  We describe and discuss the low-temperature resistivity (and the
temperature-dependent inelastic scattering rate) of several different doped 2D
semiconductor systems from the perspective of the Planckian hypothesis
asserting that $\hbar/\tau =k_\mathrm{B}T$ provides a scattering bound, where
$\tau$ is the appropriate relaxation time. The regime of transport considered
here is well-below the Bloch-Gruneisen regime so that phonon scattering is
negligible. The temperature-dependent part of the resistivity is almost
linear-in-$T$ down to arbitrarily low temperatures, with the linearity arising
from an interplay between screening and disorder, connected with carrier
scattering from impurity-induced Friedel oscillations. The temperature
dependence disappears if the Coulomb interaction between electrons is
suppressed. The temperature coefficient of the resistivity is enhanced at lower
densities, enabling a detailed study of the Planckian behavior both as a
function of the materials system and carrier density. Although the precise
Planckian bound never holds, we find somewhat surprisingly that the bound seems
to apply approximately with the scattering rate never exceeding $k_\mathrm{B}
T$ by more than an order of magnitude either in the experiment or in the
theory. In addition, we calculate the temperature-dependent electron-electron
inelastic scattering rate by obtaining the temperature-dependent self-energy
arising from Coulomb interaction, also finding it to obey the Planckian bound
within an order of magnitude at all densities and temperatures. We introduce
the concept of a generalized Planckian bound where $\hbar/\tau$ is bounded by
$\alpha k_\mathrm{B} T$ with $\alpha\sim 10$ or so in the super-Planckian
regime with the strict Planckian bound of $\alpha$=1 being a nongeneric
finetuned situation.
