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A deterministic Wigner transport equation solver with infinite correlation length

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Abstract

We propose a new formulation of the Wigner transport equation (WTE) with infinite correlation length. Since the maximum correlation length is not limited to a finite value, there is no uncertainty in the simulation results owing to the finite integral range of the nonlocal potential term. For general and efficient simulation, the proposed WTE formulation is solved self-consistently with the Poisson equation through the finite volume method and the fully coupled Newton–Raphson scheme. Through this, we implemented a quantum transport steady state and transient simulator with excellent convergence.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

I would like to thank my advisor, the late Prof. Byung Gook Park. I sincerely appreciate his precious advice and consistent encouragement during my Ph.D. course.

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  1. Department of Electrical and Computer Engineering, Seoul National University, Seoul, 08826, South Korea

    Kyoung Yeon Kim

  2. Samsung Electronics, Hwaseong, South Korea

    Kyoung Yeon Kim

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Appendix

Appendix

The Wigner function in the on/off state is shown in more detail in Figs. 19 and 20. The figures show that the first subband has the largest Wigner function, and the rest has no significant effect on the solution. Also, the 3rd valley (t, t, l) shows the largest Wigner function and has the greatest influence on device characteristics. Interestingly, in on-state, the distribution of the Wigner function is quite different in all subbands.

Fig. 19
figure 19

Wigner function at a first and b second subband of the 1st valley (l, t, t). Wigner function at c first and d second subband of the 2nd valley (t, l, t). Wigner function at a first and b second subband of the 3rd valley (t, t, l). The gate length is 10 nm, body thickness is 3 nm, and EOT is 0.5 nm. Drain voltage is 0.4 V and gate voltage is 0 V (off-state)

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Fig. 20
figure 20

Wigner function at a first and b second subband of the 1st valley (l, t, t). Wigner function at c first and d second subband of the 2nd valley (t, l, t). Wigner function at a first and b second subband of the 3rd valley (t, t, l). The gate length is 10 nm, body thickness is 3 nm, and EOT is 0.5 nm. Drain voltage is 0.4 V and gate voltage is 0.5 V (on-state)

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Kim, K.Y. A deterministic Wigner transport equation solver with infinite correlation length. J Comput Electron 22, 1377–1395 (2023). https://doi.org/10.1007/s10825-023-02079-9

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