Before revision: De is the diffusion coefficient or diffusivity is the concentration gradient of electrons there is a minus sign because the direction of difussion is opposite to that of the concentration gradient The diffusion coefficient for a charge carrier is related to its mobility by the Einstein relation: where: kB is the Boltzmann's constant T is the absolute temperature e is the electrical charge of an electron Now let's focus on the diffusive current in one-dimension along the x-axis: The electron current density Je is related to flux, F, by: Thus Similarly for holes: Notice that for electrons the diffusive current is in the same direction as the electron density gradient because the minus sign from the negative charge and Fick's Law cancel each other out.
After revision: De is the diffusion coefficient or diffusivity is the concentration gradient of electrons there is a minus sign because the direction of diffusion is opposite to that of the concentration gradient The diffusion coefficient for a charge carrier is related to its mobility by the Einstein relation: where: kB is the Boltzmann's constant T is the absolute temperature e is the electrical charge of an electron Now let's focus on the diffusive current in one-dimension along the x-axis: The electron current density Je is related to flux, F, by: Thus Similarly for holes: Notice that for electrons the diffusive current is in the same direction as the electron density gradient because the minus sign from the negative charge and Fick's Law cancel each other out.