  In contrast to semiconductors doped with transition metal magnetic elements,
which become ferromagnetic at temperatures below ~ 100K, semiconductors doped
with non-magnetic ions (e.g. silicon doped with phosphorous) have not shown
evidence of ferromagnetism down to millikelvin temperatures. This is despite
the fact that for low densities the system is expected to be well modeled by
the Hubbard model, which is predicted to have a ferromagnetic ground state at
T=0 on 2- or 3-dimensional bipartite lattices in the limit of strong
correlation near half-filling. We examine the impurity band formed by
hydrogenic centers in semiconductors at low densities, and show that it is
described by a generalized Hubbard model which has, in addition to strong
electron-electron interaction and disorder, an intrinsic electron-hole
asymmetry. With the help of mean field methods as well as exact diagonalization
of clusters around half filling, we can establish the existence of a
ferromagnetic ground state, at least on the nanoscale, which is more robust
than that found in the standard Hubbard model. This ferromagnetism is most
clearly seen in a regime inaccessible to bulk systems, but attainable in
quantum dots and 2D heterostructures. We present extensive numerical results
for small systems that demonstrate the occurrence of high-spin ground states in
both periodic and positionally disordered 2D systems. We consider how
properties of real doped semiconductors, such as positional disorder and
electron-hole asymmetry, affect the ground state spin of small 2D systems. We
also discuss the relationship between this work and diluted magnetic
semiconductors, such as Ga_(1-x)Mn_(x)As, which though disordered, show
ferromagnetism at relatively high temperatures.
