  Silicon is a leading candidate material for spin-based devices, and
two-dimensional electron gases (2DEGs) formed in silicon heterostructures have
been proposed for both spin transport and quantum dot quantum computing
applications. The key parameter for these applications is the spin relaxation
time. Here we apply the theory of D'yakonov and Perel' (DP) to calculate the
electron spin resonance linewidth of a silicon 2DEG due to structural inversion
asymmetry for arbitrary static magnetic field direction at low temperatures. We
estimate the Rashba spin-orbit coupling coefficient in silicon quantum wells
and find the $T_{1}$ and $T_{2}$ times of the spins from this mechanism as a
function of momentum scattering time, magnetic field, and device-specific
parameters. We obtain agreement with existing data for the angular dependence
of the relaxation times and show that the magnitudes are consistent with the DP
mechanism. We suggest how to increase the relaxation times by appropriate
device design.
