1

Objectives

• Efficient device modeling development for 2D Materials with atomic resolution.

• Matching Exp: Analyzing the contribution of inter-layer intra-layer e-h coupling.

2

2D materials TMDs, promising devices

Wikipedia

ü LED, Solar Cell, LASER(direct bandgap in 1layer)

ü Valleytronics(lack of inversion symmetry )

Light Generation and Harvesting in a van der Waals Heterostructure

Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides

ü FET (Finite bandgap)

Tunnel Field-Effect Transistors in 2D Transition Metal Dichalcogenide Materials2

3

Inter or intra layer coupling?

• interlayer coupling observed• Room temp• Dual gate(D=1.2V/nm)

vdW interaction between layer.Do electron hole recombine between or within layers.?

T. Chu, et al., Nano Lett., vol. 15, no. 12, pp. 8000–8007, 2015.

• Intralayer coupling observed• 10K• Single gate(D=0.5V/nm)

J. Klein, et al., Nano Lett., vol. 16, no. 3, pp. 1554–1559, 2016.

Two studies have shown contradicting resutls:

4

MLWF in NEMO5

Step 1: Calculate spread and minimize functional Ω = ∑ 𝑟% − 𝒓𝒏%)

Wannier90:To find unitary matrices that minimize the spread of the wave function.

Step 2: Calculate gradient and update Unitary matrices.

Step 3: Form new Wannier functions and calculate step 2.

DFT( e.g. VASP) relaxation + self-consistent calculation.

NEMO5Device calcuation(Electrical Gates, doping, open boundary)

Hij(r)

Bloch wave function |Ψ,-⟩  

Step 1: ReadinHamiltonian.cpp construct system Hamiltonian.

Step 2: Non-linear Poisson with subatomic resolution. (B.C. included) 5

n-layer Hamiltonian

Hamiltonian constructed for confined structure Hamiltonian extracted from

bulk TMDs

xy

z

(j loops all neighboring cells)

1-layer

2-layer

n-layern-layer

z

x y

Gate

Applying B.C. for gated structure study.

6

Subatomic  resolution  for  charge

Mo: 5 d orbitalsS: 4 sp3 orbitals

r

Delta Charge

Convergence issues !

Gaussian Charge:• Gaussian function used for finer

mesh. • Determination of Sigma:

matching of charge accumulation percentage.

Subatomic resolution of potential

r0

r0 Gaussiand-1d-2d-3d-4d-5

Gaussiansp3-1sp3-2sp3-3sp3-4

(a) (b)

Radius (Å)

Cum

ulat

ive

Char

ge (%

)

Radius (Å)

Cum

ulat

ive

Char

ge (%

)

7

Layer transferability

M/Γ

Hamiltonian is found transferable for different layer thickness (matching DFT result )

1-layer 5-layer1st Brillouin zone of monolayer MoS2

Ec -E

c,min (eV

)

ΓQ

K M

Important valleys identified for 2H TMDs.

8

Thickness dependent characteristics

0.40.20.0

-0.2-0.4-0.6

EK

–EΓ

(eV

)

0.30.20.10.0

-0.1EK

–EQ

(eV

)

Number of Layers

Thin à thick layers• Conduction band min : K à Q valley• Valence band max: K à Γ valley• K valley: m* increase• Q, Γ valley: m* decrease

54321

m*

(m0)

0.8

0.7

0.6

0.5

0.4

1.2

1.0

0.8

0.6

m*

(m0)

0.65

0.55

0.45

m*

(m0)

m*

(m0)

CB, K valley

VB, Γ valley

VB, K valley

CB,Q valley

Number of Layers9

Gated Band Structure

Eg,indirect Eg,direct

z

x y

Gate

6 layer MoS2 gated structure.• K: Degenerate states broken. • Γ,Q: resilient to gate bias.

Wavefunction localization responds to electric gate differently.

0.0

0meV0meV83meV

CB,Q valley

0.0

CB, K valley

58meV58meV125meV126meV

Localized wavefunction at K valley

Delocalized wavefunction at Γ valley:

Vg=0VVg=50VVg=100V

z (nm)

-qV

(eV

)

(c)

10

PL spectrum comparisonEc

Ev oxide

100V

50V

0V

PL In

tens

ity(a

.u.)

Eg,indirect Eg,direct

Match with Exp result (Northwestern Univ.):1. red shift of the direct gap

excitons freq.2. Unchanged indirect gap.

Photoluminescence (PL) :1. Create exciton(electron hole pairs)2. Measure the recombination, emitted

photon Laser 532nm recombined

Data from TeodorKosev Stanev

11

Inter or intra layer?

Eg,indirect Eg,direct

Ec

Ev oxide

Intralayer

Interlayer

Fermi golden rules prohibits transition between localized state of different layers.

Intralayer and interlayer band gap are both extracted. (spatially resolved wavefunction)

Intra-layer dominates transition

12

Status and PlansIn this work:• MLWF used with subatomic resolved charge calculation• Layer dependent material characteristics extracted from bulk

Hamiltonian• Stark effect comparison with the experiment with PL

Acknowledgement:The work is supported by NSF EFRI-1433510. We also acknowledge the Rosen Center for Advanced Computing at Purdue University for the use of their computing resources and technical support. This research is part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (award number ACI 1238993) and the state of Illinois.

Predicting  TMD  gated  structure  stark  effect  photoluminescence  

Kuang-Chung Wang, Daniel Valencia, James Charles, Teodor Kosev Stanev, Gerhard  Klimeck,  Tillmann Kubis