Mesh Spacing

Running

One setting, below the buttons beside the layer table: how finely the structure is divided before it is solved. It is the main accuracy control you have, and it costs far less than you would expect.

01The choice

Mesh spacing offers 0.05, 0.1, 0.25, 0.5, 1.0, 2.0 and 4.0 nm, and starts at 0.5 nm. The grid is uniform — the spacing you pick applies across the whole structure, thin layers and thick alike.

The bound-state calculation does not use it. That runs on its own, usually finer grid, set in the Schrodinger conditions panel and described in Quantised States.

02What it costs

Solving time is proportional to the number of nodes, so halving the spacing doubles it. Doubling a small number leaves a small number. A 3 µm structure, right across the range:

4.0  nm       766 nodes    0.01 s
1.0  nm     3 061 nodes    0.01 s
0.5  nm     6 121 nodes    0.02 s
0.1  nm    30 601 nodes    0.11 s
0.05 nm    61 201 nodes    0.22 s

Refining is rarely what costs you. Unless the structure is many microns thick, or you are running a sweep over many bias points, treat the mesh as cheap and choose it for accuracy rather than speed.

03Keep layer boundaries on nodes

Pick a spacing that divides your layer thicknesses. An interface that falls between two nodes is effectively moved to the nearest one, and at a large band step that position error becomes an energy error exactly where the interesting physics is.

At 0.5 nm anything specified in whole or half nanometres lands cleanly, which is much of why it is the default. The failure is easy to miss: the same 110 nm stack solved at 4 nm puts no layer boundary on a node at all, and returns a sheet density about 6 per cent low without anything looking wrong.

04Nominally identical layers

A node that lands exactly on a layer boundary has to be assigned to one layer or the other, and it goes to the layer on its substrate side. Two layers of the same thickness can therefore end up with a one-node difference between them, so a structure you built to be symmetric comes out slightly asymmetric.

It is a one-node effect, so it shrinks in proportion to the spacing. A symmetric n-GaAs / AlGaAs / n-GaAs stack at 300 K, comparing the sheet density of the two outer layers:

2.0  nm    +2.04 %
1.0  nm    +1.01 %
0.5  nm    +0.50 %
0.25 nm    +0.25 %
0.1  nm    +0.10 %
0.05 nm    +0.05 %

Halving the mesh halves the discrepancy, all the way down. If two layers you expect to be identical come out differing by a fraction of a per cent, refine the mesh before looking for a physical explanation — there almost certainly is not one.