Question

Silicon Cube, side length 3 cm. A dc voltage through it of 1v creates a current of 8mA. Assume electron mobility dominates current, mobility 1300 cm^2/Vs. Si bandgap of 1.1eV and 300k if you need it.

What's the concentration of free electrons and their drift velocity?

Answer 1

The magnitude of the electric field,

Here V=1V and d= side length of the cube = 3cm.

Hence

Hence, the magnitude of drift velocity is

Here, = the mobility of the electrons = 1300 cm^2/Vs.

Hence

The current density has a magnitude

Here, I = 8 mA.

Now, we know that , where n is the concentration of free electrons and e is the electronic charge.

Hence