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[email protected] Lecture 07 http://www.iap.uni-jena.de/multiphoton
Nanomaterials and their Optical Applications Winter Semester 2013
Lecture 07
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
[email protected] Lecture 07
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).
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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.
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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
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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
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Wavefunctions of the crystal 7
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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.
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Band structure of some semiconductors 9
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Band structure of some semiconductors 10
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Group IV semiconductors (Si,Ge) 11
• 4 electrons in the last orbital • 4 valence bands
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Group III-V semiconductors (GaAs, ) 12
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Quantum well : what is it ? 13
Thin layer of a smaller bandgap semiconductor is sandwiched between two layers of a wider bandgap semiconductor
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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
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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
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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
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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
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Quantum well : their features 18
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 :
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Quantum well : their features 19
• 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
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Quantum well : their features 20
• 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
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Quantum well : their features 21
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
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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:
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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
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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
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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
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Optical Properties related to quantum confinement
26
P. Prasad, Nanophotonics, §4.1-4.6, Wiley.
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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
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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).
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Example of confinement effects 29
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).
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Example of confinement effects 30
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
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Example of confinement effects 31
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
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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)
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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
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Lasing media for compact solid-state lasers 34
Quantum Confined semiconductors and the lasing wavelength
CD player, laser printers, telecommunications pump laser
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Lasing media for compact solid-state lasers 36
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
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Lasing media for compact solid-state lasers 37
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
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Lasing media for compact solid-state lasers 38
1. Edge emitting (also called in plane laser)
Material for laser diodes
Materials possible for blue laser: GaN, GaAs, SiC, TiO2, ZnO, MgAl2O4, MgO
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Lasing media for compact solid-state lasers 39
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
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Lasing media for compact solid-state lasers 40
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.
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Lasing media for compact solid-state lasers 41
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
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Lasing media for compact solid-state lasers 42
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
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Lasing media for compact solid-state lasers 43
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
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Quantum well 44
absorption between two subband Intersubband absorption in a multiquantum well designed for triply resonant non-linear susceptibility
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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