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Nanoscale Systems for Opto-Electronics
1.80 1.85 1.90 1.95 2.00 2.05
PL
inte
nsity
[a
rb. u
nits
]
Energy [eV]
700 675 650 625 600
Wavelength [nm]
2
Nanoscale Systems for Opto-ElectronicsLecture 7
Interaction of Light with Nanoscale Systems- general introdcution and motivation- nano-metals (Au, Ag, Cu, Al ...)
introduction to optical propertiesmie scatteringmie scattering in the near-fieldmie scattering with nano rodsresonant optical antennas
- artificial quantum structures (semiconductor quantum dots, ...)- quantum dot lasers
Optical Interactions between Nanoscale Systems- Förster energy transfer (dipole-dipole interaction)- super-emitter concept- SERS (surface enhanced Raman spectroscopy: bio-sensors)
Beating the diffraction limit with Nanoscale Systems- surface plasmon polariton (SPP) - light confinement at nanoscale- plasmonic chips- plasmonic nanolithography
3
Last Time: Resonant Optical Antenna
4
Motivation: Technology
10 nm 1-10 nm
Classical Transport Quantum Effects
100 nm
Moore’s Law !1965
2015?
10 µm
Top DownTop Down Bottom UpBottom Up
5
Motivation: Fundamental Science
bottom-up
top-down
atom
cluster-molecule
nanocrystal
bulk phase
transition 2D – 3D
changing S/V ratio
here: discuss only crystalline structures !
6
From Small to Big
Semiconductor Clusters, Nanocrystals, and Quantum Dots A. P. Alivisatos Science 1996 February 16; 271: 933-937.
Atom Cluster/ Molecule Nanocrystal Macrocrystal / bulk
Quantum chemistry EMA with confinement
7
Nanoscale Materials Science – Questions:
How does one make nanometer sized objects ?
How do you make identical copies of nanometer sized objects ?
How do the properties (optical, electrical) change as a function of object size and dimension?
How do charge carriers behave in nanoscale objects ?
Are there new (undiscovered) properties in nanoscale objects ?
Are they useful for new artificial bulk materials with nanoscale objects as their building block ?
8
Nanoscale Materials Science – Questions:
Are they useful for new artificial bulk materials with nanoscale objects as their building block ?
9
Crystal Structure of some Materialsplease note: by no means meant to be comprehensive
Bravais latticescubic
tetragonal
hexagonal
rhombohedral
orthorhombic
monoclinic
triclinic
10
Crystal Structure of Single Element Crystalsplease note: by no means meant to be comprehensive
lattice: fccbasis atom: 1e.g.: Cu, Ag, Au, Ni, Pd, Pt, Al ...
lattice: fcc, diamond unit cellbasis atom 1 (0,0,0)basis atom 2 (¼, ¼, ¼)e.g.: C,Si, Ge, Sn ...
lattice: bccbasis atom: 1e.g.: Fe, Cr, V, Nb, Ta, W, Mo ...
lattice: hcpbasis atom 1 (0, 0, 0)basis atom 2 ( ½, ¼, ½ ) e.g.: Mg, Re, Co, Zn, Cd, C ...
11
Crystal Structure of Single Compound Crystalsplease note: by no means meant to be comprehensive
lattice: fcc, rock salt unit cellbasis element 1 (0, 0, 0)basis element 2 (½, 0, 0 )e.g.: KCl, AgBr, KBr, PbS, MgO, FeO ...
lattice: fcc, ZnS unit cellbasis atom 1 (0,0,0)basis atom 2 (¼, ¼, ¼)e.g.: ZnS, GaAs, InSb, GaP ...
lattice: cubic primitiv, CsCl unit cellbasis element 1 (0, 0, 0)basis element 2 (½, ½, ½ )e.g.: CsCl, AlNi, CuZn ...
12
More on Crystal Structure: Packing Fraction...
assume: rigid, touching spheres
a
r
simple cubic case
3
3
4rVsphere π=
6
)2
(3
4
3
3
a
aVsphere
π
π
=
=
...524.06
63
3
3
==
=
=
π
π
a
a
Ratio
aV
sc
cube
13
More on Crystal Structure: Packing Fraction...
assume: rigid, touching spheres
a
r
3
33
24
2
)4
2(
3
4
a
aVsphere
π
π
=
=
...741.06
2
62
3
3
3
==
=
=
π
π
a
a
Ratio
aV
fcc
cube
fcc case
ar
rc
ac
ac
aac
4
2
4
2
2 22
222
=
==
=
+=
Corner: 8(1/8) = 1 sphereFace: 6(1/2) = 3 spheres
3
6
2
4
a
VV sphereestotalspher
π=
=
14
Inverse Power Law: surface to volume ratio
3
3
4aVsphere π=
cube cylindersphere
Surface area
Volume
Ratio
26aS =
3aV =
aa
aRatio
663
2
==
24 aS π=
aV
SRatio
3==
alS π2=
laV 2π=
aV
SRatio
2==
As the size of the system decreases, the fraction of atoms on the surface increase.
15
Power Laws ???
e.g. the proportionality between the optimal cruising speed Vopt of flying bodies (insects, birds, airplanes) and body mass M in kg raised to the power 1 /6
A power law is any polynomial relationship that exhibits the property of scale invariance.
16
Length Scale Issues
Appropriate length scale for nano stuff is a regime where the chemical, physical, optical and electrical properties of matter become size and shape dependent.
Semiconductor business:
deBroglie wavelength of exciton or Bohr radius of exciton ?
ν = E / h
λ = h / p
with
h [ J s] Planck‘s constant
6.62 x 10-34
17
Bohr Radius of an Electron (in vacuum)
from textbook:
Angstrom 528.0
1028.5
numberOrbit
10602.1
1011.9
10054.1
/1085.8
4
0
110
19
31
34
120
2
220
0
=×=
×=
×=
×=
×=
=
−
−
−
−
−
a
ma
n
Cq
kgm
Js
mF
with
mq
na
�
�
ε
πε
18
Bohr Radius of an Electron (in solid phase)
from textbook:
Cq
mmm
Js
mF
with
qma
heeff
eff
19
34
120
2
20
0
10602.1
111
10054.1
/1085.8
4
−
−
−
×=
+=
×=
×=
=
ε
επε
19
Bohr Radius of an Electron (in solid phase)
from textbook:
Cq
mmm
Js
mF
with
qma
heeff
effb
19
34
120
2
20
10602.1
111
10054.1
/1085.8
4
−
−
−
×=
+=
×=
×=
=
ε
επε GaAsme= 0.067 m0
mh = 0.45 m0ε= 12.4ab= 11.3 nm
CdSeme= 0.13 m0
mh = 0.45 m0
ε = 9.4ab= 4.97 nm
lattice constant:
ZnS unit cell with a = 0.567 nm
Screening effect in solid phase leads to large ab
20
Excitons in Semiconductors
Free Excitons (Wannier-Mott)
Radius rexciton >> a lattice constant
Moving freely in crystal (coulomb interaction screened, ε bulk,semiconductor 5-12)
Hydrogen-like Hamiltonian:
L.E. Brus, J. Chem. Phys. 80 (9), 1984
•Effective mass approximation
small mass implies that localization energies for e- and h+ are large
21
Excitons in Semiconductors
bulk exciton Bohr radius:
00
02
0
20
)(
4
am
a
m
qma
b
b
µε
µεπε
=
= �
reduced exciton mass
bulk exciton total energy:
)4
(2
1
)4
()4
(2
1
thatso
41
v
4
v
:Newtonwith
4v
2
1
0
2
0
2
0
2
0
22
20
22
0
22
r
q
r
q
r
q
r
qm
r
q
r
m
r
qm
tot
tot
tot
πεεε
πεεπεεε
πεε
πεε
πεεε
−=
−=
=
=
−=
22
Excitons in Semiconductors
bulk exciton Bohr radius:
00
02
0
20
)(
4
am
a
m
qma
b
b
µε
µεπε
=
= �
reduced exciton mass
bulk exciton total energy:
20
2
20
2220
40
2220
4
2
220
0
2
1
1)
)4((
2
1
1)
)4((
2
1
4
with
)4
(2
1
nmR
nm
qm
n
q
then
q
na
r
q
tot
tot
tot
b
tot
−=
−=
−=
=
−=
εµε
εµ
πεε
πεεµε
µπεε
πεεε
�
Orbit number n=1
Rydberg, R=13.4 eV
23
Excitons in Semiconductors
bulk exciton Bohr radius:
00
02
0
20
)(
4
am
a
m
qma
b
b
µε
µεπε
=
=
reduced exciton mass
bulk exciton total energy:
=
−=
−=
=∞
02
1
20
2
1
mR
nmR
bind
nbind
tot
εµε
εεεε
µε
Orbit number n=1
24
QM Bulk Picture
QM: HΨ = E Ψ
Potential for carriers in crystal:→ translational symmetry Va(x) = Va(x+a)
Ψ-function modulated (Bloch ansatz):
→Ψk(x) = uk(x) exp(ikx)
Energy-Dispersion
“modulation of plane waves“
unit cell delocalization
V
x
E(k)
k
CB
VB
25
Introduction – Solid State
Semiconductor
light absorption
relaxation
light emissionE
nerg
y
VB
CB
ΔEgap
E(k)
k
CB
VB
V
x
26
Introduction – Solid State
Semiconductor
light absorption
relaxation
light emissionE
nerg
y
VB
CB
ΔEgap
CB
VB
V
xFree Excitons (Wannier-Mott)
27
Free Exciton SpectroscopyA
bsor
ptio
n, α
Photon Energy
(ħω – Eg)1/2
n=1
n=2
For T < RX/kB: hydrogenic line series observable
E(n) = Eg – RX / n2
Ene
rgy
light absorption
Val
ence
Ban
dC
ondu
ctio
n B
and
28
Excitons in CdSe Bulk - Energetic Aspect
• Binding energy: RX,CdSe = (µ/m0ε) RH 15 meV
with me* = 0.119 me
0 , mh* = 0.5 me
0
→ RX,CdSe / kB = 174 K
•Exciton Bohr radius: aX = (m0 ε / µ) aH 6 nm
→ N = V/V0 = (4/3 π aX3) / (a2c) ≈ 8*105 unit cells
29
Electronic DOS does matter !
Exciton Bohr radius >> crystal dimension
3 D 2 D 1 D 0 D
E E E E
DOS
DOS
bulk
se
mic
ondu
ctor
arti
fici
al a
tom
Early motivation for semiconductor nanostructures
30
Outlook: Squeeze the Exciton Bohr radius
Energy
Small sphere
1-10nm 'particle-in-a-spherical-box' problem
31
Outlook: Synthesis - Bottom-up Approach
20 nm
TEM image of core CdSe nanocrystals Eisler HJ, unpublished data
C.B. Murray, D.J. Norris, and M.G. Bawendi, J. Amer. Chem. Soc. 1993, 115, 8706
T=330ºC
N2
TOPO
Tri-octylphosphineoxide
TOPSe
CdO
33
Outlook: Optical Properties of Artificial Atoms
1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
no
rma
l. In
ten
sity
Energy [eV]
800 700 600 500 400
1.47 470
1.85 950
2.5 2350
3.05 4220
Reff
(nm) #atoms
Wavelength [nm]
34
Outlook: Optical Properties of Artificial Atoms
35
Outlook: Optical Properties of Artificial Atoms
S. Kim, B. Fisher, H.-J. Eisler, M. G. Bawendi, J. AM. CHEM. SOC. 125, 11466 (2003)
CdSe
36
Outlook: [CdSe]core{ZnS}shell Type-I Heterostructure
M. A. Hines, P. Guyot-Sionnest, J. Phys. Chem. 1996, 100, 468-471.B. O. Dabbousi et al., J. Phys. Chem. B 1997, 101, 9463-9475.
400 500 600 700 800
Abs
orb
anc
e, P
hoto
lum
ines
cenc
e
Wavelength [nm]
400 500 600 700 800
Abs
orb
anc
e, P
hoto
lum
ines
cenc
e
Wavelength [nm]
ZnEt2
(TMS)2S
~200oCTOP/TOPO
37
Outlook: Absorption and Photoluminescence