  The scattering of conduction electrons off neutral donors depends sensitively
on the relative orientation of their spin states. We present a theory of
spin-dependent scattering in the two dimensional electron gas (2DEG) of field
effect transistors. Our theory shows that the scattering mechanism is dominated
by virtual transitions to negatively ionized donor levels. This effect
translates into a source-drain current that always gets reduced when donor
spins are at resonance with a strong microwave field. We propose a model for
donor impurities interacting with conduction electrons in a silicon transistor,
and compare our explicit numerical calculations to electrically detected
magnetic resonance (EDMR) experiments. Remarkably, we show that EDMR is optimal
for donors placed into a sweet spot located at a narrow depth window quite far
from the 2DEG interface. This allows significant optimization of spin signal
intensity for the minimal number of donors placed into the sweet spot, enabling
the development of single spin readout devices. Our theory reveals an
interesting dependence on conduction electron spin polarization p_c. As p_c
increases upon spin injection, the EDMR amplitude first increases as p_{c}^{2},
and then saturates when a polarization threshold p_T is reached. These results
show that it is possible to use EDMR as an in-situ probe of carrier spin
polarization in silicon and other materials with weak spin-orbit coupling.
