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Unformatted text preview: Semiconductor Lasers We have shown that similar to an atomic system, gain can occur in a semiconductor if we recognize that: 1. There is a nearly continuous array of states in the conduction and valence bands . 2. The occupancy of the upper and lower states are governed by Fermi statistics assuming quasi Fermi levels for the non equilibrium laser condition. 3. The optical transitions must satisfy energy and momentum conservation. The gain is then given by: Where f c (E b ) and f v (E a ) are the occupancy probabilities of the upper (conduction band) and lower (valence band) states, respectively that are separated by hn. [ ] [ ] 21 ( ) ( ) ( ) ( ) ( ) absorption coefficient ( ) ( ) ( ) ( ) red c b v a c b v a n h h B h f E f E c h f E f E γ ν ν ρ ν α ν γ ν α ν = = { t 2 t 1 r 1 r 2 r 1 r 2 E i e5 Γ L t 2 t 1 r 1 r 2 E i e3 Γ L E i t 1 E i e Γ L t 2 t 1 E i e Γ L r 2 t 1 E i e Γ L r 2 t 1 E i e2 Γ L 1 2 2 1 2 1 L i t tr L r t t E e E E rr eΓ Γ = = ∑ ~ Γ – complex propagation constant=j(n+jk) 2 π/λ o but k = α ’ λ o /4 π α ’ = g  α l ~ ~ ~ ( 29 2 ' 2 2 1 2 1 2 Oscillation 1 2 2 1 o l n L j L j g L o rr e n L m rr e π α λ α π π λ  + + → = ⇒ = = ~ t 1 E i γ th = 1 2 2 1 ln( ) 2 2 1 th l o o o o o R R m L d n dn nL n d γ α λ λ λ λ λ = + = ⇒ =  Losses in Semiconductors 1. Free carrier absorption , α fc 1. α fc = σ p p + σ n n = 10 18 (3 n + 7 p) 1. Scattering Loss – a s – due to inhomogeneities in materials Only a fraction of the semoiconductor is excited and has gain, thus only a fraction, Γ , of the photon field distribution overlaps the gain region. Gain region has loss a fc a + a s Passive region has loss α fc p + α s ε ~ ~ ~ ~ Γγ th = 1 1 Total losses (1 ) ln Only a fraction, , of the EM wave experiences gain 1 1 (1 ) ln Since ( ) varies with E = h , threshold is achieved when the maximum gain s a p l fc fc s a p th fc fc s L R L R E α α α α γ α α α γ ν = Γ + Γ + + Γ Γ = Γ + Γ + + max atisfies the threshold condition. 1 1 ( ) (1 ) ln The gain at threshold will occur at some injected carrier concentration. The current that is required to reach that carrier density a p fc fc s E L R γ α α α ⇒ Γ = Γ + Γ + + is the THRESHOLD CURRENT. The gain at threshold will occur at some injected carrier concentration . The current that is required to reach that carrier density is the THRESHOLD CURRENT. To calculate the threshold current and to investigate the dynamic properties of semiconductor lasers, we need to consider how the population of carriers is built up in the active region of a semiconductor laser.Let’s consider a double heterojunction laser under forward as our example: The forward biased current injects carriers (electrons and holes) into the active region. This creates a nonequilibrium situation in which the population of the conduction band and valence band states are altered from the equilibrium. Excess electrons and holes are available for recombination. As carriers altered from the equilibrium....
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This note was uploaded on 02/23/2011 for the course EE 474 taught by Professor Lingo during the Spring '11 term at USC.
 Spring '11
 Lingo

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