A simple expression for impurity distribution after multiple diffusion processes

There are several diffusion processes with different temperatures in modern semiconductor technology. The impurity distribution after these diffusion processes is analyzed and a simple expression for describing the distribution is given. It is found that the impurity distribution after multiple diffusion processes can be characterized with an effective diffusion length. The relation between this effective diffusion length and the diffusion lengths of each diffusion process is given and shows itself to be very simple and instructive. The results of the expression agree well with numerical simulations by using SUPREM IV. An example of the application of the expression is also shown. (semiconductor physics)