Population Inversion at a Junction:
- If a p-n junction is formed between degenerate materials, the bands under forward bias appear as shown in Fig.
- If the bias (and thus the current) is large enough, electrons and holes are injected into and across the transition region in considerable concentrations.
- As a result, the region about the junction is far from being depleted of carriers. This region contains a large concentration of electrons within the conduction band and a large concentration of holes within the valence band.
- If these population densities are high enough, a condition of population inversion results, and the region about the junction over which it occurs is called an inversion region.
- Population inversion at a junction is best described by the use of the concept of quasi-Fermi levels. Since the forward-biased condition of Fig. is a distinctly nonequilibrium state, the equilibrium equations defining the Fermi level are not applicable.
- In particular, the concentration of electrons in the inversion region (and for several diffusion lengths into the p material) is larger than equilibrium statistics would imply; the same is also true for the injected holes in the n material.
- Using Eqs. (1) and (2), we can draw Fn and Fp on any band diagram for which we know the electron and hole distributions.
- For example, in above Fig. Fn in the neutral n region is essentially the same as the equilibrium Fermi level EFn, This is true to the extent that the electron concentration on the n side is equal to its equilibrium value.
- However, since large numbers of electrons are injected across the junction, the electron concentration begins at a high value near the junction and decays exponentially to its equilibrium value np deep in the p material.
- Therefore, Fn drops from EFn as shown in Fig. We notice that, deep in the neutral regions, the quasi- Fermi levels are essentially equal.
- The separation of Fn and Fp at any point is a measure of the departure from equilibrium at that point. Obviously, this departure is considerable in the inversion region, since Fn and Fp are separated by an energy greater than the band gap (Fig. 2).