Abstract
In amorphous semiconductors and insulators, the using conductivity formulas are semi-empirical and have no satisfying physical explanations. A conductivity equation has been derived by Debye for the response of ideal materials which is rarely observed in practice, but a general conductivity equation which includes the previous empirical equations via a correct choice of arbitrary parameters and moreover totally theoretical derivation had to be generated. Hence, to determine the motion of electrons in the amorphous environment, we defined the equation of motion including viscous forces as a function of coordinates, their derivatives and time variables. We developed a fractional form of this equation over these three variables and finally obtained the most generalized equation of motion, which counts the overall interactions by a fractional form as a variation of two variable. The improved formula, called the stretched Havriliak–Negami equation, has the same form and behavior as the semi-empirical equation and reducible to the Cole–Cole and Cole–Davidson-type of conductivity.