GaN-based Devices: Physics and Simulation

Transcription

1 GaN-based Devices: Physics and Simulation Joachim Piprek NUSOD Institute Collaborators Prof. Shuji Nakamura, UCSB Prof. Steve DenBaars, UCSB Dr. Stacia Keller, UCSB Dr. Tom Katona, now at S-ET Inc. Dr. Simon Li, Crosslight Software Inc. NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 2

2 Outline 1. Nitride Material Properties 2. Light-Emitting Diodes (LED) 3. Laser Diodes (LD) NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 3 Optoelectronic Device Physics Electrical Model Photon Emission & Absorption Model Thermal Model Optical Model NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 4

3 Nitride Material Parameters needed: more than 4 material parameters as function of layer composition mobility (n,p) μ(t,n,f) bandgap E g (T) SRH lifetime (n,p) τ electron affinity χ(t) spont. recomb. coeff. B electron effective mass m Auger coefficient (n,p) C hole effective mass par. A 1 -A 6 optical dielectric constant ε valence split energies Δ 1 - Δ 3 dc dielectric constant ε o deformation potentials a, D 1 -D 4 refractive index n(λ) elastic constants C 13, C 33 absorption coefficient α(λ) lattice constant a thermal conductivity κ dopant activation energy E a LO phonon energy E LO etc. most of these parameters are not exactly known for nitride compounds => main source of uncertainty in nitride laser simulations NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 5 Direct Energy Gap 7 Band Gap Energy (ev) AlN UV blue green red GaN 1 InN In-plane Lattice Constant (nm) Al x Ga 1-x N E g =6.12x (1-x) -1.5x(1-x) In x Ga 1-x N E g =.77x (1-x) x(1-x) NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 6

4 Wurtzite Band Structure Parameters [Vurgaftman & Meyer, JAP 94, 3675, 23] NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 7 Built-in Polarization fixed interface charges due to spontaneous polarization strain induced polarization quantum well effects longer emission wavelength less transition strength [Fiorentini et al., APL 8, 124 (22)] NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 8

5 Polarization Field NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 9 Carrier Mobility μ(n,f,t) PROBLEM: doping effect μ(n) Mg acceptor E A >.17eV hole mobility < 15 cm 2 / Vs hole conductivity constant field effect μ(f) Electron Mobility [cm 2 /Vs] Nakamura et al. fit to Monte Carlo Simulation μ(n) = μ d +(μ -μ d ) / (1+(N/N r ) α ) Goetz et al Electron Density [1 18 cm -3 ] Carrier Mobility [ cm 2 / Vs ] solid: Monte Carlo Simulation electrons holes dashed: fit function μ(f) = μ o / (1+μ o F/v sat ) GaN InGaN Al.2 Ga.8 N SL Electric Field [kv/cm] NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 1

6 GaN-based Light Emitting Diodes [ Ch. 1 in Optoelectronic Devises: Advanced Simulation and Analysis, ed. J. Piprek, Springer 25] NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 11 Ultraviolet LED Design AlGaN Multi-Quantum Well (MQW) Structure [Thomas Katona, PhD Thesis, UCSB 23] NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 12

7 UV Emission Measurement E.L. Intensity (a.u.) ma 5 ma 75 ma 1 ma λ (nm) λ peak = 338 nm FWHM = 8nm NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 13 Power Measurements Max Power =.135 mw at 1mA DC Max Quantum Efficiency =.33% x 3 μm 4 x 4 μm 5 x 5 μm 1 8 Power (mw) Voltage (V) Relative η ext (%) Rseries (Ω) 3 x 3 μm.2 4 x 4 μm 1 5 x 5 μm Current (ma) J (A/cm 2 ) NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 14

8 LED Simulation three-dimensional physics-based model Drift-Diffusion model (incl. thermionic emission) for electrons n(x,y) and holes p(x,y) Spontaneous emission spectrum from wurtzite kp band structure of strained quantum wells Internal temperature T(x,y) from heat flux equation Ray tracing model for light extraction from every source point APSYS by Crosslight Software NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 15 MQW Band Diagram Al.3 Ga.7 N blocker layer: bandgap adjusted from 4.1 ev to 4.5 ev Electron Energy [ev] E C E V n-cladding blocker layer p-cladding Polarization charges Vertical Distance [μm] grey blue quantum wells no polarization charges NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 16

9 3D Simulation Results Internal Emission Rate Vertical Current Density current = 1 ma, bias= 6.5 V NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 17 Carrier Recombination Carrier Density Recombination Rate Carrier Density [1 18 cm -3 ] electrons holes Recombination Rate [1 25 cm -3 s -1 ] radiative non-radiative Vertical Distance [μm] Vertical Distance [μm] electron hole separation in QW strong non-radiative recombination non-radiative lifetime = 1 ns NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 18

10 Carrier Leakage from MQW Vertical Current Density [A/cm 2 ] hole leakage electron injection electron leakage hole injection n-cladding p-cladding Vertical Distance [μm] solid lines: E block = 4.5 ev, dashed lines: E block = 4.1 ev NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 19 LED Efficiency Quantum efficiency η det = η int η opt η cap detected eff. η det =.35 % internal eff. η int = 1. % optical eff. η opt = 4.5 % capture eff. η ext = 82 % triangles: measurement Detected Light Power [mw] Light vs. Current no polarization τ nr = 1 μs in QWs full simulation.1.5 original blocker band gap Injection Current [A] NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 2

11 GaN-based Laser Diode [ Ch. 9 in Semiconductor Optoelectronic Devises: Introduction to Physics and Simulation by J. Piprek, Academic Press, 23] NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 21 Rigde-Waveguide Laser Diode [ Nakamura et al., Jap. J. Appl. Phys, 37 (1998) L12 ] 3nm GaN contact 6nm AlGaN-SL cladding 1nm GaN waveguide 2nm AlGaN barrier 38nm InGaN active 1nm GaN waveguide 12nm AlGaN-SL cladding 1nm InGaN compliance p-contact 2 x 4nm In.15 GaN wells (1.6% cs) 3 x 1nm In.2 GaN barr. (.2% cs) n-contact 3nm GaN Sapphire ELOG substrate substrate SiO 2 ridge width = 3μm, cavity length = 45 μm, facet reflectivity =.18 /.95 NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 22

12 Laser Simulation two-dimensional physics-based model Drift-Diffusion model (incl. thermionic emission) for electrons n(x,y) and holes p(x,y) Strained-QW gain g(λ,n,p,t,x,y) from wurtzite kp band structure Internal temperature T(x,y) from heat flux equation Transversal optical mode intensity W(x,y) from effective index method LASTIP by Crosslight Software NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 23 Comparison to Measurements CW simulation vs. measurement measured near-field 6 5 dots: measurement lines: simulation mW Power [mw] st mode 6 4 Voltage [V] 8mW 1 2nd mode Current [ma] fit parameters α i = 12 cm -1 τ SRH =.5 ns (QW) R th = 75 K/W NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 24

13 Optical Modes vertical profile of index and mode near field profile Refractive Index n-gan n-ingan n-cladding p-cladding p-gan Wave Intensity (a.u.) y (micron) Vertical Position y [μm] optical confinement factor =.15 per quantum well. y (micron) NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 25 Self-Heating thermal resistance: R temperature distribution ΔT P 3K = 4 W MQW th = = 75 heat K W external R th = 3 K/W heat power profile at laser axis NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 26

14 Heat Sources heat power contributions vs. current 1 total power (U*I) light power Joule heat Heat Power [W] Thomson Cooling (negative heat) defect recombination absorption Peltier Heat Current [ma] NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 27 Optical Gain Material Gain [1/cm] (TE) N [1 19 cm -3 ] = T = 2 o C considered: wurtzite band structure incl. strain independent quantum wells self-consistent carrier density band gap renormalization: Material Gain [1/cm] (TE) Wavelength [μm] 2 o C N = 3 x 1 19 cm o C 22 o C ΔE g = (- 4.5 x 1-8 evcm) N 1/3 thermal band gap shrinkage: de g /dt = -.6 mev/k dλ e /dt =.9 nm/k Wavelength [μm] NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 28

15 Quantum Well Active Region Energy [ev] n-gan energy band diagram at power maximum conduction band InGaN/InGaN MQW electron Fermi level p-algan p-gan hole Fermi level valence band I=54mA Vertical Position y [μm] Electron Density [1 19 cm -3 ] n-side QW carrier density profile power maximum threshold QW1 QW2 p-side Vertical Position [μm] band offset ΔE c / ΔE v =.7 /.3 NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 29 Leakage Current 2D current flow 1D electron current profile y (micron) Vertical Electron Current Density j n,y [ka/cm 2 ] n-side power maximum threshold QW1 QW2 electron leakage current p-side Vertical Position [μm] (ridge center) NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 3

16 Carrier Loss Comparison vertical electron leakage into p-region limits maximum lasing power 1 Current Loss [ma] defect recombination spontaneous emission electron leakage Power [mw] Lasing Power: (thr.) 42mW Current [ma] NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 31 Optimization: Facet Coating 6 5 facet reflectance (front / back) P max = 48 mw Output Power (front) [mw] R=.2 /.95 R=.18 /.95 dots: measurement, lines: simulation Current [ma] NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 32

17 Optimization: Heat Sinking removed heat-sink (sapphire) thermal resistance (3 K/W) 8 thermal resistance temperature profile at maximum power Output Power (front) [mw] R th = 45 K/W R th = 75 K/W dots: measurement, lines: simulation Current [ma] P max = 77 mw Temperature [K] n-gan n-superlattice (SL) p-sl heat-sink thermal resistance 3 K/W K/W MQW Vertical Position [μm] NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 33 Summary 1. GaN (opto)electronics creates new opportunities and challenges for device simulation 2. Realistic results possible with careful consideration of material properties NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 34

18 Further Reading Part 1: Material Properties 1. Introduction (Piprek) 2. Electron bandstructure parameters (Vurgaftman/Meyer) 3. Spontaneous and piezoelectric polarization: basic theory vs. practical recipes (Bernardini) 4. Transport parameters for electrons and holes (Bellotti/ Bertazzi) 5. Optical constants of bulk nitrides (Goldhahn / Buchheim/Schley/Winzer/Wenzel) 6. Intersubband absorption in AlGaN quantum wells (Gunna/Bertazzi/Paiella/Bellotti) 7. Interband transitions in InGaN quantum wells (Hader/ Moloney/ Thränhardt/ Koch) 8. Electronic and optical properties of quantum wells with (11) crystal orientation (Park/Chuang) 9. Carrier scattering in quantum-dot systems (Jahnke) Part 2: Devices 1. AlGaN/GaN high electron mobility transistors (Palacios / Mishra) 11. Intersubband optical switches for optical communications (Suzuki) 12. Intersubband electroabsorption modulator (Holmström) 13. Ultraviolet light emitting diodes (Kuo/ Yen/ Chen) 14. Visible light emitting diodes (Karpov) 15. Light-emitting diodes for the generation of white light (Linder/Eisert/Jermann/Berben) 16. Fundamental characteristics of edge-emitting lasers (Hatakoshi) 17. Resonant internal transverse-mode coupling in InGaN/GaN/AlGaN lasers (Smolyakov/Osiński) 18. Optical properties of edge-emitting lasers: measurement and simulation Schwarz Witzigmann) 19. Electronic properties of InGaN vertical-cavity lasers (Piprek/ Li/ Farrell/DenBaars/Nakamura) 2. Optical design of vertical-cavity lasers (Nakwaski/Czyszanowski/Sarzala) 21. GaN nanowire lasers (Maslov/Ning) to be published in January 27 NUSOD 6 Tutorial MA2, Joachim Piprek 9/11/6 35