deriving insights from computation: molecular electronics to self-trapped excitons
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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. Son J. Neaton J. Ihm (Korea) - PowerPoint PPT PresentationTRANSCRIPT
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.