The n₀ p₀ Product

We may take the product of the general expressions for n₀ and p₀, respectively. The result is

(1)

which may be written as

(2)

As Equation (2) was derived for a general value of Fermi energy, the values of n₀ and p₀ are not necessarily equal. However, Equation (2) is exactly, which we derived for the case of an intrinsic semiconductor. We then have that, for the semiconductor in thermal equilibrium

(3)

Equation (3) states that the product of no and p₀ is always a constant for a given semiconductor material at a given temperature. Although this equation seems very simple, it is one of the fundamental principles of semiconductors in thermal equilibrium. The significance of this relation will become more apparent in the chapters that follow. It is important to keep in mind that Equation (3) was derived using the Boltzmann approximation. If the Boltzmann approximation is not valid, then likewise, Equation (3) is not valid.

An extrinsic semiconductor in thermal equilibrium does not, strictly speaking, contain an intrinsic carrier concentration, although some thermally generated carriers are present. The intrinsic electron and hole carrier concentrations are modified by the donor or acceptor impurities. However, we may think of the intrinsic concentration n_i in Equation (3) simply as a parameter of the semiconductor material.