$a$ is the simple cubic lattice constant of bulk silicon. The phosphorus layers had to be separated by a considerable amount of silicon due to the large Bohr radius of the hydrogen-like orbital introduced by P in Si ($\sim$2.5 nm). Ref. showed that this far exceeded the sub-nanometer cell side length. If desired, cells with a lower in-plane density of dopants may be constructed, by lengthening the cell in the $x$- and $y$-directions, such that more Si atoms occupy the doped monolayer in the cell.

![$\left(001\right)$ planar slice of the $c\left(2\times2\right)$ structure, at the 1/4 ML doped monolayer. One of the Si sites has been replaced by a P atom (shown in dark gray). The periodic boundaries are shown in black.[]{data-label="fig:c22schematic"}](c22){width="0.6\linewidth"}

A collection of tetragonal cells comprised of 4, 8, 16, 32, 40, 60, 80, 120, 160 and 200 monolayers were constructed, having four atomic sites per monolayer and oriented with faces in the $[110]$, $[\bar{1}10]$ and $[001]$ directions (see Fig. \[fig:diagram\_P\_layer\_pbc\]). Cells used in PW calculations began at 4 layers and ran to 80 layers; larger cells were not computationally tractable with this method. SZP and DZP models began at 40 layers to overlap with PW for the converging 