Quantum Dots in Photonic Structures Lecture 8: Semiconducotor Quantum dots www.qcadesigner.ca Jan Suffczyński cqd.eecs.northwestern.edu Wednesdays, 17.00, SDT Projekt Fizyka Plus nr POKL.04.01.02-00-034/11 współfinansowany przez Unię Europejską ze środków Europejskiego Funduszu Społecznego w ramach Programu Operacyjnego Kapitał Ludzki

Ordering in self-organized Plan for today Reminder 2. Excitons in semiconductor quantum dots 3. Ordering in self-organized Quantum Dot system

Holes Consider an insulator (or semiconductor) with a few electrons excited from the valence band into the conduction band “Deficiency” of negative charge can be treated as a positive charge Negative curvature of the band  negative hole effective mass

Semiconductor Quantum Well

Semiconductor Quantum Well

Semiconductor Quantum Well Confinement potential

Quantum Confinement in Nanostructures 1 Direction: Quantum well (thin film) Two-dimensional excitons 2 Directions: Quantum wire One-dimensional excitons 3 Directions: Quantum dot Zero-dimensional excitons Each confinement direction converts a continuous k in a discrete quantum number n. kx ky nz kx nz ny ny nz nx

Density of states Structure Degree of Confinement Bulk Material 0D Quantum Well 1D 1 Quantum Wire 2D Quantum Dot 3D d(E)

Confined levels in Quantum Wells Energy of confined levels GaAs/AlGaAs Quantum Well Decrease of the level energy when width of the Quantum Well decreased R. Dingle, Festkorperprobleme’1975

Confined levels in Quantum Dots Photoluminescence of GaAs/GaAlAs Quantum Dots QD as an artificial atom B. Piętka et al.

QD types and fabrication methods Goal: to engineer potential energy barriers to confine electrons in 3 dimensions Basic types/methods Colloidal chemistry Electrostatic Lithography Epitaxy Fluctuation Self-organized Patterned growth - „Defect” QDs

Photoluminescence spectra of GaN template on sapphire GaN grown on 11-22 direction, CEA Valbonne An evidence for narrow, discrete emission lines!

„Defect” type quantum dots

„Defect” type quantum dots HRTEM, S. Kret, IF PAN

Cubic GaN vs wurtzite GaN Structure Zinc blende Wurtzite Lattice constant at 300 K 0.450 nm a0 = 0.3189 nm c0 = 0.5185 nm Energy Gap at ~0 K 3.30 eV Ramirez-Flores et al.,1994, Ploog et al., 1995 3.50 eV Dingle et al., 1971 Monemar 1974 Energy of emission (~3.25-3.45 eV) agrees resonably with an expectation for cubic GaN inclusions in wurtzite GaN

Self-organized Semiconductor QDs Number of atoms ~ 103 - 106 C. H. Li et al, APL’2005

Epitaxy: Self-Organized Growth Lattice-mismatch induced island growth Self-organized QDs through epitaxial growth strains Stranski-Krastanov growth mode (use MBE, MOCVD) Islands formed on wetting layer due to lattice mismatch (size ~10s nm) Disadvantage: size and shape fluctuations, strain, Control island initiation Induce local strain, grow on dislocation, vary growth conditions, combine with patterning

Semiconductor Quantum Dot Klimeck et al.

QD confined electron wavefunctions Klimeck et al.

InGaAs self-assembled QDs Calculated confined eh-pair energies for InAs assuming pyramidal shape Grundmann, Bimberg et al., TU Berlin

CdTe QDs qrowth – amorfous Te deposition method J. Kobak et al. GaAs:Si substrate F. Tinjod et al., APL (2003)

CdTe QDs qrowth – amorfous Te deposition method J. Kobak et al. ZnTe buffer 1000 nm GaAs:Si substrate F. Tinjod et al., APL (2003)

CdTe QDs qrowth – amorfous Te method ZnTe buffer 1000 nm GaAs:Si substrate CdTe layer F. Tinjod et al., APL (2003)

CdTe QDs qrowth – amorfous Te deposition method J. Kobak et al. amorphous Te ZnTe buffer 1000 nm GaAs:Si substrate CdTe layer F. Tinjod et al., APL (2003)

CdTe QDs qrowth – amorfous Te deposition method J. Kobak et al. amorphous Te QDs ZnTe buffer 1000 nm GaAs:Si substrate F. Tinjod et al., APL (2003)

CdTe QDs qrowth – amorfous Te deposition method J. Kobak et al. QDs ZnTe buffer 1000 nm GaAs:Si substrate F. Tinjod et al., APL (2003)

CdTe QDs qrowth – amorfous Te deposition method J. Kobak et al. ZnTe cap 100 nm ZnTe buffer 1000 nm GaAs:Si substrate F. Tinjod et al., APL (2003)

Control of CdTe/ZnTe QD density with the temperature of CdTe deposition PL intensity µPL 6 K 0 – 2 QDs 15 – 30 QDs 30 – 60 QDs 300 – 600 QDs 3 ML Czas nakładania stały różna temperatura nakładania 80 – 160 QDs 500 – 1000 QDs 1900 2000 2100 2200 2300 2400 2500 Photon Energy (meV) J. Kobak et al., arXiv:1210.2946 (2012)

Control of CdTe/ZnTe QD density with the thickness of CdTe layer PL intensity T=334 oC µPL 6 K 1 ML 10 – 20 QDs 2 ML 100 – 200 QDs 3 ML 300 – 600 QDs 4 ML 500 – 1000 QDs 1900 2000 2100 2200 2300 2400 2500 Photon Energy (meV) J. Kobak et al., arXiv:1210.2946 (2012)

Control of CdTe/ZnTe QD density with the thickness of CdTe layer

Epitaxy: Patterned Growth Growth on patterned substrates Grow QDs in pyramid-shaped recesses Recesses formed by selective ion etching Disadvantage: density of QDs limited by mask pattern T. Fukui et al. GaAs tetrahedral quantum dot structures fabricated using selective area metal organic chemical vapor deposition. Appl. Phys. Lett. May, 1991

Excitons in Semiconductor Quantum Dots

Exciton formation The absorption of photon by an interband transition in a semiconductor or insulator creates an electron in the conduction band and hole in the valence band. Eg

Exciton formation This oppositely charged particles attract each other though Coulomb interaction, and there may be the probability of the formation of neutral electron-hole pair called an Exciton.

Exciton formation Wannier-Mott excitons Frenkel exciton A striking resemblance with the hydrogen atom is already evident at first sight; the role of the proton is played here by the hole. If we regard the electron and hole as point charges characterized by their charge and effective masses (the so-called effective mass approximation), we can apply a modified Bohr model of the hydrogen atom. We shall see that this illustrative approximation can explain the majority of the principal features observed in the optical spectra of Wannier excitons in semiconductors

Exciton – Bohr model Wannier-Mott excitons Moddified Bohr model of the hydrogen atom applies reduced mass binding energy dielectric constant

Exciton binding Energy Ry(H) = 13.6 eV Binding Energy of electron in Hydrogen atom Exciton compared to hydrogen atom: larger ratio of the effective masses electron and hole are in medium with dielectric constant ranging between 10-30,  Smaller exciton binding energy Unlike the pair of a light electron and a very heavy proton, the exciton is composed of two light quasi-particles with comparable masses me mh which entails a lower stability of the exciton in comparison with the hydrogen atom For stability of Excitons binding energy must be higher than ∼ kBT

Exciton Bohr Diameter - bulk The same size dot of different material may not assure quantum confinement

Oscillator strength of the exciton recombination confined in QD J. Hours, P. Senellart, E. Peter, A. Cavanna, and J. Bloch, PHYSICAL REVIEW B (R)2005

Oscillator strength of the exciton recombination confined in QD

How to observe excitons in Semiconductor Quantum Dots?

Spectroscopy of individual Quantum Dots Towards detector Laser beam Microscope objective Sample with QDs

Experimental setup Laser beam

Spatial resolution <1m) Microscope objective Spatial resolution <1m) J. Jasny and J. Sepioł, Chem. Phys. Lett. 273, 439 1997.

QD exciton emission QDs ensamble emission Individual QD emission spectrum

Excitonic transitions in a quantum dot Exciton (X) X X:

Excitonic transitions in a quantum dot Biexciton (XX) XX XX:

Excitonic transitions in a quantum dot Charged exciton (X+ or X-) CX CX:

X Xdark X Neutral exciton X Formed by: heavy hole and electron Jz = ±3/2 Jz = ±1/2 4 possible spin states of X Xdark X Jz = -1 Jz = +1 Jz = -2 Jz = +2

Fine structure of neutral exciton ( + )/ 2 X δ1~0.1meV ( – )/ 2 X Anisotropic exchange δ0~1meV Isotropic exchange ( + )/ 2 δ2 ≈0 Xdark ( – )/ 2

QD anisotropy AES Energy ~ XX AES V H AES X V H empty dot

Fine structure of neutral exciton Anisotropic exchange splitting: AES = 182  6eV

Excitonic states in magnetic field B = 0 - + B > 0, B||z ~gXBB XX H V X AES H V empty dot

Evolution of -PL spectrum in magnetic field

Is dark exciton emission possible? T. Smoleński et al. Spin flip to bright state due to fonon absorption? δ0 fonon Decay of X Double exponential decay of X log(PL) X Spin flip induced decay of Xdark At low temperatures small probability ~ exp(-δ0/kT) of spin flip due to phonon absorption Time

However, emission of Xdark possible at magnetic field! T. Smoleński et al. B Magnetic field in the plane of the sample induces mixing of bright and dark excitonic states 2X X- X+ Xdark X

Identification of excitonic transitions PL intensity vs excitation power measurement of anisotropic exchange splitting + correlation measurements

Ordering in self-organized Quantum Dot system

Coupled Quantum Dots G. J. Beirne et al., Phys. Rev. Lett. 96, 137401 (2006) B.D.Gerardot et al., Phys. Rev. Lett. 95, 137403 (2005)

Spontaneous ordering in self-organized Quantum Dot system orientation shape size distribution

Spontaneous ordering in self-organized Quantum Dot system P. Wojnar, IF PAN