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Introduction to Nano-materials As part of ECE-778 – Introduction to Nanotechnology 1 Outline • What is “nano-material” and why we are interested in it? • Ways lead to the realization of nano-materials • Optical and electronic properties of nano-materials • Applications 2 What is “nano-material” ? • Narrow definition: low dimension semiconductor structures including quantum wells, quantum wires, and quantum dots • Unlike bulk semiconductor material, artificial structure in nanometer scale (from a few nm’s to a few tens of nm’s, 1nm is about 2 mono-layers/lattices) must be introduced in addition to the “naturally” given semiconductor crystalline structure 3 Why we are interested in “nano-material”? • Expecting different behavior of electrons in their transport (for electronic devices) and correlation (for optoelectronic devices) from conventional bulk material 4 Stages from free-space to nano-material • Free-space SchrÖdinger equation in free-space: 2 ( ) r ,t i r ,t 2m0 t Solution: k e i ( k r Et / ) 1 2 2 |k | k 2l / L, l 1,2,3,... E 2m0 Electron behavior: plane wave 5 Stages from free-space to nano-material • Bulk semiconductor SchrÖdinger equation in bulk semiconductor: 2 [ V0 (r )] r ,t i r ,t 2m0 t e2 V0 (r ) V0 (r lR) V0 (r ) r Solution: 2 2 |k | i ( k r Et / ) E nk e nk 2meff Electron behavior: Bloch wave 6 Stages from free-space to nano-material • Nano-material SchrÖdinger equation in nano-material: 2 [ V0 (r ) Vnano (r )] r ,t i r ,t 2m0 t with artificially generated extra potential contribution: Vnano (r ) Solution: nk e iEt / Fn ,k (r ) nk 7 Stages from free-space to nano-material Electron behavior: Quantum well – 1D confined and in parallel plane 2D Bloch wave Quantum wire – in cross-sectional plane 2D confined and 1D Bloch wave Quantum dot – all 3D confined 8 A summary on electron behavior • Free space – plane wave with inherent electron mass – continued parabolic dispersion (E~k) relation – density of states in terms of E: continues square root dependence • Bulk semiconductor – plane wave like with effective mass, two different type of electrons identified with opposite sign of their effective mass, i.e., electrons and holes – parabolic band dispersion (E~k) relation – density of states in terms of E: continues square root dependence, with different parameters for electrons/holes in different band 9 A summary on electron behavior • Quantum well – discrete energy levels in 1D for both electrons and holes – plane wave like with (different) effective masses in 2D parallel plane for electrons and holes – dispersion (E~k) relation: parabolic bands with discrete states inside the stop-band – density of states in terms of E: additive staircase functions, with different parameters for electrons/holes in different band • Quantum wire – discrete energy levels in 2D cross-sectional plane for both electrons and holes – plane wave like with (different) effective masses in 1D for electrons and holes – dispersion (E~k) relation: parabolic bands with discrete states inside the stop-band – density of states in terms of E: additive staircase decayed functions, with different parameters for electrons/holes in different band 10 A summary on electron behavior • Quantum dot – discrete energy levels for both electrons and holes – dispersion (E~k) relation: atomic-like k-independent discrete energy states only – density of states in terms of E: -functions for electrons/holes 11 Why we are interested in “nano-material”? Free electrons (electrons in vacuum): highly mobile hence transportable, all in one status, with kinetic energy but no potential energy Electrons in atomic systems: having multiple status with different potentials, immobile hence untransportable, with potential energy but no kinetic energy (excluding the kinetic energy for orbiting) Electrons in semiconductors: having multiple status with different potentials, mobile hence transportable, with both potential and kinetic energies, yet having scattered energy levels at each status 12 Why we are interested in “nano-material”? Electrons in atomic systems: in highly regulated status, possible to achieve accurate result, yet hardly accessible and controllable Electrons in semiconductors: easily accessible and controllable, yet in poorly regulated status – any manipulation can hardly lead to an accurate result 13 Why we are interested in “nano-material”? • Answer: take advantage of both semiconductors and atomic systems – low dimensional semiconductor material (or nano-material), i.e., semiconductor quantum wells semiconductor quantum wires semiconductor quantum dots 14 Why we are interested in “nano-material”? • Detailed reasons: – Geometrical dimensions in the artificial structure can be tuned to change the confinement of electrons and holes, hence to tailor the correlations (e.g., excitations, transitions and recombinations) – Relaxation and dephasing processes are slowed due to the reduced probability of inelastic and elastic collisions (much expected for quantum computing, could be a drawback for light emitting devices) – Definite polarization (spin of photons are regulated) – (Coulomb) binding between electron and hole is increased due to the localization – Increased binding and confinement also gives increased electron-hole overlap, which leads to larger dipole matrix elements and larger transition rates 15 Ways lead to the realization of nano-material • Required nano-structure size: Electron in fully confined structure (QD with edge size d), its allowed (quantized) energy (E) scales as 1/d2 (infinite barrier assumed) Coulomb interaction energy (V) between electron and other charged particle scales as 1/d If the confinement length is so large that V>>E, the Coulomb interaction mixes all the quantized electron energy levels and the material shows a bulk behavior, i.e., the quantization feature is not preserved for the same type of electrons (with the same effective mass), but still preserved among different type of electrons, hence we have (discrete) energy bands If the confinement length is so small that V<<E, the Coulomb interaction has little effect on the quantized electron energy levels, i.e., the quantization feature is preserved, hence we have discrete energy levels 16 Ways lead to the realization of nano-material • Required nano-structure size: Similar arguments can be made about the effects of temperature, i.e., kBT ~ E? But kBT doesn’t change the electron eigen states, instead, it changes the excitation, or the filling of electrons into the eigen energy structure If kBT>E, even E is a discrete set, temperature effect still distribute electrons over multiple energy levels and dilute the concentration of the density of states provided by the confinement, since E can never be a single energy level Therefore, we also need kBT<E! 17 Ways lead to the realization of nano-material • Required nano-structure size: The critical size is, therefore, given by V(dc)=E(dc)>kBT (25meV at room temperature). For typical III-V semiconductor compounds, dc~10nm-100nm (around 20 to 200 mono-layers). More specifically, if dc<10nm, full quantization, if dc>100nm, full bulk (mix-up). On the other hand, dc must be large enough to ensure that at least one electron or one electron plus one hole (depending on applications) are bounded inside the nano-structure. 18 Ways lead to the realization of nano-material • Current technologies – Top-down approach: patterning etching re-growth – Bottom-top approach: patterning etching selective-growth – Uneven substrate growth: edge overgrowth, V-shape growth, interface QD, etc. – Self-organized growth: most successful approach so far – Wafer bonding 19 Electronic Properties • Ballistic transport – a result of much reduced electronphonon scattering, low temperature mobility in QW (inplane direction) reaches a rather absurd value ~107cm2/s-V, with corresponding mean free path over 100m • Resulted effect – electrons can be steered, deflected and focused in a manner very similar to optics, as an example, Young’s double slit diffraction was demonstrated on such platform 20 Electronic Properties • Low dimension tunneling – as a collective effect of multiple nano-structures, resonance appears due to the “phase-matching” requirement • Resulted effect – stair case like I-V characteristics, on the down-turn side, negative resistance shows up 21 Electronic Properties • If excitation (charging) itself is also quantized (through, e.g., Coulomb blockade), interaction between the excitation quantization and the quantized eigen states (i.e., the discrete energy levels in nano-structure) brings us into a completely discrete regime • Resulted effect – a possible platform to manipulate single electron to realize various functionalities, e.g., single electron transistor (SET) for logical gate or memory cell 22 Optical Properties • Discretization of energy levels increases the density of states • Resulted effect – enhances narrow band correlation, such as electron-hole recombination; for QD lasers, the threshold will be greatly reduced 23 Optical Properties • Discretization of energy levels reduces broadband correlation • Resulted effect – reduces relaxation and dephasing, reduces temperature dependence; former keeps the electrons in coherence, which is very much needed in quantum computing; latter reduces device performance temperature dependence (e.g., QD laser threshold and efficiency, QD detector sensitivity, etc.) 24 Optical Properties • Quantized energy level dependence on size (geometric dimension) • Resulted effect – easy tuning of optical gain/absorption spectrum 25 Optical Properties • Discretization of energy levels leads to zero dispersion at the gain peak • Resulted effect – reduces chirp, a very much needed property in dynamic application of optoelectronic devices (e.g., optical modulators or directly modulated lasers) 26 Applications • Light source - QD lasers, QC (Quantum Cascade) lasers • Light detector – QDIP (Quantum Dot Infrared Photodetector) • Electromagnetic induced transparency (EIT) – to obtain transparent highly dispersive materials • Ballistic electron devices • Tunneling electron devices • Single electron devices 27 References • The first to read – F. Owens and C. Poole Jr., “The Physics and Chemistry of Nanosolids”, Wiley-Interscience, 2008, ISBN-978-0-470-06740-6 • On solid state physics – C. Kittel, “Introduction to Solid State Physics”, Springer, ISBN-978-0-471-41526-8 • On basic quantum mechanics – L. Schiff, “Quantum Mechanics”, 3rd Edition, McGraw Hill, 1967, ISBN-0070856435 • On nano-material electronic properties – W. Kirk and M. Reed, “Nanostructures and Mesoscopic Systems”, Academic Press, 1991, ISBN0124096603 • On nano-material and device fabrication techniques – T. Steiner, “Semiconductor Nanostructures for Optoelectronic Applications”, Artech House, 2004, ISBN-1580537510 • On nano-material optical properties – G. Bryant and G. Solomon, “Optics of Quantum Dots and Wires”, Artech House, 2005, ISBN-1580537618 28