Ficks First and Second Laws of Diffusion

After ion implantation, the defects are annealed at high temperatures, and diffusion of the implanted atoms occurs. Atoms will diffuse from regions of high concentration in a solid to regions of low concentration of atoms in units of 

The parameter X is commonly referred to as the characteristic diffusion length and it increases as (Dt)1/2. It signifies the extent of the diffusion. 

Consider a volume where the flux of atoms entering is different than the flux of atoms leaving. The change with time of the concentration of diffusing atoms in that volume is given by the gradient of the flux. This can be expressed as 

This is the so-called continuity equation or Fick s second law, where C, the concentration, is generally a function of position x and time t. For the case where D is constant, 

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Equation 1 applies to stationary states, and Equation 2 to nonsta-tionary states of diffusion. Equation 2 can be derived from Equation 1 by considering the rate of accumulation of diffusate at a given point in the medium it reduces to Equation 3 when the diffusion coeflBcient is a constant (9). If the latter condition is satisfied, the diffusion process is said to be ideal, or Fickian, and Equations 1 and 3 represent Ficks first and second laws of diffusion respectively. 

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