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Low-temperature magneto-photoluminescence is a very powerful technique to characterize high purity GaAs and InP grown by various epitaxial techniques. These III-V compound semiconductor materials are used in a wide variety of electronic, optoelectronic and microwave devices. The large binding energy differences of acceptors in GaAs and InP make possible the identification of those impurities by low-temperature photoluminescence without the use of any magnetic field. However, the sensitivity and resolution provided by this technique rema1ns inadequate to resolve the minute binding energy differences of donors in GaAs and InP. To achieve higher sensitivity and resolution needed for the identification of donors, a magneto-photoluminescence system 1s installed along with a tunable dye laser, which provides resonant excitation. Donors 1n high purity GaAs are identified from the magnetic splittings of "two-electron" satellites of donor bound exciton transitions 1n a high magnetic field and at liquid helium temperature. This technique 1s successfully used to identify donors 1n n-type GaAs as well as 1n p-type GaAs in which donors cannot be identified by any other technique. The technique is also employed to identify donors in high purity InP. The amphoteric incorporation of Si and Ge impurities as donors and acceptors in (100), (311)A and (3ll)B GaAs grown by molecular beam epitaxy is studied spectroscopically. The hydrogen passivation of C acceptors in high purity GaAs grown by molecular beam epitaxy (MBE) and metalorganic chemical vapor deposition (MOCVD) 1s investigated using photoluminescence. Si acceptors ~n MBE GaAs are also found to be passivated by hydrogenation. The instabilities in the passivation of acceptor impurities are observed for the exposure of those samples to light. Very high purity MOCVD InP samples with extremely high mobility are characterized by both electrical and optical techniques. It is determined that C is not typically incorporated as a residual acceptor ~n high purity MOCVD InP. Finally, GaAs on Si, single quantum well, and multiple quantum well heterostructures, which are fabricated from III-V semiconductors, are also measured by low-temperature photoluminescence.