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The theory of the coherent excitation of optical phonons in polar semiconductors is developed by use of the Boltzmann equations in which the collective behavior of carriers is taken into account. The linearized theory gives the critical condition for which the coherent emission of optical phonons exceeds the total damping of the system. Current and phonon wave-amplitude saturations due to non-linear effects are discussed by applying a quasi-linear theory. In a sample of finite size, phonon waves reflected at the boundary give rise to a further decrease of current by the acoustoelectric effect, resulting in a negative resistance. Such a negative resistance generates a current instability having its frequency determined by the transit time across the sample. Finally, the critical conditions of phonon wave growth are examined for GaAs and InAs.