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Impact of Non-Linear Piezoelectricity on Excitonic Properties of

Impact of Non-Linear Piezoelectricity on Excitonic Properties of III-N Semiconductor Quantum Dots. Joydeep Pal Microelectronics and Nanostructures Group School of Electrical and Electronic Engineering. Outline. Contents. Introduction to Piezoelectric Effect

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Impact of Non-Linear Piezoelectricity on Excitonic Properties of

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  1. Impact of Non-Linear Piezoelectricity on Excitonic Properties of III-N Semiconductor Quantum Dots Joydeep Pal Microelectronics and Nanostructures Group School of Electrical and Electronic Engineering

  2. Outline Contents • Introduction to Piezoelectric Effect • Physical Parameters: Bulk and Strained III-N systems • Piezoelectric field in Quantum Wells: Impact of the Non-linear piezoelectric effect • Excitonic properties of Quantum Dots: Study on InGaN QDs

  3. + + + - + - + + + + Piezoelectric Polarisation Piezoelectricity in III-V semiconductors Applied Strain 4 identical sp3 orbitals Only 3 identical sp3 orbitals

  4. In-plane Strain δr Shear Strain Atomic Displacement model W. A. Harrison: Electronic Structure and Properties of Solids, Dover, New York (1989). Material parameters : αp: bond polarity ZH*: effective ionic charge (depends on αp) M. Migliorato et al, Phys. Rev. B 74, 245332 (2006), R.Garg et al,Appl. Phys. Lett. 95, 041912 (2009) J. Pal et al, Phys. Rev. B 84, 085211 (2011)

  5. Physical parameters of Group-III-Nitrides Parameters GaN AlN InN a (Ǻ) 3.155 3.063 3.523 c (Ǻ) 5.149 4.906 5.725 u (Ǻ) 0.376 0.382 0.377 Z* 2.583 2.553 2.850 αp 0.517 0.511 0.578 Z*H 0.70 0.85 0.65 e31(C/m2) -0.55 (-0.55exp) -0.6 (-0.6exp) -0.55 (-0.55exp) e33 (C/m2) 1.05 (1.12exp) 1.47 (1.50exp) 1.07 (0.95exp) e15 (C/m2) -0.57(-0.38th) -0.6 (-0.48exp) -0.65 (-0.44th) e311(C/m2) 6.185 5.850 5.151 e333(C/m2) -8.090 -10.750 -6.680 e133(C/m2) 1.543 4.533 1.280 Psp (C/m2) -0.007 (-0.029th) -0.051 (-0.081th) -0.012 (-0.032th) Total Polarization with Second Order effects J. Pal et al, Phys. Rev. B 84, 085211 (2011)

  6. Total Polarization (PT) v Strain J. Pal et al, Phys. Rev. B 84, 085211 (2011)

  7. Spontaneous Polarization (Psp) in Alloys J. Pal et al, Phys. Rev. B 84, 085211 (2011)

  8. Piezoelectric field in Binary III-N Quantum Wells Quantum Well Experiment This work Previous work Lw/Lb (MV/cm) (MV/cm) (MV/cm)  GaN/AlN 10.20 10.30 10.65 2.6/100  GaN/AlN 8.00 8.06 8.43 2.5/6 GaN/AlN 10.00 ±1.00 9.00 ±0.50 6.0 ±1.00 (0.8 ±0.26)/ (2.8±0.52) GaN/AlN 5.04 5.06 4.76 2.3/1.9 GaN/AlN 6.07 6.072 6.55 1.4/1.9 InN/GaN 9.25th(8.13 th) 9.13(5.9) 6.71 4/6  InN/GaN 5.21th(11.17th) 5.71(9.23) 4.11 6/4   InN/GaN 5.89th(8.61th) 6.4(8.57) 5.11 8/6 J. Pal et al, Phys. Rev. B 84, 085211 (2011)

  9. Piezoelectric field in Binary III-N Quantum Wells J. Pal et al, Opt Quant Electron (2011) (published online)

  10. Piezoelectric field in Ternary III-N Quantum Wells Quantum Well Experiment This work Previous work Lw/Lb (kV/cm) (kV/cm) (kV/cm) Al0.17Ga0.83N/GaN 760 760 1205 3/5 Al0.65Ga0.35N/GaN 2000 2090 2170 6/3 GaN/In0.06Ga0.94N 605 610 544 3/3 GaN/In0.09Ga0.91N 1000 960 766 3/3 GaN/In0.11Ga0.89N 1330 1310 1210 3/3 GaN/In0.12Ga0.88N 1600 1603 1500 3/6 GaN/In0.22Ga0.78N 3090 3097 3132 3/8 J. Pal et al, Phys. Rev. B 84, 085211 (2011)

  11. Excitonic Structure in III-N Alloy Quantum Dots Exciton X0 Biexciton 2X Biexcitonic Shift : Bxx = Exx - 2Ex Optimization Function: Ξ = Bxx*ln(px(x)/px(0)) • Exx and Ex calculated with full configuration interaction (CI) Hamiltonian (Ne=12, Nh=18) • parallel kppw 8 Band k.p calculation including • Strain • Spin-Orbit interaction • 2nd Order Piezoelectricity • Spontaneous Polarization • Shape (Aspect Ratio D/h) Exx: Biexciton Energy Ex: Exciton Energy A. Mohan et al, Nphoton.2010.2 (2010) S. Tomic, A. Sunderland, I. Bush, J. Mat. Chem. 16, 1963 (2006) S. Tomić & N. Vukmirović, Physical Review B 79, 245330 (2009)

  12. Excitonic Structure in III-N Alloy Quantum Dots Biexciton shift: Alloy composition dependence in InGaN Quantum dots Application : Generation of Entangled Photon Source, Multi Exciton Generation (MEG) Solar Cells

  13. Excitonic Structure in III-N Alloy Quantum Dots Exx = 2Ex D/h = 5 Bound Biexciton: Light emission at different energies by tuning the alloy content in the InGaN Quantum dots Main Application : Entangled photon source covering the visible light spectra

  14. Excitonic Structure in III-N Alloy Quantum Dots Optimization function for Single Photon Source : Tunability in the InGaN Quantum dots (based on the In content) Application : Generation of Single Photon Source

  15. Excitonic Structure in III-N Alloy Quantum Dots Maximum values of Optimization Function (Ξ) Optimization function : Best suitable light emission energy range dependent on alloy composition in InGaN Quantum dots Main Application : Widely tunable single photon source

  16. Conclusions & Acknowledgements • A new improved set of piezoelectric coefficients for III-N has been presented. Second order effects are sizeable. • Most notably the spontaneous polarization is substantially smaller than previously believed. • Predictions of the binding energy of excitons in InGaN QDs show that it is possible to obtain entangled photons for a large range of compositions • Since photons appear to be possible across the visible range our study suggests that nitride based QDs should be further investigated experimentally as single photon sources • Many thanks and gratitude go to: • Max Migliorato, Geoffrey Tse, Vesel Haxha, Raman Garg (University of Manchester) • Stanko Tomić (University of Salford) • Robert Young (University of Lancaster) • CASTEP Development Group, Matt Probert & Phil Hasnip (York) • High Performance Computing (HPC) facility in Manchester (University of Manchester) and SCARF in STFC Rutherford Appleton Lab

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