Generative Process Variation Modeling and Analysis for Advanced Technology Based on Variational Autoencoder

The development of advanced technology nodes highlights the significant impact of process variations on device electrical characteristics. To analyze and understand these variations, extensive and intensive technology computer-aided design (TCAD) simulations or costly on-wafer testing are often indispensable. This article proposes a novel generative process variation modeling method to alleviate this burden, which can learn from a few discrete sampling points and reproduce or generate analytical electrical responses for variation analysis and circuit simulation without requiring predefined domain knowledge or empirical equations. A silicon nanowire (NW) transistor is employed to showcase the strength of the proposed method, considering two complex process variabilities: metal grain granularity (MGG) and random discrete dopants (RDDs). The trained models on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Id$</tex-math></inline-formula>–<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Vg$</tex-math></inline-formula> curves achieve median percentage errors of 0.7% (best case) and 2.8% (worst case). Furthermore, the proposed framework is transfer-learnable, allowing data from a new variability source to be added to a trained model, resulting in even greater accuracy and further reducing the cost of data collection.