outline

8/19/2015 LBNL 1

Electronic structure of stable edges – the general electron

counting model

Hole transfer at MoS2/WS2 heterojunction – dephasing of

plasma in a two-state quantum capacitor.

background – TMD edges

8/19/2015 LBNL 2

Zigzag edges are most often seen in experiments

Strong PL near edges suggests that they are passivated.

Gutierrez, et al. Nano Lett. 13, 3447 (2013)

Theory predicts metallic ribbons with zigzag edges

Li, et al. JACS 130, 16739 (2008)

review: semiconducting semiconductor surface

8/19/2015 LBNL 3

0

23/4 5/4

Dangling bonds (DBs)

Fermi level

Valence band

Conduction

band

Ga DBs

As DBs

GaAs (110) surface

Zhang and Cohen, Surface Sci. 172, 754 (1986)

the electron counting model (ECM)

Pashley, PRB 40, 10481 (1989)

• As has 5 valence electrons (els) and 4 bonds; it

contributes to each bond 5/4 els

• Ga has 3 valence els and 4 bonds; it contributes to each

bond 3/4 els

• Each bond gets 5/4 + 3/4 = 2 els

• Each As DB is an acceptor (assign a number -3/4); each

Ga DB is a donor (assign a number +3/4)

• The total number should always add up to ZERO

• ECM ensures correct occupation critical to atomic

relaxation and gap opening.

8/19/2015 LBNL 4

reconstruction: ECM for GaAs(001)

PRB 40, 10481 (1989)

4

As Ga

• A number of reconstructions were

observed for GaAs(001)

• Most noticeably is 2x4 with As-As dimer

• Each As has 2 DBs. By sharing 2 els in a

dimer, each As only needs 2x(-3/4) + 1 =

-1/2 els; each dimer with 2 As is thus a

2x(-1/2) = -1 el acceptor

• Removing a pair of As exposes 4 Ga.

Each exposed Ga is a +¾ el donor

• Counting: 3 x (-1) + 4 x ¾ = 0. √

8/19/2015 LBNL 5

Top View of b(2x4)

8/19/2015 LBNL 6

ECM is HARD to understand

• It is so hard because it involves, and only involves,

arithmetic – boring, loss of attention, etc., etc.

• It is hard because it uses the concept like “removing

an electron is equivalent to adding a hole”

• It is at least not intuitive enough, because it uses the

concept of sharing electrons in a dimer bond, which

makes a poor guy look rich

• Worst of all, in many cases, it DOES NOT WORK!

8/19/2015 LBNL 7

• ECM requires tetrahedral coordination (zincblende structure).

4+

2-

Standard ECM assumes two electrons per bond

• Mo has 4 valence els and 6 bonds; each bond

has 4/6 = 2/3 els from Mo

• S also has 6 valence els but only three bonds;

each bond has 2 els from S

a general electron counting model (gECM)

• Total number of electrons per bond = 2 2/3. NO WAY!

gECM eliminates the 2-els-per-bond rule & structure dependence

• Mo donates 4 els to neighboring S, i.e., 4/6 = 2/3

• S accepts 2 els from neighboring Mo, i.e., -2/3

• For each formula unit MoS2: 6 x 2/3 + 2 x 3 x (-2/3) = 0. √

8/19/2015 LBNL 8

Mo

S

8/19/2015 LBNL 9

application to TMD zigzag edges

El counting @ ideal edges

• Mo edge: 2 DBs per Mo;

each donates 2/3 els;

2x2/3 = 4/3→ needs 3x

period to get an integer = 4

Mo Edge: electron donor

Mo

S Edge: electron acceptor

S

• S edge: 1 DB per S; each

accepts 2/3 els; 2 S per 1x;

2x(-2/3) = -4/3 → again 3x

period to get an integer (-4)

• To satisfy the gECM, the period along zigzag edges should thus

be 3x or its multiples, 6x, 9x, etc.Chem. Mater., 2015, 27, 3326

the first try of 3x period (PBE results)

8/19/2015 LBNL 10

• Adding two S atoms offers 2×(-2) = -4 els

0.17 eV

• If the counting were correct, one should be able to get a band gap when

the period is 3x. √

0.28 eV

S edge (-4)

• S2 is a 2-el acceptor, oppose to 2S being a 4-el acceptor; thus, forming 2 dimers = adding 4 els

Mo edge (+4)

8/19/2015 LBNL 11

wait again, the gap of ~0.2 eV may be too small!

It's the multi-valency that matters

8/19/2015 LBNL 12

• Depending on the local environment, Mo can be valence +4, +5, or

even +6. If 2 Mo change from +4 to +5 (or 1 Mo changes from +4 to

+6), then

S edge (-4 → -2):

an S vacancy (VS)

can donate 2 els.

1VS

0.44 eV

Chem. Mater., 2015, 27, 3326

3S

0.71 eVMo edge (+4 →

+6): 3 S adatoms

can accept 6 els.

8/19/2015 LBNL 13

thermodynamic stability

S-richS-poor S-richS-poor

• Atomic chemical

potential correlates with

growth condition, high mS

= S-rich: 1x & 2x = 6S

• Mo edge is metallic at S-

rich; semiconducting

otherwise (agree with

experiment)

• 3S may appear as 1x

• S edge is semiconducting,

but 2S2 is ferremagnetic.

8/19/2015 LBNL 14

no O

• O is isovalent to S,

so it does not

change gECM, nor

Mo multi-valency

• Larger gap due to

oxygen agrees

with experiment

• Stronger chemical

bond may be the

reason

• HSE: 1.6 & 1.8 eV.

the effect of oxygen

Mo EdgesS Edges

with O no O with O

outline

8/19/2015 LBNL 15

Electronic structure of stable edges – the general electron

counting model

Hole transfer at MoS2/WS2 heterojunction – dephasing of

plasma in a two-state quantum capacitor.

real space picture

8/19/2015 LBNL16

hole transfer upon optical excitation (~100 fs)

Hong et al., Nat Nano 9, 682 (2014)

Smallest Direct Gap (at K)

reciprocal space picture

8/19/2015 LBNL 17

ab initio MD versus TDDFT MD

TDDFT-MD: real-time ab-initio MD coupled with TDDFT

• (Ehrenfest dynamics) Electron is time-evolved quantum

mechanically, but ion is classically

See also J. Chem. Phys. 129, 054110 (2008)

ab initio MD

• Born-Oppenheimer approximation → time-independent

electronic ground state at each atomic configuration

8/19/2015 LBNL 18

TDDFT-MD simulations

• Initial occupation: optically

excited states

• Real-time electron and ion

dynamics with 24-attosecond

time steps

• Project time-evolved hole

wavefunction onto ground-

state eigenfunctions |𝑾𝑺𝟐 and

|𝑴𝒐𝑺𝟐

• Confirm hole transfer

• Increased transfer at higher T

due to electron-phonon

coupling.

77 K

300 K

Time (fs)

Ho

le P

roje

ctio

ns

|𝑊𝑆2

|𝑀𝑜𝑆2

|𝑊𝑆2

|𝑀𝑜𝑆2

dots = average over a period

8/19/2015 LBNL 19

LA branch (off Γ)

A1gA1g• Hole transfer is a

result of energy

dissipation

• Important phones

are A1g and LA-

branches with large

energy dissipation

• These phones have

substantial Raman

peaks,* exhibiting

strong electron-

phonon coupling.

*ACS Nano 4, 2695 (2010); Sci. Rep. 3, 1755 (2013)

normal modes responsible for the transfer

Mo

de

ener

gy

in

crea

se (

eV)

8/19/2015 LBNL 20

• Still see hole

oscillation, so

oscillation is not

because phonons

• Oscillation is not

sinusoidal, suggesting

the system is not a

superposition of

𝑀𝑜𝑆2 and 𝑊𝑆2

Fixed ions

|𝑊𝑆2

|𝑀𝑜𝑆2

what happens if one fixes the ions?

• Requires a new theory that can explain these observations.

• No electron-phonon interaction → no energy dissipation

8/19/2015 LBNL 21

𝐻𝑓𝑖𝑒𝑙𝑑 = 𝐸0 +𝜎 𝑡

𝜖z

ModelTDDFT

plasma in a two-state quantum capacitor

)𝑑 = ( 𝑊𝑆2 𝑧 𝑊𝑆2 − 𝑀𝑜𝑆2 𝑧 𝑀𝑜𝑆2 (effective distance)𝑀𝑧 = 𝑊𝑆2 𝑧 𝑀𝑜𝑆2 (dipole transition matrix element)

𝐻 =𝐸𝑀𝑜𝑆2

− (𝐸0 + 𝜎[𝑡 ] 𝜖 ) 𝑑 2 𝐸0 + 𝜎 𝑡 𝜖 𝑀𝑧

(𝐸0 + 𝜎 𝑡 𝜖)𝑀𝑧 𝐸𝑊𝑆2+ 𝐸0 + 𝜎 𝑡 𝜖 𝑑 2

Dipole fields due to hoe transfer

hidden criticality of hole transfer

8/19/2015 LBNL 22

hidden criticality of hole transfer

8/19/2015 LBNL 23

summary

8/19/2015 LBNL 24

Electronic structure of stable edges – the general electron

counting model Lucking, et al., Chem. Mater., 2015, 27, 3326

Dopant ionization energy – the zero jellium limit Wang, et

al., PRL 114, 196801 (2015)

Hole transfer at MoS2/WS2 heterojunction – dephasing of

plasma in a two-state quantum capacitor.