  We present an open-system quantum-mechanical 3D real-space study of the
conduction band structure and conductive properties of two semiconductor
systems, interesting for their beyond-Moore and quantum computing applications:
phosphorus $\delta$-layers in silicon and the corresponding $\delta$-layer
tunnel junctions. In order to evaluate size quantization effects on the
conductivity, we consider two principal cases: nanoscale finite-width
structures, used in transistors, and infinitely-wide structures, electrical
properties of which are typically known experimentally. For devices widths
$W<10$~nm, quantization effects are strong and it is shown 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 values. For tunnel junctions, two distinct conductivity
regimes are predicted due to the strong conduction band quantization.
