Optical Absorption, Loss and Gain

OPTICAL ABSORPTION, LOSS AND GAIN

The photon flux associated with an electromagnetic wave traveling through a semiconductor is denoted by

where α (the absorption coefficient) is usually positive and

I0ph is the incident light intensity at x = 0.

The optical intensity (which is the photon flux multiplied by the photon energy h v) falls as the wave travels. The electrons are pumped in the conduction band and holes in the valence band. The electron-hole recombination process (photon emission) can be stronger than electron-hole generation (photon absorption).

In general, the gain coefficient is defined by

gain coefficient = emission coefficient - absorption coefficient.

Let fe (Ee) and fh (Eh) the electron and hole occupation. The emission coefficient depends upon the product of fe (Ee) and fh (Eh).

Similarly, the absorption coefficient depends upon the product of (1 − fe (Ee)) and (1- fh (Eh)). Here the energies Ee and Eh are related to the photon energy by the condition of vertical k-transitions.

For these transitions we have

The occupation probabilities fe and fh are found by the quasi-Fermi levels for electrons and holes.

The gain is the difference of the emission and absorption coefficient. It is now proportional to

The optical wave has a general spatial intensity dependence:

and if g (h v) is positive, the intensity grows because additional photos are added by emission. The condition for positive gain requires "inversion" of the semiconductor system, eqn (3).

The quasi-Fermi levels must penetrate their respective bands for this condition to be satisfied.