  We present an open-system quantum-mechanical real-space study of the
conductive properties and size quantization in phosphorus $\delta$-layers
systems, interesting for their beyond-Moore and quantum computing applications.
Recently it has been demonstrated that an open-system quantum mechanical
treatment provides a much more accurate match to ARPES measurements in
highly-conductive, highly-confined systems than the traditional approaches
(i.e. periodic or Dirichlet boundary conditions) and, furthermore, it allows
accurate predictions of conductive properties of such systems from the first
principles. Here we reveal that quantization effects are strong for device
widths $W<10$~nm, and we show, for the first time, that the number of
propagating modes determines not only the conductivity, but the distinctive
spatial distribution of the current-carrying electron states. For $W>10$~nm,
the quantization effects practically vanish and the conductivity tends to the
infinitely-wide device's values.
