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The effect of hydrostatic tensile stress on the band structures of silicon have been theoretically investigated based on the first-principles calculation. The calculations demonstrate that the electron effective mass for stressed structure becomes 3.71% smaller than that for unstressed, whereas the band gap for stressed structure is 4.96% larger than unstressed one. At last, the impact of these changes on band-to-band tunneling leakage current in silicon-on-insulator MOSFET was calculated. And the calculated result shows that the tunneling leakage current decreases due to these changes.