Surface Boundary Conditions

Boundary conditions and carriers

The surface boundary condition says how the top of the structure is contacted. It is the single most consequential choice you make, because it sets where the bands start.

01The two boxes follow the mode

Beside the Surface Boundary Conditions menu sit two entry boxes. They are not fixed in meaning: both relabel themselves when you change mode, and grey out when the mode has no use for them.

So read the label rather than relying on where the box is. A box showing N/A: is inert and whatever it contains is ignored. Set the mode first, then fill in what it asks for.

02schottky

A metal contact with a barrier — the usual choice for a gated or rectifying structure. Both boxes are active.

  • Schottky barrier height (eV) — the electron barrier at the contact, measured from the conduction band edge to the metal Fermi level. It starts at 0.7 eV.
  • Contact bias, top − rear (V) — the voltage on the top contact relative to the rear. Positive bias pushes towards flat band for an n-type structure; negative bias increases depletion.

03ohmic

A non-rectifying contact. The surface is simply held at charge neutrality, so there is nothing to specify and both boxes are inert.

This is the right choice when the contact should not perturb the structure at all — a heavily doped, well-behaved contact layer — and it is a good default when you are interested in what the layers do rather than what the surface does to them.

04pinned

The surface Fermi level is pinned at a fixed position, as it is on a real free surface with a high density of surface states.

  • Surface pinning (V) — the position of the Fermi level relative to the intrinsic level at the surface. Positive drives the surface Fermi level towards the conduction band, giving more downward band bending; negative drives it towards the valence band.

Zero puts the surface Fermi level at midgap, which is a reasonable first guess for a strongly pinned semiconductor surface.

05surface charge

A fixed sheet of charge sitting at the surface, with the bands free to arrange themselves around it.

  • Surface electron sheet density (cm⁻²) — the sheet density, entered as a number of electrons per square centimetre.

Watch the sign here. The box asks for an electron sheet density, so a positive value places negative charge at the surface. If the bands bend the opposite way to what you expected, this is almost always why.

06contact bias

Two terminals with a voltage between them, for modelling a biased junction rather than a surface.

Both boxes at the top are ignored in this mode, which may surprise you. The voltages are taken instead from the Contact Voltage (V) column of the layer table — from the first and last layers, or from the substrate row. That is what marks a layer as a terminal.

This mode carries real restrictions on what it can represent, and it is worth reading them before trusting a result: see Contacts Under Bias.

07Choosing one

  • Modelling a metal gate or Schottky diodeschottky.
  • Modelling an exposed semiconductor surfacepinned, or surface charge if you know the sheet density.
  • You want the surface to not interfereohmic.
  • You are applying a voltage across a junctioncontact bias.