Impurity diffusion vs redistribution in semiconductors

[setareh]

Hi,
Could any kine soul please explain this to me:

I know that diffusion is movement of impurities (dopants) into the semiconductor especially happening during heat cycles in fabrication process. but what is the dopant redistribution? Is it movement of impurities toward the surface?

Thanks in advance

 

[jsgruszynski]

The diffusion follows diffusion laws.

The diffusion equation says:

The rate of change of concentration in time is equal to the rate of change in physical space of the the product of diffusion coefficient and the rate of change of the concentration in physical space.

If your diffusion concentration doesn't change with physical location this reduces to:

The rate of change of concentration in time is equal to the diffusion coefficient times the rate of change of the rate of change of the concentration in space.

What this means is that movement will be toward physical locations of higher concentration to less concentration - just like most familiar cases of diffusion are probably understood intuitively. Solid state diffusion is really no different from fluid diffusion in a liquid or a gas only far slower and/or more temperature dependent.