▎ 摘　　要

We report here a tight-binding theoretical study of the tunneling conductance and temperature dependent specific heat of graphene-on-substrate. The Hamiltonian consists of the electron hoppings up to third nearest neighbors in the presence of doping and on-site Coulomb interactions at two sub-lattices of honey-comb lattice. The total Hamiltonian is solved by Zubarev Green's functions technique. Then, the sub-lattice magnetizations, tunneling conductance, and specific heat are calculated from the Green's functions and are computed numerically. The effect of impurity, substrate induced gap, and repulsive Coulomb potential on tunneling conductance is discussed. The anomaly in specific heat at low temperatures is described.