A Differentiable Tight-Binding Model for Inverse Design

Differentiable tight-binding models are implemented to reveal the potential of inverse design on nano devices. The condition of the reciprocity for green's functions and its role in efficient calculations of gradients are explained through a simple case, a 1D inhomogeneous tight-string system. Further insights on reciprocity and the formalism for later discussion are provided through a 1D tight-binding model example. Algorithm details for both 1D and 2D cases are presented and bring us experimental results such as probability amplitude tunneling, resonance, and the growth of transmission rate. Finally, future works and notes worth mentioned are discussed.

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Journal

Title: ScienceOpen Preprints

Publisher: ScienceOpen

Publication date (Electronic preprint): 28 November 2022

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[1 ] ITRI

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[* ]Email: nylue2014@ 123456gmail.com .

Author information

LYU YUAN https://orcid.org/0000-0002-1862-7843

Article

DOI: 10.14293/S2199-1006.1.SOR-.PPQ8DHA.v1

SO-VID: 7782bcd0-19db-44b1-bdc4-2545e49ea1df

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This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .

History

Date received : 28 November 2022

References

Lalau-Keraly Christopher M., Bhargava Samarth, Miller Owen D., Yablonovitch Eli. Adjoint shape optimization applied to electromagnetic design. Optics Express. Vol. 21(18)2013. The Optical Society. [Cross Ref]
Thuerey Nils, Holl Philipp, Mueller Maximilian, Schnell Patrick, Trost Felix, Um Kiwon. Physics-based Deep Learning. 2021. arXiv. [Cross Ref]
Rothwell Edward J., Cloud Michael J.. Electromagnetics. 2018. CRC Press. [Cross Ref]
Miller Owen D.. Photonic Design: From Fundamental Solar Cell Physics to Computational Inverse Design. 2013. arXiv. [Cross Ref]
Levi A. F. J., Rosen I. G.. A Novel Formulation of the Adjoint Method in the Optimal Design of Quantum Electronic Devices. SIAM Journal on Control and Optimization. Vol. 48(5):3191–3223. 2010. Society for Industrial & Applied Mathematics (SIAM). [Cross Ref]

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[1] Lalau-Keraly Christopher M., Bhargava Samarth, Miller Owen D., Yablonovitch Eli. Adjoint shape optimization applied to electromagnetic design. Optics Express. Vol. 21(18)2013. The Optical Society. [Cross Ref]

[2] Thuerey Nils, Holl Philipp, Mueller Maximilian, Schnell Patrick, Trost Felix, Um Kiwon. Physics-based Deep Learning. 2021. arXiv. [Cross Ref]

[3] Rothwell Edward J., Cloud Michael J.. Electromagnetics. 2018. CRC Press. [Cross Ref]

[4] Miller Owen D.. Photonic Design: From Fundamental Solar Cell Physics to Computational Inverse Design. 2013. arXiv. [Cross Ref]

[5] Levi A. F. J., Rosen I. G.. A Novel Formulation of the Adjoint Method in the Optimal Design of Quantum Electronic Devices. SIAM Journal on Control and Optimization. Vol. 48(5):3191–3223. 2010. Society for Industrial & Applied Mathematics (SIAM). [Cross Ref]