Introduction to nano materials

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  • 1.1 Introduction to Nano-materials

2. 2 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 3. 3 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 nms to a few tens of nms, 1nm is about 2 mono- layers/lattices) must be introduced in addition to the naturally given semiconductor crystalline structure 4. 4 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 5. 5 Stages from free-space to nano-material Free-space Schrdinger equation in free-space: Solution: Electron behavior: plane wave ,...3,2,1,/2 == lLlk 1)/( Etrki k e = 0 22 2 || m k E = trtr t i m ,, 2 0 ) 2 ( = 6. 6 Stages from free-space to nano-material Bulk semiconductor Schrdinger equation in bulk semiconductor: Solution: Electron behavior: Bloch wave trtr t irV m ,,0 2 0 )]( 2 [ =+ )()( 00 RlrVrV += r e rV 2 0 )( = kne Etrki kn )/( = effm k E 2 || 22 = 7. 7 Stages from free-space to nano-material Nano-material Schrdinger equation in nano-material: with artificially generated extra potential contribution: Solution: trtrnano t irVrV m ,,0 2 0 )]()( 2 [ =++ )(rVnano knrFe kn iEt kn )(, / = 8. 8 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 9. 9 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 10. 10 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 11. 11 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 12. 12 Why we are interested in nano-material? Electrons in semiconductors: highly mobile, easily transportable and correlated, yet highly scattered in terms of energy Electrons in atomic systems: highly regulated in terms of energy, but not mobile 13. 13 Why we are interested in nano-material? Electrons in semiconductors: easily controllable and accessible, yet poor inherent performance Electrons in atomic systems: excellent inherent performance, yet hardly controllable or accessible 14. 14 Why we are interested in nano-material? Answer: take advantage of both semiconductors and atomic systems Semiconductor quantum dot material 15. 15 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 Increased confinement reduces the extent of the electron and hole states and thereby reduces the dipole moment 16. 16 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

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