We extend the two-dimension (2D) ePlace algorithm to a flat, analytic, mixed-size placement algorithm ePlace-3D , for three-dimension integrated circuits (3D-ICs) . Nonlinear optimizationis applied over the entire cuboid domain. Specifically, we develop (1) eDensity-3D: an electrostatics based 3D placement density function with globally uniform smoothness (2) a 3D numerical solution with improved spectral formulation (3) a 3D nonlinear pre conditioner for convergence acceleration (4) interleaved 2D-3D placement for quality and efficiency enhancement. We integrate all the features into our 3D-IC placement prototype ePlace-3D. Compared to the leading placers mPL6-3D and NTUplace3-3D , our algorithm produces 6.44\% and 37.15\% shorter wirelength, 9.11\% and 10.27\% fewer  vertical interconnects (VI) while runs 2.55x faster and 0.30x slower on average of all the ten IBM-PLACE circuits , respectively. We also validate ePlace-3D on the large-scale modern mixed-size (MMS) 3D circuits , which shows high performance and scalability.
We propose a flat, analytic, mixed-size placement algorithm ePlace-3D for three-dimension integrated circuits (3D-ICs) using nonlinear optimization. Our contributions are (1) electrostatics based 3D density function with globally uniform smoothness (2) 3D numerical solution with improved spectral formulation (3) 3D nonlinear pre-conditioner for convergence acceleration (4) interleaved 2D-3D placement for efficiency enhancement. Our placer outperforms the leading work mPL6-3D and NTUplace3-3D with 6.44\% and 37.15\% shorter wirelength, 9.11\% and 10.27\% fewer 3D vertical interconnects (VI) on average of IBM-PLACE circuits . Validation on the large-scale modern mixed-size (MMS) 3D circuits shows high performance and scalability.
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