  We consider spin-lattice relaxation processes for electrons trapped in
lateral Si quantum dots in a $[001]$ inversion layer. Such dots are
characterized by strong confinement in the direction perpendicular to the
surface and much weaker confinement in the lateral direction. The spin
relaxation is assumed to be due to the modulation of electron $g$-factor by the
phonon-induced strain, as was shown previously for the shallow donors. The
results clearly indicate that the specific valley structure of the ground
electron state in Si quantum dots causes strong anisotropy for both the
one-phonon and two-phonon spin relaxation rates. In addition, it gives rise to
a partial suppression of the two-phonon relaxation in comparison to the spin
relaxation of donor electrons.
