Quantised States

Reading results

Solves the Schrödinger equation across a chosen depth window to find the confined bound states in a well or channel, their energies, and the sheet density they hold.

01Turning it on

Tick Find quantised states in the Schrodinger conditions box. The bound states are solved after the Poisson solution, in the depth range you set:

• Start Depth and Stop Depth — the depth window, in nanometres, to solve within. Bracket the well or channel; you do not need to solve the whole structure, and a tight window keeps the states clean.
• Schrodinger Mesh, with a unit selector reading Angstroms or Nanometers — the grid spacing used inside that window, often finer than the Poisson mesh needs to be.
• Use Γ states — solves the electron levels on the Γ conduction-band profile. Useful for optically active Γ-like states in AlGaAs, including indirect-gap compositions.
• Quantum feedback — iterates the Poisson solution self-consistently with the bound-state charge from this region. Use it for equilibrium quantum wells and 2DEGs. It is described in section 3.

02The Schrödinger Region window

A separate Schrödinger Region window opens alongside the results. A summary line across the top gives the depth range and point count, the number of channels, the states found per channel with each channel’s barrier height, the sheet density, the temperature and any warnings.

Below it, a plot and a table share the window:

• The plot shows the band profile through the region with each bound level drawn as a horizontal mark at its energy. Show |ψ|² state envelopes overlays the probability density of each state, and Separate channel panels gives the electrons and holes their own stacked panels rather than one shared axis.
• The table, States and sheet density, has one row per level with columns Channel, Level, Confinement energy (eV), Absolute energy (eV) and Sheet density (cm⁻²). The channels are Electron, Heavy hole and Light hole, listed only where states exist.

The two energies answer different questions, as the note under the table says: confinement energy is measured up from the band edge (how deeply the state is bound), while absolute energy is on the same scale as the band diagram, referenced to the bulk Fermi level at zero. Under a two-terminal contact bias the occupation is not computed, so the last column becomes Occupation and reads omitted.

03Quantum feedback

Without feedback, the states are solved once on the finished Poisson potential — they read the bands but do not change them. With Quantum feedback on, the confined charge is fed back into Poisson and the two are iterated until they agree, so the potential reflects the real, quantised charge distribution rather than the semiclassical one. The summary line then reports whether the feedback loop converged and in how many iterations. It is meant for equilibrium wells and 2DEGs, and is ignored in contact-bias transport mode.