L2.3: Bulk MOS

Online simulations via nanoHUB: Nanoscale thermal transport via MD

In this tutorial: • Non-equilibrium MD simulations of thermal transport • Explore size effects

Keng-hua Lin and Ale Strachan [email protected] School of Materials Engineering & Birck Nanotechnology Center Purdue University West Lafayette, Indiana USA

• Launch tool by clicking on:

• Select prebuilt structures

• Or create your own structure by checking the box

We will create our own

© Alejandro Strachan – Online simulations: getting started 3 How the simulation cells are defined • Along the transport direction the simulation contains: • 2 Heat baths (blue) • The middle bin defines the hot and cold regions • Interior material (red) • This can be defined to be a superlattice • Periodic boundary conditions are applied along the transport direction Material (5 bins) Heat bath (3 bins)

Cold bin Hot bin

F. Müller-Plathe, J. Chem. Phys. 106, 6082 (1997) Keng-Hua Lin and A. Strachan, Physical Review B, 87, 115302 (2013).

• We would like to create a Si supercell by replicating the cubic Si unit cell • The tool allows users to build superlattices (laminates) so it is a bit convoluted

Along the transport the system will be divided in bins Each bin is one unit cell long

Cross-sectional area of the simulation cell (5x5 unit cells) Lattice parameter (5.43) Along the transport direction the “supercell” will have 5 Si bins (1 bin = 1 unit cell) and zero Ge (just Si) The number of Si bins will be varied to explore size effects The total simulation length in this case is: (3+5) x 2 x 5.43A = 86.88A The effective size for transport is the separation between heat baths (1/2 of the simulation cell length)

Heat baths are 3 bins long The “supercell” will be repeated only once

If you select to build your own structure In the Selections for Material Shape tab Choose to simulate the material as a bulk (superlattice thin film) or a superlattice square nanowire

3-D periodic boundary condition for the simulation cell

Periodic boundary condition along the z direction and free boundary condition along the x and y directions

We will use 3D periodic boundary conditions

Thermalize the system

For 1000 MD steps (2 ps)

This will equilibrate the system to the desired temperature before starting the thermal transport calculation

Timestep 2 fs

MD steps 120,000

Swap atomic velocities every 100 MD steps

Atomistic snapshots for visualization

Output temperature profile every this many steps for analysis

Ignore the first 20,000 steps when computing averages

Temperature profiles at different times

Average temperature profile

Remember simulation cell was ~86A

Analyze output: calculated thermal conductivity

Material thermal conductivity computer from temperature gradient inside the material (away from contacts) Use this value