  We consider quasi-two-dimensional gas of electrons in a typical Si-MOSFET,
assuming repulsive contact interaction between electrons. Magnetisation and
susceptibility are evaluated within the mean-field approach. Finite thickness
of the inversion layer results in an interaction-induced electron wave function
change, not found in both purely two-dimensional and three-dimensional (bulk)
cases. Taking this self-consistent change into account leads to an increased
susceptibility and ultimately to a ferromagnetic transition deep in the
high-density metallic regime. We further find that in the paramagnetic state,
magnetisation increases sublinearly with increasing in-plane magnetic field. In
the opposite limit of low carrier densities, the effects of long-range
interaction become important and can be included phenomenologically via
bandwidth renormalisation. Our treatment then suggests that with decreasing
density, the metal-insulator transition is preceded by a ferromagnetic
instability. Results are discussed in the context of the available experimental
data, and arguments for the validity of our mean-field scheme are presented.
