Study On The Optimization Analysis Of The Modified Drude Model Based On The Effective Mass Of Free Electrons And Its Application

The optical properties of the material can be uniquely identified and expressioned by the complex dielectric parameters. The dielectric parameters is one of the key factors which influences the transmission performance of the surface plasma wave in the micron or nanometer devices. therefore, this paper focuses on the dielectric parameters of precious metals. The dielectric parameters of the material is decided by the polarization which this material produced by the outer electric field, and it closely relations with the wavelength. the previous related experimental measuring results show that as the change of working wavelength, can present a wide range of metal complex dielectric parameters changes. The Drude model based on the ideal electron gas model expresses the relationship very well, but the complex relationship of the free electrons and that between electrons and ions in the solid, is simplified too simple by this model. There is a large gap between the calculation results and the experimental data in the infrared and visible light area.We modified the traditional Drude model based on the electron effective mass, considering the factors that the other electrons makes with the free electrons moving in the metal, then made an optimized analysis between the experimental results and theory value by using the least square error analysis in this paper. we get the optimized effective plasma frequency and effective electronic relaxation time for the noble metals. Tt the curve of the dielectric parameters get by the modified Drude model can well curve fitting to the experimental results in the200nm-2000nm wave range; The electron effective mass that get by the ratio of the optimized effective plasma frequency and the plasma frequency defined base on the electron static mass, agree well to the related professional literature that have been published, too. So we know that we must consider the function of the electron effective mass in the traditional Drude model, only this can we make the theoretical calculation results get by the model and the experimental results consistent. In addition, only using simple mathematical calculation, we get almost the same results which get by quantum mechanics, So we provide a new idea and method to get the electron effective mass in the solid state physics, then we get deepenly physical understanding of surface plasma wave. Using this method, we expand the working wavelengths to larger scope, then obtain the optimized effective plasma frequency and effective electronic relaxation time, The curve of the calculation result can also be able to fit well the experimental curve, then we furtherly confirmed the scientific rationality of this method.In the end, we put forward the minimal relative square error analysis, using the same steps we modify the traditional Drude model, then by comparing with the foregoing method, we found its application value too.