1. Rome Sept 2011 Leeds Jan 2012 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. Rome Sept 2011 Leeds Jan 2012 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. Rome Sept 2011 Leeds Jan 2012 Piezoelectricity in III-V semiconductors Piezoelectric Polarisation + + + + - Applied Strain 4 identical sp 3 orbitals Only 3 identical sp 3 orbitals + + + + -

4. Rome Sept 2011 Leeds Jan 2012 Atomic Displacement model δrδr Material parameters : α p : bond polarity Z H *: effective ionic charge (depends on α p ) In-plane Strain Shear Strain M. Migliorato et al, Phys. Rev. B 74, 245332 (2006), R.Garg et al,Appl. Phys. Lett. 95, 041912 (2009) W. A. Harrison: Electronic Structure and Properties of Solids, Dover, New York (1989). J. Pal et al, Phys. Rev. B 84, 085211 (2011)

5. Rome Sept 2011 Leeds Jan 2012 Physical parameters of Group-III-Nitrides ParametersGaNAlN InN a (Ǻ)3.1553.063 3.523 c (Ǻ)5.1494.906 5.725 u (Ǻ)0.3760.382 0.377 Z* 2.5832.553 2.850 α p 0.5170.511 0.578 Z* H 0.700.85 0.65 e 31 (C/m 2 ) -0.55 (-0.55 exp ) -0.6 (-0.6 exp ) -0.55 (-0.55 exp ) e 33 (C/m 2 )1.05 (1.12 exp ) 1.47 (1.50 exp )1.07 (0.95 exp ) e 15 (C/m 2 ) -0.57(-0.38 th ) -0.6 (-0.48 exp ) -0.65 (-0.44 th ) e 311 (C/m 2 )6.1855.8505.151 e 333 (C/m 2 ) -8.090 -10.750 -6.680 e 133 (C/m 2 )1.5434.5331.280 Total Polarization with Second Order effects P sp (C/m 2 ) -0.007 (-0.029 th ) -0.051 (-0.081 th ) -0.012 (-0.032 th ) J. Pal et al, Phys. Rev. B 84, 085211 (2011)

6. Rome Sept 2011 Leeds Jan 2012 Total Polarization (P T ) v Strain J. Pal et al, Phys. Rev. B 84, 085211 (2011)

7. Rome Sept 2011 Leeds Jan 2012 Spontaneous Polarization (P sp ) in Alloys J. Pal et al, Phys. Rev. B 84, 085211 (2011)

8. Rome Sept 2011 Leeds Jan 2012 Quantum Well Experiment This work Previous work Lw/Lb (MV/cm) (MV/cm) (MV/cm) GaN/AlN10.20 10.3010.65 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/AlN6.07 6.072 6.55 1.4/1.9 InN/GaN 9.25 th (8.13 th ) 9.13(5.9) 6.71 4/6 InN/GaN 5.21 th (11.17 th ) 5.71(9.23) 4.11 6/4 InN/GaN 5.89 th (8.61 th ) 6.4(8.57) 5.11 8/6 Piezoelectric field in Binary III-N Quantum Wells J. Pal et al, Phys. Rev. B 84, 085211 (2011)

9. Rome Sept 2011 Leeds Jan 2012 Piezoelectric field in Binary III-N Quantum Wells J. Pal et al, Opt Quant Electron (2011) (published online)

10. Rome Sept 2011 Leeds Jan 2012 Piezoelectric field in Ternary III-N Quantum Wells Quantum Well Experiment This work Previous work Lw/Lb (kV/cm) (kV/cm) (kV/cm) Al 0.17 Ga 0.83 N/GaN 760 760 1205 3/5 Al 0.65 Ga 0.35 N/GaN 2000 2090 2170 6/3 GaN/In 0.06 Ga 0.94 N 605 610 544 3/3 GaN/In 0.09 Ga 0.91 N 1000 960 766 3/3 GaN/In 0.11 Ga 0.89 N 1330 1310 12103/3 GaN/In 0.12 Ga 0.88 N 1600 1603 15003/6 GaN/In 0.22 Ga 0.78 N 3090 3097 31323/8 J. Pal et al, Phys. Rev. B 84, 085211 (2011)

11. Rome Sept 2011 Leeds Jan 2012 Excitonic Structure in III-N Alloy Quantum Dots Bxx = Exx - 2Ex Biexcitonic Shift : Exx and Ex calculated with full configuration interaction (CI) Hamiltonian (N e =12, N h = 18) parallel kppw 8 Band k.p calculation including  Strain  Spin-Orbit interaction  2 nd Order Piezoelectricity  Spontaneous Polarization  Shape (Aspect Ratio D/h) Exx: Biexciton Energy Ex: Exciton Energy Exciton X 0 Biexciton 2X S. Tomic, A. Sunderland, I. Bush, J. Mat. Chem. 16, 1963 (2006) S. Tomić & N. Vukmirović, Physical Review B 79, 245330 (2009) A. Mohan et al, Nphoton.2010.2 (2010) Ξ = Bxx*ln(p x (x) /p x (0) ) Optimization Function:

12. Rome Sept 2011 Leeds Jan 2012 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. Rome Sept 2011 Leeds Jan 2012 Excitonic Structure in III-N Alloy Quantum Dots 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 E xx = 2E x D/h = 5

14. Rome Sept 2011 Leeds Jan 2012 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. Rome Sept 2011 Leeds Jan 2012 Excitonic Structure in III-N Alloy Quantum Dots Optimization function : Best suitable light emission energy range dependent on alloy composition in InGaN Quantum dots Main Application : Widely tunable single photon source Maximum values of Optimization Function (Ξ)

16. Rome Sept 2011 Leeds Jan 2012 Conclusions & Acknowledgements 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 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