A band-near-fill scan holds the band capacity fixed and varies the electron count across three rows, checking that the empty-slot count falls to the filled-band boundary row by row. The arithmetic is exact only for the stated band capacities, electron counts, fill fractions, and rows in the ideal band model. Real measurements add defects, disorder, interactions, temperature, finite crystal size, calibration/fit choices, finite precision, and measurement uncertainty.
Near-filled rows show the last empty slot boundary. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Two empty slots remain a partial band
The finite band has the same slot budget in every row. Only the electron count changes, so the empty-slot count decides the boundary.
slots=4⋅2=8,electrons=6,empty=2
One empty slot still remains partial
The finite band has the same slot budget in every row. Only the electron count changes, so the empty-slot count decides the boundary.
slots=4⋅2=8,electrons=7,empty=1
No empty slots makes the band filled
The finite band has the same slot budget in every row. Only the electron count changes, so the empty-slot count decides the boundary.