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
Leeds
Jan 2012
Rome Sept
2011
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
Leeds
Jan 2012
Rome Sept
2011
Piezoelectricity in III-V semiconductors
+
-
+
+
Applied Strain
+
+
+
+
4
identical
sp3
orbitals
+
Only 3
identical
sp3
orbitals
Piezoelectric
Polarisation
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Jan 2012
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2011
-
Pi   eikl ekl
k ,l
Atomic Displacement model
In-plane Strain
δr
Shear Strain
direct
P
= eZH *  r
W. A. Harrison: Electronic Structure and
Properties of Solids, Dover, New York (1989).
Material parameters :
i 1
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)
Leeds
Jan 2012
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2011


Pkdipoles  2 p 1   p 2   rq  k  Rq
4
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
Psp (C/m2)
-0.007 (-0.029th)
e31(C/m2)
-0.55 (-0.55exp)
e33 (C/m2)
1.05 (1.12exp)
e15 (C/m2)
-0.57(-0.38th)
-0.051 (-0.081th) -0.012 (-0.032th)
-0.6 (-0.6exp)
-0.55 (-0.55exp)
1.47 (1.50exp)
1.07 (0.95exp)
-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
Total Polarization with Second Order effects
PTot  Psp  e33   2e31 //  e311 // 2  e333 2  e133 // 
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Jan 2012
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2011
J. Pal et al, Phys. Rev. B 84, 085211 (2011)
Total Polarization (PT) v Strain
0.3
0.3
a)GaN
0.1
0.2
0.0
-0.1
-0.2
0.3
Linear Pz
This Work
2
Polarization (in C/m )
0.2
Polarization (in C/m2)
0.1 e 
b)AlN
Linear Pz
This Work
0.2
Linear Pz
This Work
0.1
0.0
-0.1
-0.2
e
-0.3
-0.4
-0.3
0.0
-0.10
-0.05
0.00
0.05
-0.5
0.10
In-plane Strain (e//)
0.3
-0.1
-0.2
e
-0.3
-0.10
-0.10
-0.05
Linear Pz
This Work
c)InN
0.1
0.0
-0.1
-0.05
-0.2
e
0.10
0.05
0.00
In-plane Strain (e//)
-0.3
-0.10
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2011
0.00
0.05
In-plane Strain (e//)
0.2
Polarization (in C/m2)
Polarization (in C/m2)
a)GaN
-0.05
0.00
0.05
0.10
In-plane Strain (e)
J. Pal et al, Phys. Rev. B 84, 085211 (2011)
0.10
Spontaneous Polarization (Psp) in Alloys
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Jan 2012
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2011
J. Pal et al, Phys. Rev. B 84, 085211 (2011)
Piezoelectric field in Binary III-N Quantum Wells
Quantum Well
GaN/AlN
GaN/AlN
Experiment
(MV/cm)
10.20
8.00
This work
(MV/cm)
10.30
Previous work
(MV/cm)
10.65
8.06
8.43
Lw/Lb
2.6/100
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
6.072
6.55
1.4/1.9
9.25th(8.13 th)
9.13(5.9)
6.71
4/6
5.21th(11.17th)
5.71(9.23)
4.11
6/4
6.4(8.57)
5.11
8/6
GaN/AlN
InN/GaN
InN/GaN
InN/GaN
Leeds
Jan 2012
Rome Sept
2011
6.07
5.89th(8.61th)
J. Pal et al, Phys. Rev. B 84, 085211 (2011)
Piezoelectric field in Binary III-N Quantum Wells
Leeds
Jan 2012
Rome Sept
2011
J. Pal et al, Opt Quant Electron (2011) (published online)
Piezoelectric field in Ternary III-N Quantum Wells
Quantum Well
Experiment This work
(kV/cm)
Al0.17Ga0.83N/GaN
760
Al0.65Ga0.35N/GaN
2000
GaN/In0.06Ga0.94N
(kV/cm)
Previous work
Lw/Lb
(kV/cm)
760
1205
3/5
2090
2170
6/3
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
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Jan 2012
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2011
J. Pal et al, Phys. Rev. B 84, 085211 (2011)
Excitonic Structure in III-N Alloy Quantum Dots
Exciton X0
Biexciton 2X
Biexcitonic Shift :
Optimization
Function:
Bxx = Exx - 2Ex
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
Exx: Biexciton Energy
 2nd Order Piezoelectricity
Ex: Exciton Energy
 Spontaneous Polarization
A. Mohan et al, Nphoton.2010.2 (2010)
 Shape (Aspect Ratio D/h)
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Jan 2012
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2011
S. Tomic, A. Sunderland, I. Bush, J. Mat. Chem. 16, 1963 (2006)
S. Tomić & N. Vukmirović, Physical Review B 79, 245330 (2009)
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
Leeds
Jan 2012
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2011
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
Leeds
Jan 2012
Rome Sept
2011
Excitonic Structure in III-N Alloy Quantum Dots
0.20
In=20%
In=30%
In=40%
In=50%
In=60%
In=70%
1.8 2.4
1.2 1.8 2.4
0.8 1.6 2.4

0.15
0.10
0.05
0.00
2.8
3.2
2.4 2.8
2.0 2.4 2.8
Ex
Optimization function for Single Photon Source :
Tunability in the InGaN Quantum dots (based on the In content)
Application : Generation of Single Photon Source
Leeds
Jan 2012
Rome Sept
2011
6
7
8
9
10
11
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
Leeds
Jan 2012
Rome Sept
2011
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
Leeds
Jan 2012
Rome Sept
2011