Atomistic Simulation &Energy Research Group

Vibrationally Accurate Interatomic PotentialsAndrew Rohskopf

Advisor: Asegun Henry

Massachusetts Institute of Technology

Department of Mechanical Engineering

Tuesday, August 20, 2019

Atomistic Simulation &Energy Research Group

Modes (Phonons) & MD Simulations

2

0

0Q Q t dt

mod ,1 mod ,2 mod ,3e e e

QHeat flux

Thermal conductivity

Mode 1 Mode 2 Mode 3

Atomistic Simulation &Energy Research Group

3

Vibrational Modes & Heat Transfer

Aids heat transfer Inhibits heat transfer

https://lifestyleremodeling.com

Gifs courtesy of Freddy DeAngelis

Atomistic Simulation &Energy Research Group

4

Modes at Interfaces

Interface

Extended Modes

Partially Extended Modes

Isolated Modes

Interfacial Modes

Gifs courtesy of Kiarash Gordiz

Z. J. Liu, T. et al, Monolithic Integration of Algan/Gan Hemt on Led by Mocvd, IEEE Electron Device Letters, 35, 330-332 (2014).

Atomistic Simulation &Energy Research Group

5

Modes & Energy Conversion

B. Yu et al, Enhancement of Thermoelectric Properties by Modulation-Doping in Silicon Germanium Alloy Nanocomposites, Nano letters, 12, 2077-2082 (2012).

Thermoelectric generator

Gifs courtesy of Hamid Seyf

Atomistic Simulation &Energy Research Group

6

Modes Make Things Happen

MD @ T=300KMD @ T=300K + energy input to

a few selected modesLi

P

O

Ge

Movies courtesy of Kiarash Gordiz

Atomistic Simulation &Energy Research Group

7

Phonon Theory

i i ij jj

mu K u equilibrium

i i iu x x

Fre

qu

en

cy

Wave-vector k

Phonon DispersionMass X Acceleration = Harmonic Force

Atomistic Simulation &Energy Research Group Taylor Expansion Potential

8W.Weber, Phys. Rev .B 15, 4789 (1977).

Silicon Phonon Dispersion

1 1

2 3!ij i j ijk i j kij ijk

E K u u K u u u

2

iji j

EK

u u

3

ijki j k

EK

u u u

equilibriumi i iu x x

Wave vector

Atomistic Simulation &Energy Research Group Current Potentials

9

Silicon Phonon Dispersion

Wave vector

Tersoff, J. J. P. R. B. 38, 9902 (1988). Tersoff, J. J. P. R. B. 39, 5566 (1989). Tersoff, J. J. P. r. l. 64, 1757 (1990). Munetoh, S., et al. 39, 334-339 (2007). Stillinger, F. H. & Weber, T. A. J. P. r. B. 31, 5262 Lee, Y. & Hwang, G. S. J. P. R. B. 85, 125204 (2012). Justo, J et al. F. S. J. P. r. B. 58, 2539 (1998). Jiang, C et al. I. J. P. R. B. 86, 144118 (2012). Van Duin, A. C. et al. 107, 3803-3811 (2003). Bartók, A. P. et al. J. P. r. l. 104, 136403 (2010).W.Weber, Phys. Rev .B 15, 4789 (1977).

Silicon Thermal Conductivity

Atomistic Simulation &Energy Research Group

The “Phonon Potential”

1

2 ij i j anharmonicij

K EuE u

10

Morse

3-body

2

1 2 31 expE r

2 3

1 0 2 0E SNAP

0 k kk

E B

https://github.com/rohskopf

har nh mm a ar FF F

anharmF

harmF

Atomistic Simulation &Energy Research Group Silicon

11

2 2

1 2 3 4 0

11 exp

2 ij i jij

E K u u r

Harmonic part fitwith least squares

Anharmonic part fit with genetic algorithm

https://github.com/rohskopf

Atomistic Simulation &Energy Research Group

12

50 % force error

Blue: DFT force

Red: Potential force

DFT potential

DFT

Error F -F

F

Atomistic Simulation &Energy Research Group

13

3 % force error

Blue: DFT force

Red: Potential force

DFT potential

DFT

Error F -F

F

Atomistic Simulation &Energy Research Group Silicon

14

1 % error

2 2

1 2 3 4 0

11 exp

2 ij i jij

E K u u r Dispersion Thermal Conductivity

Atomistic Simulation &Energy Research Group Germanium

15

2 2

1 2 3 4 0

11 exp

2 ij i jij

E K u u r

3 % error

Thermal ConductivityDispersion

Atomistic Simulation &Energy Research Group Gallium Arsenide

16

2 2

1 2 3 4 0

11 exp

2 ij i jij

E K u u r

6 % error

Dispersion Thermal Conductivity

Atomistic Simulation &Energy Research Group Gallium Nitride

17

(SNAP)0

1

2 ij i j k kij k

E K u u B

10 % error

Dispersion Thermal Conductivity

Atomistic Simulation &Energy Research Group

Conclusion

18

A Rohskopf, H Seyf, K Gordiz, T Tadano, A Henry. "Empirical interatomic potentials optimized for phonon properties." NPJ Computational Materials 3 (2017)

M Muraleedharan, A Rohskopf, V Yang, A Henry. “Phonon optimized interatomic potential for aluminum.” AIP Advances 7 (2018)

A Rohskopf, S Wyant, A Henry. “Fast and accurate empirical interatomic potentials for describing thermal vibrations”. In progress

OPEN-SOURCEhttps://github.com/rohskopf

1

2 ij i j anharmonicij

E K u u E