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In this paper, a new model of thermionic emission current for non-ideal Schottky contacts and a method of extracting electrical parameters are presented. The Au/n-GaAs Schottky structure is fabricated and simulated using Silvaco–Atlas software in a wide temperature range. The proposed method shows series resistance $$ R_{s} $$ values close to those obtained from ln(I)–V method and ideality factor n in good agreement with the reported experimental studies. The barrier height $$ \phi_{b} $$ extracted by our method is in good agreement with those extracted from the band diagram (BD) and capacitance–voltage (C–V) characteristics. It is increased with decreasing temperature, in accordance with the band gap variation with temperature and the reported negative temperature coefficient of the barrier height. Conversely, $$ \phi_{b} $$ obtained from the classical model using ln(I)–V method shows an abnormal behavior and discordance with the $$ \phi_{b} $$ extracted from the band diagram and C–V characteristics. Finally, the proposed model shows identical characteristics with the simulation and the experimental curves, in all temperature range, while the classic model shows large deviations at high bias voltages.