The thermo-mechanical behavior of multilayer structures is a subject of perennial interest. A vast literature exists on this topic. While some useful closed-form expressions have been developed under certain sets of assumptions and using different approximations, most of them are rarely supported by experimental investigation. Among various multi-layer structures, this dissertation provided a thorough investigation on the lamination-based thick-film multilayer substrates, or the multichip module (MCM) substrates. As an increasing number of layers were laminated, the thermo-mechanical behavior was measured layer-by-layer using a laser profilometry during thermal cycling.
One of the key thermo-mechanical issues during the MCM-D substrate fabrication is substrate bowing, and another important con-cern is the thermal stress caused by the mismatch of the coefficient of thermal expansion (CTE). The thermal stress causes mechanical failure of films, such as adhesion reduction, contact peel-off, and variations in electrical properties, and the substrate bowing makes the fabrication process difficult, for example, vacuum mounting for handling and substrate sawing after fabrication. It also causes a stress concentration problem in internal structures such as via, and flip chip bump failure due to repeated thermal loading. Consequently, precise descriptions of the thermo-mechanical behavior of the thick-film multilayer substrates were necessarily required to realize high-density, high-yield, high-reliability, and low-cost MCM-D substrates.
In Chapter 1, while the majority of reports in the literature have focused on single-layer analysis using the well-known Stoney''s formula, this chapter examined the extended usage of Stoney''s formula for the multilayer analysis. A simple model, the multilayer-modified Stoney''s formula, which predicts a stress contribution from each individual layer was proposed and verified through the numerical analysis and experiments using various kinds of materials typically employed in a lamination-based MCM-D technology. The agreement between measured and calculated values suggested that the thermo-mechanical behavior of the laminated composite films on a silicon substrate was well described by the multilayer-modified Stoney''s formula.
In Chapter 2, the composite beam analysis (CBA) was newly proposed to analyze the thermo-mechanical behavior of lamination-based thick-film multilayer substrates. Since the lamination process uses relatively thick polymer films, the classical stress analyses assuming infinitesimally thin films, are no longer effective. The thermo-mechanical behavior of the laminated multilayer polymer films on a silicon substrate was better described by the proposed model, while an error as much as 30% was involved using Stoney''s formula. The results suggested that applying Stoney''s formula directly from the measured maximum bow or radius of curvature to calculate the internal stress may produce an overestimation of the calculated value of the stress by the same amount.
In Chapter 3, the magnitude and distribution of the biaxial, shear, and peel stresses in the lamination-based MCM-D substrate have been investigated using the numerical analysis, providing an in-depth look at the CBA model. While the biaxial stress value was constantly maintained throughout the whole film layers during the multilayer construction, as the total film thickness increases, more of tensile stress developed at the bottom plane of the silicon substrate and more of compression stress at the silicon/film interface. The numerical analysis showed that the peel and shear stresses were highly localized near the circumferential edge justifying the biaxial assumption for the CBA derivation, and increased with the thickness of the total dielectric layer. The result suggested that the probability of delamination was highest near the circumferential edge. Finally, the most widely-used traditional approaches for the stress analysis were briefly reviewed along with the recently developed CBA model, and their possible application areas in today''s microelectronics were suggested for user''s convenience.
In Chapter 4, by comparing the measured and calculated values from the CBA, the study could quantitatively analyzed the stress re-laxation effect of thermoplastics as lamination adhesives during sequential build-up of polymer multilayer structures. When analyzed through an analytical model, the measured thermal behavior of thermoplastics exhibited as much as 70% stress relaxation in the multilayer structures, and much contrasted with that of thermosets. The result provides an important design guideline that thermoplastics can be used as a stress relaxation layer in the lamination-based multilayer substrates.
In Chapter 5, the thermo-mechanical behavior of aluminum thin film on the laminated thick-film multilayer substrate was measured and compared with that of aluminum thin films on a bare silicon wafer and a single-layer substrate. While Stoney''s formula can still be adequately used for the film on a bare silicon wafer or the single-layer substrate, an error of as much as 50% can result using Stoney''s formula in the estimation of the amount of substrate bowing for aluminum thin film on the multilayer substrate. The results suggested that the aluminum thin film exhibited quite different thermo-mechanical behavior depending on which layer the film was deposited onto in the laminated thick-film multilayer substrates.
In Chapter 6, the thermo-mechanical behavior of multilayer structures was experimentally observed layer-by-layer during sequential build-up of alternating layers of polymer dielectric and metal conductor films. The results were compared with those of layer-by-layer measurement of polymer-only-multilayer structures (i.e., without the metal layers in-between). From the thermo-mechanical viewpoint, the actual process temperature, which could be found at the intersection point of two cooling curves, determined the overall shape of the heat cycle curves of the multilayer structures. For the lamination process, the actual process temperature was dependent on the adhering interface involved in the process. On the other hand, for the sputtering process, the process temperature increased as a number of layers increased; this was due to poor heat dissipation through the thick-film multilayer substrate. The results suggested that the characteristics of each fabrication process and the materials involved in the processes must be well under-stood to precisely describe the multilayer behavior.
In Chapter 7, while the majority of reports in the literature have focused on the thermo-mechanical behavior of the blanket-layered polyimides or metal thin film on a substrate, this chapter have mainly focused on that of the patterned metal layers. Firstly, using direction-ally patterned signal lines on a silicon substrate, the study investigated the effect of line directionality on the thermo-mechanical behavior of the structure. The maximum bow values of the directional signal lines measured vertical and parallel to the line directions was nearly the same for the uniformly distributed directional signal lines, except the first heating cycle due to intrinsic stress. Secondly, using the patterns with various line widths and distances, the line geometry effect on the substrate bow values was measured and quantitatively discussed using the numerical analysis as well as the well-known Stoney''s formula. The substrate bow values after pattering were proportional to the area fraction of the remaining metal patterns, regardless of line geometry and directionality. Stoney''s formula was modified to incorporate these results for the thermo-mechanical stress analysis of the patterned metal layers.
The results and discussions in this dissertation could be used for the stress analysis of thick-film multilayer substrates, especially lamination-based MCM-D substrates, providing design guidelines as well as material and process selection criteria.'
멀티칩 모듈 기판의 열적-기계적 거동을 정확히 기술하고 예측하는 것은 제품의 제조 공정과 신뢰성 확립에 크게 영향을 끼치며 따라서 저가의 고신뢰성 제품 제조를 가능하게 하는 매우 실질적인 문제이다. 멀티칩 모듈 기판의 제조 과정에서 발생하는 가장 중요한 열적-기계적 문제점들은 크게 두 가지를 나누어 생각할 수 있는데, 첫째는 기판의 휨 현상이며, 둘째는 기판 내부에서 열팽창계수 차이에 의해 발생하는 내부 응력이다.
먼저 기판의 휨 현상은 여러가지의 각종 기본적인 공정들을 매우 어렵게 만든다. 특히 MCM-D 공정 중에는 광식각 공정의 정밀도를 떨어뜨리고, 휘어진 기판에 대한 자동화 공정을 어렵게 만들고, 또한 웨이퍼의 크기가 커질수록 웨이퍼 절단 공정 상에서 심각한 수율의 감소가 예상된다. 이외에도 반복되는 열 하중으로 인한 비아, 저항체, 인덕터, 캐패시터 등 내부의 구조물에 대한 응력 집중 현상, 솔더볼 응력 집중 현상 및 파괴 현상 등은 모두 기판의 휨 현상으로 인하여 직접적으로 발생하는 문제들이다.
또한 기판의 내부 응력으로 나타날 수 있는 문제점들은 다음과 같이 몇 가지로 생각할 수 있다. 먼저 절연 필름의 파괴 현상으로 이것은 제품의 전기적 성능 저하와 파면에 의한 수분 흡습으로 인해 제품의 급격한 신뢰성 저하에 직접적인 원인이 되고 있다. 또한 금속선 등에 무리한 하중이 가해지게 되면 신호선 단락이 발생하고 이로 인해 제품의 전기적 성능이 불안정하게 되면 동작 불능 상태가 되기도 한다.
따라서 제품의 착안 및 초기 설계 당시부터 이러한 상황들을 고려하여 재료를 선정하고 제품을 디자인하는 것이 제조 단가 및 개발 비용을 낮추고 신뢰성 높은 제품을 실현하기 위해서 필수적이다. 따라서 본 연구에서는 이러한 저가의 고신뢰성 멀티칩 모듈 기판을 제작하기 위하여 주로 첨단 멀티칩 모듈의 설계 개념과 재료들을 이용하여 시제품을 제작하고 이의 열적-기계적 거동을 기술하는 모델을 개발하여 제품의 개발 과정 및 공정 중에 이를 연속적으로 적용하는 모델 개발을 목표로 한다.
본 연구에서 개발한 CBA 모델은 일반적인 멀티칩 모듈에서 사용될 수 있는 것으로 다양한 재료들을 고려하여 개발되었으며 일반적으로 후막 필름을 사용하는 라미네이션 공정과 금속선 형성을 위한 스퍼터링 공정 등 다양한 공정 및 형상이 복합적으로 포함된 MCM-D 기판 및 그 제조 공정을 효과적으로 설명할 수 있었다.
특히 최근에 각광을 받고 있는 열가소성 수지는 통상적으로 유리전이온도 이상에서 점탄성에 의한 응력 완화 현상을 가지는 것이 경험적으로 관찰되고 있는데, 이를 개발된 모델을 이용하며 매우 정량적으로 기술할 수 있었으며 이러한 결과를 이용하여 열가소성 수지를 응력 완화층으로 적용하는 멀티칩 모듈의 개념을 제시할 수 있었다.
또한 본 연구에서 수행한 FEM 해석 결과는MCM-D 기판 내의 다양한 응력 분포를 효과적으로 나타내고 있는데 이러한 FEM 해석 결과는 CBA 모델을 통하여 예측한 결과와 정확히 일치하고 있었다. 따라서 본 연구에서는 CBA 모델이 기존에 제시된 이론들에 비해 약 30%-50% 이상의 정확도를 나타내는 것이 실험 및 해석적으로 증명되었다.
