Optical Gain Analysis of Strain Compensated InGaN- AlGaN Quantum Well Active Region for Lasers Emitting at 46-5 nm ongping Zhao, Ronald A. Arif, Yik-Khoon Ee, and Nelson Tansu ±, Department of Electrical and Computer Engineering, Lehigh University Email: oz7@lehigh.edu, ± Email: Tansu@Lehigh.Edu Research Group: www.ece.lehigh.edu/~tansu Numerical Simulation of Optoelectronic Devices NUSOD 7 - Laser Diode II,WB3 Newark, Delaware September 6 th, 7
Outline Motivation The challenge of conventional InGaN QW Strain Compensated QW for improve gain media Theoretical Formulation of 6-band k p method for III-Nitride Incorporate SO-coupling and valence band mixing Incorporate strain effect Incorporate spontaneous and piezoelectric field Spontaneous emission and optical gain properties 46-nm Conventional Vs. Strain Compensated QW 5-nm Threshold Analysis for Laser Applications Summary
Characteristic of InGaN QW The advantages of III-Nitride based QW Cover a wide spectral range, from near-ir (InN) to UV (GaN) In x Ga 1-x N QW can cover emission from Blue, Green and Red Major challenges preventing high performance conventional InGaN QW Strain misfit dislocation density from strain-mismatch InGaN/GaN Phase separation in high-in content InGaN QW The existence of electrostatic field in III-nitrides Reduction of electron & hole wave function overlap Nanostructure Engineering Staggered InGaN QW 1, Type-II InGaN-GaNAs QW 3 1. R. A. Arif, Y. K. Ee, and N. Tansu, Appl. Phys. Lett., vol. 91 (9), Art. 9111, August 7.. R. A. Arif, Y. K. Ee, and N. Tansu, in Proc. of the IEEE/OSA Conference on Lasers and Electro-Optics (CLEO) 7, Baltimore, MD, May 7; 3. R. A. Arif, Y. K. Ee, and N. Tansu, in Proc. of the IEEE/OSA Conference on Lasers and Electro-Optics (CLEO) 6, Long Beach, CA, May 6.
Staggered / Graded InGaN QW 1, for Enhanced Radiative Recombination Rate Energy (ev).9 -. -1.3 -.4-3.5 Ψ e E c Ψ hh E v Γ e-hh = 64.14% 7.5 Å In.5 Ga.75 N QW 7.5 Å In.15 Ga.85 N QW -8-6 -4-4 6 8 z (Å) Intensity (A.U) 5 4 3 1 Room Temp CL Staggered InGaN QWs Γ e_hh e-hh = ~ 64.14% 69 % λ peak ~ = 47 nm Conventional InGaN QWs Conventional InGaN QWs Γ e_hh = 36.9 % Γ e-hh ~ 38 λ λ peak = 417 nm Peak ~ 417 nm 35 375 4 45 45 475 5 Wavelength (nm) Staggered InGaN QW with improved Γ e_hh ~ 64% Conventional QW with Γ e_hh ~ 36% Electrical Injected Staggered InGaN QW LEDs 1, (grown by MOCVD) Experiments (CL, PL, devices) show good agreement with theory 1. R. A. Arif, Y. K. Ee, and N. Tansu, Appl. Phys. Lett., vol. 91 (9), Art. 9111, August 7.. R. A. Arif, Y. K. Ee, and N. Tansu, Conference on Lasers and Electro-Optics 7, Baltimore, MD, May 7.
E g (ev) Strain compensated InGaN QW 1 7 6 5 4 3 1 AlN GaN InN 3 3.1 3. 3.3 3.4 3.5 3.6 Lattice Constant a (Å) a_inn=3.545 Å a_ingan >a_gan Compressive Strain a_gan=3.189 Å a_aln=3.11 Å a_algan <a_gan Tensile Strain Conventional InGaN QW GaN InGaN Introduce Tensile Barriers Strain Compensated InGaN QW AlGaN GaN
6 5 4 3 1 u u u u u u G K K F G K K F Δ Δ Δ Δ = λ λ 6 x 6 amiltonian matrix for valence band λ θ Δ Δ = 1 F θ λ Δ Δ = 1 G [ ] λ λ = ) ( 1 y x z k k A A k m h ) ( 1 yy xx zz D D λ = [ ] θ θ = ) ( 4 3 y x z k k A A k m h ) 4( 3 yy xx zz D D θ = = 5 5 ) ( D ik k A m K y x h = z z y x D k ik k A m 6 6 ) ( h Δ 3 Δ = yy xy xx i ± = ± yz zx z i ± = ± 1 Chuang S L and Chang C S, Physical Review B, 54 491, 1996
Polarization in III-Nitride Semiconductors Two types of Polarization existed in wurtzite crystals Spontaneous Polarization (SP) Piezoelectric Polarization (PZ) Strain induced Calculation of PZ i i i i C13 31 ( C11 C1 ) i C33 i P = d PZ i(3) xx Electric Field due to polarization in QW b b w w b ( PSP PPZ PSP PPZ ) L Ez = b w w b L L amiltonian incorporating with polarization υ [ z = υυ qe z δυυ ] gυ E gυ 1 F. Bernardini and V. Fiorentini, phys. stat. sol. (b), 16, 391 (1999).
Strain-Compensated InGaN-AlGaN QW GaN GaN 1-nm Al.1 Ga.9 N Energy (ev) 4-Ǻ In. Ga.78 N GaN 4-Ǻ In. Ga.78 N GaN Γ=9.18% Γ=34.54% z (nm) Strain-Compensated InGaN-AlGaN QW z (nm) Allows a strain-balanced structure reduction in the strain energy reduction in strain-misfit dislocation density Leads to Improved Optical Gain Larger ΔE c and ΔE v improve carrier confinement in QW advantageous for high temperature operation
Spontaneous Emission Spectrum Spontaneous emission spectrum (x1 7 s -1 cm -3 ev -1 ) In. Ga.78 N - Al.1 Ga.9 N QW In. Ga.78 N - GaN QW n=x1 19 cm -3 n=5x1 19 cm -3 g e sp q Photon Energy (ev) t t σ ( hω) ( M ) ( k ) c m π = n r ωl Strain-compensated InGaN-AlGaN QW exhibit increase in spontaneous emission rate ( )( v kt 1 fσ m ( kt ))( γ / π ) cv ( k ) ω γ c k dk f n e nm t σ = U, L n, m π w σ, nm t h ( ) E
Material Gain properties of InGaN QW Conventional Vs. Strain Compensated InGaN QW In. Ga.78 N - Al.1 Ga.9 N QW Material Gain (cm -1 ) n=x1 19 cm -3 In. Ga.78 N - GaN QW n=1x1 19 cm -3 n=5x1 19 cm -3 Peak Material Gain (cm -1 ) In. Ga.78 N-Al.1 Ga.9 N QW In. Ga.78 N-GaN QW g Photon Energy (ev) e hω ΔF ( hω) = g ( hω) 1 exp sp k B T λ~46 nm: (n=1x1 19 cm -3 ) In. Ga.78 N-Al.1 GaN: g~1889cm -1 In. Ga.78 N-GaN: g~1374cm -1 Relatively similar transparency carrier density n tr = 1.94-1.95x1 19 cm -3 Carrier Density (x 1 19 cm -3 ) 48% improvement
Gain Characteristics for Polar III-Nitride Transition with all allowed states Transition with same quantum number Material Gain (cm -1 ) Due to the transitions E1 E1 L Photon Energy (ev) Non-Polar Symmetric band lineup Zero matrix element for n c n v transitions Polar III-Nitrides Asymmetric band lineup Non-zero matrix element for all confined states transitions 1 1 Claus Klingshirn, Semiconductor Optics, Springer, 6
Differential Gain of InGaN QW dg/dn (x 1-17 cm ) 6 5 4 3 1 In. Ga.78 N-Al.1 Ga.9 N QW In. Ga.78 N-GaN QW 4 6 8 1 1 14 Carrier Density (x 1 19 cm -3 ) Differential gain near transparency Conventional Structure:4. 1-17 cm Strain-compensated structure:5.8 1-17 cm
R sp and Radiative Current Density for InGaN QW R sp (x1 7 s -1 cm -3 ) In. Ga.78 N-Al.1 Ga.9 N QW Material Gain (cm -1 ) 18 16 14 1 1 8 6 In. Ga.78 N - Al.1 Ga.9 N QW In. Ga.78 N - GaN QW In. Ga.78 N-GaN QW Carrier Density (x 1 19 cm -3 ) 4 5 1 15 5 Radiative Current Density (A/cm - ) 5%-4% improvement of spontaneous emission rate for InGaN-AlGaN structure at different carrier density J rad =qdr sp Reduction of radiative current density for strain-compensated structure
Threshold Analysis for InGaN QW Lasers Mirror Loss L cav = 7 μm R 1 ~ 17% Laser Structure R ~ 17% α m = 1 l ln 1 R R 1 R efractive index.8.7.6.5.4.3 C-plane Sapphire Substrate Threshold Gain Γ optical = 4% Γ optical ~ 3. % n-al.6 GaN E(z) Structure A Active Regions.3 μm u-gan 1-nm p-al.3 Ga.7 N Electron Blocking Layer 5-nm u-gan 1 pairs of SL.5 nm p-gan /.5 u-al.9 Ga.91 N p- Al.1 Ga.9 N 14 18 6 3 z (nm) z Γg α m 5.5 cm -1 = α α α = 6 cm i th i 1 g th = 18 cm -1 (per QW) m
Material Peak Gain (cm -1 ) 5 15 1 5 Threshold Analysis for Strain-Compensated InGaN QW A=5x1 7 s -1 In. Ga.78 N - Al.1 Ga.9 N QW In. Ga.78 N - GaN QW A=1x1 8 s -1 A=x1 8 s -1 4 6 8 1 J tot (A/cm /QW) J nr =qdr nr J Rad =qdr sp J tot =J nr J rad R nr =An J th for InGaN-GaN 4-QWs (A/cm ) J tot for InGaN-AlGaN 4-QWs (A/cm ) A=5x1 7 s -1 146.4 1, 1.3 A=1x1 8 s -1 174.4 1537.9 A=x1 8 s -1 371.4 613.1 1. S. Nagahama, N. Iwasa, M. Senoh, T. Matsushita, Y. Sugimoto,. Kiyoku, T. Kozaki, M. Sano,. Matsumura,. Umemoto, K. Chocho, T. Yanamoto, and T. Mukai, phys. stat. sol. (a) 188, No. 1, pp. 1 7 (1).. S. Nagahama, Y. Sugimoto, T. Kozaki, and T. Mukai, Proc. of SPIE Photonics West, San Jose, CA, USA, January 5.
Gain characteristics for Strain-Compensated InGaN QW at 5 nm In.7 Ga.73 N - Al.1 Ga.9 N QW Material Gain (cm -1 ) n=x1 19 cm -3 In.7 Ga.73 N - GaN QW n=1x1 19 cm -3 n=5x1 19 cm -3 Peak Material Gain (cm -1 ) In.7 Ga.73 N-Al.1 Ga.9 N QW In.7 Ga.73 N-GaN QW Photon Energy (ev) Carrier Density (x 1 19 cm -3 ) Strain-Compensated InGaN-AlGaN QW (5-nm) Improvement in peak optical gain by~ 3-35 % Reduction in the threshold carrier density (g th ~18 cm -1 ) Reduction of J nr by ~ 4% Reduction of J rad by ~56% Significantly reduce J th
Summary Strain-compensated InGaN-AlGaN QW for improved gain media (46-nm, 5-nm) Spontaneous emission rate Gain spectrum Monomolecular recombination rate Numerical Modeling using 6-band k.p formalism Threshold current density Strain-compensated InGaN QW has potential for achieving: Low threshold current density lasers Improved efficiency LEDs Future Works Epitaxy of strain-compensated InGaN-AlGaN QW structure Improving the simulation design for long wavelength emission Funding supports by: NSF ECCS Division #7141 DOD-Army Research Lab Peter C. Rossin Professorship Funds
Material Parameters Used in Simulations Parameters GaN AlN InN * m // /m at 3 K.1.3.7 m * /m at 3 K..3.7 A 1-7.1-3.86-8.1 A -.44 -.5 -.68 A 3 6.68 3.58 7.57 A 4-3.46-1.3-5.3 A 5-3.4-1.47-5.11 A 6-4.9-1.64-5.96 E g (ev) at 3 K 3.437 6..645 Δ cr (ev).1 -.7.4 Δ so (ev).17.36.5 a cz (ev) -7.1-3.4-4. a ct (ev) -9.9-11.8-4. D 1 (ev) -3.6 -.9-3.6 D (ev) 1.7 4.9 1.7 D 3 (ev) 5. 9.4 5. D 4 (ev) -.7-4. -.7 C 13 (GPa) 16 18 9 C 33 (GPa) 398 373 4 d 13 (pmv -1 ) -1. -.1-3.5 d 33 (pmv -1 ) 1.9 5.4 7.6 P sp (C/m ) -.34 -.9 -.4 1. J. Piprek., Nitride Semiconductor Devices: Physics and Applications, Wiley, 7. Chapter (Meyer and Vurgaftmann)