Branch : Computer Science and Engineering
Subject : Fundamental of Electronic Devices
Unit : Basic Electronics
Semiconductor lasers
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.
Thus,
n=N_{c}e^{-(Ec-En)/KT}=n_{i}e^{(En-Ei)/KT} equ-(1)
p=N_{v}e^{-(Ep-Ev)/KT}=n_{i}e^{(Ei-Ep)/KT} equ(2)
- 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. F_{n} in the neutral n region is essentially the same as the equilibrium Fermi level E_{Fn}, 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, F_{n} drops from E_{Fn} as shown in Fig. We notice that, deep in the neutral regions, the quasi- Fermi levels are essentially equal.
- The separation of F_{n} and F_{p} at any point is a measure of the departure from equilibrium at that point. Obviously, this departure is considerable in the inversion region, since F_{n} and F_{p} are separated by an energy greater than the band gap (Fig. 2).