  We study an Anderson impurity in a semiconducting host using the density
matrix renormalization group technique. We use the $U=0$ one--dimensional
Anderson Hamiltonian at half filling as the semiconducting host since it has a
hybridization gap. By varying the hybridization of the host, we can control the
size of the semiconducting gap. We consider chains with 25 sites and we place
the Anderson impurity (with $U>0$) in the middle of the chain. We dope the
half--filled system with one hole and we find two regimes: when the
hybridization of the impurity is small, the hole density and the spin are
localized near the impurity. When the hybridization of the impurity is large,
the hole and spin density are spread over the lattice. Additional holes avoid
the impurity and are extended throughout the lattice. Away from half--filling,
the semiconductor with an impurity is analogous to a double well potential with
a very high barrier. We also examine the chemical potential as a function of
electron filling, and we find that the impurity introduces midgap states when
the impurity hybridization is small.
