A final row can name the substrate the structure sits on. It is a reference, not a layer — it anchors the far side of the solve without being part of it.
01What the row is for
Every solve needs something to reference the deep end of the structure to. By default that is simply the last layer you listed. A substrate row lets you say instead: below all of this there is a semi-infinite body of some material, and have the solver anchor the bulk Fermi level to that material’s own charge neutrality.
It is written in the Material column of the last row, with a colon:
- substrate: GaAs — a semi-infinite GaAs rear reference.
- substrate: open — a floating, zero-field rear instead of a material reference. Explained in full below.
- substrate — with nothing after it, this is just a marker and is ignored entirely.
02It is not meshed
This is the point that matters, and the reason the row is a reference rather than a layer.
No band bending is solved inside the substrate row. It has no thickness and occupies no space in the result — it only sets the bulk and contact reference for the deep side. If you want to see depletion, band bending or charge in the substrate, you must add a real, finite layer of that material before the substrate row.
So a structure that ends substrate: GaAs answers “what is the deep reference?”, while one that ends with a 1000 nm GaAs layer and then substrate: GaAs also shows you what happens across that first micron.
03What the row accepts
Beyond the material name, the substrate row reads a few of the ordinary columns:
- Fraction (%) — required if the substrate material is an alloy.
- p-doping or n-doping — the substrate’s doping, which is what its neutrality is computed from.
- Dopant depth (eV) — optional, as for any layer.
- Contact Voltage (V) — sets a voltage on the rear reference, for biasing from the substrate side.
Thickness is meaningless here and is not read — the row is semi-infinite by definition.
04Three rules
- Only one substrate row per structure. A second one is rejected with an error.
- No gradients. Composition and doping must each be a single value; a slash expression is refused.
- Not both dopings — as with any layer, put the net doping in whichever column applies.
05An open (floating) rear
There is a third form of the row. In place of a material, write substrate: open and the far boundary becomes a zero-field rear: nothing is placed behind the structure, and the bands are free to sit wherever the surface and the charge in the layers put them.
This is the opposite of the default. The ordinary rear anchors the deep end to a neutral bulk — it insists the bands return to the charge-neutral level of some material far below. open insists on no such thing. It asks only that the electric field fall to zero at the back, and lets the surface contact set the reference instead.
Reach for it when the structure genuinely has nothing pinning its back:
- a free-standing membrane, or a thin film with no conducting substrate behind it;
- a back region already thick enough to be field-free, that you would rather not spend mesh on;
- a fully undoped stack, where anchoring to a neutral substrate imposes a reference the real device may not have — the two choices can differ by tenths of a volt toward the rear;
- reproducing a result from another solver that terminates at zero field, so that both are solving the same boundary-value problem.
An open rear needs a surface that fixes the reference — a Schottky, pinned, or ohmic surface. It cannot be paired with a fixed-surface-charge boundary: with both ends floating there is nothing to pin the potential at all, so the solve is refused with an error rather than returning an arbitrary answer.
06Do you need one?
Often not. If your deepest layer is already thick enough to be electrically bulk-like, it serves as its own reference and a substrate row adds nothing.
A material reference earns its place when the deep reference is a different material from your last layer — a device grown on a substrate you have not modelled explicitly — or when you want to apply a voltage to the rear without giving that region a thickness. An open rear earns its place in the opposite situation: when there is deliberately no reference behind the structure at all.
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