  Motivated by recent experimental work on magnetic properties of Si-MOSFETs,
we report a calculation of magnetisation and susceptibility of electrons in an
inversion layer, taking into account the co-ordinate dependence of electron
wave function in the direction perpendicular to the plane. It is assumed that
the inversion-layer carriers interact via a contact repulsive potential, which
is treated at a mean-field level, resulting in a self-consistent change of
profile of the wave functions. We find that the results differ significantly
from those obtained in the pure 2DEG case (where no provision is made for a
quantum motion in the transverse direction). Specifically, the critical value
of interaction needed to attain the ferromagnetic (Stoner) instability is
decreased and the Stoner criterion is therefore relaxed. This leads to an
increased susceptibility and ultimately to a ferromagnetic transition deep in
the high-density metallic regime. In the opposite limit of low carrier
densities, a phenomenological treatment of the in-plane correlation effects
suggests a ferromagnetic instability above the metal-insulator transition.
Results are discussed in the context of the available experimental data.
