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响应曲面法优化陶瓷—金属钎焊平面度的分析

王光辉, 刘旭, 张玉, 田皓, 宋晓国

王光辉, 刘旭, 张玉, 田皓, 宋晓国. 响应曲面法优化陶瓷—金属钎焊平面度的分析[J]. 焊接学报, 2025, 46(3): 120-126. DOI: 10.12073/j.hjxb.20231204001
引用本文: 王光辉, 刘旭, 张玉, 田皓, 宋晓国. 响应曲面法优化陶瓷—金属钎焊平面度的分析[J]. 焊接学报, 2025, 46(3): 120-126. DOI: 10.12073/j.hjxb.20231204001
WANG Guanghui, LIU Xu, ZHANG Yu, TIAN Hao, SONG Xiaoguo. Analysis of the response surface method for optimising the flatness of ceramic-metal brazing[J]. TRANSACTIONS OF THE CHINA WELDING INSTITUTION, 2025, 46(3): 120-126. DOI: 10.12073/j.hjxb.20231204001
Citation: WANG Guanghui, LIU Xu, ZHANG Yu, TIAN Hao, SONG Xiaoguo. Analysis of the response surface method for optimising the flatness of ceramic-metal brazing[J]. TRANSACTIONS OF THE CHINA WELDING INSTITUTION, 2025, 46(3): 120-126. DOI: 10.12073/j.hjxb.20231204001

响应曲面法优化陶瓷—金属钎焊平面度的分析

基金项目: 中央军委装备发展部装备项目管理中心;铝金刚石金属外壳系列项目(2209wp0001)
详细信息
    作者简介:

    王光辉,硕士,助理工程师;主要研究方向金属钎焊. Email: wangguanghui@cetc13.cn

    通讯作者:

    刘旭,硕士,高级工程师;Email: chidazhao@hit.edu.cn.

  • 中图分类号: TG 454

Analysis of the response surface method for optimising the flatness of ceramic-metal brazing

  • 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.

  • 图  1   试验外壳结构示意图: 陶瓷—金属墙体结构

    Figure  1.   Schematic construction of the test enclosure: ceramic-metal wall construction

    .

    图  2   不同瓷件边长对陶瓷—金属钎焊平面度的影响规律

    Figure  2.   Influence of different edge lengths on the flatness of ceramic—metal brazing

    图  3   不同瓷件高度对陶瓷—金属钎焊平面度的影响规律

    Figure  3.   Influence of different edge heights on the flatness of ceramic—metal brazing

    图  4   不同金属墙体厚度对陶瓷—金属钎焊平面度的影响规律

    Figure  4.   Influence of different metal wall thickness on the flatness of ceramic—metal brazing

    图  5   平面度变化回归方程的预测值与试验测量值的对比

    Figure  5.   Comparison of predicted and experimentally measured values from regression equations for changes in flatness

    图  6   不同瓷件边长下,瓷件高度与墙体厚度对瓷件平面度变化值的影响规律

    Figure  6.   Influence of porcelain height and wall thickness on the change value of porcelain flatness under different porcelain side lengths. (a) 20 mm; (b) 30 mm; (c) 40 mm

    图  7   不同瓷件高度下,瓷件边长与墙体厚度对瓷件平面度变化值的作用规律

    Figure  7.   Role of porcelain side length and wall thickness on the change value of porcelain flatness under different porcelain heights. (a) 0.8 mm; (b) 1.6 mm; (c) 2.4 mm

    图  8   不同墙体厚度下,瓷件边长与瓷件高度对瓷件平面度变化值的作用规律

    Figure  8.   Law of the role of porcelain edge length and porcelain height on the change value of porcelain flatness for different wall thicknesses. (a) 0.4 mm; (b) 0.6 mm; (c) 0.8 mm;

    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
    1302.40.60.004425
    2402.40.40.002560
    3202.40.40.001640
    4400.80.40.080680
    5400.80.80.106175
    6401.60.60.020040
    7300.80.60.073730
    8402.40.80.009400
    9200.80.80.040000
    10200.80.40.028000
    11301.60.40.011120
    12201.60.60.010300
    13301.60.80.026530
    14301.60.60.017270
    15202.40.80.004750
    下载: 导出CSV

    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 $
    下载: 导出CSV

    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
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-12-03
  • 网络出版日期:  2025-02-14
  • 刊出日期:  2025-03-24

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