Reproducing Tsai et al. 1987: trap density after nitridation in ammonia

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/tsai_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

H.-H. Tsai, L.-C. Wu, C.-Y. Wu and C. Hu, “Effects of thermal nitridation conditions on the reliability of thin nitrided oxide films”, IEEE Electron Device Lett. EDL-8, 143-145 (1987).

A study of thermally nitrided gate oxides: 250 Å of dry oxide grown at 920 °C, nitrided in ammonia at 900, 1000, 1100 and 1150 °C for 0.5 and 3 h, then put through a full polysilicon-gate process ending in forming gas at 430 °C. It is in the project's library because it measures trap density after nitridation. It does not measure trap density against oxidation history: what it reports is the trap density generated by electron injection, the flat-band voltage and the charge to breakdown. Nitridation is the first process in the challenge's system 1 that our language cannot write: there is no ammonia (or N2O) among its gases and no program for nitrogen at the interface. This page writes the history with nitrogen standing in for the heat of the nitridation, shows what the programs then predict, and records what is missing.

How well can this study be reproduced?

Low. The gate oxidation temperature, the 250 Å thickness, the 30 min nitrogen anneal, the nitridation temperatures and times, the load temperature, the reflow and the forming-gas temperature are stated. Not stated: the oxidation time, the ramp rates and ramp gas around the nitridation, the drive-in time, the reflow gas, the forming-gas time and H2 fraction, and every deposition temperature. The central step cannot be written: the language has no ammonia, and no program incorporates nitrogen. The trap densities are only plotted, against injected fluence, and the pre-stress values are not printed.

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. 4 same, 4 approximated, 2 assumed, 9 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.

Pure SiO2, 250 Å, not nitrided

Simulated time in this history: 3 h 10 min.

Across the samples

Timing the paper does not give

• Gate oxidation time at 920 °C: only the 250 Å thickness is stated.
• Pull from the oxidation furnace and transfer to the nitridation furnace: rate, gas and waiting time.
• Ramp from the 900 °C load to the nitridation temperature and back down: rate, gas (ammonia or inert) and unload temperature.
• Whether the stated 0.5 and 3 h include the ramps.
• Drive-in at 1000 °C: time and gas.
• Reflow at 1038 °C: gas and ramps (time stated, 30 min).
• Forming gas at 430 °C: time and H2 fraction.
• LPCVD polysilicon and CVD oxide: temperatures and times (both expose the interface to hydrogen-bearing gases).

What the second reading changed

• The project holds no recipe or dataset for this paper (ontology/library.json: status held, used_by empty; SOURCE.md: “Not read by us”). Everything here is from the second reading.
• SOURCE.md says the paper reports “trap density after nitridation at 900 to 1150 C”. It reports the trap density generated during electron injection after nitridation (Figure 1). The pre-stress trap density was measured (“first measured for the interface state density”) but is not printed; the curves of Figure 1 start below about 1×10^11 cm⁻² eV⁻¹.
• The 1000 °C, 3 h condition is listed in the text (“at 900, 1000, 1100, and 1150 C for 0, 0.5, and 3 h”) but has no entry in either table.
• The pure oxide was stressed at 1 mA/cm², the nitrided oxides at 10 mA/cm² (Table I and figure captions), so the paper's comparison of pure and nitrided oxide in Figure 1 mixes two stress currents.

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>.

Pure SiO2, 250 Å, not nitrided

# Pure SiO2, 250 Å, not nitrided
SAMPLE Cap_SiO2 {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    DOPING: n_type_15_25_ohm_cm
    GATE: n_plus_polysilicon_As
    AREA_UM2: 62500
}
CONTROL_TRAJECTORY History {
    EVENT Isolation KIND other TIMING assumed                    # LOCOS isolation (conventional polysilicon-gate process)
    RUN Oxidation DURATION 4200 TEMP 920->920 AMBIENT dry_O2 TIMING assumed VARY duration 2400..7200
    RUN NitrogenAnneal DURATION 1800 TEMP 920->920 AMBIENT inert_N2 TIMING stated
    EVENT PolyDeposition KIND deposition TIMING assumed          # LPCVD polysilicon, about 4500 Å
    EVENT ArsenicImplant KIND other TIMING assumed               # Arsenic implant into the polysilicon
    RUN DriveIn DURATION 1800 TEMP 1000->1000 AMBIENT inert_N2 TIMING assumed VARY duration 600..3600
    EVENT BoronImplant KIND other TIMING assumed                 # Gate lithography and self-aligned boron implant, 2×10^15 cm⁻² at 30 keV
    EVENT OxideDeposition KIND deposition TIMING assumed         # CVD SiO2
    RUN Reflow DURATION 1800 TEMP 1038->1038 AMBIENT inert_N2 TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Contact etch and metallization
    RUN FormingGas DURATION 1800 TEMP 430->430 AMBIENT forming_gas_H2 TIMING assumed VARY duration 600..3600
    EVENT Measure KIND measurement TIMING assumed                # Trap density and flat-band voltage, then constant-current stress
}

The paper lists 0 h among the nitridation times; whether the pure-oxide wafers went into the nitridation furnace is not stated, so they are written without it.

250 Å oxide nitrided in NH3 at 900 °C for 0.5 h

# 250 Å oxide nitrided in NH3 at 900 °C for 0.5 h
SAMPLE Cap_N900_0p5h {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    DOPING: n_type_15_25_ohm_cm
    GATE: n_plus_polysilicon_As
    AREA_UM2: 62500
}
CONTROL_TRAJECTORY History {
    EVENT Isolation KIND other TIMING assumed                    # LOCOS isolation (conventional polysilicon-gate process)
    RUN Oxidation DURATION 4200 TEMP 920->920 AMBIENT dry_O2 TIMING assumed VARY duration 2400..7200
    RUN NitrogenAnneal DURATION 1800 TEMP 920->920 AMBIENT inert_N2 TIMING stated
    EVENT Transfer KIND transfer TIMING assumed                  # Pulled and moved to the nitridation furnace
    EVENT Load KIND load TIMING assumed                          # Loaded into the nitridation furnace at 900 °C
    RUN Nitridation DURATION 1800 TEMP 900->900 AMBIENT inert_N2 TIMING stated
    RUN RampDown DURATION 600 TEMP 900->800 AMBIENT inert_N2 TIMING assumed VARY T_end 600..900
    EVENT PolyDeposition KIND deposition TIMING assumed          # LPCVD polysilicon, about 4500 Å
    EVENT ArsenicImplant KIND other TIMING assumed               # Arsenic implant into the polysilicon
    RUN DriveIn DURATION 1800 TEMP 1000->1000 AMBIENT inert_N2 TIMING assumed VARY duration 600..3600
    EVENT BoronImplant KIND other TIMING assumed                 # Gate lithography and self-aligned boron implant, 2×10^15 cm⁻² at 30 keV
    EVENT OxideDeposition KIND deposition TIMING assumed         # CVD SiO2
    RUN Reflow DURATION 1800 TEMP 1038->1038 AMBIENT inert_N2 TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Contact etch and metallization
    RUN FormingGas DURATION 1800 TEMP 430->430 AMBIENT forming_gas_H2 TIMING assumed VARY duration 600..3600
    EVENT Measure KIND measurement TIMING assumed                # Trap density and flat-band voltage, then constant-current stress
}

Charge to breakdown 40.8 C/cm² (Table I); no program models breakdown.

250 Å oxide nitrided in NH3 at 1000 °C for 0.5 h

# 250 Å oxide nitrided in NH3 at 1000 °C for 0.5 h
SAMPLE Cap_N1000_0p5h {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    DOPING: n_type_15_25_ohm_cm
    GATE: n_plus_polysilicon_As
    AREA_UM2: 62500
}
CONTROL_TRAJECTORY History {
    EVENT Isolation KIND other TIMING assumed                    # LOCOS isolation (conventional polysilicon-gate process)
    RUN Oxidation DURATION 4200 TEMP 920->920 AMBIENT dry_O2 TIMING assumed VARY duration 2400..7200
    RUN NitrogenAnneal DURATION 1800 TEMP 920->920 AMBIENT inert_N2 TIMING stated
    EVENT Transfer KIND transfer TIMING assumed                  # Pulled and moved to the nitridation furnace
    EVENT Load KIND load TIMING assumed                          # Loaded into the nitridation furnace at 900 °C
    RUN RampUp DURATION 600 TEMP 900->1000 AMBIENT inert_N2 TIMING assumed VARY duration 200..2000
    RUN Nitridation DURATION 1800 TEMP 1000->1000 AMBIENT inert_N2 TIMING stated
    RUN RampDown DURATION 1200 TEMP 1000->800 AMBIENT inert_N2 TIMING assumed VARY T_end 600..900
    EVENT PolyDeposition KIND deposition TIMING assumed          # LPCVD polysilicon, about 4500 Å
    EVENT ArsenicImplant KIND other TIMING assumed               # Arsenic implant into the polysilicon
    RUN DriveIn DURATION 1800 TEMP 1000->1000 AMBIENT inert_N2 TIMING assumed VARY duration 600..3600
    EVENT BoronImplant KIND other TIMING assumed                 # Gate lithography and self-aligned boron implant, 2×10^15 cm⁻² at 30 keV
    EVENT OxideDeposition KIND deposition TIMING assumed         # CVD SiO2
    RUN Reflow DURATION 1800 TEMP 1038->1038 AMBIENT inert_N2 TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Contact etch and metallization
    RUN FormingGas DURATION 1800 TEMP 430->430 AMBIENT forming_gas_H2 TIMING assumed VARY duration 600..3600
    EVENT Measure KIND measurement TIMING assumed                # Trap density and flat-band voltage, then constant-current stress
}

Charge to breakdown 0.2 C/cm² (Table I); no program models breakdown.

250 Å oxide nitrided in NH3 at 1100 °C for 0.5 h

# 250 Å oxide nitrided in NH3 at 1100 °C for 0.5 h
SAMPLE Cap_N1100_0p5h {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    DOPING: n_type_15_25_ohm_cm
    GATE: n_plus_polysilicon_As
    AREA_UM2: 62500
}
CONTROL_TRAJECTORY History {
    EVENT Isolation KIND other TIMING assumed                    # LOCOS isolation (conventional polysilicon-gate process)
    RUN Oxidation DURATION 4200 TEMP 920->920 AMBIENT dry_O2 TIMING assumed VARY duration 2400..7200
    RUN NitrogenAnneal DURATION 1800 TEMP 920->920 AMBIENT inert_N2 TIMING stated
    EVENT Transfer KIND transfer TIMING assumed                  # Pulled and moved to the nitridation furnace
    EVENT Load KIND load TIMING assumed                          # Loaded into the nitridation furnace at 900 °C
    RUN RampUp DURATION 1200 TEMP 900->1100 AMBIENT inert_N2 TIMING assumed VARY duration 400..4000
    RUN Nitridation DURATION 1800 TEMP 1100->1100 AMBIENT inert_N2 TIMING stated
    RUN RampDown DURATION 1800 TEMP 1100->800 AMBIENT inert_N2 TIMING assumed VARY T_end 600..900
    EVENT PolyDeposition KIND deposition TIMING assumed          # LPCVD polysilicon, about 4500 Å
    EVENT ArsenicImplant KIND other TIMING assumed               # Arsenic implant into the polysilicon
    RUN DriveIn DURATION 1800 TEMP 1000->1000 AMBIENT inert_N2 TIMING assumed VARY duration 600..3600
    EVENT BoronImplant KIND other TIMING assumed                 # Gate lithography and self-aligned boron implant, 2×10^15 cm⁻² at 30 keV
    EVENT OxideDeposition KIND deposition TIMING assumed         # CVD SiO2
    RUN Reflow DURATION 1800 TEMP 1038->1038 AMBIENT inert_N2 TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Contact etch and metallization
    RUN FormingGas DURATION 1800 TEMP 430->430 AMBIENT forming_gas_H2 TIMING assumed VARY duration 600..3600
    EVENT Measure KIND measurement TIMING assumed                # Trap density and flat-band voltage, then constant-current stress
}

Charge to breakdown 0.3 C/cm² (Table I); no program models breakdown.

250 Å oxide nitrided in NH3 at 1150 °C for 0.5 h

# 250 Å oxide nitrided in NH3 at 1150 °C for 0.5 h
SAMPLE Cap_N1150_0p5h {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    DOPING: n_type_15_25_ohm_cm
    GATE: n_plus_polysilicon_As
    AREA_UM2: 62500
}
CONTROL_TRAJECTORY History {
    EVENT Isolation KIND other TIMING assumed                    # LOCOS isolation (conventional polysilicon-gate process)
    RUN Oxidation DURATION 4200 TEMP 920->920 AMBIENT dry_O2 TIMING assumed VARY duration 2400..7200
    RUN NitrogenAnneal DURATION 1800 TEMP 920->920 AMBIENT inert_N2 TIMING stated
    EVENT Transfer KIND transfer TIMING assumed                  # Pulled and moved to the nitridation furnace
    EVENT Load KIND load TIMING assumed                          # Loaded into the nitridation furnace at 900 °C
    RUN RampUp DURATION 1500 TEMP 900->1150 AMBIENT inert_N2 TIMING assumed VARY duration 500..5000
    RUN Nitridation DURATION 1800 TEMP 1150->1150 AMBIENT inert_N2 TIMING stated
    RUN RampDown DURATION 2100 TEMP 1150->800 AMBIENT inert_N2 TIMING assumed VARY T_end 600..900
    EVENT PolyDeposition KIND deposition TIMING assumed          # LPCVD polysilicon, about 4500 Å
    EVENT ArsenicImplant KIND other TIMING assumed               # Arsenic implant into the polysilicon
    RUN DriveIn DURATION 1800 TEMP 1000->1000 AMBIENT inert_N2 TIMING assumed VARY duration 600..3600
    EVENT BoronImplant KIND other TIMING assumed                 # Gate lithography and self-aligned boron implant, 2×10^15 cm⁻² at 30 keV
    EVENT OxideDeposition KIND deposition TIMING assumed         # CVD SiO2
    RUN Reflow DURATION 1800 TEMP 1038->1038 AMBIENT inert_N2 TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Contact etch and metallization
    RUN FormingGas DURATION 1800 TEMP 430->430 AMBIENT forming_gas_H2 TIMING assumed VARY duration 600..3600
    EVENT Measure KIND measurement TIMING assumed                # Trap density and flat-band voltage, then constant-current stress
}

Charge to breakdown 1.2 C/cm² (Table I); no program models breakdown.

250 Å oxide nitrided in NH3 at 900 °C for 3 h

# 250 Å oxide nitrided in NH3 at 900 °C for 3 h
SAMPLE Cap_N900_3h {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    DOPING: n_type_15_25_ohm_cm
    GATE: n_plus_polysilicon_As
    AREA_UM2: 62500
}
CONTROL_TRAJECTORY History {
    EVENT Isolation KIND other TIMING assumed                    # LOCOS isolation (conventional polysilicon-gate process)
    RUN Oxidation DURATION 4200 TEMP 920->920 AMBIENT dry_O2 TIMING assumed VARY duration 2400..7200
    RUN NitrogenAnneal DURATION 1800 TEMP 920->920 AMBIENT inert_N2 TIMING stated
    EVENT Transfer KIND transfer TIMING assumed                  # Pulled and moved to the nitridation furnace
    EVENT Load KIND load TIMING assumed                          # Loaded into the nitridation furnace at 900 °C
    RUN Nitridation DURATION 10800 TEMP 900->900 AMBIENT inert_N2 TIMING stated
    RUN RampDown DURATION 600 TEMP 900->800 AMBIENT inert_N2 TIMING assumed VARY T_end 600..900
    EVENT PolyDeposition KIND deposition TIMING assumed          # LPCVD polysilicon, about 4500 Å
    EVENT ArsenicImplant KIND other TIMING assumed               # Arsenic implant into the polysilicon
    RUN DriveIn DURATION 1800 TEMP 1000->1000 AMBIENT inert_N2 TIMING assumed VARY duration 600..3600
    EVENT BoronImplant KIND other TIMING assumed                 # Gate lithography and self-aligned boron implant, 2×10^15 cm⁻² at 30 keV
    EVENT OxideDeposition KIND deposition TIMING assumed         # CVD SiO2
    RUN Reflow DURATION 1800 TEMP 1038->1038 AMBIENT inert_N2 TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Contact etch and metallization
    RUN FormingGas DURATION 1800 TEMP 430->430 AMBIENT forming_gas_H2 TIMING assumed VARY duration 600..3600
    EVENT Measure KIND measurement TIMING assumed                # Trap density and flat-band voltage, then constant-current stress
}

Charge to breakdown 18.7 C/cm² (Table I); no program models breakdown.

250 Å oxide nitrided in NH3 at 1100 °C for 3 h

# 250 Å oxide nitrided in NH3 at 1100 °C for 3 h
SAMPLE Cap_N1100_3h {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    DOPING: n_type_15_25_ohm_cm
    GATE: n_plus_polysilicon_As
    AREA_UM2: 62500
}
CONTROL_TRAJECTORY History {
    EVENT Isolation KIND other TIMING assumed                    # LOCOS isolation (conventional polysilicon-gate process)
    RUN Oxidation DURATION 4200 TEMP 920->920 AMBIENT dry_O2 TIMING assumed VARY duration 2400..7200
    RUN NitrogenAnneal DURATION 1800 TEMP 920->920 AMBIENT inert_N2 TIMING stated
    EVENT Transfer KIND transfer TIMING assumed                  # Pulled and moved to the nitridation furnace
    EVENT Load KIND load TIMING assumed                          # Loaded into the nitridation furnace at 900 °C
    RUN RampUp DURATION 1200 TEMP 900->1100 AMBIENT inert_N2 TIMING assumed VARY duration 400..4000
    RUN Nitridation DURATION 10800 TEMP 1100->1100 AMBIENT inert_N2 TIMING stated
    RUN RampDown DURATION 1800 TEMP 1100->800 AMBIENT inert_N2 TIMING assumed VARY T_end 600..900
    EVENT PolyDeposition KIND deposition TIMING assumed          # LPCVD polysilicon, about 4500 Å
    EVENT ArsenicImplant KIND other TIMING assumed               # Arsenic implant into the polysilicon
    RUN DriveIn DURATION 1800 TEMP 1000->1000 AMBIENT inert_N2 TIMING assumed VARY duration 600..3600
    EVENT BoronImplant KIND other TIMING assumed                 # Gate lithography and self-aligned boron implant, 2×10^15 cm⁻² at 30 keV
    EVENT OxideDeposition KIND deposition TIMING assumed         # CVD SiO2
    RUN Reflow DURATION 1800 TEMP 1038->1038 AMBIENT inert_N2 TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Contact etch and metallization
    RUN FormingGas DURATION 1800 TEMP 430->430 AMBIENT forming_gas_H2 TIMING assumed VARY duration 600..3600
    EVENT Measure KIND measurement TIMING assumed                # Trap density and flat-band voltage, then constant-current stress
}

Charge to breakdown 1.5 C/cm² (Table I); no program models breakdown.

250 Å oxide nitrided in NH3 at 1150 °C for 3 h

# 250 Å oxide nitrided in NH3 at 1150 °C for 3 h
SAMPLE Cap_N1150_3h {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    DOPING: n_type_15_25_ohm_cm
    GATE: n_plus_polysilicon_As
    AREA_UM2: 62500
}
CONTROL_TRAJECTORY History {
    EVENT Isolation KIND other TIMING assumed                    # LOCOS isolation (conventional polysilicon-gate process)
    RUN Oxidation DURATION 4200 TEMP 920->920 AMBIENT dry_O2 TIMING assumed VARY duration 2400..7200
    RUN NitrogenAnneal DURATION 1800 TEMP 920->920 AMBIENT inert_N2 TIMING stated
    EVENT Transfer KIND transfer TIMING assumed                  # Pulled and moved to the nitridation furnace
    EVENT Load KIND load TIMING assumed                          # Loaded into the nitridation furnace at 900 °C
    RUN RampUp DURATION 1500 TEMP 900->1150 AMBIENT inert_N2 TIMING assumed VARY duration 500..5000
    RUN Nitridation DURATION 10800 TEMP 1150->1150 AMBIENT inert_N2 TIMING stated
    RUN RampDown DURATION 2100 TEMP 1150->800 AMBIENT inert_N2 TIMING assumed VARY T_end 600..900
    EVENT PolyDeposition KIND deposition TIMING assumed          # LPCVD polysilicon, about 4500 Å
    EVENT ArsenicImplant KIND other TIMING assumed               # Arsenic implant into the polysilicon
    RUN DriveIn DURATION 1800 TEMP 1000->1000 AMBIENT inert_N2 TIMING assumed VARY duration 600..3600
    EVENT BoronImplant KIND other TIMING assumed                 # Gate lithography and self-aligned boron implant, 2×10^15 cm⁻² at 30 keV
    EVENT OxideDeposition KIND deposition TIMING assumed         # CVD SiO2
    RUN Reflow DURATION 1800 TEMP 1038->1038 AMBIENT inert_N2 TIMING stated
    EVENT Metal KIND metallization TIMING assumed                # Contact etch and metallization
    RUN FormingGas DURATION 1800 TEMP 430->430 AMBIENT forming_gas_H2 TIMING assumed VARY duration 600..3600
    EVENT Measure KIND measurement TIMING assumed                # Trap density and flat-band voltage, then constant-current stress
}

Charge to breakdown 5.2 C/cm² (Table I); no program models breakdown.

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

9 within, 15 not modelled of 24 numbers. Tolerance is stated per row; nothing was fitted for this page.

Aligning the simulation: what the unstated things would have to be

Every step whose timing or temperature the paper leaves open carries a range in the history above (VARY). scripts/align_study.py searched those ranges against the paper's numbers through the same predictor, first one unknown at a time, then all together. No parameter a program declares fitted was touched. The unknowns were chosen on N1000_0p5h, N1100_0p5h, N1150_0p5h, N900_0p5h, SiO2 only; every other number is a test they played no part in.

Together: Oxidation duration 4200 s (was 4200); DriveIn duration 1090 s (was 1800); FormingGas duration 600 s (was 1800); RampDown T end 600 °C (was 800); RampUp duration 0.4893× (was 1).

As reproduced: 9 of 24 within tolerance, median error 87.2%. Aligned: 9 of 24 within tolerance, median error 19.3%. On the held-out samples only: 3 of 9 within tolerance, median error 93.8% as reproduced, 3 of 9 within tolerance, median error 65.0% aligned.

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

Five unknowns were declared: the gate oxidation time (40 to 120 min), the ramp up to the nitridation temperature (3 to 30 °C/min), the unload temperature after the ramp down (600 to 900 °C), the drive-in time (10 to 60 min) and the forming-gas time (10 to 60 min). They were chosen on the pure oxide and the four 0.5 h wafers and tested on the three 3 h wafers. Only 9 of 24 numbers have a program at all: one thickness and eight pre-stress trap densities, the latter scored as a bound (0 to 1×10^11 cm⁻² eV⁻¹) from Figure 1. As reproduced 9 of 24 within tolerance (median error on the modelled rows 87.2%); aligned 9 of 24 (19.3%); on the 3 h wafers 3 of 9 before and after (median error 93.8% before, 65.0% after), the other 6 having no program.

The thickness pins the oxidation time and nothing else is pinned. The 250 Å is matched with 67 to 70 min at 920 °C in the thin-oxide program (25.3 nm as reproduced). Every other scan ties at 6 of 15 on the chosen wafers: the bound on the trap density is wide enough that no history unknown moves a row across it, so the values printed for the ramps, the unload temperature and the drive-in are not findings. The combined search moves the forming gas to 10 min, the low end of its range, on the median error alone: 30 min in 10% H2 at 430 °C caps about 93% of the dangling bonds hydrogen reaches (the capping rate is fitted at 400 °C and, with Brower's 1.66 eV, 3.4 times faster at 430 °C), and a shorter anneal leaves the density nearer the bound's centre. That is the centre of a bound pulling, not a measurement of the time.

The nitridation enters only as heat, and the heat lowers the predicted trap density. With nitrogen standing in for ammonia, the trap-density program's relaxation runs during the nitridation: 8.3×10^9 for the pure oxide, 7.9, 6.4, 3.8 and 3.2×10^9 after 0.5 h at 900, 1000, 1100 and 1150 °C, and 6.7, 3.1 and 3.1×10^9 after 3 h at 900, 1100 and 1150 °C (forming gas 30 min, 10% H2). Leaving the nitridation out altogether puts every wafer at the pure oxide's value (median error 83.5% against the bound's centre, from 87.2%; 2.0% with the aligned 10 min forming gas): the data cannot tell, because no pre-stress value is printed.

The fixed-charge program gives 2.54×10^10 cm⁻² for every wafer, because the 30 min reflow at 1038 °C in nitrogen sets it whatever came before. Table II's flat-band voltages run from −1.363 V (900 °C, 3 h) to +0.227 V (1150 °C, 3 h). With C_ox = 1.38×10^-7 F/cm² for 250 Å, that spread is 1.4×10^12 charges per cm², and the pure oxide to 900 °C, 0.5 h difference (−0.167 to −0.987 V) is 7.1×10^11 cm⁻² more positive charge. The program has no flat-band observable and no nitrogen; the gate work function is not stated, so the voltages were not converted to a charge and scored.

Forming gas with 5% H2 instead of 10% keeps the count (9 of 24) and moves the median error from 87.2% to 52.7% (42.1% with the aligned history): it multiplies the remaining density by 3.7 on every wafer (8.3×10^9 to 3.0×10^10 for the pure oxide), which shows how much the unstated H2 fraction matters to the program. Its capping rate is linear in p_H2, so halving it halves the exponent, and 30 min at 430 °C in 10% H2 is an exponent of 2.6.

With heating and cooling transitions the count stays 9 of 24, and every trap density moves: 11 to 13% lower with a hot push (median error 88.8%) and 37 to 44% lower, to 1.9 to 4.7×10^9, with a cold-furnace ramp (92.6%). Most of it is the forming-gas step: the transitions add a heat-up and a cool-down around it in forming gas (180 s and 600 s for the hot push, 30 and 60 min for the cold furnace), and those alone lower every wafer by 10.5% and 37%. The capping rate now has Brower's activation energy (1.66 eV; 5.6×10⁻⁶ of the 400 °C rate at 200 °C), so the ramps count as about 76 s (hot push) and 320 s (cold furnace) at 430 °C, not their full 13 and 90 min as before the 11 November hydrogen change, when they gave 30% and ten times lower. The heat-ups and cool-downs around the 900 to 1150 °C steps add up to 2.5% (hot push) and 10.6% (cold furnace) by relaxation, on the wafers whose own steps relax them least (the pure oxide and 900 to 1000 °C); nothing on the 3 h wafers at 1100 and 1150 °C.

With Quantum ESPRESSO switched on, the computed equilibrium bound after the 430 °C forming gas is 2.9 to 3.9×10^6 cm⁻² eV⁻¹, three orders of magnitude below the program's 3.1 to 8.3×10^9 and four below the Figure 1 bound of about 1×10^11. The pre-stress density is not printed, so no measured-over-bound ratio is given; what Figure 1 shows is consistent with an anneal far from equilibrium.

3 within, 6 not modelled of 9 numbers with the aligned settings (the samples used to choose the unknowns are left out).

What alignment cannot fix: the paper's results are all outside the predictor. The trap density generated by electron injection (Figure 1, 4.8 to 20×10^11 cm⁻² eV⁻¹ at 3×10^18 cm⁻²), the flat-band voltage (Table II) and the charge to breakdown (Table I) have no program, and 15 of the 24 rows say so. Reasons in order: (b) the language cannot write the nitridation (no NH3 or N2O among its gases; the runtime refuses mix:NH3=1.0) and has no electrical stress step; (c) no program models nitrogen at the interface, bulk electron traps, trap generation under injection, or a flat-band voltage.

What a nitridation program would need: a state for the nitrogen at the interface and in the film (areal density and depth, growing with time at temperature in NH3 with an activation energy, and re-oxidizing in N2O/O2), a state for hydrogen brought in by ammonia, and observation models for the fixed and trapped charge they carry. Tsai's own data would test it only through stress results, so a stress statement (STRESS CURRENT 10 mA/cm2 FLUENCE 3e18 INJECTION substrate) and a generation observable are needed before this paper can be scored.

What our language and ontology cannot yet say

• Ammonia and nitrous oxide as gases. AMBIENT mix:NH3=1.0 and mix:N2O=1.0 are refused (the gases are Ar, H2, H2O, N2, O2). Adding p_NH3 and p_N2O as controls would let a nitridation be written as done; today it can only be written as nitrogen, which carries its heat and nothing else. Every row here would then at least be run on the paper's history.
• A program for nitrogen at the interface. With the gas written, a program has to say what it does: incorporate nitrogen at the Si/SiO2 interface (rate rising with temperature, saturating with time), release hydrogen into the film, and shift fixed charge and trap generation. The paper's Table II (more negative flat-band voltage at lower nitridation temperature, positive after 3 h at 1100 and 1150 °C) is the first check such a program would have.
• An electrical stress step. Figure 1 and 2 are measured during constant-current injection; the language has no statement for it, so the paper's main result is outside any history. A STRESS statement with current density, polarity and fluence, and observables for generated trap density and flat-band shift, would make it a target.
• The gate as a sample property a program reads. A flat-band voltage needs the gate work function (As-doped polysilicon here). GATE is recorded on the sample and read by nothing; a program computing Vfb from fixed charge, trapped charge and the gate would let Table II be scored.
• The forming-gas time and H2 fraction (history). Since 11 November the capping rate has Brower's 1.66 eV (see the Reed 1989 page), so a forming-gas ramp from room temperature counts for little (the cold-furnace ramps lower the density 37%, where they gave ten times before). What still sets the predicted density is what the paper does not state: the forming-gas time (10 to 60 min) and the H2 fraction (5% gives 3.7 times the density of 10%).
• Process steps that bring hydrogen. LPCVD polysilicon (silane), CVD oxide and the ammonia itself are hydrogen sources the history records only as events. A hydrogen source on an EVENT or a deposition RUN with its gas would let them reach the trap-density program.

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 1986 nitridation furnace, would ammonia flow during the ramp from the 900 °C load to 1100 or 1150 °C, or would the tube be in nitrogen until the hold?
2. Is a positive flat-band voltage after 3 h at 1100 and 1150 °C (Table II) what you would expect from nitrogen at the interface, or from something else in the full process (the 1038 °C reflow, the boron ring)?
3. Ammonia brings hydrogen. Should a program for nitridation carry the hydrogen it releases (as electron traps, as Si-H or N-H at the interface), or is nitrogen incorporation the first thing to model?
4. The pre-stress trap density was measured but not printed. Would the curves of Figure 1 at zero fluence be the pre-stress values, or are they the generated density (a difference)?