  We theoretically investigate silicon doped bilayer graphene, Si-BLG, with
different stoichiometry of Si-BLG structures. The dangling bonds of C-Si atoms
are found at low concentration ratio of Si atoms inducing sp$^3$-hybridization
of buckled pattern in the structure. The Si-BLG with dangling bonds revel
strong mechanical response at low strain of a uniaxial load, and the fracture
strain is seen at low strain ratio. The sp$^3$-hybridization forms a small
bandgap which induces an intermediate thermal and optical response of the
system. In contrast, at higher Si concentration ratio, the Young modulus and
fracture strain are increased comparing to the low Si concentration ratio. This
is due to presence of high number of C-Si bonds which have a high tolerant
under uniaxial load. In addition, a relatively larger bandgap or an overlap
between valence and conduction bands are found depending on the Si
configurations. In the presence of gaped Si-BLG, the thermal and optical
response are high. We thus obtain a high Seebeck coefficient and a figure of
merit with low electronic thermal conductivity which are useful for
thermoelectric nanodevices, and an enhancement of optical response is acquired
with a redshift in the visible range.
