AlScN point-defect thermodynamic model notebook [SOF-8054] - #368
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…24 [SOF-8054]
Step 1 of the defect model: 41 cells, 25/25 internal checks. 244 charge-state
lines recovered from the main text and supplement as exact PDF vector segments
rather than pixel digitization - 4 compositions x 2 chemical-potential limits x
{O absent, present}, with band gaps 5.924/5.656/5.188/5.040 eV.
Validation: slopes integer to 5.6e-4; reconstructed lower envelopes match the
drawn ones to 0.031 eV; N-poor minus N-rich energies match the supplement's
chemical-potential tables to 0.004 eV without those tables entering the
extraction. Site densities are composition-weighted, which matters - using the
full cation density misplaces x = 0.042 by 1.39 decades.
Open item for step 2: Fig. 2(b) O_N reproduces only up to a factor of 24.2 +/- 1.4,
and log10(24) = 1.380 matches a site-count normalisation of one site per 48-atom
SQS rather than its 24 N sites.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
…ions) and some changes to the extraction notebook [SOF-8054] AlScN_defect_thermodynamic_model.ipynb builds the point-defect thermodynamic model on top of the numbers the extraction notebook digitises. It carries a bulk equilibrium model and a depth-resolved freeze-in model grown layer by layer, with the oxygen condition and both meshes exposed as inputs. Lee2024_AlScN_defects.ipynb gains the Balestra effective-mass section, a classification manifest separating model inputs from validation-only data, and role tags on every heading. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
…, plot fixes [SOF-8054]
Oxygen is now a (mode, value) condition rather than a hard-wired target. Either
pin the total [O_N] and back-solve mu_O, or fix mu_O and let [O_N] be predicted;
("concentration", 0.0) removes O_N entirely. Every result in section 6 is
reported both with O_N and with none, for the bulk and the film alike.
Two meshes, separated. Charge sits on lattice planes c/2 = 0.25 nm apart; Poisson
runs on a mesh m times finer. Section 6.2.3 shows m = 1 and m = 4 agree to
0.000 meV -- the FD Laplacian is exact for the piecewise-linear potential that
plane charges produce -- and sweeps the plane spacing, which is physics and not
free to refine.
The free surface now sits one plane spacing above the last occupied plane, so no
charge plane lands on the boundary node. That removes the half-weight self-term
that was lifting the first layer's Fermi level past neutral and making the second
layer freeze in negative; the profile is monotone at every spacing tested.
Formation-energy and concentration panels now carry one line per defect: the
lowest-energy charge state, and the concentration summed over charge states.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
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…r [SOF-8054] Removes SURFACE_FORMATION_ENERGY_REDUCTION. Slide 5's reduced energies are surface_formation_energies, which already exists; subtracting a further 1 eV inside surface_populations both invented a number and broke the requirement that the three dH sets start identical to the bulk values. Its removal moves the thick-film E_F by +0.333 eV and confines the most-N-poor dilute-limit breach from the whole film to the first two planes. Adds 2.1.5 Ambacher et al., J. Appl. Phys. 130, 045102 (2021): eps_33(x) measured by C-V over x = 0-0.5, replacing a guessed constant 10.5. That is the static constant along the polar axis, which is what a space-charge problem needs; at x = 0.25 it is 18.5, not 10.5. Their P_SP is deliberately not carried - it is zinc-blende referenced and would be mixed up with the measured P_r. The free-surface charge is no longer an opaque 1e12. It is now the bound charge from the measured P_r (6.2e14 e/cm^2) times UNCOMPENSATED_FRACTION, so the actual guess - 0.16%, the bottom of the documented sensitivity range - is the input. Hole mass becomes a function of composition, constant for now. Film thickness is documented as a maximum, and the occupancy threshold says what it is for. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
…es [SOF-8054]
Chemical conditions are no longer discrete strings decoded inside the results
functions. muN() takes a corner name or a number in eV and returns something
callable on composition - it has to stay a function of x, because the most N-poor
vertex moves with x and the bulk model sweeps x. muO() takes ("concentration", c)
or ("potential", eV), a bare number meaning delta mu_O, or "none". Call sites now
read bulk_results(muN("N-rich"), muO(variant), temperature=...).
T_eff,surf is threaded through as a parameter rather than read from module scope,
so it is an experimental input on the same footing as the growth temperature.
Both temperatures are named at every call site.
Depth figures are drawn on linear axes as well as log. The structure sits in the
first few nm and log is what shows it, but linear is what a result should be read
off, so both are produced.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
…al [SOF-8054]
FREE_SURFACE_CONDITION picks between the two forms, and grow_film takes it as a
parameter rather than reading a module constant:
("charge", e/cm^2) Neumann, eps dphi/dz = -sigma. The floating, unbiased case;
what survives of the bound charge sets the field.
("potential", volts) Dirichlet on the growth front. Biased deposition, where an
applied bias fixes the potential across the stack and the
charge is whatever the solution needs. Also the form the
adsorbate-reservoir picture wants.
Field is not offered as a third option: specifying the field just inside the
surface is the same statement as specifying the charge, E = sigma/eps.
The plasma sheath is documented as deliberately absent rather than merely omitted.
At ~3e8 e/cm^2 it moves the frozen profile by 0.0 meV, measured.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
…F-8054] dH = E_def - E_bulk + sum_i n_i mu_i ran over nitrogen and oxygen only. V_Al and V_Sc were given n_N = 0, so they did not move with the chemical condition at all. At the most N-poor vertex that is a 3.2 eV error, and it is why the N-poor runs put V_Sc at ~18% of its sublattice: cation vacancies should be strongly suppressed under cation-rich conditions, and instead they were unchanged. The four parallel per-species dicts become one ATOMS_REMOVED table - the literal n_i of the formula - so a defect cannot silently omit a species it touches. The vertex potentials are now read off the published panels rather than typed in: a vacancy removes one atom, so dH(N-poor) - dH(N-rich) for V_i IS Delta mu_i. That gives all three host species instead of nitrogen alone, and the panels agree that the shift is charge-independent to ~1 meV, which is what makes it a chemical potential rather than a fit. Three checks now hold the result: the nitrogen column matches the SI corner table to 50 meV, Delta mu_Al = -Delta mu_N as mu_Al + mu_N = H_f(AlN) requires, and Delta mu_Sc departs from -Delta mu_N by up to 0.49 eV - so the cations cannot be collapsed onto the nitrogen potential. Effect at x = 0.25, most N-poor: V_Sc falls from 3.3e18 to 4.5e8 cm^-3, and the depth model's dilute-limit breach goes from the whole film to 3 of 400 planes. Also restores the bulk table to 1000 K, which an earlier commit had silently moved to the deposition temperature. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
…8054] The generator assigned a fresh uuid to every cell on every build, so rebuilding an unchanged notebook showed up as all 80 cells modified. Ids are now a hash of the cell's kind and content: identical input gives a byte-identical notebook, and a diff means something actually changed. This commit is that one-time id renumbering; no content changed. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
H_f(AlScN) = mu_N + x mu_Sc + (1-x) mu_Al is one equation in two cation unknowns, so something has to close it. Treating the alloy as AlN and ScN in equilibrium adds mu_Al + mu_N = H_f(AlN) and mu_Sc + mu_N = H_f(ScN), giving Delta mu_Al = Delta mu_Sc = -Delta mu_N. One number then sets every species, which is what makes an intermediate chemical condition well defined rather than a guess about which vertex to walk towards - the previous commit could only interpolate between two named corners. Lee's published corners are not exactly on this tieline, and the reason is worth recording: Delta mu_Al sits within 50 meV of it everywhere, but Delta mu_Sc departs by up to 0.83 eV at x = 0.042 - and the ternary and quaternary panels depart in OPPOSITE directions by nearly equal amounts (+0.35/-0.35 at x = 0.125, +0.09/-0.09 at x = 0.25, +0.004/+0.001 at x = 0.333). The two published references straddle the tieline rather than sitting on one side of it. Cost of the simplification, measured against the published most-N-poor panel: 0.49 eV for V_Sc at x = 0.042, 0.09 eV at x = 0.25, few meV at x = 0.333. The build-time check now walks the tieline too, so it reports this rather than validating a conversion the model no longer performs. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
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Adds
other/experiments/alphafilm/AlScN_defect_thermodynamic_model.ipynb, the point-defect thermodynamic model built on the numbers the extraction notebook digitises, and updatesLee2024_AlScN_defects.ipynb.Model
Two flavours over one set of shared ingredients:
E_Fset self-consistently by charge neutrality.E_F(z)comes from the electrode and Poisson alone — there is no neutrality solve in the depth model.4.3.2 stubs the multi-stage flavour (slide 6) so the structure does not need rearranging later.
Controls
(mode, value)condition. Either pin the total[O_N]and back-solvemu_O, or fixmu_Oand let[O_N]be predicted;("concentration", 0.0)removes O_N entirely. Every result in section 6 is reported both with O_N and with none, for the bulk model and the film alike. Kinetic modelling of the actual transport is noted as the third option and needs research first.mtimes finer. 6.2.3 showsm = 1andm = 4agree to 0.000 meV — the finite-difference Laplacian is exact for the piecewise-linear potential that plane charges produce, so the Poisson mesh has nothing to converge — and separately sweeps the plane spacing, which is physics rather than a numerical knob.Guards on the output
Each run prints the assumptions behind the figure it produces: the chemical and oxygen conditions, the temperatures, where each defect's ground-state charge flips with depth, the screening length against the plane spacing, and a warning wherever defect occupancy breaks the dilute limit the formation energies assume. The most N-poor limit trips that warning across the whole film and is flagged rather than quietly reported.
Notebook outputs are stripped, and quiet leaf sections are collapsed so the outline stays scannable.
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