Semiconductor lasers

1
Semiconductor lasers
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Light absorption and emission in semiconductor
Pair involved in optical Transition at frequency
?
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Density of states
Allowed states
dk
Number of states that have transition Energies in
the Interval from h? to h(?d?)
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Fermi Dirac Distribution
In undoped semiconductor np
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Absorption and Emission
Absorption B12 fv(?)1- fc(?) Stim. Emission
B21 fc(?)1- fv(?) Spont . Emission A21
fc(?)1- fv(?)
Balance of carriers in the interval with
transition energy from h? to h(?d?)
Integrate over ?
Spontaneous recombination rate
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Pumping and gain
h?pgtgtEg
Pump current density (A/cm3)
k
Laser gain coeffiicent
Ev
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Gain coefficient
Transparency
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Recombination
RrecAnBn2Cn3Jrec/e
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Materials
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Gain vs frequency and carrier density
(in units of 1018cm-3)
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Peak gain vs carrier density
?0?2000-4000 cm-1 Ntr?1-2?1018 cm-3 Ns?0-.6?1018
cm-3
Approximate expression
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Differential gain
Compare with ?21?/nd?/dn
n2-4Ntr a ?/2Ntr10-15cm2
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Gain vs current density
JJrec?teRrect
t