Deriving Insights from Computation: Molecular Electronics to Self-trapped Excitons

Steven G. Louie Physics Department, UC Berkeley and MSD, LBNL

Electron Transport:

Self-trapped Excitons:

Supported by: NSF and DOE

J.-H. Choi Y.-W. SonJ. Neaton J. Ihm (Korea)K. Khoo M. Cohen

S. Ismail-Beigi (Yale)O1

Si1

Si2

Molecular Electronics

Present approach: Ab initio scattering-state method

Other ab initio approaches:NEGF methods -- (e.g., TRANSIESTA, Guo, et al., …)Lippman-Schwinger -- (e.g., di Ventra & Lang, …)Master equation -- (e.g., Gebauer & Car, …)

(Electron transport through single molecules,atomic wires, …)

Example of a Molecular Electronic Device

(For a review, see Reed & Chen, 2000)

Chen, et al (1999); Rawlett, et al (2002)

Some fundamental issues

• Open system: infinitely large and aperiodic

• Out of equilibrium: Chemical potential ill-defined across molecule

• Nanometer length scales: atomic details of contact and self-consistent electronic structure are important

µL µR

Current

R

LVscf = Vpp + VHa + Vxc

Self-consistent potential

Theoretical framework

• Compute bias-dependent transmission coefficients t

• Current from transmission of states T(E,V)

• Formalism for an open, infinite system out of equilibrium capturing the atomic-scale details of the molecular junction • Two-terminal geometry with semi-infinite leads

R leadConductor

rt

L lead

i

€

I(V)=2e

hT(E,V)

μR

μL

∫dE

First-principles Scattering-State Approach to Molecular Electronic Devices

Choi, Cohen & Louie (2004)

€

I(V)=2e

hT(E,V)

μR

μL

∫dE

Closer look at a scattering state

Example state propagating from left to right with energy E

where, e.g.,

Transmission matrix

Incident L lead stateTransmitted R lead state &

evanescent waves

Reflected L lead state &evanescent waves

Conductor C state

R leadConductor

r t

L lead

i

Conductance of Pt-H2 junction

[1] R.H.M. Smit et al., Nature 419, 906 (2002)

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Conductance (2e2/h)

Num

ber

of C

ount

s

Pt• Conductance of single H2 molecule has been interpreted by break-junction measurements to be close to 1 G0 = 2e2/h

• Single channel

Pd-H2 junction: Reduced conductance

Pd

Increasing H2 conc. x

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

PdHx PdHx

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

Cou

nts

Conductance (2e2/h)Conductance (2e2/h) Conductance (2e2/h)

Similar experiments with Pd nanojunctions yields about 0.3-0.5 G0, a factor of two or three less than Pt.

Modeling the junction

H—H?

[111]

Tip—H?

Break junction

Transmission spectra

Resonances Plateau

Khoo, Neaton & Louie (2005)

G=1.01G0

G=0.35G0

EF Pt

PdResonances

Physical picture

EF

Pt

E

Pt case

Pd casePd

E

EF

• Junction states are band-like

• Scattering is minimal over a range of energies

• Junction states are resonant

• Scattering is large and energy dependent

JunctionMetal

Local electronic structure

Pt Pd

Tra

nsm

issi

on (

2e2/h

)

H2

Tip atom

Bulk atom

Pt

Loca

l den

sity

of

stat

es

H2

Tip atom

Bulk atom

Pd

Khoo, Neaton and Louie (2005)

Local electronic structure

H2

Tip atom

Bulk atom

H2

Tip atom

Bulk atom

Pt Pd

Pt Pd

Loca

l den

sity

of

stat

esT

rans

mis

sion

(2e

2/h

)

Band-like

Localized

Khoo, Neaton and Louie (2005)

Conductance of H2 nanojunctions

Pd / H2 Pt / H2

Experiment 0.3 - 0.6G0 1.0G0

Our work

(G0 = 2e2/h)

0.35G0 (Pd)

0.14G0 (PdH)

1.01G0

H2 nanojunction conductanceStrongly lead-dependent: Tip atoms play a key roleClosed-shell molecule is a good conductor!Transport properties of small molecules are strongly affected by lead

Our calculations characterize conduction in the junction and explain experiment

Khoo, Neaton & Louie (2005)

Negative Differential Resistance and Lead Geometry Effects

Son, Choi, Ihm, Cohen and Louie (2004)

Calculated I-V Curve of a Tour Molecular Junction

unoccupiedoccupied

Dominant transmitting state

L U

L U

Potential Drop across Molecular Junction

Potential at 0.6 A above molecularplane

Forces in the Photo-Excited State: Self-trapped Exciton

Forces in Excited State

• For many systems, photo-induced structural changes are important

– differences between absorption and luminescence– self-trapped excitons– molecular/defect conformation changes– photo-induced desorption

• Need excited-state forces– structural relaxation– luminescence study– molecular dynamics, etc.

• GW+BSE approach gives accurate forces in photo-excited state

Ismail-Beigi & Louie, Phys. Rev. Lett. 90, 076401 (2003)

Excited-state Forces

ES = E0 + ΩS

∂RES = ∂RE0 + ∂RΩS

E0 & ∂RE0 : DFT

ΩS : GW+BSE

Ismail-Beigi & Louie, Phys. Rev. Lett. 90, 076401 (2003).

Verification on molecules

Ismail-Beigi & Louie, Phys. Rev. Lett. 90, 076401 (2003).

Excited-state force methodology

• Proof of principle: tests on molecules

- CO and NH3

• GW-BSE force method works well

• Forces allow us to efficiently find excited-state energy minima

SiO2 (-quartz): optical properties

• Oxygen• Silicon

[1] Ismail-Beigi & Louie (2004)[2] Philipp, Sol. State. Comm. 4 (1966)

[1]

Emission at ~ 3 eV!

Self-trapped exciton (STE) in SiO2 (-quartz)

Triplet STE has ≈ ms and ~ 6 eV Stokes shift [1]

[1] e.g. Itoh, Tanimura, & Itoh, J. Phys. C 21 (1988).

1. Start with 18 atom bulk

cell

2. Randomly displace

atoms by ±0.02 Å

3. Relax triplet exciton state4. Repeat steps 2&3: same

final config.

Ismail-Beigi & Louie (2005)

Structural Distortion from Self-Trapped Exciton in SiO2

Final configuration: Broken Si-O bond Hole on oxygen Electron on silicon Si in planar sp2 configuration

Ismail-Beigi & Louie (2005)

• Oxygen• Silicon

Self-Trap Exciton Geometry

Bond (Å)

Bulk Defect

Si1-O1 1.60 1.97 (+23%)

Si2-O1 1.60 1.68 (+5%)

Si1-Oother 1.60 1.66 (+4%)

Angles Bulk Defect

O1-Si1-Oother 109o ≈ 85o

Oother-Si1-Oother 109o ≈ 120o

O1

Si1

Si2

Atomic rearrangement for STE

No activation barrier!

Electron-Hole Wavefunction of Self-Trapped Exciton in SiO2

Hole probability distributionwith electron any where in the crystal

Electron probability distribution given the hole is in the colored box

Electron & Hole Distributions of Self-Trapped Exciton in SiO2

Final configuration: Broken Si-O bond Hole on oxygen (brown) Electron on silicon (green) Si in planar sp2 configuration

Ismail-Beigi & Louie, PRL (2005)

• Oxygen

• Silicon QuickTime™ and aGIF decompressor

are needed to see this picture.

Constrained DFT Calculations

Constrained LSDA: DFT with excited occupations

Problems:

• Relaxes back to ideal bulk from random initial displacements: excited-state energy surface incorrectly has a barrier.

• Large initial distortion needed for STE [1,2]

• Predicted Stokes shift and STE luminescence energy are very poor to correlate with experiments

[1] Song et al., Nucl. Instr. Meth. Phys. Res. B 166-167, 451 (2000).[2] Van Ginhoven and Jonsson, J. Chem. Phys. 118, 6582 (2003).

STE in SiO2: Comparison to Experiment

Luminescence freq.: T (eV)

Stokes shift (eV)

Luminescence Pol || z (*)

Expt. [1-6]2.6, 2.74, 2.75, 2.8

6.2-6.40.48, 0.65,

0.70

GW+BSE 2.85 6.37 0.72

CLSDA (forced)

4.12 2.14 ----

1. Tanimura et al., Phys. Rev. Lett. 51, 423 (1983).

2. Tanimura et al., Phys. Rev. B 34, 2933 (1986).3. Itoh et al., J. Phys. C 21, 4693 (1988).4. Itoh et al., Phys. Rev. B 39, 11183 (1989).5. Joosen et al., Appl. Phys. Lett. 61, 2260

(1992).6. Kalceff & Phillips, Phys. Rev. B 52, 3122

(1996).

(*)

€

Pol =Iz − Ixy

Iz + Ixy

Summary

First-principles calculations may be used to gain insightsinto new and old problems

• Electron transport through single molecule can exhibitdramatic negative differential resistance. (Chargerearrangement mechanism discovered.)

• Self-trapped exciton in SiO2 => broken-bond geometryand huge Stokes shifts.