nanomaterials and their optical applications...quantum wells, quantum wires, quantum dots, quantum...

[email protected] Lecture 07 http://www.iap.uni-jena.de/multiphoton

Nanomaterials and their Optical Applications Winter Semester 2013

Lecture 07

[email protected]

December 17th 2013, No lecture First Lecture in 2014: 7th of January

[email protected] Lecture 07

Schedule Oral Presentation 2

Date Room Time Speaker Title of the talk

10.12 Lecture Hall 12.15 Egor Khaidarov PALM & STORM

SR 2 Physik 12.45 Siyuan Wang Sensing with whispering gallery modes

13.15 Morozov Sergii Quantum dots and computing

13.45 Xiaohan Wang STED

27.01 Seminar Hall 16.00 Tesfaye Belete MBE and MOCVD

SR 4 Physik 16.30 Svetlana Shestaeva Nanowire as biosensor

17.00 Kai Wang Optical to plasmon Tweezers

17.30 Getnet k. Tadesse Sensing with SNOM

4.02 Lecture Hall 12.15

SR 2 Physik 12.45

13.15

13.45


Materials for what ? 3

High transparency of dielectrics like optical fibre Data transport over long distances Very high data rate

Nanoscale data storage Limited speed due to interconnect Delay times

The speed of photonics The size of electronics

Brongersma, M.L. & Shalaev, V.M. The case for plasmonics. Science 328, 440-441 (2010).


Outline: inorganic semiconductor 4

1. Crystalline structure, wave function, electronic states, band structure, DOS

2. Type of material

3. Quantum wells, quantum wires, quantum dots, quantum rings

4. Optical properties

5. Superlattices, hybrid structures (core-shell quantum dots, QD-QW)

6. Lasing media: quantum cascade

Inspired from the following references: J. Faist, ETHZ, Optical Properties of semiconductor, ETHZ, 2008 lecture notes P. Prasad, Nanophotonics, §4.1-4.6, Wiley.


Crystalline structure 5

Perfect crystal = invariant under the translational symmetry

Lattice constant =constant distance between unit cells in a crystal lattice

Revise: crystallography !

crystalline structure of GaAs ZincBlende type

The Hamiltonian of a semiconductor crystal has the translation symmetry

http://en.wikipedia.org/wiki/Translational_symmetry

R = reciprocal lattice or k-space or Fourier-space

http://www.chembio.uoguelph.ca/educmat/chm729/recip/vlad.htm


Wavefunctions of the crystal 6

where

The Bloch theorem states that the wave functions have two “good” quantum numbers, the band index n and a reciprocal vector k

n infinite periodic 1D box, we get the so-called Bloch function

http://leung.uwaterloo.ca/CHEM/750/Lectures%202007/SSNT-5-Electronic%20Structure%20II.htm


Wavefunctions of the crystal 7


Band structure of some semiconductors 8

Heavy and light holes (also - holes in so-called split-off band) are just different types of holes (like different types of atoms or molecules occupying the same volume). Concentration of heavy holes is much higher than that of light holes, due to their larger mass and thus density of states. The energy-wavevector (E-k) relationship shows the dependence of total energy (i.e. kinetic plus potential energy) on the wavevector. Wavevector k is defined as particle (electron, hole,...) momentum divided by Planck's constant. Since the absolute value of the potential energy is unimportant, you can change the scale so that E=0 at k=0.


Group IV semiconductors (Si,Ge) 11

• 4 electrons in the last orbital • 4 valence bands


Group III-V semiconductors (GaAs, ) 12


Quantum well : what is it ? 13

Thin layer of a smaller bandgap semiconductor is sandwiched between two layers of a wider bandgap semiconductor


Quantum well : 2D confinement 14

http://www.lps.umd.edu/MBEGroup/MBEHomePage.htm I

Type I :band edge discontinuities of the conduction and valence band have opposite signs

Type II: band edge discontinuities that are in the same direction confine both electrons and holes


Quantum well : 2D confinement 15

Type I : The bandgap of one semiconductor is completely contained in the bandgap of the other one: GaAs - AlGaAs system

Type II : The bandgaps overlap but change in sign : InP/InSb

Type III The bandgaps do not overlap at all. The situation for carrier transfer is like type II, just more pronounced: GaSb/InAs

A heterojunction: junctions between two different semiconductors

http://en.wikipedia.org/wiki/Heterojunction

http://www.tf.uni-kiel.de/matwis/amat/semi_en/kap_5/backbone/r5_3_1.html


Quantum well : their features 16

• Large confinement effect due to large bandgap difference • Lattice matched -> no strain

Why this material system ?

Substrate: GaAs Quantum wells: AlAs/ GaAs or AlGaAs/GaAs Epitaxy: bottum-up fabrication layer by layer by (a) Molecular beam epitaxy (MBE) (b) Metal organiv chemical vapor

deposition (MOCVD)

Z, confinement direction


Bottom-up: epitaxial growth 17

Lattice matching: avoid stress in the material

Lattice constant =constant distance between unit cells in a crystal lattice

Binary compounds

Ternary compounds

Quaternary compounds



2. Quantized energy, n =1,2,3 (sub-band index), l width of the well (solution of Schrödinger equation in a box)

3. Kinetic energy of the electron in the free to move xy plane

1. Ec = bottom of the conduction band

Finite potential barrier : modified the behaviour of the energies eigenvalues and wavefuntions compared to infinite potential

E<V : Energy levels of electrons are quantized in z In x,y energies given by the mass approximation (modification of the mass of the electrons due to the well)

Energy of the electrons in the conduction band :



• E>V : not quantization at all either in z or x, y. The total number of discrete levels depends on the barrier V and the width of the well

• Holes behave similarly but with but inverted energy and different effective mass

• 2 types of hole in this material system: heavy and light, each quantum state is split in 2 lh and hh

• Wavefunctions do not go to 0 at the boundary but

exponetially decay into the wider bandgap region • The band-to-band transition (interband) is higher than Eg

Effective bandgap for a quantum well



• Excitonic transition below the band-to-band transition • Intraband (or inter-subbands) transition : between the sub-bands within the

conduction band (applications: Quantum Cascade Laser Paper 7)

• Modification of the density of states larger than bulk close to the bandgap -> stronger optical transition allowing laser action in quantum wells

0 at the bottom of the conduction band



Exciton = when an electron in the conduction band is bound to its corresponding hole in the valence band

Tightly bound exciton: Frenkel exciton, within a single molecule Or not tighly bound: Wannier exciton, over several lattices Analogous to an hydrogen atom where an electron and a proton are bound by coulombic interactions thus quantized energy levels below the bandgap

Bohr radius

Rydberg energy usually between 1-100 meV Exciton binding energy

Reduced mass of the pair

Excitons form when kT< Ry, otherwise ionized


Quantum wires : their features 22

x y

z

2D confinement : free-electron behaviour only in one direction III-V: InP II-VI: CdSe

lx

lz

Energy of a one dimensional electron: Continuous band in y Quantized in x , y

Lowest sub-band energy:


Quantum wires : their features 23

x y

z

lx

lz

Density of states • Singularity near ky =0

• Increase of the strength of optical transition

• Improved optical efficiency = better emission

• Increase of the exciton binding energy


Quantum dots : their features 24

x y z

lx

lz

3D confinement 10nm GaAs cube contains about 40000 atoms Artificial atoms Only discrete energy levels:

ly

Density of states Series of delta function Sharp absorption and emission even at room temperature


Quantum dots : their features 25

x y z

lx

lz ly

Large surface to volume ratio Strong manifestation of surface-related phenomena Different degree of confinement for different sizes: smaller than the Bohr radius Thus energy between the subbands much larger than the exciton binding energy

Quantum rings…

External magnetic field to influence the electronic states


Optical Properties related to quantum confinement

26

P. Prasad, Nanophotonics, §4.1-4.6, Wiley.


Optical Properties related to quantum confinement

27

Size dependence of optical properties • blueshift in the bandgap • Discrete subbands

Quantum confinement produces:

Increase of oscillator strength • DOS modified

New intraband transition • Transitions within the bands

• due to presence of free carrier by impurity doping or charge injection • In the near infrared (see Paper 6 quantum cascade laser)

• Equivalent to free carrier absorption in bulk that are usually weak because

needs to be coupled with phonons

Increased Exciton Binding • About 4 times higher in QW than in bulk -> can be seen at room temperature

Increase of Transition Probability in Indirect bandgap (luminescent Silicon) • ∆x is reduced, thus ∆k is larger, thus quasi momentum is relaxed


Example of confinement effects 28

Absorption Spectra of GaAs/AlGaAs quantum wells of different width at 2K

Thick QW = like bulk Exciton

Quantization starts Exciton at each subband

Blue shift increase of subband separation splitting of n= 1 in heavy holes and light holes bands

Dingle, R., Wiegmann, W. & Henry, C. Quantum States of Confined Carriers in Very Thin Al_{x}Ga_{1-x}As-GaAs-Al_{x}Ga_{1-x}As Heterostructures. Physical Review Letters 33, 827-830 (1974).



Excitation and photolumiescence spectra of 15 nm diameter InP nanowire

Two-orthogonal polarization

Strong anisotropy

Field intensity E2

strongly attenuated for Eperp

and unaffected for Epara

Wang, J., Gudiksen, M.S., Duan, X., Cui, Y. & Lieber, C.M. Highly polarized photoluminescence and photodetection from single indium phosphide nanowires. Science (New York, N.Y.) 293, 1455-7 (2001).



Bruchez, M., Moronne, M., Gin, P., Weiss, S. & Alivisatos, A.P. Semiconductor nanocrystals as fluorescent biological labels. Science 281, 2013-2016 (1998).

InAs InP CdSe

Sizes of the nanocrystals decreases from left to right

Tunable from UV to IR With sizes and material changes

Fluorescent properties of semiconductor nanocrystals (quantum dots) of different sizes



Miller, D. et al. Electric field dependence of optical absorption near the band gap of quantum-well structures. Physical Review B 32, 1043-1060 (1985).

Effect of an applied electric field on the energy levels, thus on the optical spectra Quantum-confined Stark Effect

In bulk : Franz-Keldysh effect = change in absorption to lower energy , shift of the CB and VB, broadening of the exciton peak and ionization

In QW : in the plane (longitudinal) of the QW then similar as bulk In the direction of confinement (transverse)

• no ionization of the exciton • Interband seperation changes • Lower exciton binding • Broadening of the exciton • Mixing of allowed states • Large change in absorption thus • Large change in the real part of n

V


Superlattices 32

Miller, D. et al. Electric field dependence of optical absorption near the band gap of quantum-well structures. Physical Review B 32, 1043-1060 (1985).

Periodic array of quantum structure

Multiple quantum wells

• 9 nm width well leads to formation of minibands

• Thus change in the density of states • Tunneling of the electrons (QCL)


Core-Shell quantum dots 33

Photoluminescence spectra of InP and core-shell structures

• Wider bandgap shell : passivation, less non radiative losses

• Mostly red-shift are observed due to a lowering of the bandgap


Lasing media for compact solid-state lasers 34

Quantum Confined semiconductors and the lasing wavelength

CD player, laser printers, telecommunications pump laser



as in every LASER



1. Edge emitting (also called in plane laser)

• Cavity = cleaved crystal surfaces • Injection of electrons in the active region • Narrow gain spectrum • Small line width • Highmodulation speed • Low output power 100 mW • In arrays up to 50W

Single QW Double heterostructure semiconductor laser Multiple QW



1. Edge emitting (also called in plane laser) Principle of LED (light emitting diode)

• p-n junction devices • forward biased • the applied forward voltage on the diode of the LED drives the electrons

and holes into the active region between the n-type and p-type material, the energy can be converted into infrared or visible photons

• electron-hole pair drops into a more stable bound state, releasing energy on the order of electron volts by emission of a photon.

http://hyperphysics.phy-astr.gsu.edu/hbase/solids/pnjun2.html#c4



1. Edge emitting (also called in plane laser)

Material for laser diodes

Materials possible for blue laser: GaN, GaAs, SiC, TiO2, ZnO, MgAl2O4, MgO



1. Edge emitting (also called in plane laser) Material for laser diodes

Japan (Shuji Nakamura) developed the The 1st green, blue, violet & white LEDs with GaN semiconductors (epitaxial MOCVD on a sapphire substrate -1993) The 1st blue-light semiconductor laser (1995)

Environmentally friendly compared to Arsenic

High melting point Bandgap → blue or

UV light Photon Emission



1. Edge emitting (also called in plane laser) Issues for blue diodes

• Standard techniques (Czochralski, Bridgeman, Float Zone) used to make single crystal wafers (GaAs & Si) don't work for GaN.

• GaN has a high melting temperature and a very high decomposition pressure. • The nitrogen evaporates out of the crystal as it grows and the GaN atoms won't bond. • To keep the nitrogen in, need very high pressures (more than 1000 MPa), which are

difficult to achieve in a commercial process.



1. Edge emitting (also called in plane laser) Issues for blue diodes

The Problem GaN grown on sapphire which has 15% smaller lattice constant

Leads to high defect density

Cracking of layers when structures are cooled down after growth due to high difference in thermal expansions of the two materials

GaN is ideal choice for substrate but this is still in research

The Solution Akasaki proposed

solution:developing AlN buffer layers

Nakamura proposed solution: growth of GaAlN buffer layers



2. Surface emitting laser (SEL) : vertical laser output

Vertical External CSEL Vertical Cavity SEL

Easy to integrate to fibers Heating effects in the multiple layer structure



3. Quantum cascade laser • Electrons from the conduction band only: unipolar • Intraband transitions only • Normal laser: 1 electron produces 1 photon • QC laser: 1 electron produces 25 to 75 photons • 4 to 24 microns wavelength, more than 1W • Chemical sensing of toxic gas or pollutants


Quantum well 44

absorption between two subband Intersubband absorption in a multiquantum well designed for triply resonant non-linear susceptibility


Outlook 45

Faist, J. et al. Quantum cascade laser. Science (New York, N.Y.) 264, 553-6 (1994).

• Unipolar semiconductor laser : relies only on one type of carrier • Superlattices • Space charged effects: excess electric charge is treated as a continuum of

charge distributed over a region of space • Schawlow–Townes Linewidth: the fundamental (quantum) limit for the

linewidth of a laser (Phys. Rev. 112 (6), 1940 (1958))

Key words

nanomaterials and their optical applications...quantum wells, quantum wires, quantum dots, quantum...

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