Quantum Dots for optical applications
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1 Quantum Dots for optical applications QD Ecole Polytechnique Fédérale de Lausanne Tutorial developed with the support of
2 European Network ofexcellence on Photonic Integrated Com ponents and Circuits Integration ofresearch on: Technologies forphotonic VLSI Photonic SignalProcessing Integrated LightSources Advanced Materials N anophotonics Through: JointR esearch Activities JointEducation Program s Access to facilities: 42 Research groups 12 Affiliate Partners Exchange ofr esearchers D issem ination ofknow ledge
3 Quantum Dots E λ L Electrons in GaAs, T=3K: h E > kt L < λ * 2mkT 3 nm QD devices: 1 nm Outline: QDs: Dreams & reality The physics of single QDs Laser applications
4 Why care about QDs? Or: The QD "dream"
5 Narrower gain makes better lasers Gain calculation: Arakawa, Sakaki 1982 Asada et al., 1986 E NB: Idealized picture!!! Lower threshold current Lower temperature sensitivity Larger modulation bandwidth
6 Real QDs Or: The shattered dream?
7 Nanostructure fabrication: Quantum Dots Top-down fabrication Need high-resolution lithography Etching Nonradiative defects Bottom-up: Strain-driven self-assembly High crystal quality radiative properties Uncontrolled nucleation Size dispersion WL substrate QDs Example: InAs on GaAs (but also InAs on InP, Ge on Si,...) 15 nm High local In content 2 nm 13 nm on GaAs
8 Inhomogeneous broadening 1 µm diameter: K, 4 µ W 1 µ m PL intensity (arb. un.) MacroPL at 5K: FWHM= 31 mev E ideal meas Energy (ev) E 3 nm Inh. broad. Gain FWHM: E QDs E QWs PL counts PL counts nm diameter: Wavelength (nm) K, 4 µ W 3 nm Wavelength (nm) Dot density: 3 dots/µm 2
9 Can we do better? Controlling self-assembly SK growth on prepatterned substrates In adatoms Growth-rate anisotropy driven growth: Kohmoto et al., J. Vac. Sci. Tech. B 22 Site control Improved unif. Baier et al., APL 24 GaAs QD 4 µm Courtesy: E. Pelucchi, E. Kapon, EPFL
10 Radiative properties of self-assembled QDs Intensity (arb. un.) Intensity (arb. un.) Energy (ev) Excited states: Wavelength (µm) GS ES2 ES1 WL 9 A/cm 2 11 A/cm K 21 A/cm ka/cm 2 GaAs Energy (ev) QD characteristics: 13 nm emission on GaAs Radiative efficiency 2% at RT Long carrier lifetime 1ns Density: 3x1 1 cm -2 A. Zunger, MRS Bulletin 1998 WL ES2 ES1 GS
11 Single QD physics (and applications): Like an atom??
12 QDs behave as atoms... Discrete electronic transitions Coulomb and exchange effects... A solid-state toolbox for optical spectroscopy Single QDs generate single photons PL Intensity (cps) XXX XX X - X X + 21µW 8.3µW x2 5.3µW x2 2.5µW x3 76nW x1 3nW Energy (mev) 5µW N. photons 2 1 time See invited talk by JM Gérard this afternoon Application to Q- cryptography
13 QDs do not behave as atoms... Homogeneous linewidth: 2 2 Γ= = + Γ phonon +Γ T τ 2 life At RT: Γ 5-15 mev ( T ) Auger ( n) Borri et al., PRL 21 Birkedal et al., PRL 21 Bayer et al., PRB 22 (Bayer et al., PRB 22) Interaction with crystal and carriers must be considered
14 lasers (1): The physics of a different laser
15 A summary of laser performance TTBOMK (To The Best Of My Knowledge) On GaAs, at 13 nm: J th <3 A/cm 2 at RT (Huang et al. EL 2, Park et al. PTL 2) Linewidth enhancement factor <1 (several groups) 1 Gb/s modulation (Hatori et al. ECOC 24, Kuntz et al., EL 25) T >2 K and J th <2 A/cm 2 (Shchekin EL 22) On GaAs (metamorphic), at 15 nm: J th 1.5 ka/cm 2 at RT (Ledentsov et al., EL 23) On InP at 155 nm: J th <4 A/cm 2 at RT (Saito APL 21, Wang PTL 21) Linewidth enhancement factor <3 (Ukhanov et al., APL 22) 1 Gb/s: - T =84 K (Schwertberger PTL 22) see also A. Kovsh's talk Fr A1-1
16 The quantum side of QD lasers Quantum Dots: Are they really different (better?) than QWs? Fact: Inhomog. + homog. broadening makes gain linewidth " QWs... But still it is a different laser! Confinement-related aspects: Discrete n. states Low J tr Low max gain Excited states Intraband dynam. Localization Thermal equil.?
17 The role of the density of states Transparency current: I tr ρ τ ( E) Maximum gain per pass: g max = 2 2 cv πex ω ρ enc ( E) QWs: E QWs: 13 nm QDs on GaAs: GaAs InAs InGaAs 1 2 QDs ( ggaas S = 3x1 cm, Einh = 2meV) k t QDs: ρqd GaAs π GaAs ρqw m 2 * 2g E S inh.1 QDs have 1 ρ QW ( E)= m* times lower density of π 2 states ρ QD ( E ) Low 2 transparency g S g S : areal dot current density Low Emax inh gainh E : inhomog. broad.
18 Record threshold current density N quantum dots 2N states Room-temperature: J th =33 A/cm 2 J tr = 9 A/cm 2 Theoretical estimate for J tr : (N QD =2, g S =3x1 1 cm -2, τ=8 ps) Single facet power (mw) J 8.4 µm x 4 mm 2 QD layers tr = Current (ma) Huang et al., Electron. Lett. 2 N QD The lowest J tr of any semiconductor laser eg τ S 2 = 12 A/cm J Voltage (V) BUT: Modal gain per QD layer 3-4 cm -1 Low-loss cavities Stack many layers
19 Gain limitations Strain issues in QD stacking Strain compensation (Zhang, APL 23, Lever, JAP 24) High-T capping (Ledentsov 23, Liu APL 24) Stacking of >1 layers 5nm Ground state lasing only for low loss: 1 1 NQDgth =α+ ln L R ES2 ES1 GS Intensity (a.u.) QD layers 2 mm µm Wavelength (nm)
20 Dual-state lasing Markus et al., APL 23 Violates population clamping theory??? light population bias
21 The role of intraband relaxation ES GS Population τ τ stim 1 fgs 1 τ τ stim ES population Rate equation model: mm ES GS.5 ES threshold GS threshold Carrier injection rate (e/τ r ) Model τ 8 ps Exper. Photon number Integr. int. (arb. un.) mm total GS ES Carrier injection rate (e/τ ) r 2 mm 293 K GS total.2 ES Current (ma) Predicted by Grundmann et al., APL 2
22 A more general view Carrier accumulation in non-lasing states: Low differential gain Large gain compression g' = dg dn GS tot n capture time from WL to QD n WL WL relaxation time from ES to GS n ES capture into nonlasing QDs n nonlas QDs dg GS ngs << ntot g' = small dntot Small f rel in lasers High P sat in SOAs
23 Modulation characteristics Carriers / dot Carriers / dot tot ES GS WL Carrier injection rate (e/τ ) r QD layers 1 QD layers ES tot GS WL Carrier injection rate (e/τ ) Gb/s: 3 QD layers Exp.: Kuntz, EL 25 1 QD layers
24 Thermal equilibrium? Intensity (arb. un.) ma 2 ma 1 ma 4 ma increasing current 3 QD layers, 2 mm, pulsed 293 K Wavelength (nm) hν2 hν3 - hν1 hν2 hν3 hν1 Inhomogeneous broadening + absence of thermal equilibrium Broad laser line = many independent lasers!
25 Thermal equilibrium Occupation factor Occupation factor Holes Energy (ev) Electrons lasing line Energy (ev) τ act QDs: real space τ act >1 ps QWs: E τ SHB <1 ps QDs more prone to nonequilibrium distribution τ SHB k
26 lasers (2): Prospects for application? Low threshold current Small linewidth enhancement factor Temperature performance Broad gain, large saturation power Lasers SOAs, SLEDs
27 Linewidth enhancement factor in QD lasers α Ideally: 4π dneff / dn = = λ dg / dn Gain Energy At high bias: Excited states! α -factor ES GS Model G (el./dot/τ rad ) ES GS α -factor 12 1 Refractive index α Current (ma) Newell et al., PTL C Experiment Current (ma) Markus et al., JSTQE 23
28 Insensitivity to feedback Coherence collapse threshold: f 1 +α α 2 crit Γ 4 f 2 feedback level (db) α: linewidth enh. factor Γ: damping rate QDs: α small Γ large (gain compression) I/I th -1 O'Brien et al, Electron. Lett. 23 Reduced feedback sensitivity Potential for isolator-free modules
29 Temperature characteristics E E E v <kt Holes spread among closely-spaced levels Shcheckin No thermal et activation al., APL 22 Matthews if E>>kT et al., APL 22 T >2 K E c >kt Use p-doping T-dependence fixed by electron distribution (Shchekin EL 22) Occupation factor Gain / G max GS electrons GS holes Temperature (K) GS ES Temperature (K)
30 QDs as amplifiers Size dispersion Broad gain spectrum Carrier reservoir Large saturation power & fast recovery time WL ES2 ES1 GS Akiyama et al, OFC 24 P sat >19 dbm over 12 nm Polarisation sensitivity? Preliminary evidence of polarisation control by shape engineering (Jayavel, APL 24)
31 Intensity (a.u.) Current (mamp.) Wavelength (nm) GS: 55 nm FWHM ES: 45 nm FWHM GS + ES: > 1 nm QD superluminescent diodes 8 µm x 4mm ridge 12 nm EPFL & EXALOS AG (Li et al, Electron. Lett. 25) Chirped QD multilayers Output power (mw) C pulsed GaAs InGaAs 15% In 13.5% In 12% In 1.5% In 9% In Current (A)
32 QD lasers: Real applications coming up? QD lasers are different, in some cases better Low chirp Feedback insensitivity Low-cost 1 Gb/s transmitters Large T Broad gain SOAs, tunable lasers, SLDs
33 Acknowledgements Simulations: Alexander Markus QD lasers: M. Rossetti, L.H. Li Single QDs: B. Alloing, C. Monat, C. Zinoni Collaborations with Alcatel CIT and EXALOS AG Funding: For this tutorial: epixnet NoE For QD research at EPFL:
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