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Handout 27 1D and 0D Nanostructures: Semiconductor …

1 ECE 407 Spring 2009 Farhan Rana Cornell UniversityHandout 271D and 0d nanostructures : Semiconductor quantum Wires and quantum DotsIn this lecture you will learn: Semiconductor quantum wires and dots density of states in Semiconductor quantum wires and dotsCharles H. Henry (1937-)ECE 407 Spring 2009 Farhan Rana Cornell University1D nanostructures : Semiconductor quantum WiresSEM of 20 nm diameter GaAs nanowiresGaAs/AlGaAs quantum wires grown by electron waveguide confinementA carbon nanotube (rolled up graphene):2 ECE 407 Spring 2009 Farhan Rana Cornell UniversitySemiconductor quantum Wires12cccEEE xyzEc2Ec1 Inside: eccmkEkE22211 Outside: eccmkEkE22222 Inside: rErmErEriEecc 112211112 Outside: rErmErEriEecc 222222222 Inside: zkizeyxfAr,11 Outside: zkizeyxfAr,22 Assumed solutions.

1D and 0D Nanostructures: Semiconductor Quantum Wires and Quantum Dots In this lecture you will learn: • Semiconductor quantum wires and dots • Density of states in semiconductor quantum wires and dots Charles H. Henry (1937-) ECE 407 – Spring 2009 – Farhan Rana – Cornell University ... energy of the confined states:

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Transcription of Handout 27 1D and 0D Nanostructures: Semiconductor …

1 1 ECE 407 Spring 2009 Farhan Rana Cornell UniversityHandout 271D and 0d nanostructures : Semiconductor quantum Wires and quantum DotsIn this lecture you will learn: Semiconductor quantum wires and dots density of states in Semiconductor quantum wires and dotsCharles H. Henry (1937-)ECE 407 Spring 2009 Farhan Rana Cornell University1D nanostructures : Semiconductor quantum WiresSEM of 20 nm diameter GaAs nanowiresGaAs/AlGaAs quantum wires grown by electron waveguide confinementA carbon nanotube (rolled up graphene):2 ECE 407 Spring 2009 Farhan Rana Cornell UniversitySemiconductor quantum Wires12cccEEE xyzEc2Ec1 Inside: eccmkEkE22211 Outside: eccmkEkE22222 Inside: rErmErEriEecc 112211112 Outside: rErmErEriEecc 222222222 Inside: zkizeyxfAr,11 Outside: zkizeyxfAr,22 Assumed solutions.

2 1cE2cEECE 407 Spring 2009 Farhan Rana Cornell UniversityxyzxyzEc2Ec1 Semiconductor quantum Wires yxfmkEEyxfymxmyxfEyxfymxmmkEeyxfEeyxfmEe zceeeeezczikzikeczz,2,22,,222,,212211222 2221122222222111221 Inside:Plug in the assumed solution:Outside: yxfmkEEyxfymxmezcee,2,2222222222222 Boundary conditions at the inside-outside boundary: boundary2boundary1,,yxfyxf boundary2boundary1 .,1 .,1nyxfmnyxfmee is the unit vector normal to the boundaryn 3 ECE 407 Spring 2009 Farhan Rana Cornell UniversitySolve these with the boundary conditions to get for the energy of the confined states .

3 3,2,12,221 pmkEEkpEezpczc The electron is free in the z-direction but its energy due to motion in the x-yplane is quantized and can take on only discrete set of valuesxyzxyzEc2Ec1 Semiconductor quantum Wireszk1cE11 EEc 21 EEc 31 EEc EThe energy dispersion for electrons in the quantum wires can be plotted as shown:It consists of energy subbands ( subbands of the conduction band)Electrons in each subband constitute a 1D Fermi gasECE 407 Spring 2009 Farhan Rana Cornell UniversitySemiconductor quantum Wires: density of StatesSuppose, given a Fermi level position Ef , we need to find the electron density :We can add the electron present in each subband as follows: pfzczEkpEfdkn,22 fEIf we want to write the above as: fQWEEEfEgdEnc 1 Then the question is what is the density of states gQW(E ) ?

4 Zk1cE11 EEc 21 EEc 31 EEc E4 ECE 407 Spring 2009 Farhan Rana Cornell UniversityStart from: ezpczcmkEEkpE2,221 And convert the k-space integral to energy space: fppcpceEpfpceEEEEfEEEEEEmdEEEfEEEmdEncpc 11221222 211 This implies: EgQW1cE11 EEc 21 EEc 31 EEc Semiconductor quantum Wires: density of StatesfEzk1cE11 EEc 21 EEc 31 EEc E pfzczEkpEfdkn,22 pcppceQWEEEEEEmEg 1122 2 ECE 407 Spring 2009 Farhan Rana Cornell UniversitySemiconductor quantum wire LasersGaAs/AlGaAs quantum wires grown by electron waveguide confinementmetalA Ridge Waveguide Laser Structure5 ECE 407 Spring 2009 Farhan Rana Cornell University0D nanostructures .

5 Semiconductor quantum DotsTEM of a PbS quantum dotCore-shell colloidal quantum dots (Mostly II-VI semiconductors )CdTeCdSeGaAs substrateInAs quantum dots (MBE)ECE 407 Spring 2009 Farhan Rana Cornell UniversitySemiconductor quantum Dots12cccEEE Ec2 Inside: eccmkEkE22211 Outside: eccmkEkE22222 Inside: rErmErEriEecc 112211112 Outside: rErmErEriEecc 222222222 Inside: zyxfAr,,11 Outside: zyxfAr,,22 Assumed solutions:Ec11cE2cE6 ECE 407 Spring 2009 Farhan Rana Cornell UniversityBoundary conditions at the inside-outside boundary: boundary2boundary1,,,,zyxfzyxf boundary2boundary1.

6 ,,1 .,,1nzyxfmnzyxfmee is the unit vector normal to the boundaryn Semiconductor quantum DotsEc2Ec1 Solve these with the boundary conditions to get for the energy of the confined states : ..3,2,11 pEEpEpccThe electron is not free in any direction and its energy due to motion is quantized and can take on only discrete set of valuesIn the limit Ec the lowest energy level value for a spherical dot of radius Ris:2212 RmEe ECE 407 Spring 2009 Farhan Rana Cornell UniversitySemiconductor quantum Dots: density of StatesSuppose, given a Fermi level position Ef , we need to find the electron number N:We can add the electron present in each level as follows: pfcEpEfN2If we want to write the above as.

7 FQDEEEfEgdENc 1 Then the question is what is the density of states gQW(E ) ?Ec2Ec1 pcQDpEEEg 2 Because the dot is such a small system, at many times concept of a Fermi level may not even be appropriate!! EgQD1cE11 EEc 21 EEc 31 EEc 7 ECE 407 Spring 2009 Farhan Rana Cornell UniversityA ridge waveguide quantum dot laser structuremetalSemiconductor quantum Dot Lasers (III-V Materials)non-radiativerecombinationelec tronsN-dopedphotonstimulated andspontaneousemissionholesP-doped Only 2 electrons can occupy a single quantum dot energy level in the conduction band Only 2 holes can occupy a single quantum dot energy level in the valence band Some advantages of 0D quantum dots for laser applications.

8 Ultralow laser threshold currents due to reduced density of states High speed laser current modulation due to large differential gain Small wavelength chirp in direct current modulation Ability to control emission wavelength via quantum size effectInAsQdotsInGaAsECE 407 Spring 2009 Farhan Rana Cornell UniversityColloidal quantum Dots: Wonders of quantum Size EffectPhotoluminescence from CdSe/ZnS (core-shell colloidal) quantum dots of different sizes (~2-6 nm) pumped with the same laserPhotoluminescence from CdTe/CdSe (core-shell colloidal) quantum dots of different sizes CdSeCdTe1cE1vEE EgQDphotonphoton RmEERmEEhvvecc 2121222 8 ECE 407 Spring 2009 Farhan Rana Cornell UniversityQuantum Dots.

9 Biology ApplicationsMotion of quantum -dot-attached-RNA into cells monitored by the luminescence (the quantum dots used are CdSe (core) and ZnS (shell) CdSe/ZnS quqntum dot coated with DHLA and functionalized with maltose binding protein (MBP) and AvidinECE 407 Spring 2009 Farhan Rana Cornell UniversityQuantum Dots: Biology ApplicationsNat. Biotechnol., 22, 198-203 (2004)Invitro microscopy of the binding of EGF to erbB1erB1 bound to eGFP (enhanced green fluorescent protein)EGF (epidermal growth factor) bound to quantum dotMovie shows binding of EGF tagged with fluorescent quantum dots to erB1 tagged with the green fluorescent protein CdSeZnSPolymer coatingNat.)

10 Biotechnol., 22, 969 (2004)Imaging of antibody (PSMA) coated quantum dots targeting cancer tumors cells9 ECE 407 Spring 2009 Farhan Rana Cornell UniversityColloidal quantum Dot Electrically Pumped LEDs-1-2-3-4-5-6-7-8 NiOWO3 ZnCdSCdSeZnCdSeSnO2(ZTO) ZnSnO2 ZnOZnS0 Possibleelectron injection layersPossiblehole injection layersQuantum dot(QD)eVVacuum levelBulovic et. al. (2010)

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