Physics for Electrical Engineering: Unit IV: Optical Properties of Materials
Optical absorption, loss and gain
Optical Properties of Semiconductor
The optical intensity (which is the photon flux multiplied by the photon energy h v) falls as the wave travels.
OPTICAL ABSORPTION, LOSS AND GAIN
The
photon flux associated with an electromagnetic wave traveling through a
semiconductor is denoted by
Iph
= I0ph exp ( - ɑx) …(1)
where
ɑ (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 ƒe
(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:
Iph
= I0ph exp (hv) x)
… (4)
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).
fe
(Ee) + fh (Eh) > 1
The
quasi-Fermi levels must penetrate their respective bands for this condition to
be satisfied.
Physics for Electrical Engineering: Unit IV: Optical Properties of Materials : Tag: : Optical Properties of Semiconductor - Optical absorption, loss and gain
Physics for Electrical Engineering: Unit IV: Optical Properties of Materials
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Physics for Electrical Engineering
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