Emily's pages: Questions · Vocabulary · Language · Studies reproduced · Experiment proposal · The essay

The language: how a process history and a model are written

Written 10 November 2026 for Emily. Generated from the language's own files and a live run of the predictor; not edited by hand.

ISL, the Interface Science Language, is how this project writes down two things: what was done to a sample (the recipe) and what we think happens because of it (a model). Both are plain text. A model is a short program; it contains no built-in physics, so every rate law and every constant a prediction uses is on the page where a person can read, question and change it.

It exists so that two kinds of claim can be told apart: a model that was fitted to data and a model that was checked against data it never saw. The language labels every number with which of those it is, and refuses to run a program whose units, conservation claims or bounds do not hold.

What we would like Emily to check

1. Can you write the recipes you care about? Section 2 lists what a recipe can say today. Anything a process engineer would record and we cannot (cooling ambient, furnace and tube, moisture in the gas, pull rate, loading step, boat position) is a gap, and the answer to Question 4 on the questions page says which gaps matter most.
2. Do the six kinds of process, and the five labels on a number, cover how you would describe an interface model? Section 4 and 5.
3. Are the observables the right ones? Section 8 lists every quantity the language can predict. Say what is missing.
4. Would you trust a prediction that came with the support statement shown in Section 1?

1. From a recipe to a prediction

A recipe is a sample and a list of steps. This is the whole file for one:

# (100) silicon, dry oxidation for one hour at 1000 C, then a forming-gas anneal after metallization.
SAMPLE Wafer_A {
    FAMILY: Si_Planar
    ORIENTATION: Si100
    CLEAN: RCA
}
CONTROL_TRAJECTORY History {
    RUN Oxidation DURATION 3600 TEMP 1000->1000 AMBIENT dry_O2
    RUN PostMetalAnneal DURATION 1800 TEMP 400->400 AMBIENT forming_gas_H2
}

One command turns it into everything the project can say about the resulting interface:

python -m isl_harness.predict examples/histories/planar_si_dry_then_forming_gas.isl

which prints (shortened):

Interface: Si_Planar (challenge system 1)
Sample: FAMILY: Si_Planar; ORIENTATION: Si100; CLEAN: RCA
Recipe:
  RUN Oxidation DURATION 3600 TEMP 1000->1000 AMBIENT dry_O2
  RUN PostMetalAnneal DURATION 1800 TEMP 400->400 AMBIENT forming_gas_H2

Predictions: oxide thickness 57.94 nm [supported within scope] consumed substrate 15.37 nm [supported within scope] oxide thickness (thin-oxide program) 51.59 nm [outside the tested scope] fixed charge 1.462e+11 cm^-2 [supported within scope] interface state density at midgap 7.508e+10 cm^-2 eV^-1 [direction only] interface state density at 0.20 eV above the valence band 1.397e+11 cm^-2 eV^-1 [direction only] interface state density at 0.30 eV above the valence band 1.148e+11 cm^-2 eV^-1 [direction only] interface state density at 0.40 eV above the valence band 1.079e+11 cm^-2 eV^-1 [direction only] interface state density at 0.55 eV above the valence band 7.508e+10 cm^-2 eV^-1 [direction only] interface state density at 0.70 eV above the valence band 5.418e+10 cm^-2 eV^-1 [direction only] interface state density at 0.80 eV above the valence band 6.941e+10 cm^-2 eV^-1 [direction only] ```

Every line carries a label saying how far to trust it. Supported within scope means the program was tested on data it was not fitted to and this recipe lies inside what it was tested on. Direction only means it gets the direction of change right and the amount is not reliable. Outside the tested scope means the recipe is beyond what that program was tested on. The full output also lists, for each program, its parameters with their labels and a sentence on how it was tested.

2. What a recipe can say

A sample has a family (which of the challenge's five interfaces; SiGe and germanium are separate families) and, where they matter, an orientation, a pre-oxidation clean (one of RCA, sulfuric_aqua_regia_HF, peroxide_HF, HCl_in_situ, sulfuric_peroxide_HF, not_stated), a shape, a composition and a diameter.

A recipe is a list of steps, each RUN <name> DURATION <seconds> TEMP <start °C>-><end °C> AMBIENT <gas>. A ramp is a step whose two temperatures differ. The gases it knows by name are dry_O2, inert_N2, inert_Ar, forming_gas_H2 (10% hydrogen), pure_H2, steam, wet_O2 and vacuum. A mixture is written with its partial pressures: mix:N2=0.999998,H2O=2.0e-6 is nitrogen with 2 ppm of water, and a model may read the water pressure.

What a recipe cannot say yet: the bubbler temperature that sets the moisture of wet_O2 (so wet oxygen supplies no partial pressures), the cooling ambient as a separate field, furnace or tube, wafer loading and pull rates other than as a short step, and the state of the gate metal. Whether those matter is a question for you.

3. What a model looks like

A model is a set of named blocks. This is a real one and a short one: it says where the germanium fraction under the oxide settles while a SiGe alloy is oxidized. Read it as a sentence: there is a quantity `ge_i`, the germanium fraction just under the oxide; it starts at the alloy's composition; while the alloy is being oxidized it moves toward a value set by the starting composition; and the model is scored against these measurements.

# 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.

SAMPLE Alloy_A { FAMILY: SiGe_oxide COMPOSITION: Si0.80Ge0.20 }

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: 0.2; 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 History { RUN Oxidation DURATION 120 TEMP 850->850 AMBIENT steam }

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_A { FROZEN: true DATASET: data/derived/sige_interface_germanium.csv DATASET_DIGEST: sha256:<hash of the dataset file> SPLIT: train TARGET: Ge_at_interface = 0.482 +/- 0.05 abs } ```

An observation may read states and constants but never a control. This keeps a measurement from being a restatement of the recipe.

4. The six kinds of process

Every operator states one kind. The kinds name a form of change, not a mechanism: what relaxes, grows or is passivated is said by the quantity the operator acts on. Each word is one the sources themselves use (checked by a text search of the papers; see the vocabulary page).

A Transport operator must be written as a flux, so the amount is conserved. Exchange and Passivation must declare a conservation law: what leaves one place must arrive in another, and sites are neither made nor destroyed.

5. Every number carries a label

The 29 model files in this repository hold 311 labelled numbers:

A fit may change only fitted numbers. The runtime refuses to override a sourced one. This is how the project keeps a published constant from being quietly adjusted to match a result.

6. What is checked before a program runs

• Units. Every term of every equation must have consistent dimensions. The language has one unit per dimension (1 (a pure number), cm (length), s (time), K (temperature), eV (energy), atm (pressure)), so a scale error such as nm beside cm cannot be written; values are converted before they are put in.
• Conservation. Each declared conservation claim is checked symbolically against the operator's own terms, including boundary fluxes and sources.
• Isolation of the measurement. An observation reads states and constants only, never a control.
• Bounds. Minimum, maximum and capacity limits are enforced on every accepted solver step.
• The contract. Every target has an observation model, and a frozen contract matches its dataset's hash.

7. What the language cannot yet say

• One spatial dimension only.
• A layer whose own thickness changes, such as the growing oxide, has no grid of varying length; the oxide is a state, not a field. A front moving into a material is followed on a grid that travels with it.
• A drift velocity that varies with position.
• The pre-oxidation clean is recorded with a program but no process can read it yet.
• Nothing in the language says why a number is what it is. It says what a number is labelled, and where it came from.

8. What the language can predict

The language names 34 observables. Each serves one of the challenge's four targets:

• layer thickness (Oxide, interlayer and consumed-substrate thicknesses.): Consumed_alloy, Consumed_substrate, Core_diameter, Si_oxidized, Thickness
• composition profile (Composition against depth across the interface.): Enriched_layer_efold_width, Enriched_layer_extent, GeO2_fraction, Ge_at_10nm, Ge_at_30nm, Ge_at_interface, O16_interface, O18_film, O18_fraction_at_13A, O18_fraction_at_22A, O18_fraction_at_5A, O18_interface, O_film_total, Si_at_front, Si_in_grid
• trap density (Interface trap density, at midgap or against energy.): Dit, Dit_at_0p20eV_above_Ev, Dit_at_0p30eV_above_Ev, Dit_at_0p3eV_below_Ec, Dit_at_0p40eV_above_Ev, Dit_at_0p4eV_below_Ec, Dit_at_0p55eV_above_Ev, Dit_at_0p5eV_below_Ec, Dit_at_0p70eV_above_Ev, Dit_at_0p80eV_above_Ev, Normalized_Pb
• fixed charge (Fixed oxide charge.): Nf, Qf, Qss

Which interface each program covers, how well it did on held-out data, and which cells of the challenge have no program at all, is in the essay's scorecard.