impact of non-linear piezoelectricity on excitonic properties of
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Rome Sept 2011Leeds 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
Rome Sept 2011Leeds Jan 2012
OutlineOutline
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
Rome Sept 2011Leeds Jan 2012
Piezoelectricity in III-V semiconductorsPiezoelectricity in III-V semiconductors
,i ikl kl
k l
P e e Piezoelectric Polarisation
+
++
+- Applied Strain
4 identical
sp3
orbitals
Only 3 identical
sp3
orbitals
+
++
+-
Rome Sept 2011Leeds Jan 2012
Atomic Displacement modelAtomic Displacement model
δr
directH = eZ * rP
Material parameters :αp: bond polarity
ZH*: effective ionic charge (depends on αp)
4
2
1
2 1dipolesk p p q q
i
P r k R
��������������
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)
Rome Sept 2011Leeds Jan 2012
Physical parameters of Group-III-NitridesPhysical parameters of Group-III-NitridesParameters 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
2 233 31 // 311 // 333 133 //2Tot spP P e e e e e
Total Polarization with Second Order effects
Psp (C/m2) -0.007 (-0.029th) -0.051 (-0.081th) -0.012 (-0.032th)
J. Pal et al, Phys. Rev. B 84, 085211 (2011)
Rome Sept 2011Leeds Jan 2012
Total Polarization (PTotal Polarization (PTT) v Strain) v Strain
-0.10 -0.05 0.00 0.05 0.10-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
In-plane Strain (e//)
Po
lari
zati
on
(in
C/m
2 )a)GaN Linear Pz
This Work
e
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
-0.10 -0.05 0.00 0.05 0.10
In-plane Strain (e//)
Po
lari
zati
on
(in
C/m
2)
Linear Pz This Work
b)AlN
e
-0.10 -0.05 0.00 0.05 0.10-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3 Linear Pz
This Work
c)InN
In-plane Strain (e)
Po
lari
zati
on
(in
C/m
2)
c)InN
e
J. Pal et al, Phys. Rev. B 84, 085211 (2011)
-0.10 -0.05 0.00 0.05 0.10-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
In-plane Strain (e//)
Po
lari
zati
on
(in
C/m
2 )a)GaN Linear Pz
This Work
e
Rome Sept 2011Leeds Jan 2012
Spontaneous Polarization (Spontaneous Polarization (PPspsp) in Alloys) in Alloys
J. Pal et al, Phys. Rev. B 84, 085211 (2011)
Rome Sept 2011Leeds Jan 2012
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
Piezoelectric field in Binary III-N Quantum Wells Piezoelectric field in Binary III-N Quantum Wells
J. Pal et al, Phys. Rev. B 84, 085211 (2011)
Rome Sept 2011Leeds Jan 2012
Piezoelectric field in Binary III-N Quantum Wells Piezoelectric field in Binary III-N Quantum Wells
J. Pal et al, Opt Quant Electron (2011) (published online)
Rome Sept 2011Leeds Jan 2012
Piezoelectric field in Ternary III-N Quantum Wells 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)
Rome Sept 2011Leeds Jan 2012
Excitonic Structure in III-N Alloy Quantum DotsExcitonic Structure in III-N Alloy Quantum Dots
Bxx = Exx - 2ExBiexcitonic Shift :
•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 EnergyEx: Exciton Energy
Exciton X0
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(px(x)/px
(0))Optimization
Function:
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Excitonic Structure in III-N Alloy Quantum DotsExcitonic Structure in III-N Alloy Quantum Dots
Biexciton shift: Alloy composition dependence in InGaN Quantum dotsApplication : Generation of Entangled Photon Source,
Multi Exciton Generation (MEG) Solar Cells
Rome Sept 2011Leeds Jan 2012
Excitonic Structure in III-N Alloy Quantum DotsExcitonic 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
Exx = 2Ex
D/h = 5
Rome Sept 2011Leeds Jan 2012
Excitonic Structure in III-N Alloy Quantum DotsExcitonic 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
2.8 3.20.00
0.05
0.10
0.15
0.20
2.4 2.8 2.0 2.4 2.8 1.8 2.4 1.2 1.8 2.4 0.8 1.6 2.4
6 7 8 9 10 11
In=70%In=60%In=50%In=40%In=30%In=20%
Ex
Rome Sept 2011Leeds Jan 2012
Excitonic Structure in III-N Alloy Quantum DotsExcitonic 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)
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Conclusions & AcknowledgementsConclusions & Acknowledgements
Many thanks and gratitude go to: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
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