In this paper, we present a tight-binding model based on DFT calculations for investigation the electronic and optical properties of monolayer Germanene. The thermal properties are investigated using Green function method. The required tight binding parameters including the onsite energies and third nearest neighbors hopping and overlap integrals are obtained based on our DFT calculations. Germanene is a semiconductor with zero band gap and linear band dispersion around the K point. The band gap opening occurs in the presence of bias voltage. The band gap is increased linearly with increase of the bias voltage strength. The tight binding results for position of the two first peaks in the optical Infrared region is same with the DFT results. By applying and increasing bias voltage, the dielectric function shows the blue shift by reduction the peak intensity in the energy range E < 1 eV. The thermal conductivity and heat capacity increase with increasing the temperature due to the increasing of thermal energy of charge carriers and excitation them to the conduction bands. The thermal properties of Germanene in the absence of bias U = 0 is larger than that U ≠ 0 and they decrease by further bias strength increasing, due to the increasing band gap with bias.
