Jumping of impurities in Silicon is-

1. Thermally activated (temperature dependent)
2. Random
3. Direction of motion occurs by diffusion in the presence of concentration gradient

The simplest description of diffusion is given by Fick's laws, which were developed by Adolf Fick in the 19th century.

The first law states that the molar flux due to diffusion is proportional to the concentration gradient.

$J=-D \frac{dN}{dx}$

where $\text{J = flux density} \bigg(\frac{atoms}{cm^2}\bigg) \\ \text{D = Diffusion coefficient} \bigg(\frac{cm^2}{s}\bigg) \\ \text{N = volume concentration} \bigg(\frac{atoms}{cm^3}\bigg) \\ \text{x = distance (cm)}$

The negative sign indicates that the diffusion is down the concentration gradient.