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The main purpose of this paper is mathematical analysis on time-periodicflows of electrons and holes in semiconductors. The flows appear in a situationthat alternating-current voltages are applied to devices. In this paper, westudy the drift-diffusion model for semiconductors in a three-dimensionalbounded domain and investigate the existence and stability of time-periodicsolutions. We first derive the uniform-in-time estimate of time-globalsolutions, and then prove by the relative entropy method that the difference ofany two solutions decays exponentially fast as time tends to infinity. Thesefacts enable us to show the unique existence and global stability oftime-periodic solution.

Time-periodic flows of electrons and holes in semiconductor devices