impact of non-linear piezoelectricity on excitonic properties of

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


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


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

+

++

+-


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)


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)



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


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


-0.10 -0.05 0.00 0.05 0.10-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3


Po

lari

zati

on

(in

C/m

2 )a)GaN Linear Pz

This Work

e


Spontaneous Polarization (Spontaneous Polarization (PPspsp) in Alloys) in Alloys



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



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)


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



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:



Biexciton shift: Alloy composition dependence in InGaN Quantum dotsApplication : Generation of Entangled Photon Source,

Multi Exciton Generation (MEG) Solar Cells



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



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



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)


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

impact of non-linear piezoelectricity on excitonic properties of

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