How a pattern of laser-cut slits in a Ginestium™ film teaches heat to race along one direction and stay blocked along the other — and how to read what the tool computes for you, without being a thermal engineer.
On an EFFIBLUE chip, you often want the heat from a hot spot to drain quickly along one direction (toward a heat sink, a housing edge) without spreading along the other (toward a sensitive neighbouring component). A solid metal film conducts the same in every direction — no use for this kind of directional sorting.
The solution: cut the Ginestium™ film with very fine laser slits, in a regular pattern. Chosen well, this pattern lets heat flow almost freely in one direction and strongly holds it back in the other. The simulator computes, for a given pattern and settings, how well that sorting works — before anything is actually ablated.
The tool answers a concrete question: "if I cut this slit pattern, at this film thickness and on this substrate, what will conduction be in the direction I want to favour (x), and in the one I want to block (y)?" It also gives two practical sanity checks: will the design hold together mechanically, and could differential film/substrate expansion fatigue it over thermal cycling?
It is an exploration tool before fabrication: you set a pattern, look at the result, adjust, and once satisfied, export the drawing in the format used by the laser-ablation machine.
Picture the film from above, as solid strips separated by fine, regular slits (filled with air, vacuum, or another insulator). Along the strips, heat flows almost without obstacle: that's the x direction, the one to favour. To go the other way, it must systematically cross a slit — an insulator — which slows it down sharply: that's the y direction, the one to block.
The result of this calculation is two numbers: k_xx (effective conductivity in the favoured direction) and k_yy (effective conductivity in the blocked direction). Their ratio k_xx / k_yy is the anisotropy achieved — the larger it is, the better the sorting works.
The film doesn't float in a vacuum: it sits on a noticeably thicker EFFIBLUE substrate. Heat can therefore leave in two different directions, and the tool handles them with two distinct models.
In practice: system k_xx and system k_yy account for this dilution by the substrate, while out-of-plane R_th answers "if heat must cross the stack vertically, what total resistance does it meet?"
In a very thin film, heat no longer flows quite like it would in a bulk block: the heat carriers (phonons) are hindered by the film's nearby edges. The thinner the film relative to their "mean free path" (a characteristic distance specific to each material), the more its real conductivity falls below the bulk material's value. The "Correct k for confinement" checkbox applies this correction when ticked — it is off by default, to be enabled deliberately for very thin films.
A model is only useful if you know what it assumes. Here are the assumptions behind each calculation.
The calculation assumes a slit pattern that repeats identically as far as the eye can see (a single "cell" is solved and then mentally tiled). At an actual chip edge, the pattern stops: the tool does not model these boundary effects.
k_xx and k_yy are conductivities at thermal equilibrium (the system has had time to settle). This simulator says nothing about the speed at which heat spreads over time — that's the role of the thermal diffusion comparator, a companion tool. Direct consequence, detailed in the note (§10): heat capacity does not enter this calculation anywhere.
Junction bridges often measure a few micrometres — too fine for the calculation grid. Their local thermal short-circuit effect is added through a calibrated analytical formula (validated to within 5% against a high-resolution solver), not resolved cell by cell like the rest of the pattern.
The confinement correction assumes "diffusive" heat transport — valid for a film with a sufficiently thick interior. Below 5 nm, this assumption becomes questionable (transport becomes more two-dimensional/ballistic); the tool does not silently disable the correction — it flags that you've left its domain of validity.
"Mechanical fragility" and "CTE risk" are simple qualitative scores (void fraction, bridge density, thermal-expansion mismatch × cycling amplitude), meant to quickly flag a risky configuration — not the output of a finite-element mechanical simulation or an actual fatigue test.
Interface resistance (R_th interface) is a single number supplied by the user, not a physical contact model — handy for exploring its sensitivity, but to be calibrated against a real measurement before drawing final conclusions. It only acts on the vertical path: see the note (§10).
The tool never hides an edge case: it still calculates, but warns you.
k_yy becomes unreliable. Increase grid resolution or widen the pitch.Settings (JSON) — exports all of the tool's settings (material, geometry, substrate, bridges…), not the calculation results. Useful to resume a session later or hand it to a colleague, who re-imports it identically.
Gerber (.gbr) — exports the actual vector drawing of the ablation pattern, in the format expected by the laser-ablation machine. This is the practical endpoint of the process: once the pattern is validated virtually, this file goes straight to fabrication.
This section is the guide's technical reference: it describes the formulas actually executed by the server engine, in the order they run, and justifies each modelling choice. It is not required to use the tool.
If the size-effect correction is checked, the entered 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 structure's walls (path limited to L_c). Collision rates add, so the inverse lengths add: 1/Λ_eff = 1/Λ + 1/L_c, i.e. Λ_eff = Λ·L_c/(Λ + L_c). Since conductivity is proportional to the mean free path, k_eff/k = Λ_eff/Λ = L_c/(L_c + Λ).
The minimum in L_c tells which of the two confinements bites: the film thickness, or the wall of material left between two slits. On this simulator, unlike the parametric sweep, both are plausible — which is why the minimum is taken explicitly.
The same factor is applied to out-of-plane conductivity k_z: confinement suppresses transport in both directions.
The ratio k_x/k_y does equal A, as required. But crucially, the product k_x·k_y stays equal to k_eff²: the geometric mean is preserved. Turning the anisotropy dial therefore does not surreptitiously change the total amount of heat the material can carry, only its split between the two directions. With A = 1, you get exactly k_eff in both directions.
A partial-depth etch leaves material below the slit. Across the film's thickness, fraction p of the top is filled by the slit medium and fraction (1 − p) of the bottom is still solid film. Seen from lateral transport, these two layers conduct side by side — in parallel — hence the thickness-weighted arithmetic mean, not the harmonic mean. At full-depth etch (p = 1), you recover k_gap.
The pattern is reduced to a repeating unit cell: width = bridge period (or pitch × aspect ratio for hexagonal), height = 2 × pitch. Each cell is assigned k_slit if it falls in a slit, otherwise k_x and k_y. A pure-conduction problem is then solved on this cell, twice: once along x, once along y.
Between two neighbouring cells, heat crosses half of one cell then half of the other: these are two resistances in series, and the equivalent conductivity of two equal halves is their harmonic mean. Taking the arithmetic mean instead would let heat "leak" across a material/slit boundary and systematically overestimate k_yy — precisely the quantity the tool is supposed to make small. Another useful property: the harmonic mean drops to zero as soon as one of the two conductivities is zero, which turns a high-vacuum cell into a true barrier.
(5) is the finite-volume flux balance: at equilibrium, what enters a cell through its four faces leaves it again, so its temperature is the neighbours' average, weighted by face conductances. Sweeping every cell while reusing already-updated values is the Gauss-Seidel method; it converges, but slowly on a fine grid. The factor ω > 1 (successive over-relaxation) extrapolates beyond the computed correction and cuts the iteration count by roughly an order of magnitude. ω must stay within ]1 ; 2[ for the scheme to remain stable; 1.9 is the value used here.
Boundary conditions: temperature fixed at 1 and 0 on the two faces perpendicular to the tested direction, periodicity on the other two — the numerical translation of the "infinite pattern" assumption. Total flux is measured every 50 iterations, and the calculation stops once its relative variation drops below 2×10⁻³, with a 6,000-iteration cap.
Since the imposed temperature difference is exactly 1 across the cell's full length, this flux is the effective conductivity, with no further normalisation needed. The mesh is sized to give several cells across the slit (44 to 220 cells in height, 24 to 220 in width) and capped at 46,000 cells total; beyond that, the grid is scaled down proportionally, which triggers the "under-resolved slit" warning.
For an infinite lamellar stack of alternating bands, these are not approximations but the exact solutions: along the bands conductances add, across them it's the resistances that add. These are also the Wiener bounds — no microstructure of the same void fraction can exceed k_xx^ideal or fall below k_yy^ideal. Hence their dual use: instant display (no solver to run) and a sanity check on the numerical result, which must always fall between the two.
The step-4 solver runs without bridges. Their effect is added back afterward, analytically:
A bridge is a few micrometres across, on a grid whose cells run several dozen micrometres. Resolving it directly would require refining the grid everywhere — roughly a ×100 cost in cell count for one localised detail. Correction (8) does more with less: it recovers the slit band's conductivity as the solver actually computed it, adds the bridge as a parallel short-circuit within that band alone, then reassembles. The 0.88 factor captures the brick offset: staggered bridges don't line up into one continuous path and so short-circuit a little less. The whole scheme is calibrated to within 5% against a high-resolution solver.
k_xx is untouched: a bridge adds material across the bands, it changes nothing about conduction along the bands.
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 is also the mechanical explanation for dilution: with t_f 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 anisotropy drowns in the average. Substrate grooving exists to make the substrate itself anisotropic — the only way to bring K_xx/K_yy back up.
Vertically, heat crosses the three layers one after the other: areal resistances add, unweighted. This is the only place in the model where interface resistance enters — see the note (§10). Note that k_z is genuinely the material's out-of-plane conductivity, independent from the in-plane one: for a lamellar material like graphene, the gap reaches a factor of 100, and using the in-plane value would make R_z absurdly optimistic.
(12) has a clear physical meaning: it's the differential strain accumulated between film and substrate over a thermal cycle. 2,500 ppm is a 0.25% expansion mismatch — the order of magnitude where thin-film delamination is documented. The score is coarse but anchored.
(11) makes no such claim: it's an empirical ranking that pits removed material (φ, which weakens) against bridge density (b, which reinforces), with two surcharges for tougher geometries. The coefficients 2 and 3 are unitless and come from no mechanical model. Treat it as a traffic light, never as a sizing criterion.
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 |
|---|---|---|
| Thermal Anisotropy Simulator | steady state | does not enter |
| Parametric Sweep | steady state | does not enter |
| Thermal Diffusion Comparator | transient | enters explicitly |
For this tool, this is therefore neither an oversight nor an implicit inclusion: the equation solved in step 4 is ∇·(k∇T) = 0, in which ρ·c_p does not appear — and the simulator doesn't carry 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. This simulator's R_th interface parameter (0 to 100 ×10⁻⁶ m²·K/W, default 10; the same slider in the diffusion comparator) enters in series into the out-of-plane resistance — this is equation (10) from §09, restated here:
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 — true for Ginestium™ too, whose high k_z (1,000 W/m·K) makes the film term negligible.
What is neglected, and this is a deliberate assumption. R_th,if enters neither the step-4 k_xx/k_yy homogenisation, nor step-7's K_xx/K_yy, nor the comparator's diffusion-front diffusivity α_eff, which states this explicitly under the relevant slider. The parametric sweep, for its part, 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. It is already implicit in equation (9), which assigns a single conductivity to the film + substrate pair.
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 cannot see. Sensitivity to R_th interface can be tested right here, but it will only show up on the out-of-plane R_th.
You don't need to handle these units to use the tool: the sliders and numeric fields do most of the work. This glossary just helps decode the results shown.