Electrical Engineering ⇒ Topic : Graded Semiconductor and Its Potential Variation

GRADED SEMICONDUCTOR AND ITS POTENTIAL VARIATION

Consider a semiconductor bar shown in Figure (a) in which hole concentration is not uniform. This type of semiconductor bar is called graded semiconductor. Two points P₁ and P₂ separated by a distance d have been considered. Let us calculate the potential difference V₂₁ between these points

                       Figure (a) Semiconductor bar.

Since net current is zero,

                                ............. (1)

where D_p is called diffusion constant for holes and its unit is m²/s. Diffusion and mobility are not independent of each other and in fact are related by the Einstein relation.

                                                                        ................ (2)

                                                                   ...............(3)

Using Eqs. (2) and (3), Eq. (3) can be obtained as:

                                 ............ (4)

Equation (4) can also be written as:

                                      ................(5)

Equation (5) is same as the Boltzmann relation in kinetic gas theory.

Let us consider a P-N junction diode as shown in Figure (b). Let the hole concentration at P₁ be NA and the electron concentration at P₂ be N_D. The hole concentration at P₂ is, therefore, n_i²/N_D.

                                  Figure (b) P-N junction diode.

From Eq. (4),

                          ............ (6)

Equation (6) gives the barrier potential of the diode and it is denoted by the symbol V₀.