Channel Characteristic-Based Deep Neural Network Models for Accurate Eye Diagram Estimation in High Bandwidth Memory (HBM) Silicon Interposer

In this article, for the first time, we propose channel characteristic-based deep neural network (DNN) models for accurate eye-height (EH) and eye-width (EW) estimation of high bandwidth memory (HBM) silicon interposer channels. The proposed models preprocess the design parameters that are highly relevant to the characteristics of the HBM channels. By taking account of the contribution of each design parameter to the eye diagram, the proposed models can accurately estimate the EH and EW of the channels even with a limited number of datasets. For verification, the proposed DNN models were applied to the microstrip and stripline channels of an HBM silicon interposer. Only redistributed layer (RDL) was used to clearly see the effect of reflecting the channel characteristics of the proposed method. We compared the proposed DNN models with various regression methods and a conventional fully connected multilayer DNN model. As a result, the proposed DNN models reduced the EH and EW error rates by 22.7 and 43.9% compared to the other regression methods. In addition, the proposed DNN models not only reduced the error rates by 22.0-28.4% but also reduced the computing cost by 8.0-9.4%, compared to the conventional DNN model. Moreover, we compared the proposed models with various DNN models having other preprocessing structures. By showing 26.7 and 28.8% lower EH and EW error rates than the other DNN models, we validated that the proposed models properly consider the most dominant design factors in preprocessing.