where *'E*_{a}' is the activation energy measured in 'eV' of the dopant or impurity being diffused and *'D*_{0}' is the diffusion coefficient extrapolated to infinite temperature. The activation energy is dependent on both the element being diffused and the specific semiconductor that it is being diffused into.
Fick's second law or the continuity equation can be solved for a variety of different initial and boundary conditions. Each solution represents a different diffusion profile. Two of the most common profiles are available as part of this calculator.

**Constant-Surface-Concentration Diffusion**

The initial condition for this profile is a dopant concentration of zero inside the semiconductor substrate. For this profile the dopant concentration at the surface of the semiconductor remains constant, and the concentration eventually goes to zero at some point in the semiconductor. These conditions can be summarized mathematically as

This profile is a Gaussian distribution and is the other diffusion profile supported by this calculator and graph.
**Extrinsic vs. Intrinsic Diffusion**

The profiles calculated here are based on intrinsic diffusion. Intrinsic diffusion is represented by constant diffusivities, and doping concentrations being less than then intrinsic-carrier concentration at the diffusion temperature. The intrinsic-carrier concentration for silicon at 1000°C is 5 X 10^{18} cm^{-3} and 5 X 10^{17} cm^{-3} for gallium arsenide. If the dopant-impurity concentration exceeds the intrinsic-carrier concentration at the diffusion temperature, then the diffusion becomes extrinsic, and the profiles become more complicated. **This calculator does not verify whether the diffusion conditions inputted meet the constraint of intrinsic diffusion. It is assumed the user is knowledgeable as to whether or not the conditions meet the intrinsic diffusion requirement. This calculator is entirely theoretical and predicts the diffusion profiles mathematically; however, some diffusion profiles may not be experimentally possible depending on the impurity, the semiconductor, and other diffusion parameters such as temperature.**

**References**

H.C. Casey, and G.L. Pearson, "Diffusion in Semiconductors," in J.H. Crawford, and L.M. Slifkin, Eds.,*Point Defects in Solids,* Vol. 2, Plenum, New York, 1975.

S.M. Sze, *Semiconductor Devices: Physics and Technology,* 2^{nd} Ed., Wiley, New York, 2002.