Poisson finds the equilibrium band diagram of a layered structure. Knowing what that includes — and what it deliberately leaves out — is the key to reading its results correctly.
01The band diagram, from a layer stack
You describe a device as a stack of layers — each with a material, a thickness and a doping — and choose how the surface is contacted. From that, Poisson solves Poisson’s equation through the structure and returns the equilibrium band diagram: the electrostatic potential, the conduction and valence band edges, the electron and hole densities, and the sheet charge in each layer, all as a function of depth.
That is the core calculation. Everything else in the tool either feeds it (the layer table, the materials database, the boundary condition) or reads from its result (the plots, the transport summary, the export).
02One Fermi level, at thermal equilibrium
The solve is an equilibrium one: a single Fermi level sets the carrier populations everywhere, and the bands arrange themselves so the structure is charge-neutral overall. This is exactly right for a device sitting at rest, and it is what makes the calculation fast and robust.
The one place a second Fermi level appears is a deliberately biased junction — covered under Contacts Under Bias. Everywhere else, read the results as an equilibrium picture.
03What it does, and what it doesn’t
The scope is worth stating plainly, because the model is honest about its limits rather than guessing past them.
It computes
the equilibrium electrostatics
- Band edges and potential vs. depth
- Carrier densities, electrons and holes
- Depletion, accumulation and band bending
- Sheet charge and sheet resistance per layer
- Quantised states in a chosen region
- Capacitance vs. voltage
It doesn’t
no current, no time
- Current flow — it is a zero-current model
- Transport — no drift–diffusion or Monte Carlo
- Forward-biased conducting junctions
- Transient or time-dependent behaviour
- Recombination or generation currents
- Self-heating or thermal effects
The single most useful thing to remember: Poisson tells you where the bands sit and how the carriers distribute. If your question is about how much current flows, or how the device responds over time, that is a transport problem and needs a drift–diffusion or Monte Carlo tool instead. Poisson often gives the input to such a question — the field profile and the band line-up — but not the current itself.
04The two optional add-ons
Quantised states. Over a region that you nominate, a Schrödinger solver finds the bound states — energies and wavefunctions — in the potential the band solution produced. This is how you get the confined levels of a quantum well or a triangular notch.
Capacitance–voltage. A C–V sweep steps the contact voltage and reports the small-signal capacitance at each point — the standard way to extract doping profiles and barrier heights from a real device, reproduced here in the model.
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