Electrical and dielectric properties of Au/n-Si metal-semiconductor structures with high dielectric have been examined by capacitance/conductance-voltage (C/G-V) measurements in the frequency range of 5-500 kHz at room temperature. Voltage-dependent profiles of interface states (N-ss) and resistance (R-i) were extracted from the C and G data using the low-high-frequency capacitance and Nicollian-Brews methods, respectively. The real and imaginary components of the complex dielectric constant (epsilon', epsilon ''), electric modulus (M' and M ''), and ac conductivity (sigma(ac)) were calculated from the C and G data. All parameters have a strong relation with frequency and voltage, especially at low frequencies due to Maxwell-Wagner relaxation and N-ss. The observed peaks in the N-ss-V and R-i-V plots can be ascribed by the special distribution of N-ss at M/S interface. These results confirmed that [2% graphene cobalt-doped (Ca3CO4Ga0.001Ox] interlayer has high-dielectric constant and can be used an interlayer instead of the traditional SiO2 at M/S interface to increase their capacitance or more charges/energy storage and reduce both the values of N-ss and series resistance (R-s). The values of a are almost constant at lower-intermediate frequencies, but they start to increase at high frequencies that are corresponding to the dc and ac conductivity, respectively.