  We investigate theoretically 2D electronic transport in Si:P $\delta$-doped
layers limited by charged-dopant scattering. Since the carrier density is
approximately equal to the dopant impurity density, the density dependent
transport shows qualitatively different behavior from that of the well-studied
2D Si-MOSFETs where the carrier density is independent of the impurity density.
We find that the density dependent mobility of the Si:P system shows
non-monotonic behavior which is exactly opposite of the non-monotonicity
observed in Si-MOSFETs --- in the Si:P system the mobility first decreases with
increasing density and then it increases slowly with increasing density above a
typical density $10^{14}$ cm$^{-2}$ (in contrast to Si MOSFETs where the
mobility typically increases with density first and then slowly decreases at
high density as surface roughness scattering dominates). In the low density
limit (or strong screening limit) mobility decreases inversely with increasing
density, but in the high density limit (or weak screening limit) it slowly
increases due to the finite width effects of the 2D layer. In the intermediate
density regime ($1/a < 2 k_F < q_{TF}$, where $a$, $k_F$, and $q_{TF}$ are the
confinement width of the $\delta$-layer, Fermi wave vector, and Thomas-Fermi
screening wave vector, respectively) the density dependent mobility is
approximately a constant at the minimum value. However, the calculated mean
free path increase monotonically with density. We also compare the transport
scattering time relevant to the mobility and the single particle relaxation
time relevant the quantum level broadening, finding that the transport
scattering time could be much larger than the single-particle scattering time
unlike in Si MOSFETs where they are approximately equal.
