Instead of dialling in one ablation pattern by hand and seeing what comes out, this tool tries the thousand-odd combinations at once and lets the numbers point to the best one. This guide explains the principle, the calculation behind it, and how to read the recommendation without being a thermal engineer.
The thermal anisotropy simulator answers "how good is this pattern?" — great for fine-tuning, slow for exploring: every trial needs a setting, a calculation, a reading. The parametric sweep flips the question: among every manufacturable groove geometry, which one is best for this material?
In one pass it evaluates 1,008 combinations — 12 slit widths × 21 pitches × 4 patterns — then designates the optimum according to a priority slider you set: lean toward strong conduction in the favoured direction, lean toward strong blocking in the other, or anywhere in between.
Two concrete uses, in this order.
Framing before simulating. Before opening the anisotropy simulator, you want to know which zone to search: a 90 µm slit or a 200 µm one? a 500 µm pitch or a 1,500 µm one? The sweep answers this in a few seconds, with a trade-off curve that shows why the optimum sits where it does and nowhere else.
Comparing the four patterns on equal footing. Each design (straight, tapered, herringbone, hexagonal) has its own best setting, which differs from one design to the next. Comparing them at one arbitrary shared setting would be unfair; the sweep compares each design at its own optimum.
The sweep's bounds aren't arbitrary: the lower slit-width bound (90 µm) is the process's declared laser kerf capability, and the pitch range covers what remains drawable on a 49 × 49 mm chip. In other words, everything the tool proposes is manufacturable.
Solving the full numerical solver 1,008 times would take several minutes and make the sliders unusable. So the tool proceeds in two stages, and that split is the key to both its speed and its reliability.
The analytical base is the exact solution for an infinite stack of alternating material/slit bands: parallel along the bands, series across them. It stays reliable at every slit proportion, including the finest — precisely where the numerical solver becomes sensitive to how fine its grid is.
The design factor answers "how much better (or worse) does this pattern do than straight slits, at equal void fraction?". It is a ratio, and a ratio between two calculations run on the same grid: shared inaccuracies cancel out. This keeps the information that matters — how designs rank against each other — without inheriting the solver's weaknesses in absolute value.
The one parameter that governs everything is the void fraction φ: slit width divided by pitch. Widening the slits (large φ) blocks the y direction better and better — anisotropy climbs — but removes material, so conduction along x collapses. Narrowing the slits does the opposite. There is no absolute optimum: there is a trade-off curve, and a choice to make on it.
The figures above concern the film alone. On the chip, this film sits on a much thicker EFFIBLUE substrate, which conducts in every direction and therefore "dilutes" the anisotropy so hard-won. The right-hand panel shows the three numbers that matter: film anisotropy, system anisotropy, and the dilution factor between the two. This is very often where the design's real feasibility is decided, far more than in the choice of pattern.
Two levers act on this dilution, both adjustable: thinning the substrate, and grooving the substrate in alignment with the film's slits. Without one or the other, system anisotropy stays close to 1 whatever pattern is chosen.
Every quantity here is a conductivity at thermal equilibrium. The tool says nothing about the time heat takes to propagate — that's the role of the thermal diffusion comparator. Direct consequence: heat capacity does not enter this calculation at all (see the note, §09).
As with the anisotropy simulator, the calculation assumes a pattern that repeats identically; edge effects at the chip's border are not modelled.
The sweep does not model junction bridges. Yet these, essential for mechanical strength, short-circuit the blocked direction: in the full simulator, a film's real anisotropy typically falls back to around ×100. The sweep's values should therefore be read as a ranking between configurations, not as final performance.
When the phonon correction is enabled, the characteristic length used is the film thickness alone. This is legitimate here because the residual wall between two slits is at least 300 µm across the entire swept domain — a thousand times more than a typical film. The anisotropy simulator, by contrast, takes the minimum of the two, because its own setting range allows for much thinner walls.
Only substrate thickness and its groove fraction are adjustable here; its conductivity is fixed at the EFFIBLUE reference value. To vary it, switch to the anisotropy simulator.
Results (CSV) — all 1,008 swept combinations, one row each: design, slit width, pitch, φ, k_xx, k_yy, anisotropy. This is the raw sweep, not just the optimum: enough to build your own sorts, plot other trade-offs in a spreadsheet, or archive the run exactly as it was computed.
There is deliberately no settings export or fabrication-file export here: this tool exists to choose a geometry, not to produce it. The chosen pattern is replayed and exported as Gerber from the thermal anisotropy simulator.
This section is the guide's technical reference: it describes the formulas actually executed, in order, and justifies each modelling choice. It is not required to use the tool.
If the size-effect correction is enabled, the catalogue conductivity is first scaled down:
This is Matthiessen's rule applied to heat transport. Two mechanisms independently hinder phonons: internal collisions within the material (mean free path Λ) and bounces off the film's faces (path limited to t_f). Collision rates add, so the inverse lengths add: 1/Λ_eff = 1/Λ + 1/t_f, i.e. Λ_eff = Λ·t_f/(Λ + t_f). Since conductivity is proportional to the mean free path, k_eff/k = Λ_eff/Λ = t_f/(t_f + Λ), which is (1).
The characteristic length used is the film thickness alone, without comparing it to the residual wall between two slits the way the anisotropy simulator does. This is justified by the swept domain: the wall there is at least 500 − 200 = 300 µm, three orders of magnitude above a typical film. It can therefore never be the limiting factor.
Below 5 nm of thickness, the diffusive-transport assumption behind (1) is no longer defensible — transport becomes two-dimensional or ballistic. The tool still applies the correction, but flags it: silently swapping in a different model would be worse.
For a given void fraction φ, the pattern is first treated as an infinite stack of alternating material/slit bands:
These are not approximations: for an infinite lamellar composite, they are the exact solutions. Along the bands, material and slit conduct side by side and conductances add in proportion to width — arithmetic mean. Across them, heat must cross one then the other and it is the resistances that add — harmonic mean. These are also the Wiener bounds: no microstructure of the same φ can exceed k_xx⁰ or fall below k_yy⁰.
This base was chosen over the numerical solver as the sweep's foundation precisely because it stays exact at small φ, exactly where the solver becomes sensitive to resolution: a fine slit only spans a few cells there and its barrier is underestimated. With the sweep going down to φ = 0.06, that would have been disqualifying.
Base (2) makes no distinction between straight slits, tapered slits, herringbone, or a hexagonal array — it only knows φ. Differentiation comes from a calibration run once, at sweep launch, against the full numerical solver (finite volumes + over-relaxation, the same engine as the anisotropy simulator):
That's 5 φ values × 4 designs × 2 directions = 40 solver runs, cached server-side and indexed on the pair (film conductivity, slit-medium conductivity).
The solver has a known, systematic resolution bias: it underestimates the barrier effect of a slit that spans only a few cells. This bias depends mostly on φ and the grid — so it is very largely shared between the tested design and the "straight" reference computed at the same φ on the same grid. Taking the ratio of the two cancels it out. This keeps the information sought — how much this pattern differs from the reference — without inheriting the imprecision that would make the absolute value hard to defend. It's also why "straight" is 1 by construction: it's the yardstick, not a design like the others.
If the solver fails, the tool falls back to an offline-calibrated factor table rather than interrupting the sweep. Between the 5 calibration points, factors are interpolated linearly in φ, and held constant beyond the bounds.
This is the operation — three multiplications — repeated 1,008 times, hence the sweep's instantaneity.
These 1,008 points now need ranking against two opposing objectives. That's the role of the figure of merit F, which the tool maximises:
Two normalised terms. Each is scaled to its maximum over the sweep, so it sits between 0 and 1: two dimensionless quantities are compared instead of adding W/m·K to a bare ratio, which would make no sense.
A product, not a sum. This is a weighted geometric mean. Its decisive property: if either term tends to zero, the product tends to zero. A configuration with spectacular anisotropy that conducts almost nothing therefore scores zero — the desired behaviour. An arithmetic mean would instead have ranked it first on the strength of its second term alone.
A logarithm on anisotropy. Over the swept domain, k_xx varies by a factor of roughly 2, while anisotropy spans two to four decades. Without the log, the second term would completely swamp the first, and the figure of merit would only ever point to the "widest possible slits" corner, regardless of the priority setting.
The guard rails. The bases are floored at 1 (k_xx and A) and the log's denominator at 10, so that no fractional power ever applies to a negative number and no logarithm ever vanishes.
The main recommendation is searched among straight slits only. This is not an oversight: at equal conduction, tapered and herringbone patterns gain anisotropy only through a geometric effect — their non-uniform geometry locally tightens φ — with no real conduction gain. Recommending them would mean asking for extra ablation complexity for an advantage that isn't one. All four designs remain swept, and the "best config per design" table shows all of them, each at its own optimum.
The formulas are exactly those of the anisotropy simulator, applied to the recommended configuration alone:
Film and substrate are two conductive sheets stacked together: laterally they conduct in parallel, each contributing its conductance k·t. Dividing the sum by total thickness converts it back to an equivalent conductivity, directly comparable to the film's alone. This also explains the dilution: with t_f of a few hundred nanometres against t_s on the order of a millimetre, the substrate term weighs thousands of times more, and the film's fine anisotropy dissolves in the average. Substrate grooving exists precisely to make the substrate itself anisotropic — the only way to bring K_xx/K_yy back up.
A warning appears once system anisotropy drops below ×3: below that, the film's geometry simply no longer shows at chip scale, and the pattern choice becomes secondary to substrate thickness.
Two questions recur regularly about the deposited materials: where does their heat capacity come in, and what is done about interfacial thermal resistances. Straight answers, with the assumptions actually made across the three thermal tools.
The regime decides. At steady state, heat capacity has no effect at all: once the temperature field has settled, only conductivity governs how heat is distributed. In the transient regime, by contrast, it is heat capacity that, together with conductivity, sets the thermal diffusivity α = k/(ρ·c_p) and hence the speed at which temperature evolves.
The three tools split accordingly:
| Tool | Regime | Film ρ·c_p |
|---|---|---|
| Parametric Sweep | steady state | does not enter |
| Thermal Anisotropy Simulator | steady state | does not enter |
| Thermal Diffusion Comparator | transient | enters explicitly |
For this tool, as for the anisotropy simulator, this is therefore neither an oversight nor an implicit inclusion: both solve an equation — ∇·(k∇T) = 0 — in which ρ·c_p does not appear, and neither carries these fields in its parameters at all. The material catalogue shared by all three tools does record ρ and c_p for every material, but only the diffusion comparator consumes them.
In the diffusion comparator, capacity enters through the film-plus-substrate system's effective diffusivity:
Two explicit assumptions are made here about the deposited layers. First, the ablated fraction of the film stores nothing: the slit medium (air, vacuum, aerogel) is treated as having no meaningful capacity at these scales, hence the (1 − ψ) factor. Second, ρ and c_p are taken at 300 K and held constant — no temperature dependence is modelled.
Values come from the shared server catalogue:
| Material | ρ (kg/m³) | c_p (J/kg·K) | Data status |
|---|---|---|---|
| Ginestium™ | 2,100 | 710 | stand-in — oriented synthetic pyrolytic carbon at 300 K; not a Ginestium™ measurement |
| Few-layer CVD graphene | 2,200 | 700 | literature |
| Nanocrystalline CVD diamond | 3,400 | 536 | measured on an NCD film at 302 K |
| Copper (control) | 8,960 | 385 | literature, bulk copper |
| Substrate | user-entered (defaults 3,900 / 880) | — | |
A "custom" material has neither ρ nor c_p: in that case the comparator explicitly returns "no diffusivity" rather than guessing a value.
Thickness-weighting crushes the film's contribution. With the comparator's default settings — Ginestium™ 400 nm on 10 µm of substrate — the film accounts for only ≈ 1.6 % of the system's capacity; push the substrate to 2 mm and its share drops below 0.01 %. Effective diffusivity is therefore, in practice, "the system's lateral conductivity divided by the substrate's capacity."
A direct consequence: the diffusion front is very insensitive to the film's c_p. Not because it is neglected — it is genuinely in the formula — but because the stack's geometry leaves it little weight. The film matters through its k·t, in the numerator, far more than through its capacity in the denominator.
They are not ignored, but their treatment is partial, and out-of-plane only.
What exists. The anisotropy simulator and the diffusion comparator both expose an R_th interface parameter (0 to 100 ×10⁻⁶ m²·K/W, default 10), which enters in series into the out-of-plane resistance:
This is a single, global film/substrate interface. The geometric model has only two layers: there is no multilayer stack with one resistance per interface, and no lateral resistance between grains or between pattern features.
A useful order of magnitude: for graphene (k_z = 6 W/m·K over 1.675 nm), the film term is ≈ 3×10⁻¹⁰ m²·K/W, five orders of magnitude below a typical interface resistance. In R_z, it is always the interface and the substrate that dominate, never the film.
What is neglected, and this is a deliberate assumption. R_th,if enters neither the k_xx/k_yy homogenisation, nor K_xx, nor therefore the lateral diffusion front's diffusivity α_eff. The comparator states this explicitly under the relevant slider. As for the parametric sweep — the tool this guide covers — it carries no interface resistance at all: it is a purely in-plane tool.
For lateral transport, interface resistance is not a series resistance on the heat's path: it's a coupling between two parallel paths, the film and the substrate. Neglecting it is exactly equivalent to assuming perfect coupling along z — film and substrate at the same local temperature at every abscissa, what's called the equivalent-plate assumption. That's consistent for the thicknesses and observation times targeted here.
The regime where it breaks is identifiable: short times, or a highly conductive film on a poorly conductive substrate. There, the film would race ahead of the substrate instead of dragging it along — an effect the model structurally cannot see. If your case approaches that regime, sensitivity to the R_th interface parameter can be tested in the anisotropy simulator, but only on the out-of-plane R_z.