The dielectric response function of semiconductors is derived for an isotropic model characterized by an effective Fermi energy, EF, corresponding to a mean valence electron density, and an energy gap of width Eg. The response to the fields set up by impurity atoms and by moving charged particles is investigated. The screening of impurities changes with the energy gap: as Eg increases from zero, the potential expands in range and approaches the bare Coulomb potential, while the Friedel oscillations in the induced electron density about the impurity are suppressed. The contribution of electronic excitations from the valence band of semiconductors to their stopping power for swift heavy particles is calculated.