Reproducing Yano et al. 2002: interface states on wet-oxidized 4H-SiC (03-38) and (0001)

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/yano_2002.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. Yano, T. Hirao, T. Kimoto, H. Matsunami and H. Shiomi, “Interface properties in metal-oxide-semiconductor structures on n-type 4H-SiC(03-38)”, Appl. Phys. Lett. 81, 4772 (2002).

A second laboratory's interface-state densities on SiC, after wet oxidation, a low-temperature argon anneal and a forming-gas anneal: three steps no SiC program we hold was built for. The page records what the predictor returns and why it should not be trusted here.

How well can this study be reproduced?

Moderate. Every furnace step has its temperature, time and gas class: wet oxidation at 1150 °C (25 or 120 min), argon in situ at 1150 °C for 30 min, forming gas at 400 °C for 30 min. What a simulation must supply: how the steam was made, the heat-up and cooling around each step, and the switch from steam to argon. The two samples also differ in doping and oxide thickness, not only in face.

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, 2 approximated, 2 assumed, 6 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.

4H-SiC (0001) Si face, wet 1150 °C 120 min

Simulated time in this history: 3 h 00 min 01 s.

Across the samples

Timing the paper does not give

• Wait between the RCA clean and loading: “immediately”.
• Load temperature, heat-up and the gas during it: not stated.
• How the steam was made (bubbler or pyrogenic), its partial pressure and flow: not stated.
• The switch from steam to argon before the in-situ anneal: not stated.
• Cooling after the argon anneal, and unload temperature: not stated.
• Ramps of the 400 °C forming-gas anneal, and time from metal deposition to it: not stated.

What the second reading changed

• The project held this paper as “held, not yet transcribed”: there was no stored recipe and no dataset. The Dit values here are the second reader's digitization of Figure 3 (pixel calibration), not a project dataset.
• The project's note calls the paper “interface state density against energy on two faces … (and the effect of anneals)”. The paper has one process for both faces and no anneal comparison: one wet oxidation, one argon anneal and one forming-gas anneal for every sample.
• The two faces were not oxidized for the same time (25 against 120 min) and carry different doping (3.2×10¹⁷ against 8.7×10¹⁶ cm⁻³) and oxide thickness (67 against 45 nm); a face comparison is also a comparison of these.
• The (11-20) points on Figure 3 are from another paper (the authors' ref. 13) and are not reproduced here.

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>.

4H-SiC (0001) Si face, wet 1150 °C 120 min

# 4H-SiC (0001) Si face, wet 1150 °C 120 min
SAMPLE SiC_0001 {
    FAMILY: SiC_SiO2
    ORIENTATION: 4H_SiC_Si_face
    CLEAN: not_stated
    DOPING: n_type_8.7e16
}
CONTROL_TRAJECTORY History {
    EVENT Epitaxy KIND deposition TIMING assumed                 # n-type epilayer by CVD at 1520 °C
    EVENT Clean KIND clean TIMING assumed                        # RCA clean
    EVENT Load KIND load TIMING assumed                          # Loaded immediately into the furnace
    RUN WetOxidation DURATION 7200 TEMP 1150->1150 AMBIENT mix:H2O=0.842,O2=0.158 TIMING stated
    RUN Purge DURATION 1 TEMP 1150->1150 AMBIENT mix:H2O=0.842,O2=0.158 TIMING assumed VARY duration 1..600
    RUN ArgonAnneal DURATION 1800 TEMP 1150->1150 AMBIENT inert_Ar TIMING stated
    EVENT Unload KIND other TIMING assumed                       # Cooled and unloaded
    EVENT Metal KIND metallization TIMING assumed                # Al gate (300 µm) and Al back contact
    RUN PMA DURATION 1800 TEMP 400->400 AMBIENT forming_gas_H2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # C-V at 300 and 100 K; conductance at 300 K
}

4H-SiC (03-38) face, wet 1150 °C 25 min

# 4H-SiC (03-38) face, wet 1150 °C 25 min
SAMPLE SiC_0338 {
    FAMILY: SiC_SiO2
    ORIENTATION: 4H_SiC_03-38_face
    CLEAN: not_stated
    DOPING: n_type_3.2e17
}
CONTROL_TRAJECTORY History {
    EVENT Epitaxy KIND deposition TIMING assumed                 # n-type epilayer by CVD at 1520 °C
    EVENT Clean KIND clean TIMING assumed                        # RCA clean
    EVENT Load KIND load TIMING assumed                          # Loaded immediately into the furnace
    RUN WetOxidation DURATION 1500 TEMP 1150->1150 AMBIENT mix:H2O=0.842,O2=0.158 TIMING stated
    RUN Purge DURATION 1 TEMP 1150->1150 AMBIENT mix:H2O=0.842,O2=0.158 TIMING assumed VARY duration 1..600
    RUN ArgonAnneal DURATION 1800 TEMP 1150->1150 AMBIENT inert_Ar TIMING stated
    EVENT Unload KIND other TIMING assumed                       # Cooled and unloaded
    EVENT Metal KIND metallization TIMING assumed                # Al gate (300 µm) and Al back contact
    RUN PMA DURATION 1800 TEMP 400->400 AMBIENT forming_gas_H2 TIMING stated
    EVENT CV KIND measurement TIMING assumed                     # C-V at 300 and 100 K; conductance at 300 K
}

The programs the predictor ran on these histories: experiments/song_sic/oxide_growth_sic.isl.template.

The model itself, experiments/sic_interface_states/one_way_anneal.isl.template, as it is written. Every equation the simulation uses is in this text; the runtime holds no physics.

# ==============================================================================
# ISL MODEL: INTERFACE STATES OF SiC/SiO2 THROUGH ARGON ANNEALS
#
# Two parts. One is stable. The other is removable: a hold in argon takes it down to a level
# set by the anneal temperature, and it does not come back at a lower temperature. The density
# at each energy below the conduction band is the stable part plus the removable part, each
# with its own weight at that energy.
#
# The form was chosen among three (decay to nothing, a reversible equilibrium, a one-way level)
# by scripts/run_sic_interface_states.py, on the samples oxidized at 1150 C. How fast the level
# is reached is not resolved by any source we hold (the anneals are "1 to 10 min"), so the rate
# is a hypothesis: fast enough to finish within a minute.
# Fields in {{braces}} are filled by the runner.
# ==============================================================================
SAMPLE {sample_id} {{
    FAMILY: SiC_SiO2
    ORIENTATION: 4H_SiC_Si_face
    CLEAN: not_stated
}}
STATE removable {{ UNIT: 1; INITIAL: 1; MIN: 0; MAX: 1 }}
CONTROL T {{ UNIT: K }}
CONTROL p_Ar {{ UNIT: atm }}
PARAMETER log_level {{ VALUE: -0.3; UNIT: 1; STATUS: fitted }}
PARAMETER E_level {{ VALUE: 1.0; UNIT: eV; STATUS: fitted }}
PARAMETER log_S_0p3 {{ VALUE: 11.8; UNIT: 1; STATUS: fitted }}
PARAMETER log_S_0p4 {{ VALUE: 11.5; UNIT: 1; STATUS: fitted }}
PARAMETER log_S_0p5 {{ VALUE: 11.2; UNIT: 1; STATUS: fitted }}
PARAMETER log_R_0p3 {{ VALUE: 12.4; UNIT: 1; STATUS: fitted }}
PARAMETER log_R_0p4 {{ VALUE: 12.3; UNIT: 1; STATUS: fitted }}
PARAMETER log_R_0p5 {{ VALUE: 12.1; UNIT: 1; STATUS: fitted }}
PARAMETER settle_rate {{ VALUE: 0.1; UNIT: s^-1; STATUS: hypothesis }}
PARAMETER way {{ VALUE: {way}; UNIT: 1; STATUS: constant }}
PARAMETER soft {{ VALUE: 1.0e-3; UNIT: 1; STATUS: constant }}
PARAMETER T_ref {{ VALUE: 1573.15; UNIT: K; STATUS: constant }}
PARAMETER D_unit {{ VALUE: 1.0; UNIT: cm^-2 eV^-1; STATUS: constant }}
PARAMETER p_ref {{ VALUE: 1.0; UNIT: atm; STATUS: constant }}
PARAMETER ln10 {{ VALUE: 2.302585092994046; UNIT: 1; STATUS: constant }}
PARAMETER k_B {{ VALUE: 8.617333262e-5; UNIT: eV K^-1; STATUS: constant }}
# The level the anneal temperature allows, as a fraction of the as-oxidized removable part.
QUANTITY raw_level {{ UNIT: 1; EQUATION: raw_level = exp(ln10 * log_level) * exp((E_level / k_B) * (1 / T - 1 / T_ref)) }}
# Never more than the as-oxidized amount.
QUANTITY level {{ UNIT: 1; EQUATION: level = (raw_level + 1 - sqrt((raw_level - 1) * (raw_level - 1) + soft * soft)) / 2 }}
# way = 1: one-way (acts only while above the level). way = 0: reversible (moves to the level from either side).
QUANTITY above {{ UNIT: 1; EQUATION: above = (1 - way) + way * (1 + (removable - level) / sqrt((removable - level) * (removable - level) + soft * soft)) / 2 }}
CONTROL_TRAJECTORY {trajectory_id} {{
{runs}
}}
OPERATOR F_ArgonAnneal : Relaxation {{
    EQUATION: d(removable)/dt = -settle_rate * (p_Ar / p_ref) * above * (removable - {target})
}}
OBSERVATION_MODEL Obs_0p3 {{ TARGET: Dit_at_0p3eV_below_Ec; UNIT: cm^-2 eV^-1; EQUATION: Dit_at_0p3eV_below_Ec = D_unit * (exp(ln10 * log_S_0p3) + removable * exp(ln10 * log_R_0p3)) }}
OBSERVATION_MODEL Obs_0p4 {{ TARGET: Dit_at_0p4eV_below_Ec; UNIT: cm^-2 eV^-1; EQUATION: Dit_at_0p4eV_below_Ec = D_unit * (exp(ln10 * log_S_0p4) + removable * exp(ln10 * log_R_0p4)) }}
OBSERVATION_MODEL Obs_0p5 {{ TARGET: Dit_at_0p5eV_below_Ec; UNIT: cm^-2 eV^-1; EQUATION: Dit_at_0p5eV_below_Ec = D_unit * (exp(ln10 * log_S_0p5) + removable * exp(ln10 * log_R_0p5)) }}
EVALUATION_CONTRACT {contract_id} {{
    FROZEN: true
    DATASET: data/derived/kobayashi_2017_sic_dit.csv
    DATASET_DIGEST: sha256:{dataset_sha256}
    SPLIT: {split}
{targets}
}}

Our simulation against the paper

2 off, 4 not modelled of 6 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. There are no held-out samples here: the unknowns were chosen on the same numbers they are scored on, so the aligned score is an upper bound, not a test.

Together: Purge duration 600 s (was 1).

As reproduced: 0 of 6 within tolerance, median error 89.7%. Aligned: 0 of 6 within tolerance, median error 88.7%.

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

As reproduced, nothing is predicted that should be. With the oxidation written as the paper states it (wet; Deal and Grove's bubbler mixture as our assumption), the interface-state program returns nothing: it accepts only histories with a dry-oxygen step. The growth program grows from the oxygen fraction alone with dry constants and labels the result outside its tested scope: 7.6 nm on (0001) after 120 min (paper 45 nm) and 2.4 nm on (03-38) after 25 min (paper 67 nm; the program runs this face as the Si face). 0 of 6 within tolerance; 4 of the 6 numbers have no program.

What was searched. One unknown, steam still in the tube at the switch to argon (1 s to 10 min). It cannot reach the Dit rows, and on thickness it moves the numbers from 7.6 to 8.1 nm and from 2.4 to 3.1 nm. The search counts stayed at 0 of 6 everywhere; the combined search still moved it to 10 min on median error alone (89.7% to 88.7%). That move is not evidence.

The interface-state program's numbers, run on a counterfactual history (the oxidation written as dry oxygen, everything else as stated): 3.23×10¹² cm⁻² eV⁻¹ at 0.3 eV and 2.32×10¹² at 0.4 eV below the conduction band, the same on both faces, labelled outside the tested scope. Measured (Figure 3): 1.38×10¹² and 6.3×10¹¹ on (0001), 7.9×10¹¹ and 6.9×10¹¹ on (03-38). The program is 2.3 and 3.7 times high on (0001) and 4.1 and 3.4 times high on (03-38): 0 of 6, median error 185%. The reason is scope, not a number to fix: the program was fitted to Kobayashi 2017's dry-oxidized (0001) samples and argon anneals at 1300 to 1500 °C. Here the oxide is wet, the argon anneal is at 1150 °C (below the program's range, so it reduces nothing and the program returns its as-oxidized level), there is a 400 °C forming-gas anneal no SiC program reads, and one of the faces is one the program has never seen. The 2.3 to 4 times lower density after this wet process than after Kobayashi's dry oxidation is consistent with the known benefit of wet oxidation on SiC, but this page cannot separate the wet oxide, the forming gas and the laboratory.

Quantum ESPRESSO switched on. The computed record (evaluations/atomistic/si_dangling_bond_hydrogen.json) is for a silicon dangling bond with three silicon back-bonds, the Pb centre of Si/SiO2. Run through the silicon hydrogen-capping program with this paper's forming-gas step (400 °C, 30 min, 10% H2), its equilibrium bound is 2.7×10⁵ cm⁻² eV⁻¹ at midgap, six to seven orders of magnitude below the 6×10¹¹ to 2.6×10¹³ cm⁻² eV⁻¹ measured here. The comparison is not one of like with like, and the page does not show a computed section because no SiC program uses the record: the paper itself attributes the states near the SiC conduction band to “carbon clusters, near-interface oxide traps, dangling bonds, and so on”, and a forming-gas anneal capping silicon dangling bonds would not be expected to reach them. What remains after the hydrogen step here is not limited by the Si–H bond.

Heating and cooling transitions (above): no number moves by more than 2% in any scenario. The assumed heat-ups and cool-downs are in nitrogen; the growth program grows nothing in nitrogen and the interface-state program returns nothing for a wet history.

2 off, 4 not modelled of 6 numbers with the aligned settings.

Wet oxidation of SiC has no program. For thickness, Gupta and Akhtar's wet Si-face constants at 1150 °C (B = 1.2×10⁻³ µm²/h, B/A = 0.885 µm/h, 85 °C bubbler) give 48.3 nm after 2 h against the 45 nm measured here, a 7% difference between two laboratories; a wet SiC program built from them would be the first test of transfer for wet SiC. Nothing in our library gives constants for the (03-38) face.

For interface states, a SiC program would need: the oxidizing gas (wet against dry) as a factor, an argon anneal whose effect starts below 1300 °C or is known to be nil there, the 400 °C forming-gas step, the face (here (03-38) and (0001); Kobayashi's program knows only (0001)), and energies shallower than 0.3 eV, where this paper's face comparison lies (4 to 8 times lower on (03-38) at 0.1 to 0.2 eV). The program reports only 0.3, 0.4 and 0.5 eV.

No program reads the flat-band shift, hysteresis or effective charge on SiC, which are this paper's other printed results.

What our language and ontology cannot yet say

• A SiC face vocabulary beyond Si, C and a: (03-38) is written here as 4H_SiC_03-38_face, a new word no program or ontology entry knows. Faces should be Miller indices (with polytype and off-cut), so a program can say which it has constants for and the runtime can refuse a misspelling.
• The interface-state program's energies should be the sample's to choose (OBSERVE Dit AT Ec-0.15 eV), or the program should report the whole curve it can support; today only 0.3, 0.4 and 0.5 eV exist, and this paper's result lies at 0.1 to 0.2 eV.
• The sic_interface_states program returns nothing (not even a refusal with a reason) when a history has no dry-oxygen step. A wet history should be refused with a stated reason, so the page can say why, rather than appear as “no program”.
• In situ steps: a statement that two RUNs are in the same tube with no unload between them (IN_SITU), against Kobayashi's anneal in another furnace (a transfer through air). Here the argon anneal is in situ, and the gas switch in between is an unknown we had to write as an extra step.
• The measurement temperature and method on an observable (MEASURE Dit METHOD conductance AT 300 K; C-V at 100 K): the same sample gives different counts of shallow states by method and temperature, which is how this paper argues.

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. Kyoto's wet oxidation around 2002: pyrogenic or bubbler? It decides the water pressure we would need for a wet SiC program.
2. Is a 30 min argon anneal at 1150 °C, in situ after wet oxidation, expected to change the interface-state density, or is it there to remove water from the oxide?
3. Does a 400 °C forming-gas anneal reduce Dit near the conduction band of 4H-SiC at all, as it does for silicon dangling bonds?