Reading results
The plot shows you the details of the solution. The results window is where the values resulting from the model appear, and where the solver states what it actually did.
01Four tabs
Model Results opens beside the plot after an ordinary solve, with four tabs: Electrostatics, Boundary Conditions, Layer Transport and Derived. It is a separate window from the main one, but only one exists at a time: a second solve replaces it. Copy the report before re-running if you want to keep a result to compare against.
The first line of the first tab sets the convention for everything else:
All energies referenced to bulk Fermi level = 0 eV.Every energy in this window and on the plot is measured from that zero. A surface conduction band of +0.72 means the band edge sits 0.72 eV above the bulk Fermi level, not above vacuum and not above the band edge somewhere else. It is important to understand this before comparing two structures.
02Electrostatics
The solution itself, and the surface it produced.
Lattice temperature and the convergence pair are described in Running a Simulation — check these are correct.
Below those, the applied bias appears in one of two forms, and which one you get tells you which model ran:
- Applied bias, surface relative to rear — the ordinary single-surface case. One number, referenced to a rear that sits at zero.
- Top contact voltage, Rear contact voltage and Potential drop across structure — the two-terminal contact-bias case, where both ends are real terminals and both can be driven.
Then the surface itself: Surface conduction band energy and Surface valence band energy, both on the convention above, and Surface band bending — the amount the bands move between the bulk and the surface, positive when they bend upward at the surface. Band bending is omitted in contact-bias mode, where it would simply restate the terminal voltage.
If any material in the structure carries a note in the database, it appears here as a Material note row. That is the mechanism by which a provisional or unusual parameter set announces itself, so read one if it appears.
03Boundary Conditions
This tab echoes the boundary condition: it reports the boundary the solver used, in words, so a misread combo box or a stale setting shows up as a sentence rather than as a puzzling band diagram.
Surface boundary condition states the condition used — Schottky contact, Ohmic contact, Pinned surface, Fixed surface charge, or Two-terminal contact bias. One further row follows, appropriate to the surface: the Schottky barrier height, the Surface Fermi level below mid-gap for a pinned surface, or the Surface electron sheet density for fixed charge. In contact-bias mode you get the role of each contact and, when the two quasi-Fermi levels have split, their values at the contact.
Rear reference is worth reading carefully, as it takes one of three forms and each is a different rear boundary:
- Set by the last meshed layer — no substrate row, so the rear reference is simply the bulk of the bottom layer.
- A named substrate material, with the reminder that it is a semi-infinite reference reservoir and not a meshed layer.
- Open (zero-field) rear — the bands terminate at zero field and the reference is taken from the surface contact, with no rear reservoir at all. This is the boundary selected by
substrate: open.
The three can move the whole band diagram relative to one another, so the row is worth a glance whenever the rear is not the default; see The Substrate Row.
04Derived
Four quantities are extracted from the solution, each reported with the depth and the layer at which it occurs — the layer being the more useful of the two.
- Maximum electron concentration and Maximum hole concentration, each as a density with its depth and layer.
- Peak electric field, as a magnitude, with where it occurs. In a depleted structure this normally falls at a junction or the surface, and it is the figure to check against the breakdown field of the material.
- Net space charge across structure — the ionised and free charge integrated over the whole stack, per unit area.
This last one doubles as a consistency check. A globally neutral structure integrates to near zero; a depleted surface integrates to the charge balanced at the contact. A large net charge on a structure that should be neutral indicates that the rear reference is not set as intended.
A maximum is not evidence that anything is there. Maximum hole concentration is reported for every structure, including a uniformly n-type one where the true hole population is negligible. It will name a depth and a layer, and the figure will still sit around twenty orders of magnitude below the electron density.
The same trap appears on the plot, more convincingly, if you switch the carrier axis to a log scale: the minority carrier draws a smooth peak that looks exactly like a confined gas. Read the exponent before trusting the shape. A real two-dimensional gas and a minority-carrier artefact are the same picture on a log axis and entirely different things in fact.
These densities are semiclassical, even in a quantum well. Every carrier density on the plot, and every sheet density in the Layer Transport table, is read from the band edge and the Fermi level in the ordinary way. It takes no account of quantum confinement, so in a narrow well it is an approximation: it puts charge where the band edge is lowest, not in the shape of a bound state.
A Find Quantised States run reports the confined charge separately, as its own two-dimensional sheet density beside the subband energies; see Quantised States. That is the physically meaningful occupancy of the well, and it is normally somewhat lower than the semiclassical density integrated over the same depth, because the lowest state a carrier can actually occupy sits above the band edge. The two are different quantities and are meant to be read as such.
Quantum feedback does not change which one appears here. With it on, the confined charge is allowed to shape the potential self-consistently, so the bands, and therefore these densities, shift; but the density shown is still the semiclassical one, now read from the corrected bands. The confined sheet density stays the separate quantised-states figure.
The Layer Transport tab is a table rather than a field list: see Sheet Resistance and Transport. Both Copy Report and Save Results… at the foot of the window are covered in Copying, Saving and Exporting.
