Applying a voltage changes what sets the carrier populations. Most of it is handled for you — but there are structures a zero-current model cannot represent, and it is worth knowing which.
01Where the carriers come from
With no bias applied, one Fermi level describes the whole structure and there is nothing to think about. Apply a voltage and that stops being true: the two ends of the device are now held at different energies, and each carrier population is set by whichever reservoir actually supplies it.
That is the idea underneath everything on this page. A contact can only pin a carrier it can genuinely exchange — and which carrier that is depends on the doping either side of it.
02A biased Schottky contact
A metal is a reservoir for both electrons and holes, but a Schottky barrier blocks one of them. The other has no comparable supply elsewhere in the structure. Thermal generation does produce minority carriers throughout — that never stops — but it only ever sustains the small background level the material’s intrinsic concentration allows, and it cannot hold a population at a defined energy against an applied bias. A contact can. So in an n-type structure it is the metal that governs the hole population, and in a p-type structure the electron population.
Poisson recognises this and handles it automatically. When the metal is the only possible source of a carrier, that carrier is referenced to the metal instead of to the bulk of the structure. There is no setting to change — it simply applies when it should.
The practical consequence is that a reverse-biased blocking contact solves cleanly at any bias, and the minority-carrier density right at the contact is fixed by the barrier height alone. It does not grow as you increase the voltage, which is the physically correct behaviour and the reason deep reverse bias is well behaved.
03Contact-bias mode and its terminals
In contact bias mode you mark terminals yourself, by putting a voltage in the Contact Voltage (V) column of the first and last layers — or of the substrate row. Poisson then classifies each terminal from its doping: n-type, p-type, undoped, or a gate if the material is an insulator.
Those classifications decide whether the structure is one the model can represent.
Solves properly
a well-posed zero-current problem
- One n-type and one p-type terminal — a real junction, each contact supplying its own carrier
- A gate or insulator terminal — a field-effect structure
- Both terminals undoped — too few mobile carriers to carry a current, so the bias is essentially a field tilt
- Any structure at zero bias — plain equilibrium
Cannot be represented
these need a transport solver
- Two terminals of the same type with carriers between them
- One doped, one undoped terminal with carriers between them
- A forward-biased junction that is conducting
- Anything where the answer you want is a current
04The warning you may see
If you bias a structure in the right-hand column above, Poisson tells you rather than quietly producing a number. The dialog is titled Biased contacts need a junction, and it says:
Biasing contacts that aren’t an n-type/p-type pair, with mobile carriers between them, makes a current-carrying resistor this zero-current model cannot represent. Use an n-type and a p-type contact, or bias only an undoped structure.
The reasoning is worth understanding, because it is not a limitation of this program so much as of the question. Two same-type contacts at different voltages, with conducting material between them, form a resistor. A resistor carries current. This model solves the case where no current flows, so there is no correct answer for it to give — and inventing one would be worse than declining.
The warning carries a Don’t show this again for this session option, for when you are deliberately exploring and already know.
05If your question really is about current
Then this is the wrong tool, but it can be useful in showing the unbiased structure. Poisson gives you the electrostatics — the field profile, the band line-up, where the carriers sit — which is very often the input to a transport calculation. For the current itself, take those results to a drift–diffusion or Monte Carlo solver.
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