Driven by the demand for increasing the operating frequency and data rates, a large number of researches on a three dimensional integrated circuit (3D-IC) are conducted, which is a promising technology that leads to a shortened interconnect length, a high clock frequency, and a low power consumption. Power and ground noise (P/G noise), however, becomes a more serious in 3D-ICs and packages because the high clock frequency and data rates result in the wideband spectra of P/G noise. Electromagnetic bandgap (EBG) structures can be a solution for suppression of wideband P/G noise in 3D-ICs and packages due to their wideband suppression characteristics, ease of fabrication, simplicity in design, low cost, and compatibility with power distribution networks. Estimating the performance of EBG structures embedded in the 3D-ICs and packages is a key of the 3D-IC free from the P/G noise, which results in the performance improvement.
In this dissertation, we propose a hybrid analytical modeling method based on a segmentation method to predict the P/G noise coupling coefficient of EBG structures in 3D-ICs and packages. The proposed modeling method remarkably reduces the computation time of calculating the P/G noise coupling coefficient of the EBG structures with high accuracy compared to the finite-difference time-domain (FDTD) method and finite element method (FEM). The proposed modeling method consists of three steps of segmentation, segment modeling, and recombination of the segments. In the first step, the EBG structure is divided into multiple segments such as the unit cell of the EBG structure, rectangular power/ground planes, and power/ground planes having an aperture. In the next step, the segments are modeled analytically using a modal decomposition and a resonant cavity model. In the final step of the proposed modeling method, the impedance matrices of the segmented EBG structure are recombined. In the recombination step, generalized impedance matrices (GIM) for multi-port multi-array segments and multi-cascading segments are derived. To further improve the computational efficiency, a simplified impedance matrix (SIM) for combination of repetitive identical multi-port segments is derived.
To validate the proposed modeling method and its superiority of computational efficiency, five original EBG structures are introduced, which are 1) a wideband EBG structure using defected ground structure (DGS), 2) a miniaturized EBG structure using a vertical inductive branch, 3) vertical stepped impedance EBG (VSI-EBG) structure, 4) On-interposer EBG structure using through silicon via (TSV), and 5) vertical-stepped impedance EBG (VSI-EBG) filter for common-mode suppression. We experimentally verified the proposed modeling method for the original EBG structures by good agreements between the calculated result and the measurements. The computation time of the proposed modeling method for the calculation of the noise coupling coefficient is greatly reduced by 98.7%, compared to the full wave simulation. For the accuracy improvement, the proposed modeling method significantly reduced the errors of predicting the fL and fU by 92.1%, compared to the dispersion equation based method.
최근 들어 삼차원 반도체는 시스템의 성능을 향상시키기 위한 유망한 기술로 많은 관심을 받고 있다. 하지만 지속적으로 증가하는 동작 주파수와 데이터 전송 속도에 의해서 삼차원 반도체 내 노이즈 문제는 갈수록 심각해지고 있다. 이를 해결하기 위한 좋은 방법으로는 electromagnetic bandgap 구조 (EBG 구조)가 있다. EBG 구조는 package나 PCB에 구현하기 용이한 구조이며, 노이즈 감쇠 특성 역시 우수하지만, 이 특성을 빠르고 정확하게 예측하는 것은 매우 도전적인 일이다.
이에 본 연구에서는 EBG 구조가 package나 PCB에 구현되었을 때, 노이즈 감쇠 특성을 빠르고 정확하게 예측하기 위한 모델링 방법을 제안한다. 제안하는 모델링 방법에서는 구조분할방법을 기반으로 하여, 다층 EBG 구조에 대한 새로운 해석적 모델을 제시하고 구조분할방법을 EBG 구조에 적용할 수 있도록 재결합 임피던스 매트릭스를 유도하고 있다. 또한, 제안하는 모델링 방법을 보다 포괄적으로 검증하기 위하여 전원 노이즈 감쇠를 위한 VSI-EBG 구조, VIB-EBG 구조, TSV-EBG 구조, 그리고 동상 신호 노이즈 감쇠를 위한 VSI-EBG 필터에 대해서도 제안하는 모델링 방법을 적용하였다.
측정을 통하여 검증된 제안하는 모델링 방법은 기존 방법 대비 92.1% 정확도 개선과 98.7%의 계산 시간 단축을 이루었다. 이처럼 제안하는 모델링 방법을 사용할 경우, EBG 구조의 특성을 빠르고 정확하게 예측할 수 있고, 이를 바탕으로 EBG 구조를 포함하는 시스템의 설계 및 설계 최적화를 이룰 수 있을 것으로 기대된다.
