We show from theoretical calculations that three-dimensional photonic crystals constructed with close-packed air spheres in a semiconductor matrix can exhibit a complete photonic band gap (CPBG) in the near-infrared range. The CPBG is easily tunable by using the free-carrier density dependence of plasma frequencies of semiconductors. The frequency of the defect mode created by inserting a slab of semiconductor into inverted opals is also found to be tunable by changing the density of free carriers of the semiconductor.