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Semiconductor Laser Lasing Conditions and Design Exercise

Discusses conditions and calculations for semiconductor lasers, including optical power output and cavity types. Includes quantum well lasers and distributed feedback lasers. Explains threshold current density and gain coefficients. Provides insights into population inversion and resonant cavity conditions for lasing. Contains formulas for stimulated emission and absorption rates. Refers to GaAs laser diode parameters and Band-to-band transitions. Mentions Quantum efficiency and active layer width influence. Engages with mathematical simplifications and semiconductor laser models.

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Semiconductor Laser Lasing Conditions and Design Exercise

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  1. L9 10272015 ECE 5212 Fall 2014 UConn F. Jain Lasers • Conditions of Lasing • Threshold Current Density Jth • Reduction of Jth: Heterostructure Lasers • Optical Power-Current Behavior • Carrier confinement in a double Heterostructure (DH) laser • Laser Design Exercise • Quantum Well/Wire/dot Lasers • Distributed Feedback Lasers Operating parameters: Operating wavelength: green, red, blue, fiber optic wavelength 1.55 microns Optical power output, expected external and wall conversion efficiency, Operating structure Cavity or Distributed Feedback type Edge emitting or surface emitting.

  2. General Conditions of Lasing: Rate of emission = Rate of absorption Rate of spontaneous emission + rate of stimulated emission =Rate of absorption A21N2 + B21 r(hn12) N2 = B12 r(hn12) N1 (1) Rate of stimulated emission >> rate of absorption gives B21 r(hn12) N2 >> B12 r(hn12) N1 Or, ( N2 /N1) >> 1 ………Condition known as population inversion. (Using Planck’s distribution law, we can show that B12=B21). (2) Rate of stimulated emission >> rate of spontaneous emission gives B21 r(hn12) N2 >> A21N2 Or, r(hn12) >> A21/B21 Photon density higher than a value.

  3. Conditions of Lasing:

  4. General Conditions of Lasing:

  5. General Conditions of Lasing: • Representing the amplitude/magnitude • (b) Phase condition

  6. Resonant Cavity: Condition I for Lasing Figure2. Cavity with parallel end faces

  7. The emission spectrum high lighting cavity modes Figure3 shows the emission spectrum highlighting cavity modes (also known as the longitudinal or axial modes) for the GaAs laser diode. Conditions and Calculations: GaAs λ = 0.85μm nr = 3.59 L = 1000μm  Δλ=2.01 Å

  8. Equivalent of population inversion in semiconductor lasers: Condition II for Lasing This condition is based on the fact that the rate of stimulated emission has to be greater than the rate of absorption. (23) Strictly speaking, the rate of stimulated emission is proportional to: (i) the probability per unit time that a stimulated transition takes place (B21) (ii) probability that the upper level E2 or Ec in the conduction band is occupied (27) , Efn = quasi-fermi level for electrons. (24) (iii) joint density of states Nj(E=hv12) (iv) density of photons with energy hv12, ρ(hv12) (v) probability that a level E1 or Ev in the valence band is empty (i.e. a hole is there) (25) The rate of stimulated emission: (26) Similarly, the rate of absorption: (27)

  9. [1]M.G.A. Bernard and G.Duraffourg, Physica Status Solidi, vol. 1, pp.699-703, July 1961 Using the condition that the rate of stimulated emission > rate of absorption; (assuming B21=B12), simplifying Equation (26) and Equation (27) (28) Further mathematical simplification yields if we use (29) (30) Bernard - Douraffourg Condition[1] (31) Equation (31) is the equivalent of population inversion in a semiconductor laser. For band to band transitions (32)

  10. Definition of quasi Fermi-levels Gain coefficient g and Threshold Current Density Jth The gain coefficient g is a function of operating current density and the operating wavelength λ. It can be expressed in terms of absorption coefficient α(hv12) involving, for example, band-to-band transition.

  11. Derivation of JTH Rate of stimulated emission = B21feNj(E=h) (h12) fh (Where (h12) = P v hs) = B21fefh (vg) nNs Rate of absorption = (1-fh)(1-fe) vg nNs B12 Net rate = Stimulated – absorption = [fe fh – (1-fe)(1-fh)] vg nNs B21 = -[1-fe-fh]  vg nNs B21 and also note that B12 = B21) The gain coefficient is Rate of spontaneous emission (34)

  12. where: αovg = probability of absorbing a photon Nv = number of modes for photon per unit frequency interval Δvs = width of the spontaneous emission line Equation (34) gives (35) The total rate of spontaneous emission (36) (37) where: Rc = Rate per unit volume η = quantum efficiency of photon (spontaneous) emission d = active layer width A = junction cross-section Equations (33), (35), (36) and (37) give (38)

  13. (39) (40) Substituting for Nv and , we get (41) The condition of oscillation, Equation (15), gives (15)

  14. Threshold current density Using Equation (15) and Equation (42) (43) (44) When the emitted stimulated emission is not confined in the active layer thickness d, Equation (44) gets modified by Γ, the confinement factor (which goes in the denominator).

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