高温下硅与玻璃键合的机械应力估算
Mechanical Stresses Estimation in Silicon and Glass Bonded at Elevated Temperature
摘要：
在静电键合过程中，也称为阳极键合，通过施加外部电压并同时加热到200 ℃，将硅键合到玻璃上。450 $°$ C.粘接后冷却到工作温度时，发生了相互变形。由于阳极键合的玻璃和硅样品的线性热膨胀系数不匹配，产生内部应力状态。这种应力称为热失配应力。本文的目的是确定的技术和设计解决方案，以实现最小的热失配应力在所得债券。键合试样材料的线性热膨胀系数与温度的非线性关系使得很难通过选择在特定温度范围内具有相近平均热膨胀系数的材料来减小热失配应力。为了评估降低热失配应力的方法，本文采用了两种不同的方法来描述组件：两个薄的粘合层和多层复合材料。基于两种品牌玻璃（LK 5，Borofloat 33）和硅的性质，使用所描述的数学模型，评估了在几个不同温度$T_b$下结合的样品中在温度$T_w$下的热失配应力。研究了玻璃与硅片厚度比对键合硅表面应力的影响。基于这样的评估，可以说，通过改变与硅结合的玻璃的厚度，可以在材料的特定深度处获得零热失配应力，或者在该深度处获得某一限定值的应力。本文所用的装配描述模型可用于优化阳极键合工艺参数。这种使用的目的是最大限度地减少器件工作温度下的热失配应力。
英文摘要：
During electrostatic bonding, also known as anodic bonding, silicon is bonded to glass by applying an external voltage and simultaneous heating to temperatures of 200...450 $°$C. While cooling to working temperature after bonding happened pieces are mutually deformed. Due to linear thermal expansion coefficients mismatch of anodically bonded glass and silicon samples an internal stress state is generated. Such stresses are called thermal mismatch stresses. The aim of this paper is a determination of technological and design solutions to achieve minimal thermal mismatch stresses in resulting bond. The nonlinear dependence of linear thermal expansion coefficients of bonded samples' materials on temperature makes it difficult to minimize thermal mismatch stresses by chosing materials with close average thermal expansion coefficients in particular temperature range. To assess means of lowering thermal mismatch stress in this paper two different ways to describe assembly are used: two thin bonded layers and multilayered composite material. Based on properties of two brands of glass (LK5, Borofloat 33) and silicon used with described mathematical models thermal mismatch stresses at temperature $T_w$ in samples bonded at several different temperatures $T_b$ are evaluated. Bonded silicon surface stress dependence of glass to silicon wafer thickness ratio is evaluated. Based on such evaluations one can say that by varying thickness of glass bonded to silicon one can obtain zero thermal mismatch stress at a particular depth of material or obtain stress of some defined value at this depth. Models of assembly description used in this paper can be used to optimize anodic bonding process parameters. Such usage aimed to minimize thermal mismatch stresses at device working temperatures is presented in this paper.
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