nanomaterials – electronic properties
DESCRIPTION
Nanomaterials – Electronic Properties. Keya Dharamvir. Modifications due to :. Quantum confinement Quantum size effect Energy bands and electronic transition Charge quantization. Nanostructures. Microstructure vs. Nanostructure. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/1.jpg)
Nanomaterials –Electronic Properties
Keya Dharamvir
![Page 2: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/2.jpg)
•Quantum confinement
•Quantum size effect
•Energy bands and electronic transition
•Charge quantization
Modifications due to :
![Page 3: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/3.jpg)
Nanostructures
STRUCTURE SPATIAL DIMENSION
CONFINEMENT DIMENSION
Bulk 3 0
Surface/ Film (Quantum Well)
2 1
Nanotubes, -wires (Quantum wire)
1 2
Nano-particles, clusters (Quantum dots)
0 3
![Page 4: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/4.jpg)
Microstructure vs. Nanostructure
Microstructure Nanostructure/ Bulk
• Physics Semi-classical Q. mechanical• Electron’s nature Particle-like Wave-like• E or k-space Continuous Discrete• Current Continuous Quantized• Decision Deterministic Probabilistic• Fabrication Micro-fabrication Nano-fabrication •Surface:volume Small Very large• Packing Low Very high
![Page 5: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/5.jpg)
Electrons’ Behaviour in Smaller Sizes
• Energy quantization d ~ Fermi wave length of electron in a metal (F)
or exciton diameter in a semionductor • Charge quantization Charging energy (Ec) >> Thermal energy (kT)
• Ballistic d<mean free path ()
Free electron case (3D box):exp(ikr) where k =2n/L; E= ħ2k2/2m N = 2x (4kF
3/3)/(2/L)3 = VkF3/32
electron concentration N = N/VEF= (ħ2/2m) kF
2 = (ħ2/2m) (32 N) 2/3; kF = (32 N)1/3
F= 2kF= 2 (32 N)-1/3
![Page 6: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/6.jpg)
Exciton : e-h pair bounded by attractive electrostatic interaction (H atom-like)
E
Eg
Conductionband
Valence band
Exciton levels
•Binding energy: Eex =e4/2ħ2n2
•Bohr (exciton) radius: r = n2ħ2/e21/me
+1/mh
Si Ge GaAs CdSe KClEex (meV) 14.7 3.8-4.1 4.2 15 400r (nm) 4.3 11.5 12.4
E
Eg
0
Exciton bindingenergy: EexEg-Eex
n=1n =2
k
![Page 7: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/7.jpg)
Quantum Confinement
Exciton radius
R
•R<< r: Strong Confinement - 1st term (localization) dominant - Electron and hole are quantized - Energy gap ~1/R2
eg) Si<4.3 nm, Ge<11.5 nm, GaAs<12.4
•R>> r: Weak confinement - 2nd term (coulomb attraction) dominant - Exciton confinement character
L.E. Brus, J. Chem. Phys. 80, 4403(1984)
Energy for the lowest excited state relative to Egap
E(R) = h22/2R2 – 1.8e2/2R …
r
dot
Particle in a box problem
![Page 8: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/8.jpg)
Density of State: # of states per unit energy range
N =2n2/L2 N =8n3/3L3
dN /dE = const dN /dE ~ E 1/2
k=2n/LE = ħk2/2mk =(2mE)ħN = 2xn/L= k/ = (ħ)2mE)
dN /dE = ((2m)/2ħ)(E)
dN /dE ~ E
N = 2n/L
DO
SDO
SDO
S
1D 2D 3D
E = ħk2/2m= ħ/2m(kx2+ky2+kz2)
• k is discreet in confinement directions only
![Page 9: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/9.jpg)
Size Effect: Energy Levels and DOS
A.P. Alivisatos, Science 271, 933 (1996)
3d 2d 1d 0d
EnergyD
OS
EF
Bulk Nano atom particle
Size controlled band gap tuningDiscrete Energy levels
CB
VB
Semiconductor
LUMO
HOMO
Band gap
![Page 10: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/10.jpg)
Size Effect:1D-Quantum well states
F.J. Himpsel et al, Adv. Phys. 47, 511 (1998)
![Page 11: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/11.jpg)
Size Effect: Optical Spectra
A.P.Alivisatos, J. Phys. Chem. 100, 13227 (1996)
• Shift to higher energy in smaller size• Discrete structure of spectra• Increased absorption intensity
![Page 12: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/12.jpg)
Size effect: Tunable Band Gap
Optical excitation is significantly enhanced, both, in frequency and intensity, in smaller sizes.
S. Ogut et al, Phys. Rev. Lett. 79, 1770 (1997)
Bulk Si = 1.14 eV GaAs =1.5 eV
![Page 13: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/13.jpg)
Energy Bands
![Page 14: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/14.jpg)
Go to P. 7 – 10 of Doc2
![Page 15: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/15.jpg)
Energy Band Structure: Energy vs. k
Cnn
VCn V n
(h2/2V Ej= cos 2j/N index j = 0, 1, 2 … Define a new index k = 2j/Na: wave vector E(k) = coska, k = eiknan : Bloch wave function (symmetry adapted LCAO)
/a k=0 /a
E
= 2/k = 2a
= ∞ ….
….
….
….
a
01
2
![Page 16: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/16.jpg)
/a k=0 /a
E
Electronic Transition
i
fif
•Direct transition (k=0)•In phase •Added transition dipole•Electronically allowed transition
i
fif
•Indirect transition (k ≠ 0)•Out of phase•Cancelled transition dipole•Electronically forbidden but vibronically allowed
Electric Transition dipole moment if = <f |er i>
•Band width: overap of wave functions•Slope dE/hdk = hk/m = vg: group velocity of electron
![Page 17: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/17.jpg)
Electronic absorption spectra for three sizes of CdSe nanocrystals, in the wurtzite (direct) and rock salt (indirect) structures. In each instance the direct gap spectrum is structured and intense, while the indirect gap one is featureless and relatively weaker. The relative absorption efficiencies do not change, despite the concentration of oscillator strength due to quantum
confinement.
Absorption spectra: Direct and Indirect Transition
![Page 18: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/18.jpg)
Size Effect: Enhanced Absorption
k
E
E
N(E)
For quantum dot,•Energy levels: discrete•DOS: delta function
• xp ~ h• x: well defined• p=hk: Not well-defined• k is not an exact quantum number for QD
•Envelope functions sample larger k-space
•Overlap of wave functions
- Increased absorption intensity
M.S. Hybersten, Phys. Rev. Lett. 72, 1514 (1994)
![Page 19: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/19.jpg)
Photon absorption: Direct vs. Indirect Transition
Selection rulek’ = kk = 0) k’ = k + qk ≠ 0)Energy relationship hv = Eg hv = Eg + hv(q)Interaction electronic: two body vibronic: three bodyTransition rate fast ~ 10 -7 sec slow ~ 10-2 secRadiative efficiency high lowExample GaAs (Eg (dir.) =1.4 eV) Si (Eg (ind.) = 1.1 eV)
(Eg (dir.) = 3.37 eV)
E
kEg
q
hv
phonon
![Page 20: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/20.jpg)
• P. 26, 27 of doc2(Optical properties of semiconductor
nanoparticles)
![Page 21: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/21.jpg)
![Page 22: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/22.jpg)
• P. 18 of doc2• (optical properties of metal
nanoparticles)
![Page 23: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/23.jpg)
Charge Quantization
•Charging energy: Ec = e2/2C >> kT At T =300K kT = 26 meV C<< 3.1x10-19 F C = 4d 4= 1.1x10-10 J -1 C2m-1
•For charge quantization, the diameter of dot (d) must be << 28 nm
ee
d
N=0
321
![Page 24: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/24.jpg)
Tunneling Spectroscopy of InAs QD
Ec=0.11 eV: single electron charging energyEg=1.02 eV: nanocrystal band gap
d = 32A
T=4.2K
U. Banin et al, Nature, 400, 926 (2000)
S-like
P-like
STM
Optical
![Page 25: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/25.jpg)
• P. 21, 22, 23 of doc2 forConduction through metal
nanoparticles.
• P. 30 forComparison table
![Page 26: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/26.jpg)
Property: Melting Temperature of Nanocrystal
A.P.Alivisatos, J. Phys. Chem. 100, 13227 (1996)
![Page 27: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/27.jpg)
Y.J. Lee et al, J. Comp. Chem 21, 380 (2000), Phys. Rev. Lett. 86, 999 (2001)
• As the cluster size decreases, the melting temperature (Tm) monotonically decreases, However, when the cluster size is small enough, Tm does not vary monotonically with cluster size.• The absence of a premelting peak in heat capacity curves for some clusers.• Premelting: surface melting, partial melting, orientational melting, and isomerization
Property: Thermodynamic Behaviors of Metal Clusters
![Page 28: Nanomaterials – Electronic Properties](https://reader035.vdocument.in/reader035/viewer/2022062407/56812eab550346895d944c53/html5/thumbnails/28.jpg)
• THANK YOU