EE 529 Semiconductor Optoelectronics – Semiconductor

EE529 Semiconductor Optoelectronics

Semiconductor Lasers 1. Optical spectrum 2. threshold, power and efficiency 3. Modulation characteristics 4. Advanced laser structures Reading: Liu, Sec. 13.3-13.4, 13.9-13.10 Ref: Bhattacharya, Sec. 6.7, 7.2, 7.13; Liu, Sec. 4.3, 5.1 Lih Y. Lin EE 529 Semiconductor Optoelectronics – Semiconductor Lasers Laser Operation

Lasing process in a

Process: 1. Population inversion ― Through or carrier injection. 2. Seed ― From and initiate the process. 3. ― Resonant enhancement and define the output wavelength. 4. Gain saturation – Population inversion decreases as stimulated emission increases. → Steady state. 5. Output coupling ― Let some of the photons out at each round trip. Lih Y. Lin 2 EE 529 Semiconductor Optoelectronics – Semiconductor Lasers Basic Semiconductor Laser Structure

p+ Juncti on n+

Ec + + E p n g eV o Ec EF n Inversion E E region c v Holes in V B Eg E EF n F p Electrons in C B eV Ec

EF p

Ev (a) (b)

Current V Cleaved surface mirror Photograph of an edge emitting

L Electrode

p+ GaAs L

+ n GaAs Electrode

Active region (stimulated emission region) 500 µm 3 Lih Y. Lin

EE 529 Semiconductor Optoelectronics – Semiconductor Lasers Different Regimes of Operation Energy

Optical gain E − E CB F n F p E Pumped electrically or F n Electrons E c i n CB optically until population inversion happened. eV 0 υ h → Emission > Absorption. Eg E Hol es i n VB v = Empty states At T > 0 EF p VB At T = 0 Optical absorption

Density of stat es Optical Power Laser Opti cal Power

Optical Power LED Stimulated emission λ

Optical Power Laser Spontaneous

λ emission I 0 I th λ

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EE 529 Semiconductor Optoelectronics – Semiconductor Lasers Optical Gain Spectrum

Optical gain coefficient g: Fractional change in the power (or intensity) per unit distance

* 3/2 2 1/2 2(mcr ) g(ν ) = 222 (hν− Egc) [ fE (21 )− fE v ( )] nhντsp

∆EF

Lih Y. Lin 5 EE 529 Semiconductor Optoelectronics – Semiconductor Lasers Threshold Gain gth Shown on the right is a typical output power-Injection current characteristics of a laser diode. PO When does lasing happen? Steady-state condition: Laser power is constant → Round-trip gain = Round-trip loss Lasing

Reflecting Pf Pi Reflecting I I → g surface E surface th th f Ei

2 Steady state EM oscillations 1 Cavity axis x

R R 2 L 1 Where does the loss come from? Reflection loss at the mirrors. Losses in the cavity medium (scattering at defects, absorption by impurities, absorption by free carriers …)

Pfi= PR12 Rexp[ g (2 L )]exp[ −α (2 L )]

α : Loss coefficient of the laser medium 11 PPf= i → g th =α+ ln  2L RR12

Lih Y. Lin 6 EE 529 Semiconductor Optoelectronics – Semiconductor Lasers Threshold Current and Efficiency

Laser diode active layer thickness = d

Determine Nth from the gain spectrum edR() N edNth sp th Jth = or Jth = ητinj s ηηinj i Above threshold, under steady state,

hν (1 / 2L ) ln(1 / RR12 ) P0ut=ηη i inj () II − th e α+(1 / 2L ) ln(1 / RR12 ) External quantum efficiency

dP(out /) hν (1 / 2L ) ln(1 / RR12 ) ηe = =ηηi inj d( I− Ith ) / e α+(1 / 2L ) ln(1 / RR12 )

Slope efficiency n Po dP hν out Threshold population η=se =η nth VdI eV n inversion Power conversion efficiency P = Lasing output power ∝ Nph PIhν  o η=out =η − th Slope represents efficiency ce1 I VI eV I Ith Lih Y. Lin 7

EE 529 Semiconductor Optoelectronics – SemiconductorExercise: Lasers Threshold Current Density of a GaAs Laser Calculate the threshold current of a GaAs laser with an undoped active region of width d = 0.2 µm starting from g(E) and Rsp(E): 1/2 − 1/2 41(EEg ) − 29 −−1 3 − 1 g(E )= 3×− 10 [fE ( ) fE ( )] cm Rsp ( E )=×− 1.15 10 EEE( g) fE c (21 )[1 − fEv ( )] s cm (eV) E cv21 3 -1 Assuming the following parameters for the laser: L = 400 µm, R1 = R2 = 0.9, α = 10 cm , Γ = 0.95, ηi = 0.9, ηinj=1 . Along your calculation, verify that you obtain the following results:

Lih Y. Lin 8 EE 529 Semiconductor Optoelectronics – Semiconductor Lasers Exercise: Efficiencies of an InP Laser

An InP Fabry-Perot laser emits at wavelength ~λ=920nm. It has an

injection efficiency η=inj 90% and an internal quantum efficiency

η=i 95%. The voltage applied to the device is 2.5V. The reflectivity

of both cavity ends are R1 = 100% and R2 = 70%. The loss coefficient of the laser medium is α=1cm-1. Its threshold current is

characterized to be Ith = 1mA. (a) The semiconductor laser has a cavity length L = 400 µm. Assume the refractive index n = 3.3. What should be the exact emission wavelength? At which longitudinal mode does lasing occur? (b) Calculate the extraction efficiency, external quantum efficiency, and slope efficiency of the device. (c) If the laser is operated at an injection level twice the threshold, find its power conversion efficiency and output power.

Lih Y. Lin 9 EE 529 Semiconductor Optoelectronics – Semiconductor Lasers Transient Response

Transient phenomena occur because of the time required for the and photon populations to come into equilibrium. As the photon population builds up rapidly, the carrier density is depleted until it falls below transparency condition.  Photon population decreases.  Carrier population starts to build up again, this time from a higher initial value, and so does the photon population.

Lih Y. Lin 10 EE 529 Semiconductor Optoelectronics – Semiconductor Lasers Frequency Response under Small-signal Modulation As the initial oscillations cease, the situation becomes periodic small-signal modulation of a laser. mγγ Complex response function: iϕ cn r()||Ω= re = 22 Ω−Ω+Ωγrri 222 2 m γγ Modulation power spectrum: cn Rf()= rf () = 4 2 22 2 22 16π (ff −rr ) +π 4 f γ

2 1/2 2 γr Resonance peak: ffpk= r − 2 3-dB modulation bandwidth: 8π 2 1/2 1/2 2 γr ff3dB =+−(1 2 ) r 82π2

Lih Y. Lin 11 EE 529 Semiconductor Optoelectronics – Semiconductor Lasers Exercise: Modulation Characteristics

A GaAs QW VCSEL has the following parameters: Emission wavelength = 850 nm, refractive index n = 3.52, gain overlap factor Γ=0.2, threshold gain coefficient 41− gth =8.16 × 10 m , excess carrier spontaneous lifetime τ=s 3.02 ns, gain cross-section σ=2.2 × 10−19 m 2 .

(a) Find the values of spontaneous carrier relaxation rate γs and cavity decay rate γc .

What is the photon lifetime τc ? −18 3 (b) If the laser output power Pout =60.6 µW, the mode volume Vmode =4.74 × 10 m ,

the emitted and photon extraction efficiency η=t 89%. Find the intracavity photon

density S0 .

(c) Find the values of differential gain parameter gn . Assume the nonlinear gain

parameter ggpn= − , find the values of differential carrier relaxation rate γn and

nonlinear carrier relaxation rate γ p .

(d) Find the values of relaxation resonance frequency fr and total carrier relaxation rate

γr .

(e) Find the resonance peak of the modulation spectrum f pk . What is the 3-dB

modulation bandwidth f3dB ?

Lih Y. Lin 12 EE 529 Semiconductor Optoelectronics – Semiconductor Lasers Lasers

n p p Ith for homostructure laser diode extremely high (a) AlGaAs GaA s AlGaAs → Not practical for room temperature operation

(~ 0.1µm)

Electrons in CB Ec Heterostructure laser: Enhance carrier ∆Ec Ec confinement and photon confinement 2 eV 1.4 eV 2 eV Cleaved reflecting surface (b) E v W Ev

Holes in VB L Refractive Stripe electrode in dex ∆n ~ 5% (c) A ctiv e Oxide insulator region p-GaAs (Contacting layer) p-Al Ga As (Confining layer) Photon x 1-x density p-GaAs (Active layer) n-Al Ga As (Confining layer) 2 x 1-x 1 3 Substrate n-GaAs (Substrate) Current (d) pathsSubstrate Electrode

Elliptical Cleaved reflecting surface la ser Active region where J > J . beam th (Emission region)

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EE 529 Semiconductor Optoelectronics – Semiconductor Lasers DBR Laser and DFB Laser Output spectrum of a typical Fabry-Perot (F-P) laser Optical Power Laser 2L = q L λ → Many wavelengths are possible, as long as they are within the gain spectrum λ How do we obtain single-frequency semiconductor lasers? Distributed Bragg reflector (DBR) laser Distributed Bragg Λ refl ector

A q(λB/2 n) = Λ B

Active layer Corrugated (a) dielectric structure (b) c Distributed feedback (DFB) laser νmB ≈ν ±()m +µ Ideal lasing emission Optical power 2nlB Λ Corrugated grating Guiding layer

Acti ve l ayer 0.1 nm

λ λ ( nm) (a) (b) λ B (c)

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EE 529 Semiconductor Optoelectronics – Semiconductor Lasers Typical Grating Coupler Structure and Coupled-Mode Theory

Coherent coupling between forward- and backward-propagating waves results in selection of longitudinal modes.

δ=βB −β() ω

2 sinh2 ( |κ |L 1 −δ / κ ) R = 22 cosh2 ( |κ |L 1 −δ / κ) −δ / κ

Lih Y. Lin 15 EE 529 Semiconductor Optoelectronics – Semiconductor Lasers Exercise: DBR Laser

A DBR laser has gain section of length l = 400µm and two identical DBRs as

end mirrors, each of length lDBR =150 µm. The grating period of the DBR is

Λ=225 nm. The effective indices for the laser modes are nNββ= = 3.45. The DBR coupling coefficient is |κ= | 50 cm−1. The gain spectrum peaks ~1550 nm. (a) Find the Bragg wavelength and frequency near the gain peak. (b) Find the peak reflectivity and the bandwidth of the two DBRs. (c) Find the effective phase length of the DBRs and that of the DBR laser to determine the longitudinal mode spacing of the laser. (d) Assume the gain bandwidth is much broader than the DBR frequency bandwidth, how many longitudinal modes can exist? (e) If the laser is pumped right at the threshold, only one mode can oscillate. What’s its wavelength? Calculate the DBR reflectivity at this lasing wavelength.

Lih Y. Lin 16 EE 529 Semiconductor Optoelectronics – Semiconductor LasersVertical Cavity Surface Emitting Laser (VCSEL) Dielectric mirrors → Distributed Bragg reflector structures A 1st-order square grating of a 50% duty factor has the largest coupling coefficient 2∆n ||κ= Λ=λ /2n λ B Contact

λ/4n2 Dielectric mirror λ/4n1

Active layer

Dielectric mirror

Substrate

Contact

SEM (Scanning electron micrograph) of a VCSEL array. Surface emission

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