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.Two-dimensional (2D) monolayer structures have been an active field of research due to their electronic, optical, and thermal properties. Graphene is a planar atomic layer of carbon atoms which they are arranged in a honeycomb lattice with 1.42 A° interatomic distance between two adjacent C atoms. Graphene has been an active field of research due to its important physical properties such as electronic structure with gapless properties, room temperature quantum Hall effects 1 and high intrinsic mobility 2 .In the graphene, the existence of a zero gap is due to the crossing between the valence and conduction bands at the K point (Dirac point). Near the K point, graphene exhibits linear energy dispersion in terms of momentum and its charge carriers behave as relativistic massless Dirac fermions described by a Dirac-like equation 3 . Note that, Materials with a zero band gap energy exhibit some fascinating and superior electronic properties compared to materials with a non-zero energy gap and they have intriguing physical properties and numerous potential practical applications in spintronics, electronics, optics and sensors 4 . The Dirac Spin-gapless semiconductors, have high carrier mobility and due to their real massless fermions and dissipation-less transport properties, they are regarded as promising candidates for applications in ultra-fast and ultra-low-power spintronic devices 5,6 .Several studies on electronic and optical properties of monolayer graphene have been reported via Density functional Theory (DFT) and Tight binding Theory (TB) 7-11 . Due to the zero band gap in graphene, the light absorption occurs in a wide range of spectra from infrared (IR) to ultraviolet which lead to the use of graphene in electro-optical devices. Using the first nearest neigh...

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