Analysis of the response surface method for optimising the flatness of ceramic-metal brazing
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摘要:
陶瓷—金属封装作为电子真空器件中的关键工艺在集成电路封装,医疗设备、国防等得到了广泛应用,两者连接后的平面度决定了芯片的可靠性,预测并控制封装后陶瓷平面度变化对半导体行业的发展具有重大意义. 基于一种高温共烧陶瓷—金属结构,采用响应曲面法对陶瓷金属钎焊的试验进行设计,以同时研究多个试验变量对陶瓷金属钎焊平面度的影响. 将钎焊前后陶瓷平面度变化作为响应值,采用中心组合设计(centralcomposite design,CCD)建立了二次多项式回归方程的预测模型,研究了陶瓷尺寸、金属尺寸对平面度变化的影响. 结果表明,增大陶瓷高度或者减小陶瓷边长、墙体厚度均使平面度变化减小;同时发现陶瓷尺寸对平面度影响较为显著,而墙体厚度对平面度影响作用较小,该结果为陶瓷钎焊平面度的预测及控制提供了参考.
Abstract:Ceramic-to-metal packaging is widely used as a key process in electronic vacuum devices in integrated circuit packaging, medical devices, and defence.The flatness of the two connections determines the reliability of the chip, and it is of great significance for the development of the semiconductor industry to predict and control the change of ceramic flatness after encapsulation.Design of experiments for ceramic-metal brazing based on a high-temperature co-fired ceramic-metal structure using the response surface method to simultaneously investigate the effects of multiple experimental variables on the flatness of ceramic-metal brazing.The change in ceramic flatness before and after brazing was taken as the response value, and a prediction model with quadratic polynomial regression equations was developed using a CCD combinatorial design to investigate the effect of ceramic size and metal size on the change in flatness.The results show that increasing the height of the ceramic or decreasing the length of the ceramic sides and the thickness of the wall reduces the change in flatness.At the same time, the ceramic size has a more significant effect on flatness, while the wall thickness plays a smaller role in affecting flatness. The results provide a reference for the prediction and control of ceramic brazing flatness.
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Keywords:
- ceramic-to-metal packages /
- planarity /
- response surface methodology
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表 1 CCD试验设计及瓷件平面度变化值
Table 1 CCD test design and flatness change value of porcelain parts
试验
编号输入变量 响应值 瓷件边长a/mm 瓷件高度b/mm 墙体厚度h/mm 平面度变化值d/mm 1 30 2.4 0.6 0.004425 2 40 2.4 0.4 0.002560 3 20 2.4 0.4 0.001640 4 40 0.8 0.4 0.080680 5 40 0.8 0.8 0.106175 6 40 1.6 0.6 0.020040 7 30 0.8 0.6 0.073730 8 40 2.4 0.8 0.009400 9 20 0.8 0.8 0.040000 10 20 0.8 0.4 0.028000 11 30 1.6 0.4 0.011120 12 20 1.6 0.6 0.010300 13 30 1.6 0.8 0.026530 14 30 1.6 0.6 0.017270 15 20 2.4 0.8 0.004750 表 2 平面度方差分析
Table 2 Analysis of variance (ANOVA) for flatness
Source 误差平方和SSE/mm2 自由度df 均方R/mm2 组间方差/组内方差F-value 显著值p-value Model 0.0144 9 0.0016 32.78 0.00060 瓷件边长a 0.0018 1 0.0018 36.82 0.00180 瓷件高度b 0.0094 1 0.0094 191.31 < 0.00010 墙体厚度h 0.0004 1 0.0004 8.08 0.03610 ab 0.0016 1 0.0016 32.82 0.00230 ah 0.0000 1 0.0000 0.7587 0.04236 bh 0.0001 1 0.0001 1.94 0.02224 a² 0.0000 1 0.0000 0.8618 0.39590 b² 0.0010 1 0.0010 20.75 0.00610 c² 3.961E-07 1 3.961E-07 0.0081 0.93180 $ \mathrm{\mathit{R}}^{\mathrm{2}}=0.983\; 3,\mathrm{Adjusted\; \mathit{R}}^2=0.953\; 3,\mathrm{Predicted\; \mathit{R}}^2=0.840\; 2 $ 表 3 修改后平面度方差分析
Table 3 Modified analysis of variance (ANOVA) for flatness
Source 误差平方和SSE/mm2 自由度df 均方R/mm2 组间方差/组内方差F-value 显著值p-value Model 0.0144 7 0.0021 49.01 < 0.0001 瓷件边长a 0.0018 1 0.0018 42.97 0.0003 瓷件高度b 0.0094 1 0.0094 223.23 < 0.0001 墙体厚度h 0.0004 1 0.0004 9.43 0.0180 ab 0.0016 1 0.0016 38.29 0.0005 ac 0.0000 1 0.0000 0.8853 0.0371 bc 0.0001 1 0.0001 2.26 0.0171 b² 0.0011 1 0.0011 26.02 0.0014 R2 = 0.98,Adjusted R2 = 0.96,Predicted R2 = 0.8822 -
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