The most important factor for compound semiconductors such as the III–V and II–VI compounds is the deviation from the stoichiometric composition, because the deviation corresponds to imperfections in the crystals which cause large changes in characteristics. The specific vapor pressure at which the crystal becomes stoichiometric was determined in the cases of heat-treatment and of crystal growth using LPE and melt growth techniques. The temperature difference method under controlled vapor pressure (TDM-CVP) is the most suitable growth method which can control the deviation from the stoichiometric composition by applied vapor pressure, even without direct contact to the solid. The optimum vapor pressures to produce nearly perfect crystals with very low dislocation densities were found as a function of temperature and were on the same straight line. The most important point defect for GaAs at high arsenic vapor pressure was found to be As interstitial atoms which play a very important role in inducing many kinds of deep levels, not only by anti-site arsenic atoms. The use of liquid encapsulation at the rotating seed shaft rather than at the melt surface has been introduced for Czochralski pulling. Nearly perfect GaAs crystals with a diameter of 15 cm were grown with very brilliant surfaces. Deep levels, in concentrations as low as 10 15 cm -3, are decreased with the application of optimum vapor pressure, and somewhat reversed with an increase of the impurity concentration. The theory for the mechanism of vapor pressure control is described by the concept that the chemical potentials of As in the three phases, vapor liquid and solid, are set equal to each other.