The Diffusion process in Semiconductors

Diffusion is defined as a process of movement of charges from high density or concentration to low density or concentration. And there is nothing wrong in that definition per se. It’s just incomplete. There is one more reason for Diffusion of charges apart from density gradience.

Where does the energy for movement of charges come from? Unlike Drift current, density gradient does not create a field so, energy is not coming from the potential difference. Then, what is the source of energy for all that work done?

The source of energy is common and it’s Thermal Energy. We all know that at room temperature Atoms vibrate and move in a random direction. This is common in every material. In fact, this random movement of atoms at room temperature is the reason why sugar cubes in the milk will dissolve without stirring. And this random movement of atoms is the reason why we see all that bumps-and-jumps in the boiling milk. Atoms get agitated only above 0 degrees Kelvin, as that is when they get extra energy from heat.

Thus, for Diffusion to happen we need two things.
1. A density gradient.
And temperature of at least higher than 0 degrees Kelvin.

In Diffusion, atoms are moving to nowhere; they are just trying to release out the energy they have gain from outside temperature. If temperature around atoms rises above 0 degrees Kelvin, they become agitated because of energy gain and try to release out that by vibrating. When the concentration is higher they will vibrate and collide with each other; shove the neighbours away; thus creating a charge movement(Diffusion). Once concentration becomes low enough where they can comfortably vibrate without colliding, the Diffusion ceases.

The dependence of Diffusion on temperature can be confirmed from the formula of Diffusion Constant(D):

  D = Mobility of charge carrier  *  Thermal Voltage

As we can see Diffusion Constant of a material depends on Thermal Voltage, it means Diffusion depends on the temperature of surrounding and as temperature increases, Diffusion Constant of material will also change. We can see that Diffusion Constant is not so constant and changes with temperature.

well, does that mean Diodes and BJT Transistors will fail to work at 0 Kelvin?
Yes, certainly. Both diodes and BJTs need difusion-current for their working (Base-Current is diffusion-current). It can be confirmed from the nature of current equation of Diode; it’s exponential. And this exponential nature comes from the dependence on diffusion. Current due to fields are linear if the field is constant.

Diffusion is not only due to density gradience but also because inherently, atoms of material move in the random direction at a temperature higher than 0 degrees Kelvin. As a result, the Work Done by charge carriers in contributing Diffusion Current is just a transformation of thermal energy into electrical current.




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