We focus in this review on the theoretical description of the probability of electron transmission at metal/semiconductor at the interface depending on the quantum theory and density functional theory .Electronic devices technology largely rely on metal/ semiconductor system interfaces, whose most important coefficient parameters for the probability of electron transmission such that :reorientation free energy , potential barrier height ( ),work function ,affinity of semiconductor ,coupling coefficient matrix element, concentration of electron ,volume of unit cell for semiconductor ,petration factor , and temperature T(K) . The probability of electron transport rate constant in Au/ Ge ,and Au/Si interface system has been calculated and the transmission through interface is examined .A Mat lab program has been used to calculate the rate constant of electron transfer and all parameters of transmission by solvingthe suitable formulas .Our results data show that the probability of the rate constant for electron transfer increases with the increasing of the coupling coefficient and temperature, and decreasing of the reorganization energy