fitted to the distribution profile. (Initially, a three-parameter Gaussian fit similar to that used in Ref. was tested, but the Lorentzian gave a better fit to the curve.)

![Planar average of the donor-electron density as a function of $z$-position for the 1/4 ML doped, 80-layer cell calculated using the DZP basis set. The fitted Lorentzian function is also shown.[]{data-label="fig:d1dzprho"}](d1dzprho){width="0.8\linewidth"}

Table \[tab:ldosrho\] summarizes the maximum donor-electron density and the full width at half maximum (FWHM) for the 1/4 ML doped cells, each calculated from the Lorentzian fit. Both of these properties are remarkably consistent with respect to the number of layers, indicating that they have converged sufficiently even at 40 layers.

  -------- ------------------------- ------
   No. of    $\rho_{\textrm{max}}$    FWHM
   layers   ($\times 10^{-3}$ $e$/)    ()
     40               3.8             6.2
     60               3.9             6.2
     80               3.9             6.5
  -------- ------------------------- ------

  : Calculated maximum donor-electron density, $\rho_{\textrm{max}}$, and full width at half maximum, FWHM, as a function of the number of layers in the 1/4 ML doped cells. The DZP basis was used.[]{data-label="tab:ldosrho"}

Our results differ from a previous DFT calculation [@Carter11] which cited a FWHM of 5.6 for a 1/4 ML doped, 80-layer cell calculated using the SZP basis set (and 10$\times$10$\times$1 $k$-points). We note that 