  A theoretical study of the band gap reduction under tensile stress is
performed and validated through experimental measurements. First-principles
calculations based on density functional theory (DFT) are performed for
uniaxial stress applied in the [001], [110] and [111] directions. The
calculated band gap reductions are equal to 126, 240 and 100 meV at 2$\%$
strain, respectively. Photoluminescence spectroscopy experiments are performed
by deformation applied in the [110] direction. Microfabricated specimens have
been deformed using an on-chip tensile technique up to ~1$\%$ as confirmed by
back-scattering Raman spectroscopy. A fitting correction based on the band gap
fluctuation model has been used to eliminate the specimen interference signal
and retrieve reliable values. Very good agreement is observed between
first-principles theory and experimental results with a band gap reduction of,
respectively, 93 and 91 meV when the silicon beam is deformed by 0.95$\%$ along
the [110] direction.
