The diffusion constant for holes in silicon is 13 cm²/s. What is the diffusion current if the gradient of the hole concentration \(\frac{dP}{dX} = -2 \times 10^{14}\) holes per cm³ per cm?

Concept:

Diffusion

1) Diffusion is a natural phenomenon.

2) The migration of charge carriers from higher concentration to lower concentration or from higher density to lower density is called diffusion.

3) Diffusion is mainly due to the concentration gradient and is always negative.

It is given by:

\(\frac{dp}{dx}\) for holes and

\(\frac{dn}{dx}\) for electrons.

Diffusion current is calculated by:

\(I=-qD_p\frac{dp}{dx}\) -----(1)

where,

D_p is hole diffusion constant in cm²/sec

and q is charge in Coulomb.

Calculation:

Given:

D_p = 13 cm²/s

\(\frac{dp}{dx}=-2 × 10^{14} holes/cm^3\)

From Equation (1):

I_D = -1.6 × 10^-19 × 13 × (-2 × 10¹⁴)

I_D = 0.416 mA.