Quantum Dot Lasers. Andrea Fiore. Ecole Polytechnique Fédérale de Lausanne

Transcription

1 Quantum Dot Lasers Ecole Polytechnique Fédérale de Lausanne Outline: Quantum-confined active regions Self-assembled quantum dots Laser applications

2 Electronic states in semiconductors Schrödinger eq.: ψ = k ( r ) u ( r ) χ( r ) k m + V crist()+ r V het () r ψ()= r Eψ() r p u k : Bloch function χ : envelope function p + V m* het χ = ( r ) ( r ) Eχ( r ) CB E bulk : V het E = = 0, χ k m* ( r ) = e ik r VB k

3 Energy quantization χ ik r ( r ) = e kl x kl y kl z = mπ x = mπ y = mπ z L E k 4π E = = x y + m* m* L ( m + m m ) z E 4π m* L Wavefunction confinement with heterostructure potential: E 1 L E>>kT at RT L<<30 nm

4 D nanostructures: Quantum Wells k x ky > 1> > 1> E z AlGaAs GaAs AlGaAs k x, k y V het = V i( k x+ k y) x y = e χ z kx + k y E = En + m * ( z), χ( r ) ( ) ( ) Confinement in one dimension Continuum of energy states

5 1D nanostructures: Quantum Wires k y > 1> > 1> E AlGaAs GaAs AlGaAs k y V het = V χ k y E = En + m * ik y y ( x, z), χ( r ) = e ( x, z)

6 0D nanostructures: Quantum Dots > E 1> AlGaAs GaAs AlGaAs > 1> V het ( x, y, z), ( r ) = χ( x, y z) = V χ, E = E n Only in a 0D nanostructures the energy levels are completely discrete! Semiconductor atoms

7 Electronic transitions Fermi's golden rule: w f H'i u r χ r A r pu r χ r if c ( ) c( ) ( ) v( ) v( ) + = = ( ) ˆ ( ) χc( r) χv( r) χc( r) ˆ χv ( r) u ( r) uv ( r) A uc r e p uv r e p c A u r u r c ( ) eˆ p v( ) χc ( r) χv ( r) =0 Material Heterostructure NB: Dimensionality has little influence on transition probability (apart from selection rules)! Neglecting excitonic effects!

8 Density of states Memo: Born-von-Karman boundary conditions k-space density of states g ( k) = const. k + dispersion relation: E = g( E) m * Bulk: ρc ( E ) E Ec Density of states E c Energy

9 Density of states QWs ρ c ( E) = const. ρ c QWires ( E) 1 E E n c s ( E) ( E En) ρ δ Density of states E 1 E Density of states E 1 E Density of states E 1 E Energy Energy Energy > 1> AlGaAs GaAs AlGaAs More confinement Less degrees of freedom Density of states more singular

10 Quantization: What for? Photonics: Shape of density of states Gain spectral width Number of states Transparency current 3D carrier confinement Energy tuning

11 Density of states and carrier distribution n ( E) = g( E) f ( E) Bulk: Density of states Fermi distribution Carrier distribution f(e) n(e) g(e) Problem with bulk: Continuous and increasing g(e) Broad carrier distribution Energy

12 Carrier distribution in nanostructures Carrier distribution f(e) n(e) QWs g(e) Carrier distribution f(e) QWires n(e) g(e) Carrier distribution f(e) s n(e) g(e) Energy Energy Energy Gain calculation: Proposed by Asada et al., JQE 1986 NB: Idealized picture!!!

13 Number of states In a semiconductor laser: Need to reach transparency must fill at least half of the available states Transparency current: I tr = eg ( E ) E τ g( E ) N quantum dots N states With low-dimensional heterostructures we can "engineer" the number of states Reduce I tr NB: Small g(e) Small max gain!

14 Carrier confinement Lateral carrier confinement in 0D nanostructures Suppressed carrier diffusion Can fabricate smaller devices

15 Outline Quantum-confined active regions Self-assembled quantum dots: growth and physical properties Laser applications

16 Nanostructure fabrication: Quantum Dots "Straightforward" approach: Fabrication on the nanoscale Need high-resolution lithography Etching Nonradiative defects "Self-organized" methods: Making Nature work for us! Growth on patterned substrates substrate Strain-driven growth on planar substrates substrate

17 Self-assembled growth Epitaxial growth: Interplay of surface energy and strain "Standard" (Frank-van der Merve) D epitaxial growth: GaAs substrate AlAs Stranski-Krastanow 3D growth mode (strain-driven): InAs substrate

18 Self-assembled quantum dots MBE growth of InAs on GaAs: 15 nm Atomic Force Microscopy 00 nm Transmission Electron Microscopy Simple growth technique, no pre-growth patterning required High crystalline quality High radiative efficiency at RT Random nucleation sites no control of island position Size dispersion Emission energy dispersion 1.3 µm operation possible

19 Self-assembled quantum dots Idealized picture: E E>>kT Arakawa, Sakaki 198 Asada et al., 1986 Real s: 15 nm 00 nm PL intensity (arb. un.) FWHM= 31 mev E ideal meas Energy (ev) E

20 Electronic structure holes electrons s-like p-like d-like Atomistic pseudo-potential approach (Williamson et al, PRB 000)

21 Emission spectrum 0 1 Intensity (arb. un.) Low excitation level 93 K 1 A/cm Energy (ev) filling: max electrons per state 1 0 Intensity (arb. un.) QW 900 A/cm 110 A/cm 7. ka/cm GaAs Energy (ev)

22 Relaxation bottleneck? Prediction of very slow relaxation from excited states to ground state (Benisty et al., PRB 1991) If E h ω opt ph cannot relax from excited to ground state no PL Experiment: Picosecond relaxation times! 1 0 E E Explanation: Auger effect P av =110 mw, 3.1x10 1 cm - el-hole pairs per pulse resolution: 3.5 ps 5 K Intensity (a.u.) ev ev 1.47 ev laser Time (ps) Morris et al, APL 1999

23 Radiative properties of optimized s Intensity (arb. un.) W/cm Wavelength (nm) 5K 100K 150K 00K 50K 300K Decay time (ps) K Time [ps] Temperature (K) Markus et al., APL 80, 911 (00) Material properties: High radiative efficiency 0% at RT Long carrier lifetime 1 ns 1300 nm emission at RT Density cm -

24 excitons: Homogeneous linewidth Single- photoluminescence: (Bayer et al., PRB 00) Γ= = +Γ T τ life Radiative dephasing phon T ( ) Phonon scattering T< K: lifetime-limited K<T<60 K: acoustic phonons T>60 K: optical phonons

25 Outline Quantum-confined active regions Self-assembled quantum dots: growth and physical properties Laser applications

26 s: Laser applications Potential advantages: Narrow gain spectrum? No, inhomogeneous broadening Wavelength tuning: Reaching µm on GaAs substrate InAs Local In content can be high with low average strain Low density of states Low transparency current

27 s vs QWs: Gain Maximum gain per pass in a D system: g max = πe x cv ω e 0 nc ρ( E) ρ( E): density of states per unit energy per unit area QWs: QWs: GaAs InGaAs GaAs E k t InAs s s: GaAs GaAs ρ QW ( E)= m* π ρ ( E) g S E inh g S : E inh : areal dot density inhomogeneous broadening

28 Max gain g g QW ρ ρ QW π m * g S E inh 0.1 ( 10 g = 3x10 cm, E = mev ) S inh 0 g QW (1 pass) 1% (1 quantum well) g (1 pass) 0.1% (1 layer, 3x10 10 cm - ) (measured: g =0.03% with 3x10 10 cm -, E=35 mev (Birkedal et al, 000)) s have lower gain than QWs! (at 1300 nm) Laser applications: Minimize losses Stack many layers

29 stacking for max gain 10 nm spacing: s aligned 5 nm spacing: s not aligned 50nm 50nm Intensity (a.u.) K 1 3 s d=5 nm 3 s d=10 nm Strain interaction between dot layers produces vertical alignment and PL broadening Wavelength (nm)

30 lasers EPFL lasers: Laser performance: J th <100 A/cm η ext =30-40% CW up to 80 C Intensity (a.u.) As-cleaved, RT: mm, 3 layers, RT 147 A/cm 136 A/cm Wavelength (nm) Power (mw) 600 µm, HR coated 95%: J (A/cm ) pulsed C 30C 40C 50C 60C 70C 80C Current (A) HR coatings and measurements: O. Gauthier-Lafaye, Opto+

31 Record threshold current density Single facet power (mw) 8.4 µm x 4 mm layers Current (ma) Huang et al., Electron. Lett. 000 J Voltage (V) Room-temperature: J th =33 A/cm J tr = 9 A/cm The lowest J tr of any semiconductor laser? Theoretical estimate for J tr : (N =, g S =3x10 10 cm -, τ=800 ps) J tr = N eg τ S = 1 A/cm

32 Gain problem in lasers Ground state lasing only for low loss (L>1.5 mm): Intensity (a.u.) layers mm 600 µ m Wavelength (nm) 1 0 N High T Higher optical loss Wavelength switch g th 1 1 = α + ln L R L= 600µm, HR/HR coated, P= 3 mw. Device width= 3µm 5 C 45 C 65 C Wavelength (nm) Ground state Excited state Device length (mm) Powe r (dbm) Wa ve le ng th (nm)

33 Max modal gain in lasers g mod 3 cm -1 per layer Klopf et al., PTL 001 N g = α ln L R L min = ln N ( 1/ R) g α 600 µm Need a factor of two in gain for applications

34 Effect of inhomogeneous broadening Intensity (arb. un.) ma 00 ma 100 ma 40 ma increasing current 3 layers, mm, pulsed 93 K - hν - - hν3 - hν1 hν hν3 hν Wavelength (nm) Inhomogeneous broadening + absence of thermal equilibrium No population clamping at threshold Broad laser line = many independent lasers!

35 Dual-wavelength lasing Markus et al., APL 003 Violates population clamping theory??? light population bias

36 Interpretation of dual-λ lasing "Slow" intraband relaxation (Benisty et al., PRB 1991) τ 0 τ 0 10 ps in our s (PL rise time) Photoluminescence: Laser: τ 0 τ spont 1 1 >> τ0 τ spont no relax. bottleneck τ 0 τ stim 1 fgs 1 τ τ 0 stim ES population Behaviour predicted by Grundmann et al., APL 000

37 Modeling -λ lasing Rate equation model: WL ES GS τ 0 f WL f ES f GS Model τ 0 8 ps Photon number mm total GS ES Carrier injection rate (e/τ ) r Population mm 1.5 ES 1 GS 0.5 ES threshold GS threshold Carrier injection rate (e/τ ) r Exper. Integr. int. (arb. un.) mm total K GS ES Current (ma)

38 3D carrier confinement in s Carrier diffusion limits device scaling: QW s Al O 3 Au GaAs AlGaAs s 300 nm current aperture oxid. edge oxid. edge Fiore et al., Appl. Phys. Lett. (00)

39 Ultrasmall LEDs: Scaling InGaAs quantum well: Current density (A/cm ) Area = aperture area QWs 93 K 9.0 µm.0 µm 940 nm 70 nm 530 nm Voltage (V) L diff Current density (A/cm ) Quantum dots: Area = aperture area s 93 K 30 µm 9.1 µm 1.8 µm 1.0 µm 830 nm 600 nm Voltage (V) Current density (A/cm ) Area = aperture area + diffusion QWs, L diff =.7 µ m 93 K 9.0 µm.0 µm 940 nm 70 nm 530 nm Voltage (V) Diffusion length:.7 µm in QWs < 100 nm in s! s for nanoscale devices

40 Real applications for lasers Disadvantage: Low gain Difficult to get VCSELs Advantages: Low threshold currents Low linewidth enhancement factor? Low chirp, insensitivity to optical feedback Broad gain spectrum & high saturation power SOAs, tunable lasers, superluminescent LEDs

41 Laser chirp Direct laser modulation: Problem: Spectral broadening Laser "chirp": laser mode gain λ nl m cav λ m = α dn / dn ν = Γvg g 1 N with : α 4π dn /dn λ λ = n n I N g n I= I() t n= n() t λ =λ() t i Kramers- Kronig linewidth-enhancement factor

42 Linewidth enhancement factor in lasers Ideally: 4π dneff / dn α = = λ dg / dn 0 Gain Refractive index Energy At low bias: GS population only low α PTL 1999

43 A more complete picture... Gain (arb. un.) G=0 G=10 G=5 G= Energy (ev) 1 10 Linewidth enhancement factor in lasers Model α -factor Experiment: C Current (ma) Markus et al., JSTQE 003 α -factor G (el./dot/τ ) rad Need to operate well below GS saturation to have low α

44 Key features for SOA applications Inhomogeneous broadening from size dispersion: Broad gain spectrum Large reservoir of carriers for replenishing the s: WL ES ES1 GS Large saturation power Polarisation sensitivity? Preliminary evidence of polarisation control by shape engineering (Jayavel, APL 004)

45 Semiconductor Optical Amplifiers Fujitsu, presented at OFC 004: Large gain bandwidth: Large saturation power:

46 lasers: Real applications coming up? s do not compete with QWs for high-gain devices (e.g. VCSELs) Threshold current lower in s, but no so useful Practical advantages over QWs for: Broad gain devices (amplifiers, tunable lasers) Long-wavelength on GaAs (1.3 µm OK µm?) Temperature-insensitive operation?