**Branch :**Computer Science and Engineering

**Subject :**Fundamental of Electronic Devices

## Steady State Carrier Generation: Quasi-Fermi Levels

We emphasized the transient decay of an excess EHP population. However, the various recombination mechanisms are also important in a sample at thermal equilibrium or with a steady state EHP generation-recombination balance.

**Quasi Fermi Levels:**

For example, a semiconductor at equilibrium experiences thermal generation of EHPs at a rate g(T) = g_{i} This generation is balanced by the recombination rate so that the equilibrium concentrations of carriers n_{0 }and p_{0} are maintained:

This equilibrium rate balance can include generation from defect centers as well as band-to-band generation. If a steady light is shone on the sample, an optical generation rate g_{op} will be added to the thermal generation, and the carrier concentrations n and p will increase to new steady state values. We can write the balance between generation and recombination in terms of the equilibrium carrier concentrations and the departures from equilibrium ∂n and ∂p:

For steady state recombination and no trapping, Then ∂n = ∂p

The term α_{r}n_{0}P_{0} is just equal to the thermal generation rate g(T).Thus, neglecting the ∂n^{2} term for low-level excitation, we can rewrite the above equ

The excess carrier concentration can be written as

It is often desirable to refer to the steady state electron and hole concentrations in terms of Fermi levels, which can be included in band diagrams for various devices.The Fermi level E_{F} is meaningful only when no excess carriers are present. However, we can write expressions for the steady state concentrations in the same form as the equilibrium expressions by defining separate quasi-Fermi levels F_{n} and F_{p} for electrons and holes. The resulting carrier concentration equations

can be considered as defining relations for the quasi-Fermi level.

**Diagram of the fermi levels:
**

The quasi-Fermi levels illustrate dramatically the deviation from equilibrium caused by the optical excitation; the steady state F_{n} is only slightly above the equilibrium E_{F}, whereas F_{p} is greatly displaced below E_{F}. From the figure it is obvious that the excitation causes a large percentage change in minority carrier hole concentration and a relatively small change in the electron concentration.

In summary, the quasi-Fermi levels F_{n} and F_{p }are the steady state analogues of the equilibrium Fermi level E_{F}. When excess carriers are present, the deviations of F_{n} and F_{p} from E_{F} indicate how far the electron and hole populations are from the equilibrium values n_{0} and p_{0} A given concentration

of excess EHPs causes a large shift in the minority carrier quasi-Fermi level compared with that for the majority carriers. The concept of quasi-Fermi levels is very useful in visualizing minority and majority carrier concentrations in devices where these quantities vary with position.