The mechanism of the optical transition without phonons between the conduction band and the valence band in doped SiGe alloy is investigated, and the model of no phonon optical transition originated from the statistical distribution of the impurities is suggested. The dipole matrix elements of the transition are calculated based on this model and the upper limits of the dipole matrix elements are calculated. The mechanism of no phonon optical transition in undoped SiGe alloy is also suggested that it is the collectivity action of the deformation wavefunction around Ge atoms.