1

5µm

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