Reproducing Thornton et al. 2022: germanium running down the oxidizing sidewall of SiGe fins

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/thornton_2022.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

C. S. Thornton, B. Tuttle, E. Turner, M. E. Law, S. Pantelides, G. T. Wang and K. S. Jones, “The Diffusion Mechanism of Ge During Oxidation of Si/SiGe Nanofins”, ACS Appl. Mater. Interfaces (2022); OSTI 1877137, accepted manuscript SAND2022-8627J (the copy read).

The challenge's SiGe system includes nanostructures, and this is the one paper we hold that measures how germanium moves on an oxidizing SiGe nanostructure as a function of time and temperature. It tests whether our SiGe programs can be pointed at a fin at all: the predictor runs every SiGe sample as a planar alloy, and the nanowire program's flat-sidewall handling is written for silicon in steam.

How well can this study be reproduced?

Low. The stack (four periods of 15 nm Si / 15 nm Si0.7Ge0.3, strained, on a 110 nm Si fin base), the gas and the four temperatures are stated. Which fin width was measured, the sidewall plane, the oxidation times (only 5, 10, 20 and 50 min at 900 °C are printed; the rest sit on a √t axis), the furnace push and pull, the oxide grown on each sample, and the conditions of the forming-gas control are not. The paper's quantity, a length along the sidewall to a 3% germanium contour, is measured on a two-dimensional cross-section that no program of ours represents.

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, 3 approximated, 6 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.

Si/Si0.7Ge0.3 fin, 900 °C, about 10 min

Simulated time in this history: 20 min.

Across the samples

Timing the paper does not give

• Oxidation times other than 5, 10, 20 (Figure 4) and 50 min (Figure 2) at 900 °C: read from the √t axis of Figure 5.
• Push and pull of the tube furnace: load temperature, rate, gas.
• Time between the Bosch etch and oxidation; any clean or polymer removal.
• The forming-gas control: temperature and times are in the supplement (Figure S5), not in this PDF.
• Oxide thickness of each sample: only “approximately 16 to 34 nm” for the sets and two sentences at 900 °C, 10 min.

What the second reading changed

• SOURCE.md and ontology/library.json say “at 900 C”. The paper oxidizes at 750, 800, 850 and 900 °C and its result is an Arrhenius plot over the four.
• The challenge brief and library.json call these SiGe fins; the germanium the paper measures moves down the silicon base of a Si/SiGe superlattice fin. The oxidizing interface where the length is measured is Si/SiO2, fed from SiGe layers above.
• Figure 4 (5, 10, 20 min at 900 °C) does not match Figure 5's 900 °C abscissae (about 10, 15, 20, 25 min).
• The low-oxygen control is a vacuum-sealed ampule in the text (PDF p. 9) and “an anneal under forming gas” in the Figure 7 caption.
• No dataset holds this paper; it is listed as skimmed, unused.

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>.

Si/Si0.7Ge0.3 fin, 900 °C, about 10 min

# Si/Si0.7Ge0.3 fin, 900 °C, about 10 min
SAMPLE Fin_900C_10min {
    FAMILY: SiGe_oxide
    COMPOSITION: Si0.7Ge0.3
    ORIENTATION: Si100
    CLEAN: not_stated
    SHAPE: fin
    FILM: Si_Si0.7Ge0.3_superlattice_4x(15nm+15nm)_on_Si_fin_base_110nm
    DOPING: undoped
}
CONTROL_TRAJECTORY History {
    EVENT Growth KIND deposition TIMING assumed                  # Four periods of 15 nm Si / 15 nm Si0.7Ge0.3 by CVD on 300 mm (100) Si
    EVENT Pattern KIND other TIMING assumed                      # Electron-beam lithography: fins 70-280 nm wide, about 5 µm long
    EVENT Etch KIND etch TIMING stated                           # Bosch deep reactive ion etch, 60 s: fins about 230 nm tall
    EVENT Storage KIND storage TIMING assumed                    # Native oxide on the fin
    EVENT Load KIND load TIMING assumed                          # Into the tube furnace
    RUN RampUp DURATION 300 TEMP 600->900 AMBIENT dry_O2 TIMING assumed VARY duration 60..1200
    RUN Oxidation DURATION 600 TEMP 900->900 AMBIENT dry_O2 TIMING bound
    RUN RampDown DURATION 300 TEMP 900->600 AMBIENT dry_O2 TIMING assumed VARY duration 60..1200
    EVENT Section KIND other TIMING stated                       # FIB lamella, 5 min plasma clean
    EVENT Measure KIND measurement TIMING assumed                # HAADF-STEM length and width of the Ge contrast; EDS end point at about 3% Ge
}

Si/Si0.7Ge0.3 fin, 900 °C, about 15 min

# Si/Si0.7Ge0.3 fin, 900 °C, about 15 min
SAMPLE Fin_900C_15min {
    FAMILY: SiGe_oxide
    COMPOSITION: Si0.7Ge0.3
    ORIENTATION: Si100
    CLEAN: not_stated
    SHAPE: fin
    FILM: Si_Si0.7Ge0.3_superlattice_4x(15nm+15nm)_on_Si_fin_base_110nm
    DOPING: undoped
}
CONTROL_TRAJECTORY History {
    EVENT Growth KIND deposition TIMING assumed                  # Four periods of 15 nm Si / 15 nm Si0.7Ge0.3 by CVD on 300 mm (100) Si
    EVENT Pattern KIND other TIMING assumed                      # Electron-beam lithography: fins 70-280 nm wide, about 5 µm long
    EVENT Etch KIND etch TIMING stated                           # Bosch deep reactive ion etch, 60 s: fins about 230 nm tall
    EVENT Storage KIND storage TIMING assumed                    # Native oxide on the fin
    EVENT Load KIND load TIMING assumed                          # Into the tube furnace
    RUN RampUp DURATION 300 TEMP 600->900 AMBIENT dry_O2 TIMING assumed VARY duration 60..1200
    RUN Oxidation DURATION 900 TEMP 900->900 AMBIENT dry_O2 TIMING bound
    RUN RampDown DURATION 300 TEMP 900->600 AMBIENT dry_O2 TIMING assumed VARY duration 60..1200
    EVENT Section KIND other TIMING stated                       # FIB lamella, 5 min plasma clean
    EVENT Measure KIND measurement TIMING assumed                # HAADF-STEM length and width of the Ge contrast; EDS end point at about 3% Ge
}

Si/Si0.7Ge0.3 fin, 900 °C, about 20 min

# Si/Si0.7Ge0.3 fin, 900 °C, about 20 min
SAMPLE Fin_900C_20min {
    FAMILY: SiGe_oxide
    COMPOSITION: Si0.7Ge0.3
    ORIENTATION: Si100
    CLEAN: not_stated
    SHAPE: fin
    FILM: Si_Si0.7Ge0.3_superlattice_4x(15nm+15nm)_on_Si_fin_base_110nm
    DOPING: undoped
}
CONTROL_TRAJECTORY History {
    EVENT Growth KIND deposition TIMING assumed                  # Four periods of 15 nm Si / 15 nm Si0.7Ge0.3 by CVD on 300 mm (100) Si
    EVENT Pattern KIND other TIMING assumed                      # Electron-beam lithography: fins 70-280 nm wide, about 5 µm long
    EVENT Etch KIND etch TIMING stated                           # Bosch deep reactive ion etch, 60 s: fins about 230 nm tall
    EVENT Storage KIND storage TIMING assumed                    # Native oxide on the fin
    EVENT Load KIND load TIMING assumed                          # Into the tube furnace
    RUN RampUp DURATION 300 TEMP 600->900 AMBIENT dry_O2 TIMING assumed VARY duration 60..1200
    RUN Oxidation DURATION 1200 TEMP 900->900 AMBIENT dry_O2 TIMING bound
    RUN RampDown DURATION 300 TEMP 900->600 AMBIENT dry_O2 TIMING assumed VARY duration 60..1200
    EVENT Section KIND other TIMING stated                       # FIB lamella, 5 min plasma clean
    EVENT Measure KIND measurement TIMING assumed                # HAADF-STEM length and width of the Ge contrast; EDS end point at about 3% Ge
}

Si/Si0.7Ge0.3 fin, 900 °C, about 25 min

# Si/Si0.7Ge0.3 fin, 900 °C, about 25 min
SAMPLE Fin_900C_25min {
    FAMILY: SiGe_oxide
    COMPOSITION: Si0.7Ge0.3
    ORIENTATION: Si100
    CLEAN: not_stated
    SHAPE: fin
    FILM: Si_Si0.7Ge0.3_superlattice_4x(15nm+15nm)_on_Si_fin_base_110nm
    DOPING: undoped
}
CONTROL_TRAJECTORY History {
    EVENT Growth KIND deposition TIMING assumed                  # Four periods of 15 nm Si / 15 nm Si0.7Ge0.3 by CVD on 300 mm (100) Si
    EVENT Pattern KIND other TIMING assumed                      # Electron-beam lithography: fins 70-280 nm wide, about 5 µm long
    EVENT Etch KIND etch TIMING stated                           # Bosch deep reactive ion etch, 60 s: fins about 230 nm tall
    EVENT Storage KIND storage TIMING assumed                    # Native oxide on the fin
    EVENT Load KIND load TIMING assumed                          # Into the tube furnace
    RUN RampUp DURATION 300 TEMP 600->900 AMBIENT dry_O2 TIMING assumed VARY duration 60..1200
    RUN Oxidation DURATION 1500 TEMP 900->900 AMBIENT dry_O2 TIMING bound
    RUN RampDown DURATION 300 TEMP 900->600 AMBIENT dry_O2 TIMING assumed VARY duration 60..1200
    EVENT Section KIND other TIMING stated                       # FIB lamella, 5 min plasma clean
    EVENT Measure KIND measurement TIMING assumed                # HAADF-STEM length and width of the Ge contrast; EDS end point at about 3% Ge
}

Si/Si0.7Ge0.3 fin, 850 °C, about 24 min

# Si/Si0.7Ge0.3 fin, 850 °C, about 24 min
SAMPLE Fin_850C_24min {
    FAMILY: SiGe_oxide
    COMPOSITION: Si0.7Ge0.3
    ORIENTATION: Si100
    CLEAN: not_stated
    SHAPE: fin
    FILM: Si_Si0.7Ge0.3_superlattice_4x(15nm+15nm)_on_Si_fin_base_110nm
    DOPING: undoped
}
CONTROL_TRAJECTORY History {
    EVENT Growth KIND deposition TIMING assumed                  # Four periods of 15 nm Si / 15 nm Si0.7Ge0.3 by CVD on 300 mm (100) Si
    EVENT Pattern KIND other TIMING assumed                      # Electron-beam lithography: fins 70-280 nm wide, about 5 µm long
    EVENT Etch KIND etch TIMING stated                           # Bosch deep reactive ion etch, 60 s: fins about 230 nm tall
    EVENT Storage KIND storage TIMING assumed                    # Native oxide on the fin
    EVENT Load KIND load TIMING assumed                          # Into the tube furnace
    RUN RampUp DURATION 300 TEMP 600->850 AMBIENT dry_O2 TIMING assumed VARY duration 60..1200
    RUN Oxidation DURATION 1440 TEMP 850->850 AMBIENT dry_O2 TIMING bound
    RUN RampDown DURATION 300 TEMP 850->600 AMBIENT dry_O2 TIMING assumed VARY duration 60..1200
    EVENT Section KIND other TIMING stated                       # FIB lamella, 5 min plasma clean
    EVENT Measure KIND measurement TIMING assumed                # HAADF-STEM length and width of the Ge contrast; EDS end point at about 3% Ge
}

Si/Si0.7Ge0.3 fin, 800 °C, about 38 min

# Si/Si0.7Ge0.3 fin, 800 °C, about 38 min
SAMPLE Fin_800C_38min {
    FAMILY: SiGe_oxide
    COMPOSITION: Si0.7Ge0.3
    ORIENTATION: Si100
    CLEAN: not_stated
    SHAPE: fin
    FILM: Si_Si0.7Ge0.3_superlattice_4x(15nm+15nm)_on_Si_fin_base_110nm
    DOPING: undoped
}
CONTROL_TRAJECTORY History {
    EVENT Growth KIND deposition TIMING assumed                  # Four periods of 15 nm Si / 15 nm Si0.7Ge0.3 by CVD on 300 mm (100) Si
    EVENT Pattern KIND other TIMING assumed                      # Electron-beam lithography: fins 70-280 nm wide, about 5 µm long
    EVENT Etch KIND etch TIMING stated                           # Bosch deep reactive ion etch, 60 s: fins about 230 nm tall
    EVENT Storage KIND storage TIMING assumed                    # Native oxide on the fin
    EVENT Load KIND load TIMING assumed                          # Into the tube furnace
    RUN RampUp DURATION 300 TEMP 600->800 AMBIENT dry_O2 TIMING assumed VARY duration 60..1200
    RUN Oxidation DURATION 2280 TEMP 800->800 AMBIENT dry_O2 TIMING bound
    RUN RampDown DURATION 300 TEMP 800->600 AMBIENT dry_O2 TIMING assumed VARY duration 60..1200
    EVENT Section KIND other TIMING stated                       # FIB lamella, 5 min plasma clean
    EVENT Measure KIND measurement TIMING assumed                # HAADF-STEM length and width of the Ge contrast; EDS end point at about 3% Ge
}

Si/Si0.7Ge0.3 fin, 750 °C, about 105 min

# Si/Si0.7Ge0.3 fin, 750 °C, about 105 min
SAMPLE Fin_750C_105min {
    FAMILY: SiGe_oxide
    COMPOSITION: Si0.7Ge0.3
    ORIENTATION: Si100
    CLEAN: not_stated
    SHAPE: fin
    FILM: Si_Si0.7Ge0.3_superlattice_4x(15nm+15nm)_on_Si_fin_base_110nm
    DOPING: undoped
}
CONTROL_TRAJECTORY History {
    EVENT Growth KIND deposition TIMING assumed                  # Four periods of 15 nm Si / 15 nm Si0.7Ge0.3 by CVD on 300 mm (100) Si
    EVENT Pattern KIND other TIMING assumed                      # Electron-beam lithography: fins 70-280 nm wide, about 5 µm long
    EVENT Etch KIND etch TIMING stated                           # Bosch deep reactive ion etch, 60 s: fins about 230 nm tall
    EVENT Storage KIND storage TIMING assumed                    # Native oxide on the fin
    EVENT Load KIND load TIMING assumed                          # Into the tube furnace
    RUN RampUp DURATION 300 TEMP 600->750 AMBIENT dry_O2 TIMING assumed VARY duration 60..1200
    RUN Oxidation DURATION 6300 TEMP 750->750 AMBIENT dry_O2 TIMING bound
    RUN RampDown DURATION 300 TEMP 750->600 AMBIENT dry_O2 TIMING assumed VARY duration 60..1200
    EVENT Section KIND other TIMING stated                       # FIB lamella, 5 min plasma clean
    EVENT Measure KIND measurement TIMING assumed                # HAADF-STEM length and width of the Ge contrast; EDS end point at about 3% Ge
}

Si fin base sidewall, 900 °C, 10 min, dry O2

# Si fin base sidewall, 900 °C, 10 min, dry O2
SAMPLE si_base_900C_10min {
    FAMILY: Si_Planar
    ORIENTATION: Si110
    CLEAN: not_stated
    DOPING: undoped
    FILM: sidewall_of_Si_fin_base_under_Si_Si0.7Ge0.3_superlattice_4x(15nm+15nm)_on_Si_fin_base_110nm
}
CONTROL_TRAJECTORY History {
    EVENT Growth KIND deposition TIMING assumed                  # Four periods of 15 nm Si / 15 nm Si0.7Ge0.3 by CVD on 300 mm (100) Si
    EVENT Pattern KIND other TIMING assumed                      # Electron-beam lithography: fins 70-280 nm wide, about 5 µm long
    EVENT Etch KIND etch TIMING stated                           # Bosch deep reactive ion etch, 60 s: fins about 230 nm tall
    EVENT Storage KIND storage TIMING assumed                    # Native oxide on the fin
    EVENT Load KIND load TIMING assumed                          # Into the tube furnace
    RUN RampUp DURATION 300 TEMP 600->900 AMBIENT dry_O2 TIMING assumed VARY duration 60..1200
    RUN Oxidation DURATION 600 TEMP 900->900 AMBIENT dry_O2 TIMING bound
    RUN RampDown DURATION 300 TEMP 900->600 AMBIENT dry_O2 TIMING assumed VARY duration 60..1200
    EVENT Section KIND other TIMING stated                       # FIB lamella, 5 min plasma clean
    EVENT Measure KIND measurement TIMING assumed                # HAADF-STEM length and width of the Ge contrast; EDS end point at about 3% Ge
}

The oxide the paper reports is measured on the silicon below the superlattice (the dashed line in Figures 4 and 7). The programs for planar silicon are the only ones in the predictor that grow oxide in dry oxygen on silicon; the nanowire program grows nothing in dry oxygen.

Si fin base sidewall, 900 °C, 10 min, sealed ampule (~35 mtorr)

# Si fin base sidewall, 900 °C, 10 min, sealed ampule (~35 mtorr)
SAMPLE si_base_ampule_900C_10min {
    FAMILY: Si_Planar
    ORIENTATION: Si110
    CLEAN: not_stated
    DOPING: undoped
    FILM: sidewall_of_Si_fin_base_under_Si_Si0.7Ge0.3_superlattice_4x(15nm+15nm)_on_Si_fin_base_110nm
}
CONTROL_TRAJECTORY History {
    EVENT Growth KIND deposition TIMING assumed                  # Four periods of 15 nm Si / 15 nm Si0.7Ge0.3 by CVD on 300 mm (100) Si
    EVENT Pattern KIND other TIMING assumed                      # Electron-beam lithography: fins 70-280 nm wide, about 5 µm long
    EVENT Etch KIND etch TIMING stated                           # Bosch deep reactive ion etch, 60 s: fins about 230 nm tall
    EVENT Storage KIND storage TIMING assumed                    # Native oxide on the fin
    EVENT Load KIND load TIMING assumed                          # Sealed in a quartz ampule pumped to about 35 mtorr
    RUN RampUp DURATION 300 TEMP 600->900 AMBIENT mix:O2=9.6e-06,N2=3.6e-05 TIMING assumed VARY duration 60..1200
    RUN Oxidation DURATION 600 TEMP 900->900 AMBIENT mix:O2=9.6e-06,N2=3.6e-05 TIMING stated
    RUN RampDown DURATION 300 TEMP 900->600 AMBIENT mix:O2=9.6e-06,N2=3.6e-05 TIMING assumed VARY duration 60..1200
    EVENT Section KIND other TIMING stated                       # FIB lamella, 5 min plasma clean
    EVENT Measure KIND measurement TIMING assumed                # HAADF-STEM length and width of the Ge contrast; EDS end point at about 3% Ge
}

The control without flowing oxygen. The residual gas is written as air at 35 mtorr; the paper does not say what it was.

The programs the predictor ran on these histories: experiments/deal_qss/two_equilibria.isl.template, experiments/rabie_sige/legoues_800C_14Ge.isl, experiments/sige_interface/interface_enrichment.isl.template, experiments/sige_inventory/conserved_germanium.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/sige_interface/interface_enrichment.isl.template, as it is written. Every equation the simulation uses is in this text; the runtime holds no physics.

# ==============================================================================
# ISL MODEL: GERMANIUM AT THE OXIDE INTERFACE OF A SiGe ALLOY
#
# While the alloy is being oxidized, the germanium fraction just under the oxide moves to a
# value set by the starting alloy: a floor plus a share of the starting fraction. The two
# numbers are fitted to one laboratory's two planar measurements (Mueller et al. 2023, 20% and
# 50% alloys) and the program is then scored on other laboratories.
#
# This is a relation written as a relaxation, not a transport model: it says where the
# interface composition settles, not why. How fast it settles is not measured by any source we
# hold (the shortest oxidation is two minutes), so the settling time is a hypothesis.
# Fields in {{braces}} are filled by scripts/run_sige_interface.py.
# ==============================================================================
SAMPLE {sample_id} {{
    FAMILY: SiGe_oxide
    COMPOSITION: {composition}
}}
STATE ge_i {{ UNIT: 1; INITIAL: ge_start; MIN: 0; MAX: 1 }}
CONTROL T {{ UNIT: K }}
CONTROL p_N2 {{ UNIT: atm }}
CONTROL p_Ar {{ UNIT: atm }}
PARAMETER ge_start {{ VALUE: {ge_start}; UNIT: 1; STATUS: sourced; SOURCE: the sample's stated composition }}
PARAMETER floor_ge {{ VALUE: 0.3; UNIT: 1; STATUS: fitted }}
PARAMETER share_ge {{ VALUE: 0.8; UNIT: 1; STATUS: fitted }}
# No source measures the interface earlier than two minutes into an oxidation.
PARAMETER settle_time {{ VALUE: 30.0; UNIT: s; STATUS: hypothesis }}
PARAMETER p_ref {{ VALUE: 1.0; UNIT: atm; STATUS: constant }}
# The interface moves only while the alloy is being oxidized: not during a hold in nitrogen or argon.
QUANTITY oxidizing {{ UNIT: 1; EQUATION: oxidizing = 1 - (p_N2 + p_Ar) / p_ref }}
CONTROL_TRAJECTORY {trajectory_id} {{
{runs}
}}
OPERATOR F_InterfaceEnrichment : Relaxation {{
    EQUATION: d(ge_i)/dt = -oxidizing * (ge_i - (floor_ge + share_ge * ge_start)) / settle_time
}}
OBSERVATION_MODEL Obs_Ge_At_Interface {{ TARGET: Ge_at_interface; UNIT: 1; EQUATION: Ge_at_interface = ge_i }}
EVALUATION_CONTRACT {contract_id} {{
    FROZEN: true
    DATASET: data/derived/sige_interface_germanium.csv
    DATASET_DIGEST: sha256:{dataset_sha256}
    SPLIT: {split}
    TARGET: Ge_at_interface = {target} +/- {tolerance} abs
}}

Our simulation against the paper

1 near, 4 off, 14 not modelled of 19 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 si_base_900C_10min only; every other number is a test they played no part in.

Together: RampUp duration 1200 s (was 300); RampDown duration 1200 s (was 300).

As reproduced: 0 of 19 within tolerance, median error 65.7%. Aligned: 0 of 19 within tolerance, median error 57.5%. On the held-out samples only: 0 of 17 within tolerance, median error 65.7% as reproduced, 0 of 17 within tolerance, median error 65.7% aligned.

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

Two timing unknowns were searched, the furnace push (1 to 20 min) and pull (1 to 20 min), chosen on the one silicon-base oxidation whose oxide the paper states (about 20 nm after 10 min at 900 °C); the sealed-ampule control and the 50% germanium of the condensed layer are the test. Three variants were tried: push and pull in nitrogen, no push or pull, and a (100) instead of (110) sidewall for the silicon base. Of 19 numbers, 14 have no program (the lengths and widths), so the search works on five.

Nothing moves into tolerance. As reproduced 0 of 19 within tolerance, median error 65.7%; aligned 0 of 19, median 57.5%; on the test cases 0 of 17 before and after. The search takes both ramps to their 20 min limit, because only the thin-oxide program responds: it grows 6.9 nm in the stated 10 min plus the assumed ramps, and 8.5 nm with 20 min ramps, against about 20 nm. The planar silicon program gives 25.4 nm (26.5 nm aligned), but almost all of it is the 23 nm initial offset of Deal and Grove's dry law: it consumes 1.05 nm of silicon. The same offset gives 23.0 nm in the sealed ampule, where about 5 nm grew; the thin-oxide program gives 1.7 nm there. Nitrogen ramps, no ramps and a (100) sidewall each leave all five numbers where they were (median 65.7% alone, 57.5% on the aligned history).

The germanium at the condensed interface is 56.6% for every history (planar relation, 0.331 + 0.783 × 0.30), against the paper's “enhanced (50%)”: 13% high, near tolerance. It has no time, no temperature and no geometry, so no unknown here can move it.

With heating and cooling transitions (the section above): 0 of 19 within tolerance in every scenario, median 65.7%, and no number moves by more than 2% (the heat-up is in nitrogen, in which neither silicon program grows oxide): the planar silicon program's oxide is set by its offset, the interface relation has no time, and the lengths have no program.

The SiGe programs run on the fins as planar alloys and label nothing outside their scope, because they flag only SHAPE nanosheet and nanowire, not fin. The Rabie program grows 18 to 31 nm on the fins at 900 °C (10 to 25 min), 30 nm at 850 °C, 42 nm at 800 °C and 97 nm at 750 °C (105 min), where the paper keeps every set within about 16 to 34 nm: its wet constants and 0.71 eV oxidant diffusion give the thickest oxide at the lowest temperature.

1 near, 2 off, 14 not modelled of 17 numbers with the aligned settings (the samples used to choose the unknowns are left out).

What alignment cannot fix: the paper's quantity has no program. The length down the sidewall (27 to 38 nm at 900 °C, √t, 1.1 eV) and the lateral width (1.5 to 2.5 nm, 1.6 eV) are 14 of the 19 numbers, and the predictor reports neither. This is case (c): no program in the predictor models the quantity. A fin program would need, in order of importance:

(1) Germanium as an interfacial species. A surface concentration of germanium living on the Si/SiO2 interface, with a diffusivity along it (Thornton's effective D, about 5e-15 cm²/s at 900 °C, 1.1 eV) and a source that exists only while SiGe is being oxidized: the germanium the inventory program releases (x N_ox X per unit area of oxidized alloy) feeds it instead of all going straight down into the alloy. The sealed-ampule control (little motion with 5 nm of oxide) is then a test of the source term, not a separate assumption.

(2) A reinsertion sink. Exchange of interfacial germanium into substitutional sites of the silicon below the interface, with its own activation energy (1.6 eV measured, 1.3 to 1.8 eV by DFT), giving the lateral width.

(3) A coordinate along the sidewall. The present runtime has one depth grid that travels with a planar front. A fin needs at least a second coordinate (height along the sidewall) for the interfacial species, and the boundary where the SiGe layers meet the sidewall; the full problem is a 2D cross-section with the oxide front moving on two faces and the top.

(4) Dry oxidation on a silicon sidewall. The nanowire program's flat-sidewall handling grows oxide only in steam (Mueller's 850 °C rate); in dry oxygen it grows nothing. The planar programs grow either 25 nm (from Deal and Grove's 23 nm offset) or 7 to 8.5 nm (thin-oxide program) where about 20 nm is reported. The sidewall plane is not stated.

(5) A layered sample and strain. Four 15 nm Si0.7Ge0.3 layers between silicon, pseudomorphic, are a FILM string; the programs see an infinite alloy.

(6) An observation model for a contour. The paper measures where the germanium falls to about 3% (EDS) along the sidewall. That is a level-set length, not a value at a depth.

What our language and ontology cannot yet say

• Interface-resident species and operators that act along an interface. A FIELD on an interface (surface concentration of mobile germanium) with Transport along it, a source tied to the oxidation flux, and an exchange into the crystal below. Without it, the paper's mechanism and every one of its 14 measured lengths and widths cannot be written.
• A second spatial coordinate, or a sidewall coordinate. GRID is one-dimensional and travels with a planar front; a fin needs height along the sidewall and lateral depth.
• SHAPE read by every program, with a refusal. The SiGe programs check only nanosheet and nanowire; a SHAPE: fin sample is run as a planar alloy without a label. Every program should state which shapes it accepts and label the rest outside its scope.
• Layered samples. LAYER blocks (composition, thickness, strain) for a superlattice on a silicon base, so that a program knows each SiGe layer holds 15 nm of alloy.
• A contour observable. OBSERVATION_MODEL ... EQUATION: L = extent(x_Ge > 0.03 along sidewall): an observable defined by a level of a field.
• Residual gas of a sealed ampule. The ambient was written as air at 35 mtorr; a statement for “sealed, pumped to P, gas unknown” with the oxygen partial pressure as an unknown (VARY p_O2) would let alignment search it.
• Sidewall orientation. ORIENTATION is a wafer property; a fin's sidewall plane is a separate property that the growth programs should read.

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. Which fin width (70 to 280 nm) do Figures 4-6 come from, and does the length depend on it?
2. What is the sidewall plane, {110} for a fin along <110>, and does the 20 nm in 10 min at 900 °C refer to the silicon base sidewall?
3. Is a Si sidewall growing 20 nm in 10 min of dry oxygen at 900 °C plausible without germanium's help? Planar Si(100) grows about 6 nm in our thin-oxide program.
4. Should the conserved inventory get a sink: germanium leaving the condensed layer along the interface, at a rate set by the oxidation, so that the planar layer and the fin's sidewall triangle share one dose?