1. Predictive Modeling and Simulation of Charge Mobility in 2D Material Based Devices
Altaf Karim
Department of Physics, COMSATS Institute of Information Technology, Islamabad

2. Outline
2D Materials
Conductivity and Mobility in Nano & Micro Devices
Drude picture
Classical mechanics and statistical mechanics approaches to model charge transport.
Molecular dynamics
Kinetic Monte Carlo

4. Drude Picture
Graphene possess a large charge carrier density (n > 1012/cm2), enabling fast electrical charge transport with charge mobility value upto150,000 cm2/Vs

5. top gated graphene field effect transistor: A schematic configuration of experimental setup is shown in figure. The transparent blue drop represents the polymer electrolyte (PEO + LiPF6). The hexagonally patterned channel represents the graphene sample underneath the electrodes. Ref: Khushbakhat, Sadia Manzoor et.al.

6. AFM images obtained for different molar concentrations of phosphine stabilized Au nanoparticles (Ph-AuNPs) spin coated on graphene.

8. Molecular Dynamics (MD)
Classical Mechanics
MD carries out a numerical integration of the classical equations of motion.

9. We use Coulomb or Lennard Jones as interaction potentials
General Scheme of MD
We initialize the system (i.e., we select initial positions, velocities, interaction potentials and boundary conditions).
Boundary Conditions
We use Coulomb or Lennard Jones as interaction potentials
Crystal Preparation
(100)
(110)
(111)
Velocities are selected randomly from Maxwell-Boltzmann distribution at the temperature of interest
We compute the forces on all particles and integrate equations of motion.
After completion of the central loop, we compute the averages of measured quantities.

10. The Nordsieck-Gear Predictor-Corrector Method
Predict the positions, velocities, accelerations etc. at time t + δt, using the current values of these quantities.
Evaluate the forces, and hence acceleration aic = fi/mi , from the new positions and calculate the size of error in predicted acceleration.
Correct the predicted positions, velocities, accelerations etc., using the error in acceleration.
Calculate any variable of interest, such as the energy, virial, order parameters.

11. Kinetic Monte Carlo Γ 𝑖𝑗 = Γ 0 exp ( Δ 𝜖 𝑖𝑗 + Δ𝜖 𝑖𝑗 2 𝑘 𝐵 𝑇 ) (1)
energy difference Δϵij=ϵj−ϵi between the initial site i and final site j
Γ 𝑖𝑗 = Γ 0 exp ( Δ 𝜖 𝑖𝑗 + Δ𝜖 𝑖𝑗 2 𝑘 𝐵 𝑇 ) (1)
𝜖 𝑖 =𝑒 𝑉 𝑥,𝑖 + 𝑒 2 4𝜋𝜀 Φ 𝑖 (2)
Φ 𝑖 𝑥 = 𝑗≠𝑖 𝑠 𝑖 . 𝑠 𝑗 𝑥 𝑖 − 𝑥 𝑗 (3)
p 𝑖𝑗 = Γ 𝑖𝑗 Γ 𝑖𝑗 (4)
where Γ 𝑖𝑗 is the total rate of all possible transitions.

14. Conductivity (simulation vs experiment)
Simulation Results
Experimental Results
Khushbakhat et.al
Conductivity vs. carrier concentration for pristine and three different coverages of AuNP’s on graphene samples.

15. Mobility (simulation vs experiment)
Pristine 3%
15%
Simulation Results
Experimental Results
Khushbakhat et.al
Carrier mobility as a function of carrier concentration calculated by Drude model based KMC simulations for three different top gated coverages of AuNPs on graphene samples.

16. Summary
Drude Model based predictive modeling and simulations worked well and found to be in good agreement with our experimental finding.
Simulations have shown that gold nanoparticles deposited on graphene at room temperature behave as cluster like charge impurities.
Charge mobility can be modify by manipulating size and distribution of impurity centers on graphene.

17. Thank You