Nanomaterials and their Optical Applications

Transcription

1 Nanomaterials and their Optical Applications Winter Semester 2013 Lecture 07 December 17 th 2013, No lecture First Lecture in 2014: 7 th of January rachel.grange@uni-jena.de

2 Schedule Oral Presentation 2 Date Room Time Speaker Title of the talk Lecture Hall SR 2 Physik Egor Khaidarov PALM & STORM Siyuan Wang Sensing with whispering gallery modes Morozov Sergii Quantum dots and computing Xiaohan Wang STED Seminar Hall SR 4 Physik Lecture Hall SR 2 Physik Tesfaye Belete MBE and MOCVD Svetlana Shestaeva Nanowire as biosensor Kai Wang Optical to plasmon Tweezers Getnet k. Tadesse Sensing with SNOM

3 Materials for what? 3 The speed of photonics The size of electronics 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 Brongersma, M.L. & Shalaev, V.M. The case for plasmonics. Science 328, (2010).

4 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, , Wiley.

5 Crystalline structure 5 Perfect crystal = invariant under the translational symmetry crystalline structure of GaAs ZincBlende type Translational_symmetry The Hamiltonian of a semiconductor crystal has the translation symmetry R = reciprocal lattice or k-space or Fourier-space Lattice constant =constant distance between unit cells in a crystal lattice Revise: crystallography!

6 Wavefunctions of the crystal 6 n infinite periodic 1D box, we get the so-called Bloch function The Bloch theorem states that the wave functions have two good quantum numbers, the band index n and a reciprocal vector k where rachel.grange@uni-jena.de Lecture 07

7 Wavefunctions of the crystal 7

8 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.

9 Band structure of some semiconductors 9

10 Band structure of some semiconductors 10

11 Group IV semiconductors (Si,Ge) 11 4 electrons in the last orbital 4 valence bands

12 Group III-V semiconductors (GaAs, ) 12

13 Quantum well : what is it? 13 Thin layer of a smaller bandgap semiconductor is sandwiched between two layers of a wider bandgap semiconductor

14 Quantum well : 2D confinement 14 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 I

15 Quantum well : 2D confinement 15 A heterojunction: junctions between two different semiconductors 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

16 Quantum well : their features 16 Why this material system? Large confinement effect due to large bandgap difference Lattice matched -> no strain 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

17 Bottom-up: epitaxial growth 17 Lattice matching: avoid stress in the material Binary compounds Ternary compounds Quaternary compounds Lattice constant =constant distance between unit cells in a crystal lattice

18 Quantum well : their features 18 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 : 1. Ec = bottom of the conduction band 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

19 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

20 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

21 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 Rydberg energy usually between mev Exciton binding energy Bohr radius Reduced mass of the pair Excitons form when kt< Ry, otherwise ionized

22 Quantum wires : their features 22 z lx lz x y 2D confinement : free-electron behaviour only in one direction III-V: InP II-VI: CdSe Energy of a one dimensional electron: Quantized in x, y Continuous band in y Lowest sub-band energy:

23 Quantum wires : their features 23 z lx lz x y Density of states Singularity near k y =0 Increase of the strength of optical transition Improved optical efficiency = better emission Increase of the exciton binding energy

24 Quantum dots : their features 24 lz lx ly x z y 3D confinement 10nm GaAs cube contains about atoms Artificial atoms Only discrete energy levels: Density of states Series of delta function Sharp absorption and emission even at room temperature

25 Quantum dots : their features 25 lz lx ly x z y 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

26 Optical Properties related to quantum confinement 26 P. Prasad, Nanophotonics, , Wiley.

27 Optical Properties related to quantum confinement 27 Quantum confinement produces: Size dependence of optical properties blueshift in the bandgap Discrete subbands 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

28 Example of confinement effects 28 Absorption Spectra of GaAs/AlGaAs quantum wells of different width at 2K Exciton Thick QW = like bulk 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, (1974).

29 Example of confinement effects 29 Excitation and photolumiescence spectra of 15 nm diameter InP nanowire Two-orthogonal polarization Strong anisotropy Field intensity E 2 strongly attenuated for E perp and unaffected for E para 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, (2001).

30 Example of confinement effects 30 Fluorescent properties of semiconductor nanocrystals (quantum dots) of different sizes InAs InP CdSe Sizes of the nanocrystals decreases from left to right Tunable from UV to IR With sizes and material changes Bruchez, M., Moronne, M., Gin, P., Weiss, S. & Alivisatos, A.P. Semiconductor nanocrystals as fluorescent biological labels. Science 281, (1998).

31 Example of confinement effects 31 Quantum-confined Stark Effect Effect of an applied electric field on the energy levels, thus on the optical spectra 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 Miller, D. et al. Electric field dependence of optical absorption near the band gap of quantum-well structures. Physical Review B 32, (1985).

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

33 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

34 Lasing media for compact solid-state lasers 34 CD player, laser printers, telecommunications pump laser Quantum Confined semiconductors and the lasing wavelength

35 Lasing media for compact solid-state lasers 35 as in every LASER

36 Lasing media for compact solid-state lasers Edge emitting (also called in plane laser) Single QW Double heterostructure semiconductor laser Multiple QW 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

37 Lasing media for compact solid-state lasers 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. rachel.grange@uni-jena.de Lecture 07

38 Lasing media for compact solid-state lasers Edge emitting (also called in plane laser) Material for laser diodes Materials possible for blue laser: GaN, GaAs, SiC, TiO 2, ZnO, MgAl 2 O 4, MgO

39 Lasing media for compact solid-state lasers Edge emitting (also called in plane laser) Material for laser diodes Japan (Shuji Nakamura) developed the The 1 st green, blue, violet & white LEDs with GaN semiconductors (epitaxial MOCVD on a sapphire substrate -1993) The 1 st blue-light semiconductor laser (1995) Environmentally friendly compared to Arsenic High melting point Bandgap blue or UV light Photon Emission

40 Lasing media for compact solid-state lasers 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.

41 Lasing media for compact solid-state lasers 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 The Solution Akasaki proposed solution:developing AlN buffer layers Nakamura proposed solution: growth of GaAlN buffer layers GaN is ideal choice for substrate but this is still in research

42 Lasing media for compact solid-state lasers Surface emitting laser (SEL) : vertical laser output Vertical Cavity SEL Vertical External CSEL Easy to integrate to fibers Heating effects in the multiple layer structure

43 Lasing media for compact solid-state lasers 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

44 Quantum well 44 absorption between two subband Intersubband absorption in a multiquantum well designed for triply resonant non-linear susceptibility

45 Outlook 45 Faist, J. et al. Quantum cascade laser. Science (New York, N.Y.) 264, (1994). Key words 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))