this history: 40 min 06 s.

Across the samples

Timing the paper does not give

• The push into the 900 °C furnace and the wafer's warm-up: time and gas.
• The cooling in the silica tube after the 6 s pull: how long and how fast.
• Which oxidation time made which measured device: only Figure 1 links time to thickness.
• The time between the HF strip and the oxidation, and between oxidation and metallization (the native oxide and the storage).
• The wafer temperature during evaporation from a tungsten filament.

What the second reading changed

• The project held no recipe and no digitized value for this paper. SOURCE.md says pages 2 and 5 were read and that the paper reports only the peak density near the band edges, “not comparable with midgap quasi-static values”. Figure 3 (PDF p. 3) does reach 0.50 to 0.58 eV for the 93 and 125 Å n-type devices (about 3.1 and 2.7×10^11 cm⁻² eV⁻¹ at 0.55 eV), so two midgap values exist, by another technique (admittance, not quasi-static).
• SOURCE.md does not mention Figure 1: a thickness-against-time series at 900 °C, 79 to 211 Å over 20 to 140 min, on the same wafers. It is a second laboratory's thin dry oxides at the temperature the thin-oxide program holds out (900 °C).
• The library's conditions record the clean as not_stated. The paper states degreasing, ultrasonic cleaning, acid etching and a sacrificial 1100 °C oxide stripped in HF.
• The library records the pull correctly (6 s, cooled in dry oxygen in the tube). It does not record that there was no anneal of any kind, which decides whether the predictor writes a spectrum.

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>.

900 °C, 20 min (Figure 1)

# 900 °C, 20 min (Figure 1)
SAMPLE Wafer_growth_20min {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: not_stated
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Degreased in hot solvents, ultrasonic clean, acid etch
    EVENT PreOxidation KIND other TIMING stated                  # Sacrificial oxidation, dry O2, 1100 °C, 30 min, Thermco furnace
    EVENT Strip KIND etch TIMING assumed                         # Preoxide etched in HF, ultrasonic clean, rinse in 14-18 MΩ cm water, dry in filtered N2
    EVENT Load KIND load TIMING assumed                          # Into the 900 °C furnace
    RUN Push DURATION 300 TEMP 25->900 AMBIENT inert_N2 PROFILE settling TAU 60 TIMING assumed VARY duration 60..900
    RUN Oxidation DURATION 1200 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 6 TEMP 900->800 AMBIENT dry_O2 TIMING stated VARY T_end 650..880
    RUN TubeCool DURATION 900 TEMP 800->25 AMBIENT dry_O2 PROFILE settling TAU 180 TIMING assumed VARY duration 120..3600
    EVENT NoAnneal KIND other TIMING stated                      # No post-oxidation or post-metallization anneal
    EVENT Measure KIND measurement TIMING assumed                # Optical MOS admittance, dark and under tungsten-lamp light, 30 Hz-100 kHz
}

Figure 1 does not say whether these are n or p wafers; the metallization is not part of this history.

900 °C, 30 min (Figure 1)

# 900 °C, 30 min (Figure 1)
SAMPLE Wafer_growth_30min {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: not_stated
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Degreased in hot solvents, ultrasonic clean, acid etch
    EVENT PreOxidation KIND other TIMING stated                  # Sacrificial oxidation, dry O2, 1100 °C, 30 min, Thermco furnace
    EVENT Strip KIND etch TIMING assumed                         # Preoxide etched in HF, ultrasonic clean, rinse in 14-18 MΩ cm water, dry in filtered N2
    EVENT Load KIND load TIMING assumed                          # Into the 900 °C furnace
    RUN Push DURATION 300 TEMP 25->900 AMBIENT inert_N2 PROFILE settling TAU 60 TIMING assumed VARY duration 60..900
    RUN Oxidation DURATION 1800 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 6 TEMP 900->800 AMBIENT dry_O2 TIMING stated VARY T_end 650..880
    RUN TubeCool DURATION 900 TEMP 800->25 AMBIENT dry_O2 PROFILE settling TAU 180 TIMING assumed VARY duration 120..3600
    EVENT NoAnneal KIND other TIMING stated                      # No post-oxidation or post-metallization anneal
    EVENT Measure KIND measurement TIMING assumed                # Optical MOS admittance, dark and under tungsten-lamp light, 30 Hz-100 kHz
}

Figure 1 does not say whether these are n or p wafers; the metallization is not part of this history.

900 °C, 40 min (Figure 1)

# 900 °C, 40 min (Figure 1)
SAMPLE Wafer_growth_40min {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: not_stated
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Degreased in hot solvents, ultrasonic clean, acid etch
    EVENT PreOxidation KIND other TIMING stated                  # Sacrificial oxidation, dry O2, 1100 °C, 30 min, Thermco furnace
    EVENT Strip KIND etch TIMING assumed                         # Preoxide etched in HF, ultrasonic clean, rinse in 14-18 MΩ cm water, dry in filtered N2
    EVENT Load KIND load TIMING assumed                          # Into the 900 °C furnace
    RUN Push DURATION 300 TEMP 25->900 AMBIENT inert_N2 PROFILE settling TAU 60 TIMING assumed VARY duration 60..900
    RUN Oxidation DURATION 2400 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 6 TEMP 900->800 AMBIENT dry_O2 TIMING stated VARY T_end 650..880
    RUN TubeCool DURATION 900 TEMP 800->25 AMBIENT dry_O2 PROFILE settling TAU 180 TIMING assumed VARY duration 120..3600
    EVENT NoAnneal KIND other TIMING stated                      # No post-oxidation or post-metallization anneal
    EVENT Measure KIND measurement TIMING assumed                # Optical MOS admittance, dark and under tungsten-lamp light, 30 Hz-100 kHz
}

Figure 1 does not say whether these are n or p wafers; the metallization is not part of this history.

900 °C, 50 min (Figure 1)

# 900 °C, 50 min (Figure 1)
SAMPLE Wafer_growth_50min {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: not_stated
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Degreased in hot solvents, ultrasonic clean, acid etch
    EVENT PreOxidation KIND other TIMING stated                  # Sacrificial oxidation, dry O2, 1100 °C, 30 min, Thermco furnace
    EVENT Strip KIND etch TIMING assumed                         # Preoxide etched in HF, ultrasonic clean, rinse in 14-18 MΩ cm water, dry in filtered N2
    EVENT Load KIND load TIMING assumed                          # Into the 900 °C furnace
    RUN Push DURATION 300 TEMP 25->900 AMBIENT inert_N2 PROFILE settling TAU 60 TIMING assumed VARY duration 60..900
    RUN Oxidation DURATION 3000 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 6 TEMP 900->800 AMBIENT dry_O2 TIMING stated VARY T_end 650..880
    RUN TubeCool DURATION 900 TEMP 800->25 AMBIENT dry_O2 PROFILE settling TAU 180 TIMING assumed VARY duration 120..3600
    EVENT NoAnneal KIND other TIMING stated                      # No post-oxidation or post-metallization anneal
    EVENT Measure KIND measurement TIMING assumed                # Optical MOS admittance, dark and under tungsten-lamp light, 30 Hz-100 kHz
}

Figure 1 does not say whether these are n or p wafers; the metallization is not part of this history.

900 °C, 70 min (Figure 1)

# 900 °C, 70 min (Figure 1)
SAMPLE Wafer_growth_70min {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: not_stated
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Degreased in hot solvents, ultrasonic clean, acid etch
    EVENT PreOxidation KIND other TIMING stated                  # Sacrificial oxidation, dry O2, 1100 °C, 30 min, Thermco furnace
    EVENT Strip KIND etch TIMING assumed                         # Preoxide etched in HF, ultrasonic clean, rinse in 14-18 MΩ cm water, dry in filtered N2
    EVENT Load KIND load TIMING assumed                          # Into the 900 °C furnace
    RUN Push DURATION 300 TEMP 25->900 AMBIENT inert_N2 PROFILE settling TAU 60 TIMING assumed VARY duration 60..900
    RUN Oxidation DURATION 4200 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 6 TEMP 900->800 AMBIENT dry_O2 TIMING stated VARY T_end 650..880
    RUN TubeCool DURATION 900 TEMP 800->25 AMBIENT dry_O2 PROFILE settling TAU 180 TIMING assumed VARY duration 120..3600
    EVENT NoAnneal KIND other TIMING stated                      # No post-oxidation or post-metallization anneal
    EVENT Measure KIND measurement TIMING assumed                # Optical MOS admittance, dark and under tungsten-lamp light, 30 Hz-100 kHz
}

Figure 1 does not say whether these are n or p wafers; the metallization is not part of this history.

900 °C, 90 min (Figure 1)

# 900 °C, 90 min (Figure 1)
SAMPLE Wafer_growth_90min {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: not_stated
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Degreased in hot solvents, ultrasonic clean, acid etch
    EVENT PreOxidation KIND other TIMING stated                  # Sacrificial oxidation, dry O2, 1100 °C, 30 min, Thermco furnace
    EVENT Strip KIND etch TIMING assumed                         # Preoxide etched in HF, ultrasonic clean, rinse in 14-18 MΩ cm water, dry in filtered N2
    EVENT Load KIND load TIMING assumed                          # Into the 900 °C furnace
    RUN Push DURATION 300 TEMP 25->900 AMBIENT inert_N2 PROFILE settling TAU 60 TIMING assumed VARY duration 60..900
    RUN Oxidation DURATION 5400 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 6 TEMP 900->800 AMBIENT dry_O2 TIMING stated VARY T_end 650..880
    RUN TubeCool DURATION 900 TEMP 800->25 AMBIENT dry_O2 PROFILE settling TAU 180 TIMING assumed VARY duration 120..3600
    EVENT NoAnneal KIND other TIMING stated                      # No post-oxidation or post-metallization anneal
    EVENT Measure KIND measurement TIMING assumed                # Optical MOS admittance, dark and under tungsten-lamp light, 30 Hz-100 kHz
}

Figure 1 does not say whether these are n or p wafers; the metallization is not part of this history.

900 °C, 110 min (Figure 1)

# 900 °C, 110 min (Figure 1)
SAMPLE Wafer_growth_110min {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: not_stated
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Degreased in hot solvents, ultrasonic clean, acid etch
    EVENT PreOxidation KIND other TIMING stated                  # Sacrificial oxidation, dry O2, 1100 °C, 30 min, Thermco furnace
    EVENT Strip KIND etch TIMING assumed                         # Preoxide etched in HF, ultrasonic clean, rinse in 14-18 MΩ cm water, dry in filtered N2
    EVENT Load KIND load TIMING assumed                          # Into the 900 °C furnace
    RUN Push DURATION 300 TEMP 25->900 AMBIENT inert_N2 PROFILE settling TAU 60 TIMING assumed VARY duration 60..900
    RUN Oxidation DURATION 6600 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 6 TEMP 900->800 AMBIENT dry_O2 TIMING stated VARY T_end 650..880
    RUN TubeCool DURATION 900 TEMP 800->25 AMBIENT dry_O2 PROFILE settling TAU 180 TIMING assumed VARY duration 120..3600
    EVENT NoAnneal KIND other TIMING stated                      # No post-oxidation or post-metallization anneal
    EVENT Measure KIND measurement TIMING assumed                # Optical MOS admittance, dark and under tungsten-lamp light, 30 Hz-100 kHz
}

Figure 1 does not say whether these are n or p wafers; the metallization is not part of this history.

900 °C, 140 min (Figure 1)

# 900 °C, 140 min (Figure 1)
SAMPLE Wafer_growth_140min {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: not_stated
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Degreased in hot solvents, ultrasonic clean, acid etch
    EVENT PreOxidation KIND other TIMING stated                  # Sacrificial oxidation, dry O2, 1100 °C, 30 min, Thermco furnace
    EVENT Strip KIND etch TIMING assumed                         # Preoxide etched in HF, ultrasonic clean, rinse in 14-18 MΩ cm water, dry in filtered N2
    EVENT Load KIND load TIMING assumed                          # Into the 900 °C furnace
    RUN Push DURATION 300 TEMP 25->900 AMBIENT inert_N2 PROFILE settling TAU 60 TIMING assumed VARY duration 60..900
    RUN Oxidation DURATION 8400 TEMP 900->900 AMBIENT dry_O2 TIMING stated
    RUN Pull DURATION 6 TEMP 900->800 AMBIENT dry_O2 TIMING stated VARY T_end 650..880
    RUN TubeCool DURATION 900 TEMP 800->25 AMBIENT dry_O2 PROFILE settling TAU 180 TIMING assumed VARY duration 120..3600
    EVENT NoAnneal KIND other TIMING stated                      # No post-oxidation or post-metallization anneal
    EVENT Measure KIND measurement TIMING assumed                # Optical MOS admittance, dark and under tungsten-lamp light, 30 Hz-100 kHz
}

Figure 1 does not say whether these are n or p wafers; the metallization is not part of this history.

n-Si/SiO2/Au, 93 Å

# n-Si/SiO2/Au, 93 Å
SAMPLE Wafer_n93 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type_1_ohm_cm_epi
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Degreased in hot solvents, ultrasonic clean, acid etch
    EVENT PreOxidation KIND other TIMING stated                  # Sacrificial oxidation, dry O2, 1100 °C, 30 min, Thermco furnace
    EVENT Strip KIND etch TIMING assumed                         # Preoxide etched in HF, ultrasonic clean, rinse in 14-18 MΩ cm water, dry in filtered N2
    EVENT Load KIND load TIMING assumed                          # Into the 900 °C furnace
    RUN Push DURATION 300 TEMP 25->900 AMBIENT inert_N2 PROFILE settling TAU 60 TIMING assumed VARY duration 60..900
    RUN Oxidation DURATION 1800 TEMP 900->900 AMBIENT dry_O2 TIMING assumed
    RUN Pull DURATION 6 TEMP 900->800 AMBIENT dry_O2 TIMING stated VARY T_end 650..880
    RUN TubeCool DURATION 900 TEMP 800->25 AMBIENT dry_O2 PROFILE settling TAU 180 TIMING assumed VARY duration 120..3600
    EVENT FrontMetal KIND metallization TIMING assumed           # Semitransparent Au dots, about 100 Å, 0.5 mm, evaporated from a tungsten filament at 1.0×10⁻⁶ Torr
    EVENT BackStrip KIND etch TIMING assumed                     # Back oxide removed in HF, front protected by apiezon wax
    EVENT BackMetal KIND metallization TIMING assumed            # Al back contact evaporated
    EVENT NoAnneal KIND other TIMING stated                      # No post-oxidation or post-metallization anneal
    EVENT Store KIND storage TIMING assumed                      # Kept in a dry box, shielded from electric fields
    EVENT Measure KIND measurement TIMING assumed                # Optical MOS admittance, dark and under tungsten-lamp light, 30 Hz-100 kHz
}

The oxidation time (30 min) is ours: the time at which Figure 1(b) reaches 93 Å. The spectrum rows are compared with the predictor's rows at the same energies; the predictor writes those rows only after a hydrogen anneal, which this history does not have.

n-Si/SiO2/Au, 125 Å

# n-Si/SiO2/Au, 125 Å
SAMPLE Wafer_n125 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type_1_ohm_cm_epi
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Degreased in hot solvents, ultrasonic clean, acid etch
    EVENT PreOxidation KIND other TIMING stated                  # Sacrificial oxidation, dry O2, 1100 °C, 30 min, Thermco furnace
    EVENT Strip KIND etch TIMING assumed                         # Preoxide etched in HF, ultrasonic clean, rinse in 14-18 MΩ cm water, dry in filtered N2
    EVENT Load KIND load TIMING assumed                          # Into the 900 °C furnace
    RUN Push DURATION 300 TEMP 25->900 AMBIENT inert_N2 PROFILE settling TAU 60 TIMING assumed VARY duration 60..900
    RUN Oxidation DURATION 2400 TEMP 900->900 AMBIENT dry_O2 TIMING assumed
    RUN Pull DURATION 6 TEMP 900->800 AMBIENT dry_O2 TIMING stated VARY T_end 650..880
    RUN TubeCool DURATION 900 TEMP 800->25 AMBIENT dry_O2 PROFILE settling TAU 180 TIMING assumed VARY duration 120..3600
    EVENT FrontMetal KIND metallization TIMING assumed           # Semitransparent Au dots, about 100 Å, 0.5 mm, evaporated from a tungsten filament at 1.0×10⁻⁶ Torr
    EVENT BackStrip KIND etch TIMING assumed                     # Back oxide removed in HF, front protected by apiezon wax
    EVENT BackMetal KIND metallization TIMING assumed            # Al back contact evaporated
    EVENT NoAnneal KIND other TIMING stated                      # No post-oxidation or post-metallization anneal
    EVENT Store KIND storage TIMING assumed                      # Kept in a dry box, shielded from electric fields
    EVENT Measure KIND measurement TIMING assumed                # Optical MOS admittance, dark and under tungsten-lamp light, 30 Hz-100 kHz
}

The oxidation time (40 min) is ours: the time at which Figure 1(b) reaches 125 Å. The spectrum rows are compared with the predictor's rows at the same energies; the predictor writes those rows only after a hydrogen anneal, which this history does not have.

n-Si/SiO2/Au, 148 Å

# n-Si/SiO2/Au, 148 Å
SAMPLE Wafer_n148 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: n_type_1_ohm_cm_epi
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Degreased in hot solvents, ultrasonic clean, acid etch
    EVENT PreOxidation KIND other TIMING stated                  # Sacrificial oxidation, dry O2, 1100 °C, 30 min, Thermco furnace
    EVENT Strip KIND etch TIMING assumed                         # Preoxide etched in HF, ultrasonic clean, rinse in 14-18 MΩ cm water, dry in filtered N2
    EVENT Load KIND load TIMING assumed                          # Into the 900 °C furnace
    RUN Push DURATION 300 TEMP 25->900 AMBIENT inert_N2 PROFILE settling TAU 60 TIMING assumed VARY duration 60..900
    RUN Oxidation DURATION 3000 TEMP 900->900 AMBIENT dry_O2 TIMING assumed
    RUN Pull DURATION 6 TEMP 900->800 AMBIENT dry_O2 TIMING stated VARY T_end 650..880
    RUN TubeCool DURATION 900 TEMP 800->25 AMBIENT dry_O2 PROFILE settling TAU 180 TIMING assumed VARY duration 120..3600
    EVENT FrontMetal KIND metallization TIMING assumed           # Semitransparent Au dots, about 100 Å, 0.5 mm, evaporated from a tungsten filament at 1.0×10⁻⁶ Torr
    EVENT BackStrip KIND etch TIMING assumed                     # Back oxide removed in HF, front protected by apiezon wax
    EVENT BackMetal KIND metallization TIMING assumed            # Al back contact evaporated
    EVENT NoAnneal KIND other TIMING stated                      # No post-oxidation or post-metallization anneal
    EVENT Store KIND storage TIMING assumed                      # Kept in a dry box, shielded from electric fields
    EVENT Measure KIND measurement TIMING assumed                # Optical MOS admittance, dark and under tungsten-lamp light, 30 Hz-100 kHz
}

The oxidation time (50 min) is ours: the time at which Figure 1(b) reaches 148 Å. The spectrum rows are compared with the predictor's rows at the same energies; the predictor writes those rows only after a hydrogen anneal, which this history does not have.

p-Si/SiO2/Al, 79 Å

# p-Si/SiO2/Al, 79 Å
SAMPLE Wafer_p79 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: p_type_1_ohm_cm_epi
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Degreased in hot solvents, ultrasonic clean, acid etch
    EVENT PreOxidation KIND other TIMING stated                  # Sacrificial oxidation, dry O2, 1100 °C, 30 min, Thermco furnace
    EVENT Strip KIND etch TIMING assumed                         # Preoxide etched in HF, ultrasonic clean, rinse in 14-18 MΩ cm water, dry in filtered N2
    EVENT Load KIND load TIMING assumed                          # Into the 900 °C furnace
    RUN Push DURATION 300 TEMP 25->900 AMBIENT inert_N2 PROFILE settling TAU 60 TIMING assumed VARY duration 60..900
    RUN Oxidation DURATION 1200 TEMP 900->900 AMBIENT dry_O2 TIMING assumed
    RUN Pull DURATION 6 TEMP 900->800 AMBIENT dry_O2 TIMING stated VARY T_end 650..880
    RUN TubeCool DURATION 900 TEMP 800->25 AMBIENT dry_O2 PROFILE settling TAU 180 TIMING assumed VARY duration 120..3600
    EVENT FrontMetal KIND metallization TIMING assumed           # Semitransparent Al dots, about 100 Å, 0.5 mm, evaporated from a tungsten filament at 1.0×10⁻⁶ Torr
    EVENT BackStrip KIND etch TIMING assumed                     # Back oxide removed in HF, front protected by apiezon wax
    EVENT BackMetal KIND metallization TIMING assumed            # Au back contact evaporated
    EVENT NoAnneal KIND other TIMING stated                      # No post-oxidation or post-metallization anneal
    EVENT Store KIND storage TIMING assumed                      # Kept in a dry box, shielded from electric fields
    EVENT Measure KIND measurement TIMING assumed                # Optical MOS admittance, dark and under tungsten-lamp light, 30 Hz-100 kHz
}

The oxidation time (20 min) is ours: the time at which Figure 1(b) reaches 79 Å. The spectrum rows are compared with the predictor's rows at the same energies; the predictor writes those rows only after a hydrogen anneal, which this history does not have.

p-Si/SiO2/Al, 148 Å

# p-Si/SiO2/Al, 148 Å
SAMPLE Wafer_p148 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: p_type_1_ohm_cm_epi
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Degreased in hot solvents, ultrasonic clean, acid etch
    EVENT PreOxidation KIND other TIMING stated                  # Sacrificial oxidation, dry O2, 1100 °C, 30 min, Thermco furnace
    EVENT Strip KIND etch TIMING assumed                         # Preoxide etched in HF, ultrasonic clean, rinse in 14-18 MΩ cm water, dry in filtered N2
    EVENT Load KIND load TIMING assumed                          # Into the 900 °C furnace
    RUN Push DURATION 300 TEMP 25->900 AMBIENT inert_N2 PROFILE settling TAU 60 TIMING assumed VARY duration 60..900
    RUN Oxidation DURATION 3000 TEMP 900->900 AMBIENT dry_O2 TIMING assumed
    RUN Pull DURATION 6 TEMP 900->800 AMBIENT dry_O2 TIMING stated VARY T_end 650..880
    RUN TubeCool DURATION 900 TEMP 800->25 AMBIENT dry_O2 PROFILE settling TAU 180 TIMING assumed VARY duration 120..3600
    EVENT FrontMetal KIND metallization TIMING assumed           # Semitransparent Al dots, about 100 Å, 0.5 mm, evaporated from a tungsten filament at 1.0×10⁻⁶ Torr
    EVENT BackStrip KIND etch TIMING assumed                     # Back oxide removed in HF, front protected by apiezon wax
    EVENT BackMetal KIND metallization TIMING assumed            # Au back contact evaporated
    EVENT NoAnneal KIND other TIMING stated                      # No post-oxidation or post-metallization anneal
    EVENT Store KIND storage TIMING assumed                      # Kept in a dry box, shielded from electric fields
    EVENT Measure KIND measurement TIMING assumed                # Optical MOS admittance, dark and under tungsten-lamp light, 30 Hz-100 kHz
}

The oxidation time (50 min) is ours: the time at which Figure 1(b) reaches 148 Å. The spectrum rows are compared with the predictor's rows at the same energies; the predictor writes those rows only after a hydrogen anneal, which this history does not have.

p-Si/SiO2/Al, 176 Å

# p-Si/SiO2/Al, 176 Å
SAMPLE Wafer_p176 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: not_stated
    DOPING: p_type_1_ohm_cm_epi
}
CONTROL_TRAJECTORY History {
    EVENT Clean KIND clean TIMING assumed                        # Degreased in hot solvents, ultrasonic clean, acid etch
    EVENT PreOxidation KIND other TIMING stated                  # Sacrificial oxidation, dry O2, 1100 °C, 30 min, Thermco furnace
    EVENT Strip KIND etch TIMING assumed                         # Preoxide etched in HF, ultrasonic clean, rinse in 14-18 MΩ cm water, dry in filtered N2
    EVENT Load KIND load TIMING assumed                          # Into the 900 °C furnace
    RUN Push DURATION 300 TEMP 25->900 AMBIENT inert_N2 PROFILE settling TAU 60 TIMING assumed VARY duration 60..900
    RUN Oxidation DURATION 4200 TEMP 900->900 AMBIENT dry_O2 TIMING assumed
    RUN Pull DURATION 6 TEMP 900->800 AMBIENT dry_O2 TIMING stated VARY T_end 650..880
    RUN TubeCool DURATION 900 TEMP 800->25 AMBIENT dry_O2 PROFILE settling TAU 180 TIMING assumed VARY duration 120..3600
    EVENT FrontMetal KIND metallization TIMING assumed           # Semitransparent Al dots, about 100 Å, 0.5 mm, evaporated from a tungsten filament at 1.0×10⁻⁶ Torr
    EVENT BackStrip KIND etch TIMING assumed                     # Back oxide removed in HF, front protected by apiezon wax
    EVENT BackMetal KIND metallization TIMING assumed            # Au back contact evaporated
    EVENT NoAnneal KIND other TIMING stated                      # No post-oxidation or post-metallization anneal
    EVENT Store KIND storage TIMING assumed                      # Kept in a dry box, shielded from electric fields
    EVENT Measure KIND measurement TIMING assumed                # Optical MOS admittance, dark and under tungsten-lamp light, 30 Hz-100 kHz
}

The oxidation time (70 min) is ours: the time at which Figure 1(b) reaches 176 Å. The spectrum rows are compared with the predictor's rows at the same energies; the predictor writes those rows only after a hydrogen anneal, which this history does not have.

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

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

Our simulation against the paper

9 near, 7 off, 30 not modelled of 46 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 growth_20min, growth_30min, growth_40min, growth_50min only; every other number is a test they played no part in.

Together: Push duration 300 s (was 300); Pull T end 650 °C (was 800); TubeCool duration 120 s (was 900).

As reproduced: 0 of 46 within tolerance, median error 19.7%. Aligned: 0 of 46 within tolerance, median error 19.6%. On the held-out samples only: 0 of 42 within tolerance, median error 22.8% as reproduced, 0 of 42 within tolerance, median error 22.8% aligned.

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

Three unknowns were declared: the push into the 900 °C furnace (1 to 15 min, in nitrogen), the temperature at the end of the 6 s pull (650 to 880 °C) and the cooling in the tube (2 to 60 min). They were chosen on the four Figure 1 oxides of 20 to 50 min; the 70 to 140 min oxides and the six measured devices are the test. As reproduced: 0 of 46 numbers within tolerance (median error 19.7% over the 16 rows a program answers). Aligned: 0 of 46 (19.6%). On the held-out rows: 0 of 42 before and after (median 22.8%). 30 of the 46 rows have no program: the density at fixed energies and the peak heights of an unannealed oxide.

The data cannot see any of the three unknowns. Every scan is flat to 0.1 point of median error. The push is written in nitrogen, and the thin-oxide program grows nothing without oxygen; the trap-density program relaxes by under 3% in 15 min at 900 °C. The pull and the cooling happen in oxygen below 900 °C, where neither program moves a number within the ranges. The aligned values printed above (pull to 650 °C, 120 s of cooling) are ties broken by hundredths of a percent; they are not findings.

Variants. A push in oxygen adds 0.5 nm to every oxide (12.5 against 9.3 nm for the 93 Å device, worse) and makes the trap-density program refuse: it takes the oxidation temperature from the first oxygen step's start, 25 °C, and its second population overflows. The 1965 law puts every oxide at 26 to 43 nm (median +104%); it starts from 23 nm. A furnace 20% slower than Massoud's, written as 80% oxygen because the program's rate is proportional to the oxygen pressure, brings 11 of 46 within tolerance: the Figure 1 oxides at 20 to 90 min (+4% to +9%) and five of the six device thicknesses. It is a stand-in, not the paper's gas, and is not used for the aligned numbers.

With heating and cooling transitions (section above). None of the four assumed scenarios moves any number by more than 2%: a hot push or a cold-furnace ramp in nitrogen grows nothing in the thin-oxide program, and the cooling knots after the paper's own pull are in oxygen below 800 °C, where nothing here changes.

Dit(E) against the predictor's spectrum. The predictor writes its energy rows only after a hydrogen anneal, as its midgap value times the shape of one measured curve (Vitkavage 1990, annealed p-type (111), from data/primary_sources/vitkavage_irene_1990_onr_tr34/figure2_agent_read_UNVERIFIED.csv). Kar's oxides had no anneal, so every energy row on this page is “no program”. Set beside it by hand: the shape's ratios to midgap (1.86, 1.53, 1.44, 0.72 and 0.92 at 0.20, 0.30, 0.40, 0.70 and 0.80 eV) are within 20% of Kar's at 7 of 10 points on the 93 and 125 Å n-type devices. They miss the peaks: 2.73 measured against 1.44 at 0.40 eV for 93 Å, 2.88 against 1.86 at 0.20 eV for 125 Å. On the 148 Å n-type device and the p-type devices the peaks reach 2.8 to 3.8×10^12, five to ten times the background, and move with thickness; no single smooth shape can give them. With the program's midgap (4.28×10^11 for 93 Å) the shape would put the rows 21 to 67% high, most of it the midgap error.

6 near, 6 off, 30 not modelled of 42 numbers with the aligned settings (the samples used to choose the unknowns are left out).

What alignment cannot fix. Thickness: the thin-oxide program is 15 to 25% high through 90 min and 36 to 50% high at 110 and 140 min. Kar's oxide grows 0.22 nm/min between 20 and 50 min and 0.075 nm/min between 50 and 140 min; the program grows 0.24 and 0.17 nm/min. An early offset of about 20% (a slower furnace, or a thickness method that reads low) and a late slowing the program does not have are both needed; the authors read it as a change from a logarithmic to a linear phase near 200 Å. 900 °C is the temperature the program holds out on Massoud's data (18 of 25 there).

Midgap density: 39% and 59% high (4.28 and 4.24×10^11 against 3.08 and 2.67×10^11). The program's value falls by 1% between 30 and 40 min at 900 °C; Kar's falls by 13%. Kar's values are from admittance under illumination, the program's training values from quasi-static C-V, and the program was fitted on oxidations of one hour or more.

Dit(E): not modelled. A program for it would need (1) the dangling-bond population the midgap program already carries, spread over two levels, a donor peak near 0.3 eV and an acceptor peak near 0.85 eV above the valence band, with positions and widths as parameters; (2) a separate U-shaped background of band tails, rising toward both edges, which hydrogen does not remove (the annealed Vitkavage curve and Fukuda's Figure 1 are this background); (3) peak heights and energies that depend on the oxide's growth: Kar's peak density falls then rises with thickness (minimum near 110 Å, maximum near 155 Å) and its energy moves between 0.26 and 0.43 eV, so a state tied to thickness or growth rate, which no trap program here has; (4) an observation model that knows which half of the gap a technique on n- or p-type silicon can reach. The data we hold to fit it: Kar's six unannealed curves, Vitkavage's unannealed and annealed (111) curves, Fukuda's three unannealed rapid thermal oxides.

What our language and ontology cannot yet say

• Which step is the oxidation. Writing the push in oxygen, which may be what was done, makes the trap-density program read the oxidation temperature as 25 °C and refuse. A ROLE oxidation|load|pull|anneal on each RUN would let a push be written as the heating it is.
• An etch that removes oxide. The 1100 °C sacrificial oxide is grown and stripped in HF before the gate oxide; it had to be an event. ETCH REMOVE ALL (or TO <nm>) after a RUN would let the preoxidation be simulated, so that its heat reaches the programs and its oxide does not.
• Dit(E) as an observable. The predictor's energy rows are fixed target names written only after hydrogen. An observation Dit AT_ENERGY <eV> ABOVE Ev BY admittance|quasistatic with the substrate type would let a paper's distribution be stated as what was measured, and let a program say it cannot answer at that energy rather than be silent.
• Peaks and cross sections. The paper's central results are a peak's height and energy and a capture cross section against thickness. The ontology has no observable for any of them.
• A device tied to a calibration series. Each measured device is known by its thickness; its oxidation time comes only from Figure 1. A sample field OXIDE_NM read as a measured property, and a way to say a RUN's duration is whatever makes that thickness (an inverse VARY), would replace the times inferred by hand here.
• Doping and gate metal as inputs. DOPING is recorded and read by no program; here it decides which half of the gap was measured. The gate metal (Au on n-type, Al on p-type) is not recordable; an aluminium gate can release hydrogen at the interface even without an anneal.
• A clean word. The vocabulary has no sacrificial_oxide_HF for “preoxidation was part of the surface cleaning”; CLEAN had to be not_stated although the paper states it.

With heating and cooling transitions

No paper we hold states how its wafers heated up or cooled down. The project owner specified scenarios for one Vitkavage wafer (isl_harness/vitkavage_transitions.py); isl_harness/thermal_transitions.py applies the same numbers to every sample here: a heat-up in nitrogen before the first furnace step (a hot push of 1 to 5 min, or a cold-furnace ramp of 60 to 120 min), the owner's radiative cooling knots after the last furnace step or after the paper's own pull (fast, or every time multiplied by 5), and ramps around an anneal at 300 to 500 °C. The paper's own steps are kept as written. All transitions are assumptions, written in the history with TIMING assumed.

The paper's own conclusions

What we would like Emily to check

1. Would a 900 °C dry furnace oxide of 1987 normally be pushed in oxygen or in nitrogen, and over how many minutes? For 20 min oxides it is a sizeable fraction of the time.
2. The peak near 0.3 to 0.4 eV above the valence band in these unannealed oxides: is it the Pb0 donor level (the dangling bond's lower level near 0.3 eV), so that a two-level Pb distribution could be the program for Dit(E)?
3. Is admittance-derived density at 0.55 eV comparable with quasi-static midgap density within a factor of two, so that Kar's midgap values can be scored against a program fitted on quasi-static data?
4. Kar finds the peak density falling then rising with thickness (minimum near 110 Å, maximum near 155 Å). Is that likely a property of the oxidation, or of the batch (the two n-type sets put the minimum at different thicknesses)?