2004 Debye Lecture 3C. B. Murray

Semiconductor NanocrystalsQuantum Dots Part 1

Basic Physics of Semiconductor Quantum DotsC. R. Kagan, IBM T. J. Watson Research Center,

Yorktown Heights, NY

Bulk Semiconductor

ConductionBand

ValenceBand

EnergyGap

Quantum DotLike a

Molecule

HighestOccupiedMolecularOrbital

LowestUnoccupiedMolecularOrbital

Quantum ConfinementLow Dimensional Structures

( ) ( )Cc EEE −∝ρ ( ) tconsEc tan=ρ ( )( )n

c EEE

−∝

1ρ ( ) ( )nc EEE −∝ δρ

Particle-in-a-Sphere

ais a spherical harmonic( )φθ ,m

lY

( ) ( ) ( )rYrkj

Crm

llnl φθφθ

,,, ,=Φ

is the lth order spherical Bessel function( )rkj lnl ,

ak ln

ln,

,α

=

2

2,

22,

2

, 22 ammk

Eo

ln

o

lnln

αηη==

solutions givehydrogen-like orbitals with

quantum numbersn (1, 2, 3 …)l (s, p, d …)

m size-dependence

0

∞

Pot

entia

l V

r

1s

2s

Discrete energy levels

The Quantum Dot is a Semiconductor

The Effective Mass Approximationparabolic conduction and valence bands

Direct Bandgap Semiconductor

E

Eg

k

( ) ( ) ( )rkirur nknk

ρρρρ⋅=Ψ exp

Bloch’s Theorem

with periodicity of crystal lattice

veff

vk m

kE2

22η−=

gceff

ck E

mkE +=

2

22ηn=conduction band

n=valence band

Free particles treatedby effective mass:

• describing graphically the curvature of the bands

• representing the potential presented by the lattice

Combining the Effective Mass Approximation with a Spherical Boundary Condition

Ehν

E

Eg

k

Single Particle (sp) Wavefunction

( ) ( ) ( )∑ ⋅=Ψk

nknksp rkiruCrρρρρ

exp(1)

linear combination of Bloch functions

Envelope Function Approximationvalid for rQD > lattice constant

which for QDs is given bythe “Particle-in-a-Sphere”

( ) ( ) ( ) ( ) ( )rfrurkiCrur spnk

nknspρρρρρρ

00 exp =⋅=Ψ ∑(2)

assume unk has weak k-dependence

( ) ( )∑ −=i

innin rrCruρρρ

ϕ0(3)

linear combination of atomic orbitals withatomic wavefunctions ϕn (n= CB or VB)i=lattice sites

Coulomb Attraction

Bulk semiconductors, Coulomb attraction

creates bound excitons

e-h• e-

h•

Confinement Energy ∝ 1/a2

Coulomb Attraction ∝ 1/a

For small a:• Confinement Energy>Coulomb Attraction

electron and hole are treated independently• Coulomb interaction added as a correction

( ) coulombceff

Lnveff

Lngeehhehp E

mmaELnLnE eehh −

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

++=22

2

2,,

2ϕϕη

For 1Se pairs of states Ecoulomb=1.8e2/εa

Brus, J. Phys. Chem. 90, 2555 (1986).

Size Dependence of Electronic Structure

Ehν

E

Eg

k

Ehν

E

Eg

k

Decreasing Dot Diameter

p-orbitals form π-bonds with associated energy levels

with an energy separation in the visible

πGround

π*

HOMOHighest Occupied Molecular Orbital

LUMOLowest Unoccupied Molecular Orbital

Development of Electronic Structure Similar to Length Dependence in 1D polyenes

Example of alternating double/single bondπ-bond extends over many C atoms

Polyene’s with increasingchain length

Energy (eV)1.5 2.0 2.5 3.0 3.5

Abs

orba

nce

(arb

itrar

y un

its)

Energy (eV)1.5 2.0 2.5 3.0 3.5

Absorbance (arbitrary units)

17Å

150Å

17 Å

21 Å

29 Å

33 Å

45 Å

55 Å

72 Å

90 Å

150 Å

Size Dependent AbsorptionExample: CdSe

Semiconductor Materials

Range from 30 nm QDs to bulk crystal

Graph from H. Weller, Pure Appl. Chem. 72, 295 (2000).

Absorption Spectra of Semiconductor Nanocrystals

800 1200 1600 2000 2400 2800

IR A

bsor

ptio

n (A

rb. U

nit)

Wavelength (nm)

3.5 nm

4.0 nm

5.0 nm

6.0 nm

8.0 nm

12 nm

7.0 nm

3.0 nm800 1200 1600 2000

IR A

bsor

ptio

n (A

rb. U

nit)

Wavelength (nm)800 1200 1600 2000 2400

IR A

bsor

ptio

n (A

rb. U

nit)

Wavelength (nm)

7.4 nm

8.5 nm5.2 nm

4.0 nm

3.0 nm8 nm

C. B. Murray, IBMO. Micic, A. Nozik, NREL

InP

PbSe PbS PbTe

HgS

NRL group

Core

Changing the Core

InAs

A. P. Alivisatos, UC Berkeley

Real Band Structure

Example: CdSe

E

Eg

k

Cd 5s orbitals2-fold degenerate at k=0

Se 4p orbitals6-fold degenerate at k=0Introduces splitting of bands

hh

lh

so

heavy hole

light hole

spin-orbit splitoff J=1/2

J=3/2∆so

∆cfcrystal field splitting

J = L + S where L=orbital angular momentumS=spin angular momentum

J good quantum number due to strong spin-orbit coupling

J=1/2

F=J+L where L=envelope angular momentumJ=Bloch-band edge angular momentum

Hole states labeled by nhLF [LF=L + (L+2)]Electron states labeled neLe

Size Evolution of Electronic States

D. J. Norris, M. G. Bawendi, Phys. Rev. B 53, 16338 (1996).

CdSe InAs

U. Banin et al., J. Chem. Phys. 109, 2306 (1998).

Low Band gap InAs modeling must alsoaccount for valence-

conduction band coupling

2S3/21Se

1S3/21Se1S3/21Se

1P3/21Pe

2S3/21Se

1P3/21Pe

Selection Rules

2ˆ he peP Ψ⋅Ψ=ρ

polarization vector of light

momentumoperator

acts only on unit cell portion of wavefunction

22ˆ hevc ffupeuP ⋅=ρ

hehe LLnnvc upeuP ,,2ˆ δδ⋅=

ρ

Overlap of the electron and hole wavefunctions within the QDs

Towards the Homogeneous Distribution: Photoluminescence and Photoluminescence Excitation

Wavelength (nm)

400 450 500 550 600 650 700

Abso

rban

ce (a

rbitr

ary

units

)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Abs

orpt

ion

Wavelength

Lum

ines

cenc

e

Wavelength

10 K

Wavelength (nm)

600 650 700 750 800Lum

ines

cenc

e (a

rbitr

ary

units

)

0.0

0.2

0.4

0.6

0.8

1.0

Photoluminescence“largest” QDS

Photoluminescence Excitation“smallest” QDS

10 K

Distribution in ensemble from size, structure, and environmental inhomogeneities

Fluorescence Line Narrowing and Photoluminescence Excitation

D. J. Norris, Al. L. Efros, M. Rosen, M. G. Bawendi, Phys. Rev. B 53, 16347 (1996)

Band Edge Exciton Structure

Splitting due to crystal field, non-spherical shape, and exchange interactions of quantum dots

Single Molecule Spectroscopy

Diffraction Limited Spot

M. Nirmal, L. E. Brus, Acc. Chem. Res. 32, 407 (1999).

Fluorescence Intermittancy in CdSe QDs

QDs “blink” like molecules

On-period decreases with increasing illumination intensity

Off-period intensity independent

Excitation every 10-5 secRelaxation every 10-8 sec

But occasionallyTwo electron-hole pairs mayexist in a single QD

Auger ionizationProbability of photoionization/excitation 10-6

Neutralization time ~0.5 sec

Auger Ionization

Al. L. Efros, M. Rosen, Phys. Rev. Lett., 78, 1110 (1997).

Consistent with single molecule spectroscopy and photodarkening observed in QD doped glasses

Single Dot Spectroscopy

Individual quantum dots

Single Quantum Dot Emission

Histogram of 513 43 Å QDs

Including all phonon lines

Spectral diffusion driven by environment

S. A. Empedocles, M. G. Bawendi, Acc. Chem. Res. 32, 389 (1999).

Metal Nanoparticles

MetalParticle-- -

-------

- ---

-------- -

Surface Plasmon Resonance

• dipolar, collective excitation between negatively charge free electrons and positively charged core

• energy depends on free electron density and dielectric surroundings

• resonance sharpens with increasing particle size as scattering distance to surface increases

Au nanoparticle absorption

Electronic Properties of Semiconductor and Metal Nanoparticles

Charge not completely solvatedas in infinite solid

ε

a

aC oεπε4=Nanoparticle capacitance

Charging Energy)(2

2

aCeEc =

Courtesy of C. T. Black, Thesis, Harvard U.

10 nm Al NC

Coulomb blockade atkBT<Ec

Structure from discrete electronic states of metal NC

STM Measurements on Single QDs

U. Banin et al. Nature 400, 542 (1999).

InAs QDs

Synthesis of monodisperse CdSe nanocrystals

...CdSePSe)(oct)Cd(CH 300323 +⎯⎯⎯⎯⎯⎯⎯⎯ →⎯+ °−− C,TOPTOPOHDA

UV-Vis and PL spectra of CdSe nanocrystals in growth at 300°C

400 600 800

abso

rban

ce, P

L in

tens

ity [a

.u.]

wavelength [nm]

add. inj.

add. inj.

200 min

120 min

60 min

12 min

0.5 min

TEM and HRTEM images of as-prepared CdSe nanocrystals.

D. V. Talapin, A. L. Rogach, A. Kornowski, M. Haase, H. Weller. Nano Lett. 2001, 1, 207.

Wet Chemical Synthesis of PbSe Nanocrystals and Superlattices

oleic acid, Synthesis Pb(OAc)2 + R3PSe

R3P, T=150 C

PbSeR= octyl

Size SelectiveProcessing

Size selective precipitation in solvent/ non solvent pairs like hexane-methanol

Self Assembly Evaporation of the solvent

T. J. Watson Research Center

PbSe Nanocrystals and Nanowires

Nanocrystals:

1.5 – 10 nm diameters100 – 100 000 atoms

Conduction band

HOMO

LUMO

Valence band

bulk nanocrystals molecular clusters

PbSe Nanocrystal

Small Bandgap (0.28 eV, cf CdSe : 1.70 eV) ⇒ IR detector, IR diode Laser MaterialLarger Bohr Radius (PbSe 46 nm, CdSe 12nm) ⇒ Strong Confinement of Electron-Hole PairLarger Optical Nonlinearity, Thermoelectric Cooling (ZT = 1 : PbTe)Semiconducting, Solar Cells, Thermoelectric, Biological Application

PbSe Nanowire

Solution Phase Synthesis using the Nanoparticles as a Building BlockFormation of the Nanowires from the Self Assembling the ParticlesControlling the wire Properties by Changing the Size and Shape of the ParticlesSemiconducting device, Interconnect, Building Blocks for the Nanodevice

Seconds0 200 400 600 800 1000

Con

cent

ratio

n of

Pre

curs

ors

(arb

itrar

y un

its)

Nucleation Threshold

Staturation

Inje

ctio

nN

ucle

atio

n

Gro

wth

Fr

om S

olut

ion

Ostwald Ripening

Monodisperse Colloid Growth (La Mer)

A

Size selective processing:

M ajor D iam eter <002>

0 10 20 30 40 50 60

Nor

mal

ized

Cou

nts

0

20

40

60

80

100

M ajor D iam eter <002>

0 10 20 30 40 50 60

Nor

mal

ized

Cou

nts

0

20

40

60

80

100

M eOH

HexaneBuO H

Growth Solution

Size Selected

39Å M ajor D ia.σ =4.5%

37Å M ajor D ia.σ = 12%

A

B

C

Center to Center Distance R (arbitrary units)

Ene

rgy

(arb

itrar

y un

its)

Steric Repulsion (R-12

)

van der Waals (R-6

)Attraction

P=Se0=P

0=P0=P0=P

P=O

P=0

Se=P

0=P

0=P0=P

0=P0=PSe=P

0=P

P=0P=0

P=0P=0

P=0

P=0

P=0P=0

P=0

/\/\/\/\/\/\/\/\

\/\/\/\//\/\/\/\/\/\/\/\\/\/\/\/

/\/\/\/\

/\/\/\/\\/\/\/\/

/\/\/\

/\/\/

\/\/\

\/\/\/\/

/\/\/\/\

\/\/\/

\/

/\/\/\/\

/\/\/\/\

\/\/\/

\/

/\/\/\/\/\/\/\/\ \/\/\/\/

/\/\/\/\

/\/\/\/\\/\/\/\/

/\/\/\/\\/\/\/\//\/\/\/\

/\/\/\/\

/\/\/\/\

\/\/\/\/

/\/\/\/\

/\/\/\

/\

/\/\/\

/\

\/\/\/\//\/

\/\/\

/\/\/\

/\

/\/\/\/\

\/\/\/

\/

\/\/\/\/

/\/\/\/\/\/\/\/\

\/\/\/\/\/\/\/\/

/\/\/\/\

\/\/\/\/

/\/\/\/\

/\/\/\

/\/\/

\/\/\\/\

/\/\/

/\/\/\/\

\/\/\/\//\/\/\/\ P=Se

0=P

0=P0=P0=P

P=O

P=0Se=P

0=P

0=P0=P

0=P0=PSe=P

0=P

P=0P=0

P=0P=0

P=0

P=0

P=0P=0

P=0

/\/\/\/\/\/\/\/\

\/\/\/\//\/\/\/\/\/\/\/\\/\/\/\/

/\/\/\/\

/\/\/\/\\/\/\/\/

/\/\/\

/\/\/

\/\/\

\/\/\/\/

/\/\/\/\

\/\/\/

\/

/\/\/\/\ /\/\

/\/\

\/\/\/

\/

/\/\/\/\/\/\/\/\ \/\/\/\/

/\/\/\/\

/\/\/\/\\/\/\/\/

/\/\/\/\\/\/\/\//\/\/\/\

/\/\/\/\

/\/\/\/\

\/\/\/\/

/\/\/\/\

/\/\/\

/\

/\/\/\

/\

\/\/\/\//\/

\/\/\

/\/\/\

/\

/\/\/\/\

\/\/\/

\/

\/\/\/\/

/\/\/\/\/\/\/\/\

\/\/\/\/\/\/\/\/

/\/\/\/\

\/\/\/\/

/\/\/\/\

/\/\/\

/\/\/

\/\/\\/\

/\/\/

/\/\/\/\

\/\/\/\//\/\/\/\r r

R

ab

c

d

Wavlength (nm)400 500 600 700 800

Abs

orba

nce

(arb

itrar

y un

its)

Wavelength (nm)400 500 600 700 800

Absorbance (arbitrary units)

A B

(a) 37Å+12%

(b) 39Å+8%

(c) 40Å+5%

(d) 42Å+<4%

(e) 39Å+11%

(f) 41Å+6%

(g) 45Å+<4%

Results of size selected Percipitation

PbSe nanowires1 0 0 0 2 0 0 0 3 0 0 0

( f )

( g )

( e )

( d )

( c )

( b )

( a )

Abso

rban

ce (a

rbitr

ary

units

)

W a v e l e n g t h ( n m )

1 0 0 0 1 5 0 0

2 9 8 K

7 7 K

Relative intensity

size: 4.0 nm

Wavelength (nm)

800 12001600200024002800

IR A

bsor

ptio

n (A

rb. U

nit)

Wavelength (nm)

3.5 nm

4.0 nm

5.0 nm

6.0 nm

8.0 nm

12 nm

7.0 nm

3.0 nm

PbSe Nanocrystals

Absorption and Photoluminescenceof PbSe Nanocrystals

0 10 20 30 40 50 60 700.0

0.5

1.0

1.5

2.0

Con

finem

ent E

nerg

y (e

V)

Equivalent Radius (A)

Based on IR & TEM Calculated using Scherrer

Formula (XRD) PbSe in Phosphate Glass (1)

Effective Mass Approx.

50 nm 5 nm

10 nm50 nm

1 2 3 4 5 6

103

104

105

106

107

Experiment Sphere Particle D = 9.8 nm, Rg = 3.8 nm

(σ = 8 %)

Ref

lect

ed In

tens

ity (A

rb. U

int)

2θ (Degree)

1 2 3 4 5 6

103

104

105

106

107

Experiment Cubic Particle L = 10.5 nm, Rg = 5.25 nm

(σ = 10 %)

Ref

lect

ed In

tens

ity (A

rb. U

nit)

2θ (Degree)

Shape Change from Sphere to Cubic and SAXS in Polymer Matrix

T. J. Watson Research Center

K.-S. Cho, W. Gaschler

PbSe Quantum Cubes

20 30 40 50 60 70

Ref

lect

ed In

tens

ity (A

rb. U

nit)

2θ (Degree)

(111) (200) (220)(311)(222)

< 3 nm

4.3 nm

7.6 nm

8.3 nm

9.5 nm

13.2 nm

Sphere

Cube

(200)

> 16 nm

5.1 nm

20 25 30 35 40 45

(200)

(220)

inte

nsity

/ a.

u.

2Θ

20 25 30 35 40 45

(200)

(220)

inte

nsity

/ a.

u.

2Θ

32 34 36

Ref

lect

ed In

tens

ity (A

rb. U

nit)

2θ (Degree)

WAXS of 10 nm PbSe quantum cubes slowly deposited from toluene (top) and rapidly precipitated from methanol (bottom)

Shape evolution of PbSe Nanocrystals

100

111

Highly symmetric rock salt structure

Modeling of x-ray diffraction:

The Debye equation which is valid in the kinematical approximation is shown in equation 4.6 (8).

(4.6)Where I(q) is the scattered intensity , Io is the incident intensity, q is the scattering parameter [q = 4πsin(θ)/l] for X-rays of wavelength l diffracted through angle θ. The distance between atoms m and n is rmn . A discrete form of the Debye is shown in eguation (4.7)(9). (4.7)

where is the incident intensity, f(q) is the angle dependent scattering factor q is the scattering parameter[4πsin(θ)/λ] for X-rays of wavelength λ diffracted through angle θ. The sum is over all inter atomic distances, and ρ(rk) is the number of times a given interatomic distance rk occurs. Since the number of discreteinteratomic distances in an ordered structure grows much more slowly than the total number of distances, using the discrete form of the equation is significantly more efficient in the simulation of large crystallites(9).

I q I F Fqr

qrmnm nm n

m n

( )sin( ),

,

= ∑∑0

( ) ( )I q I f qq

rr

qrok

kk

( ) ( ) sin= ∑2 ρ

Modeling NP Shape

2θ

10 20 30 40 50 60

Sca

ttere

d In

tens

ity (a

rbitr

ary

units

)

Equivalent Diameter ~63Å

Spherical1:1

Prolate1.22

(a)

(b)

Modeling Stacking faults

Small angle X-ray Scattering SAXS

(4.8)

Where ρ and ρo are the electron density of the particle and the dispersing medium respectively. Io is the incident intensity and N is the number of particles. F(q) is the material form factor (the fourier transform of the shape of the scattering object) and is the origin of the oscillations observed. Thus for a spherical particle of radius R

(4.9)

(4.10)

I q I N F qo o( ) ( ) ( )= −ρ ρ 2 2

F q R qR qR qRqR

( ) [ sin( ) cos( )( )

]=−4

333

3π

I q I N R qR qR qRqRo o( ) [( ) [ sin( ) cos( )

( )]]= −

−ρ ρ π2 33

243

3

Combined SAXS and WAXS Modeling.

Qunatum cubes:Cubic 12 nm PbSe nanocrystals Assembling into a superlattice.

(100) (112)

(111) (101)

Self-assembled CdSe nanorod solids

20 µm20 µm

withcrossed

polarizers

withoutpolarizers

Optical micrograph of self-assembled CdSe nanorods (between crossed polarizers).

III-V semiconductor nanocrystals : InP

400 600 800

~8nm

<2nm

InP

abso

rban

ce, a

.u.

wavelength, nm

Size-dependent evolution of absorption spectra of InP colloidal quantum dots

...InPPSi])(CH[P)(octInCl 2601803333 +⎯⎯⎯⎯⎯⎯⎯ →⎯+⋅ °−− CTOP,TOPO

PL quantum efficiency ~25-40%

J. Phys. Chem. B, 2002, 106, 12659.

etching agent

hν

) strong InP) weakprepared,-(as InP PLPL hTOPO,HF (, ⎯⎯⎯⎯⎯ →⎯ ν

CdSe/CdS quantum dot - quantum rods

CdSe coresCdSe/CdS

40 nm

CdSe/CdS

Cd:S=1:1 Cd:S=1:3

CdSe coresCdSe/CdS

40 nm

CdSe/CdS

Cd:S=1:1 Cd:S=1:3

CdSe CdS

0° 180°

||

⊥

⊥||

Luminescent II-VI nanocrystalsRoom temperature PL quantum efficiencies 50-70%

Colloidal solutions of CdSe/ZnS core-shell nanocrystals.

CdSe/CdS core-shell nanocrystals in a polymer matrix

Single particle luminescence of CdSe/ZnS nanocrystals