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Article(id=1321927206138401419, tenantId=1146029695717560320, journalId=1220038251117760515, issueId=1321927171292123557, articleNumber=null, orderNo=null, doi=10.11868/j.issn.1001-4381.2024.000241, pmid=null, cstr=32421.14.j.issn.1001-4381.2024.000241, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1711987200000, receivedDateStr=2024-04-02, revisedDate=null, revisedDateStr=null, acceptedDate=1715788800000, acceptedDateStr=2024-05-16, onlineDate=1793101606162, onlineDateStr=2026-10-27, pubDate=1773936000000, pubDateStr=2026-03-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793101606162, onlineIssueDateStr=2026-10-27, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793101606162, creator=13701087609, updateTime=1793101606162, updator=13701087609, issue=Issue{id=1321927171292123557, tenantId=1146029695717560320, journalId=1220038251117760515, year='2026', volume='54', issue='3', pageStart='1', pageEnd='272', issueExtLink='null', onlineDate='null', pubDate='1773936000000', pubDateStr='2026-03-20', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793101597855, creator='13701087609', updateTime=1793101597855, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=252, endPage=260, ext={EN=ArticleExt(id=1321927206327145100, articleId=1321927206138401419, tenantId=1146029695717560320, journalId=1220038251117760515, language=EN, title=Preparation of monodisperse micron-sized spherical copper particles based on pulsated orifice ejection method, columnId=1220689384450478826, journalTitle=Journal of Materials Engineering, columnName=RESEARCH ARTICLE, runingTitle=null, highlight=null, articleAbstract=

3D microelectronic packaging imposes extremely stringent requirements on the size and precision of Cu core balls. To obtain Cu core balls that meet these requirements， it is essential to ensure the stability during the droplet jetting process and to precisely control the droplet size as needed. This study employs the pulsated orifice ejection method to prepare monodisperse Cu particles. The key parameters affecting particle size are determined based on the Hagen-Poiseuille law， and the relationship between these key parameters and the stability and size of Cu droplet jetting is investigated in detail. The influence of temperature and differential pressure determines whether droplets can be jetted， while the pulse waveform and the rod distance primarily control the particle size. Orthogonal experiments reveal that the particle size is co-influenced by multiple parameters， among which the voltage of the pulse waveform has the most significant impact， and the the particle size increases with the increase of the voltage. Adjusting the rod distance can regulate the stability of the jetting process. Through the analysis of the jetting window and orthogonal experiments， appropriate key parameters are selected to prepare Cu particles with target sizes of 100 μm and 200 μm. The actual obtained particle sizes are 96.27 μm and 200.69 μm， with standard deviations of approximately 2.67 μm and 2.64 μm， respectively， and sphericity values both exceeding 0.95. The prepared Cu particles exhibit uniform size and high sphericity， meeting the requirements for Cu core balls.

, authors=Wei DONG1, Cen JIANG1, Fumin XU1, Yang ZHAO2, authorsList=Wei DONG, Cen JIANG, Fumin XU, Yang ZHAO, authorCompany=null, correspAuthors=Fumin XU, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1321927210500477598, articleId=1321927206138401419, tenantId=1146029695717560320, journalId=1220038251117760515, language=CN, title=基于脉冲微孔喷射法制备单分散微米级球形铜粒子, columnId=1220689384622445292, journalTitle=材料工程, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=

3D微电子封装对Cu核球尺寸及精度提出非常严格的要求，为获得满足要求的Cu核球，必须确保液滴喷射过程中的稳定性，并根据需要精确控制液滴的大小。本研究采用脉冲微孔喷射法制备单分散Cu粒子，通过哈根泊肃叶定律确定影响粒径的关键参数，细致探讨关键参数与Cu液滴喷射的稳定性与尺寸之间的关系。温度和差压的影响决定液滴能否喷射，而脉冲波形和杆距主要是对微粒大小的控制，正交实验表明：粒径是由多个参数协同影响，其中脉冲波形的电压影响最为显著，粒径大小随电压的增加而增大；调整杆距可调控喷射过程稳定性。通过喷射窗口和正交实验，选择适当关键参数制备目标粒径为100 μm和200 μm的Cu粒子，获得的实际粒径为96.27 μm和200.69 μm，标准偏差分别约为2.67 μm和2.64 μm，球形度均大于0.95，所制备Cu微粒的粒径均一，球形度高，满足Cu核球的要求。

, authors=董伟1, 江岑1, 许富民1, 赵阳2, authorsList=董伟, 江岑, 许富民, 赵阳, authorCompany=null, correspAuthors=许富民, authorNote=null, correspAuthorsNote=
许富民（1969—），男，副教授，博士，主要从事单分散粉末制备及相关研究，联系地址：辽宁省大连市甘井子区凌工路2号大连理工大学新三束实验室208（116024），E-mail：
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（a）average particle size 96.27 μm；（b）SEM images of copper particles around 100 μm；（c）average particle size 200.69 μm；（d）SEM images of copper particles around 200 μm

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（a）平均粒径96.27 μm；（b）100 μm左右铜微粒SEM图；（c）平均粒径200.69 μm；（d）200 μm左右铜微粒SEM图

, figureFileSmall=0kmoAkCFpmh7+kgYw/BFWw==, figureFileBig=aGopbgDGv5czMiML8lGWUg==, tableContent=null), ArticleFig(id=1321927219501454039, tenantId=1146029695717560320, journalId=1220038251117760515, articleId=1321927206138401419, language=EN, label=Table 1, caption=

Key technical parameters and regulation range of POEM

, figureFileSmall=null, figureFileBig=null, tableContent=
Temperature/℃Orifice diameter/µmFrequency/Hztrise/µsthold/μstfall/μsPressure/kPaVoltage/VRod distance/mm
1200100/200/30010050-300125022500-930-750.1-2.0
), ArticleFig(id=1321927219585340120, tenantId=1146029695717560320, journalId=1220038251117760515, articleId=1321927206138401419, language=CN, label=表1, caption=

POEM关键技术参数及调控范围

, figureFileSmall=null, figureFileBig=null, tableContent=
Temperature/℃Orifice diameter/µmFrequency/Hztrise/µsthold/μstfall/μsPressure/kPaVoltage/VRod distance/mm
1200100/200/30010050-300125022500-930-750.1-2.0
), ArticleFig(id=1321927219681809113, tenantId=1146029695717560320, journalId=1220038251117760515, articleId=1321927206138401419, language=EN, label=Table 2, caption=

Process parameter influencing factors and levels

, figureFileSmall=null, figureFileBig=null, tableContent=
LevelVoltage（A）/VRising edge time（B）/μs

Rod distance

（C）/mm

170500.4
2601000.8
3501501.2
), ArticleFig(id=1321927219937661658, tenantId=1146029695717560320, journalId=1220038251117760515, articleId=1321927206138401419, language=CN, label=表2, caption=

工艺参数影响因素及水平

, figureFileSmall=null, figureFileBig=null, tableContent=
LevelVoltage（A）/VRising edge time（B）/μs

Rod distance

（C）/mm

170500.4
2601000.8
3501501.2
), ArticleFig(id=1321927220038324955, tenantId=1146029695717560320, journalId=1220038251117760515, articleId=1321927206138401419, language=EN, label=Table 3, caption=

Results and polar analysis of orthogonal experiments

, figureFileSmall=null, figureFileBig=null, tableContent=
Test numberVoltage（A）/VRising edge time（B）/μsRod distance（C）/mmParticle size/μm
170500.4229.1
2701000.8214.5
3701501.2216.6
460500.8237.9
5601001.2234.2
6601500.4230.6
750501.2204.9
8501000.8207.1
9501500.4210.4
K1660.2671.9670.1
K2702.7655.8659.5
K3622.4657.7655.7
k1220.1224.0223.4
k2234.2218.6219.8
k3207.5219.2218.6
R80.316.114.4
), ArticleFig(id=1321927220344509148, tenantId=1146029695717560320, journalId=1220038251117760515, articleId=1321927206138401419, language=CN, label=表3, caption=

正交实验结果及极差分析

, figureFileSmall=null, figureFileBig=null, tableContent=
Test numberVoltage（A）/VRising edge time（B）/μsRod distance（C）/mmParticle size/μm
170500.4229.1
2701000.8214.5
3701501.2216.6
460500.8237.9
5601001.2234.2
6601500.4230.6
750501.2204.9
8501000.8207.1
9501500.4210.4
K1660.2671.9670.1
K2702.7655.8659.5
K3622.4657.7655.7
k1220.1224.0223.4
k2234.2218.6219.8
k3207.5219.2218.6
R80.316.114.4
), ArticleFig(id=1321927220428395229, tenantId=1146029695717560320, journalId=1220038251117760515, articleId=1321927206138401419, language=EN, label=Table 4, caption=

Particle size and process parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
Target particle size/μmVoltage/V

Rising edge

time/μs

Rod distance/mmActual particle size/μm
100502000.696.27
200501500.8200.69
), ArticleFig(id=1321927220747162334, tenantId=1146029695717560320, journalId=1220038251117760515, articleId=1321927206138401419, language=CN, label=表4, caption=

粒径与工艺参数

, figureFileSmall=null, figureFileBig=null, tableContent=
Target particle size/μmVoltage/V

Rising edge

time/μs

Rod distance/mmActual particle size/μm
100502000.696.27
200501500.8200.69
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基于脉冲微孔喷射法制备单分散微米级球形铜粒子
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董伟 1 , 江岑 1 , 许富民 1 , 赵阳 2
材料工程 | 研究论文 2026,54(3): 252-260
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材料工程 |研究论文 2026 , 54 (3) : 252 -260
基于脉冲微孔喷射法制备单分散微米级球形铜粒子
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董伟1, 江岑1, 许富民1 , 赵阳2
作者信息
  • 1.大连理工大学 材料科学与工程学院，辽宁 大连 116024
  • 2.陆军装甲兵学院 装备再制造技术国防科技重点实验室，北京 100072
通讯作者:
许富民（1969—），男，副教授，博士，主要从事单分散粉末制备及相关研究，联系地址：辽宁省大连市甘井子区凌工路2号大连理工大学新三束实验室208（116024），E-mail：
Preparation of monodisperse micron-sized spherical copper particles based on pulsated orifice ejection method
Wei DONG1, Cen JIANG1, Fumin XU1 , Yang ZHAO2
Affiliations
  • 1.School of Materials Science and Engineering，Dalian University of Technology，Dalian 116024，Liaoning，China
  • 2.National Key Laboratory for Remanufacturing，Army Academy of Armored Forces，Beijing 100072，China
出版时间: 2026-03-20 doi: 10.11868/j.issn.1001-4381.2024.000241
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3D微电子封装对Cu核球尺寸及精度提出非常严格的要求，为获得满足要求的Cu核球，必须确保液滴喷射过程中的稳定性，并根据需要精确控制液滴的大小。本研究采用脉冲微孔喷射法制备单分散Cu粒子，通过哈根泊肃叶定律确定影响粒径的关键参数，细致探讨关键参数与Cu液滴喷射的稳定性与尺寸之间的关系。温度和差压的影响决定液滴能否喷射，而脉冲波形和杆距主要是对微粒大小的控制，正交实验表明：粒径是由多个参数协同影响，其中脉冲波形的电压影响最为显著，粒径大小随电压的增加而增大；调整杆距可调控喷射过程稳定性。通过喷射窗口和正交实验，选择适当关键参数制备目标粒径为100 μm和200 μm的Cu粒子，获得的实际粒径为96.27 μm和200.69 μm，标准偏差分别约为2.67 μm和2.64 μm，球形度均大于0.95，所制备Cu微粒的粒径均一，球形度高，满足Cu核球的要求。

脉冲微孔喷射  /  球形金属Cu粒子  /  粒径控制  /  正交实验  /  喷射稳定性

3D microelectronic packaging imposes extremely stringent requirements on the size and precision of Cu core balls. To obtain Cu core balls that meet these requirements， it is essential to ensure the stability during the droplet jetting process and to precisely control the droplet size as needed. This study employs the pulsated orifice ejection method to prepare monodisperse Cu particles. The key parameters affecting particle size are determined based on the Hagen-Poiseuille law， and the relationship between these key parameters and the stability and size of Cu droplet jetting is investigated in detail. The influence of temperature and differential pressure determines whether droplets can be jetted， while the pulse waveform and the rod distance primarily control the particle size. Orthogonal experiments reveal that the particle size is co-influenced by multiple parameters， among which the voltage of the pulse waveform has the most significant impact， and the the particle size increases with the increase of the voltage. Adjusting the rod distance can regulate the stability of the jetting process. Through the analysis of the jetting window and orthogonal experiments， appropriate key parameters are selected to prepare Cu particles with target sizes of 100 μm and 200 μm. The actual obtained particle sizes are 96.27 μm and 200.69 μm， with standard deviations of approximately 2.67 μm and 2.64 μm， respectively， and sphericity values both exceeding 0.95. The prepared Cu particles exhibit uniform size and high sphericity， meeting the requirements for Cu core balls.

pulsated orifice ejection  /  spherical metallic Cu particle  /  particle size control  /  orthogonal experiment  /  jetting stability
董伟, 江岑, 许富民, 赵阳. 基于脉冲微孔喷射法制备单分散微米级球形铜粒子. 材料工程, 2026 , 54 (3) : 252 -260 . DOI: 10.11868/j.issn.1001-4381.2024.000241
Wei DONG, Cen JIANG, Fumin XU, Yang ZHAO. Preparation of monodisperse micron-sized spherical copper particles based on pulsated orifice ejection method[J]. Journal of Materials Engineering, 2026 , 54 (3) : 252 -260 . DOI: 10.11868/j.issn.1001-4381.2024.000241
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当前，微电子工业已经进入集成电路（integrated circuit，IC）发展的后摩尔定律时代，超大规模IC无限接近其物理极限，如何继续推动电子产品向微型化、集成化和多功能化发展是微电子技术面临的核心问题与巨大挑战［1］。作为新兴的先进封装技术，3D封装已成为解决上述问题与挑战的主要出路［2-4］。然而在3D电子封装领域，经过多次钎焊回流后，凸点往往会因为过度熔融而强度较低，使得芯片的凸点出现压溃现象，造成短路。铜核焊锡球即以铜球为核心，一定厚度钎料包覆所形成的具有核壳结构的焊球，作为3D封装互连焊点的关键材料，兼具良好的机械支撑性能、导热性能和导电性能，是3D封装的重要技术解决方案。铜的熔点约为1080 ℃，铜核球能够确保其在回焊炉中反复回流时仍维持原有形状，从而为3D封装保持必要的内部空间。尽管该领域研究已取得一定进展，但作为铜核焊锡球的核心，铜核球对尺寸精度要求极高，即使铜核球粒径有小的差别，也会造成封装的平整性降低，无法起到有效的机械支撑作用，因此如何生产满足电子封装领域需要的球形铜粒子，已成为制约该技术进一步发展的瓶颈［5-11］。
传统的球形粒子制备技术，如气雾化法［12］和离心雾化法制备［13］的粒子，由于粒径呈分布范围很宽的正态分布，即使通过筛分也无法得到满足3D封装用高精度铜球形粒子。为满足高精度铜球的尺寸要求，人们制备高精度金属粒子的方式主要是均匀液滴喷射（uniform droplet spray，UDS）和按需喷射（drop-on-demand，DOD）。UDS是利用Rayleigh射流不稳定原理在高频扰动作用下产生液滴的一种方法。Islier［14］通过UDS制备了粒径范围在300~500 μm的球形Cu粒子，利用成核动力学模型，研究了凝固路径对球形度及微球表面的影响；Joumaa［15］开发了一种高温UDS装置，研究了该装置的结构对喷射的影响，并制备了粒径范围在300~700 μm的铜液滴；Lee［16］则在低熔点锡铅合金UDS装置的基础上进行改进，实现了铜液滴的喷射，并研究了不同振动频率与进气压力对粒子的影响规律。由此看出基于UDS所制备的粒子仍存在尺寸分布较宽，且圆球度不高的问题，难以满足封装用铜核球的精度要求。与UDS相比，DOD在制备粒子粒径与精度的可控性上更具优势，Simonelli等［17］利用磁流体力学提出了一种生产直径小于80 μm、熔点高于1000 ℃的高温金属微滴的金属喷射技术，并对Sn和Ag的喷射稳定性及沉积成型结果进行了讨论；Liu等［18］通过采用气动式液滴喷射技术对金属3D打印成型中热累积效应演变与消除进行了分析；Qi等［19］通过对气动式按需喷射建立3D数值模型探究液滴沉积碰撞轨迹；Yi等［20］利用气动式液滴喷射技术提出了一种基于空间分布的螺旋轨迹的液滴沉积方法，研究了沉积距离和频率对形成质量的影响机制；Yi等［21］还基于体积分数法揭示了沉积液滴之间重熔的详细机制，优化了液滴喷射沉积过程及成型质量；Zhong等［22］利用气动式制备了不同粒径的Cu粒子，研究了不同脉冲宽度及峰值压力对Cu液滴断裂形成的影响，并对所制备的Cu粒子粒径大小及偏差做了评价，但制备的Cu粒子粒径偏差仍然较大，制备精度和效率有待提升。近年来，在DOD中开发了脉冲微孔喷射法（pulsated orifice ejection method，POEM）这种新颖的微米级粒子制备技术［23-24］，因其制备粒子具有球形度高，粒径均一且热历史一致等特点而被研究人员所青睐［25-27］。
目前，利用POEM制备低熔点Sn-Ag-Cu（SAC305）成分焊球的研究过程中，对工艺参数的影响做了详细分析［28］。在POEM制备高熔点球形Cu粒子研究中，Hu等［29］制备了Cu球形粒子并对其冷却凝固行为进行了研究，结果表明粒子粒径和球形度精度都远高于UDS和气动式DOD制备的Cu粒子。王延洋［30］制备了不同粒径的Cu粒子并通过模拟计算对冷却过程进行了分析。以上研究均探讨了铜粒子制备的工艺参数及其影响条件，然而对制备过程中影响因素的剖析尚不够完整和系统，亦未充分考虑相关因素之间的协同作用，因而难以指导通过POEM制备出符合3D封装要求的铜核球，最终导致无法实现对微滴的精确控制，限制了该方法在3D封装中的实际应用。
本研究旨在通过建立POEM液滴喷射的物理模型，系统探究影响液滴喷射与粒径控制的关键因素，综合分析熔体温度、差压、脉冲波形及杆距等参数的作用机制，从而阐明适用于制备满足3D封装要求的铜核球的参数调控规律。基于所得规律，进一步采用脉冲微孔喷射法开展铜微滴生成实验，以验证该参数调控体系在实际喷射过程中的可行性与有效性，以期为高质量微米级铜微粒的制备提供指导，并为该技术的进一步应用奠定基础。
1 实验材料与方法
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1.1 实验装置与方法
脉冲微孔喷射装置如图1（a）所示，包括压电式液滴按需喷射系统、温度控制系统、真空与差压控制系统与收集系统。实验材料为纯铜（Cu≥99.999%，质量分数），购自中诺新材（北京）科技有限公司。
为了防止原料在实验过程中氧化，首先将腔室抽至5×10-3 Pa左右，然后向腔室内部充入氩气至一个大气压。利用高频感应加热将坩埚内原料熔化，保温20 min以保证熔体温度均匀。实验中，压电陶瓷按照波形发生器预设的梯形波带动传动杆运动，波形图如图1（b）所示。对于脉冲波形调整的主要手段是通过改变电压与上升沿时间，其中电压控制压电陶瓷的变形，继而影响传动杆位移大小；而上升沿时间则是传动杆下落冲击时间。在差压控制器使坩埚内外产生的差压辅助下，传动杆作用于微孔附近熔体的脉动压力打破微孔附近的压力平衡时，一定体积的熔体脱离束缚，从坩埚底部的微孔喷出，形成液滴。液滴在下落的过程中，由于液体本身表面张力的作用，形成球形。与此同时，球形液滴会与周围环境进行热交换，以无容器状态下快速凝固形成球形金属微粒子。实验中所涉及相关参数如表1所示。实验结束后对制备的粒子进行分析，在带有底部光源的光学显微镜（Axioscope 5）下获得粒子的轮廓信息；利用图形分析软件（WinRoof 2018）对粒子的直径、球形度、粒径分布进行测量分析；采用扫描电子显微镜（SU5000）观察粒子的表面形貌。
1.2 物理模型建立与理论推算
为采用POEM制备满足要求的球形Cu粒子，首先需要确定影响粒子粒径的工艺参数。参照以往研究工作［31-32］，建立脉冲微孔喷射设备的坩埚喷射底部模型，如图2所示，模型中d0为小孔直径，l0为小孔材料的厚度，dR为传动杆直径，d为坩埚内部直径，Δz为传动杆位移距离，lc为传动杆两侧狭缝高度，Pi （i=1，2，3）分别为点1、2、3处压强。
在此基础上，为简化计算，另外做了一些假设，如下所示：（1）坩埚内流体为定常不可压缩流体；（2）坩埚内流体为层流，只有轴向流动并且是轴对称等径匀流；（3）坩埚模型内充满流体。
当传动杆向下运动时，其排开的熔体一部分通过小孔喷出形成液滴，一部分沿坩埚与传动杆间缝隙向上回流，根据哈根泊肃叶定律（Hagen-Poiseuille’s law），通过喷嘴的相应流量QN可表示为：
QN=πd04128μl0ΔPN
式中：μ为坩埚内熔体黏度；ΔPN为点2与点3之间的压强差。
除去从微孔中排出液体外，余下熔体将顺着坩埚壁与传动杆之间的狭缝回流，具体回流液体流量可以由公式（2）［32］表示：
QC=π8μlcd4-d04+d2-dR2lndR-lndΔPp
式中ΔPp为点1与点2之间的压强差。
根据质量守恒，则有：
Q=QN+QC
点1处压强即为熔体上部施加差压Pb，传动杆振动位置与小孔距离很近，点2即为传动杆下方微孔上方处的压强，点3处为坩埚外视为0压强。根据各点之间压强关系可以得到：
ΔPN=P2
ΔPp=P2-P1;ΔPN-ΔPp=P1
根据以上公式，可得到：
QN=Q+π8μlcd4-d04+d2-dR2lndR-lndPb1+d4-d04+d2-dR2lndR-lnd16l0d04lc
对于圆柱形的传动杆，有如下表达式：
Q=v⋅π4
式中v为速度。
对于传动杆单次运动，有如下表达式：
Δz=v⋅t
式中：Δz为传动杆单次运动的位移量，对应于脉冲波形电压；t为单次运动时间，对应于实验中脉冲波形上升沿项。
因此，微滴体积V可由式（6）进行积分得到，如式（9）所示：
V=∫0tQNdt=Δz⋅πdR2/41+d4-d04+d2-dR2lndR-lnd16l0d04lc+π8μlcd4-d04+d2-dR2lndR-lndPbt1+d4-d04+d2-dR2lndR-lnd16l0d04lc
整理可得：
V=2πμlcdR2d04Δz+πd04(d4-d04)Pbt(lndR-lnd)+πd04(d2-dR2)Pbt8μlcd04+128μl0(d4-d04)(lndR-lnd)+128μl0(d2-dR2)
杆距作为传动杆与坩埚底部之间的距离，可以通过传动杆两侧狭缝高度lc体现。由此可见，在同一尺寸微孔孔径下，传动杆单次运动排出液滴大小受脉冲波形中电压和上升沿、杆距以及差压的影响。
为方便后续讨论，根据工艺参数对粒子制备的影响，本研究将实验过程中各工艺参数分为喷射启动因素、粒径控制因素及喷射稳定因素三类，其中喷射启动因素对应能否喷射，粒径控制因素对应喷射液滴大小，喷射稳定因素对应液滴喷射过程中的束流状态。而基于上述的理论定性分析，可以发现液滴喷射过程中，主要的阻力是表面张力引起的Laplace力，而针对实验中同一种材料，影响表面张力的是熔体温度；当熔体与微孔材料间润湿角过大时，通过在熔体上方提供的一定的差压可促使微孔处液面达到稳定状态，以利于喷射。因此温度与差压可作为喷射启动因素。根据式（10），单个液滴大小则是受脉冲波形与杆距影响，因此将脉冲波形与杆距归为粒径影响因素。此外，杆距还会影响传动杆运动时微孔处熔体实际受力变化，这对喷射稳定性都会有影响，因此将杆距归为喷射稳定因素。
2 结果与分析
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2.1 工艺参数对微粒制备的影响
喷射启动因素主要包括熔体加热温度和差压。需要说明的是，在哈根泊肃叶模型中，差压会影响喷射液滴的大小，似乎应该属于粒径控制因素。然而在实际工作中发现，差压对喷射液滴大小的影响极小，而对液滴能否顺利稳定喷射却起到非常重要的影响，因此差压实际上属于喷射启动因素。同时，研究表明［33］，利用POEM制备金属液滴时，熔体与微孔处材料间润湿性这一物性参数非常重要。润湿角太小，会使得熔体铺展在微孔材料外表面而无法喷射；随着润湿角的增大，当润湿角达到90°及以上时，熔体在微孔处更倾向于缩回微孔内部，这有利于后续的液滴喷射，但润湿角也并非越大越好，当润湿角位于150°以上时，其微孔处液面始终处于不稳定状态，这对后续的稳定喷射有很大的影响，此时则需要外加差压用以消除这种不稳定区的存在。在本研究中，铜与石墨之间的润湿角为163°，在微孔处液面处于不稳定状态，因此需要施加一定的差压来消除影响。
而加热温度主要影响在坩埚内熔体的物性。若要达到液流喷射的效果，首要前提即是要满足冲破该熔体表面张力引起Laplace力的条件，而作为自身所具有的固有属性值，可以起到影响作用的就是熔体温度，根据公式（11）［34］：
σ=A1-TBn
式中：A、B、n均为常量，对于本研究使用的纯铜，A=1712.134，B=7000，n=1.206042；T为温度。由此可见，纯铜金属熔体的表面张力随着加热温度的增加而降低，在1085 ℃下，其表面张力值为1319.95 mN/m，而当温度加热至1200 ℃时，其表面张力值为1287.58 mN/m。因此，在金属熔点以上，随着加热温度的增加，其表面张力减小，液滴喷射受到的阻碍力减小，越容易实现液滴喷射。另外，加热温度不仅影响材料表面张力，同时还对熔体黏度产生影响，进而影响喷射启动。根据公式（12）［35］
lg(η/η0)=-a1+a2T
式中：η为黏度；η0、a1、a2均为常量，材料为纯铜时，η0=1 mPa·s，a1=0.4220，a2=1393.4 K。随着温度的上升，熔体的黏度值会相应减小，使得熔体的流动性大幅度提高，对于喷射启动也会有一定帮助。由于铜与坩埚间的高润湿角，需要施加一定的差压，促使微孔处液面稳定，以配合达到最佳喷射效果。此外，在液滴喷射过程中，坩埚内熔体随着杆的运动存在回流现象，此时熔体回流来不及补足下一次液滴的排出，可能会造成喷射不畅或是喷射断流的情况发生，而差压的存在则为避免这种情况提供了保障。
为了确定喷射启动中温度和差压的工艺窗口范围，设计了不同温度和差压下的喷射实验。在本实验中，分别设置了加热温度为1150、1175、1200、1225、1250 ℃，并在不同温度下分别设置不同差压，依次为0、2.0、4.0、6.0、8.0 kPa（杆距0.5 mm，脉冲波形为电压70 V上升沿100 μs，孔径为200 μm），如图3所示。
由图3可见，当差压值为4.0 kPa以下时，无论处于何种温度之下，都没有液滴喷射。当温度为1150 ℃时，分别在6.0 kPa和8.0 kPa下有液滴喷射，当温度为1200 ℃时，在4.0、6.0 kPa和8.0 kPa下都有液滴喷射，当温度为1250 ℃时，与1200 ℃时相同，在差压值为4.0、6.0 kPa和8.0 kPa时都有液滴喷射，由此可见，随着温度升高，熔体表面张力与黏度下降，喷射所需差压值相应降低；而当温度超过1200 ℃后，表面张力与黏度的变化趋于平缓，所需施加的最小差压值也随之稳定。因此，在制备纯铜液滴时，为获得最佳喷射条件，通常将温度设定为1200 ℃，并根据实际喷射效果，将差压值调至4.0 kPa或更高进行调试。
在粒径影响因素中，孔径是最主要的影响因素，微孔的尺寸很大程度决定了喷射液滴的粒径范围。然而有研究表明，利用同一孔径制备同一种材料的液滴时，仅依靠孔径难以精准控制喷射液滴大小，通常情况下，需要以孔径值为基准，协同脉冲波形（电压、上升沿）与杆距的调整，以此来获得更为精准的粒度，正如实验方法所描述的，改变了脉冲波形即是改变了传动杆的位移大小及运动快慢，对熔体的影响作用便是熔体破碎所获得的能量大小。在金属熔体中，黏滞阻力的存在使得传动杆向下运动过程中发生能量损耗，当传动杆的杆距较大时，传动杆的机械能在传递过程中随着杆距的增加而逐渐减小，使得微孔处所接收到的能量降低；相反，若传动杆的杆距较小时，能量传递所造成的衰减则会相应减少。
为探究比较脉冲波形中电压、上升沿以及杆距3个工艺参数的影响程度，设计了正交实验。本研究中考虑的主要测试因素是电压、上升沿与杆距，每个因素有3个水平（表2），并选择使用L9（33）正交表。
表3显示了正交实验分析结果，其中Ki （i=1，2，3）表示任一列上i水平所对应的实验结果之和；ki = Ki /s，s为任一列上i水平出现的次数，ki 表示任一列上i水平所对应的实验结果之和的平均值；此外，R为极差，R=Kj （max）－Kj （min），表示相应因素的影响程度。在表3中，RA （80.3）>RB （16.1）>RC （14.4），表明驱动电压对于粒子粒径大小的影响最大，脉冲波形上升沿和杆距的影响相近，远小于驱动电压的影响。
由正交实验结果分析可知，对粒径影响最显著的因素为驱动电压。为进一步探究电压对粒子粒径的影响，设计单一变量控制实验。在氩气保护下使用孔径200 μm的陶瓷片，保持差压4.42 kPa、上升沿50 μs和杆距0.45 mm参数不变，改变电压大小进行粒子制备，对收集的粒子进行粒径分析，结果如图4所示。
从图4中可以看出，粒子粒径随驱动电压的增大呈现单调递增的趋势。当驱动电压增大时，压电陶瓷变形增大；连接在压电陶瓷上的传动杆运动距离增加，排开液体的体积增大，即所制备的Cu粒子粒径增大。图4中误差棒体现了Cu粒子粒径的标准差，可以看到标准差随着驱动电压增加而增大，在30 V和35 V较低电压条件下制备的粒子分布更加均一，其原因在于电压增大后，作用于微孔处对金属熔体的扰动幅度过高，此时粒子形成和喷射过程不稳定，容易形成卫星滴，影响最终整体粒子的粒径分布均匀性，因此，在确保能够产生液滴的前提下，驱动电压宜采用较小值。
在探究对单一因素的影响时，同时也研究了上升沿对Cu粒子粒径的影响。以孔径为100 μm的陶瓷片在电压为70 V时改变上升沿制备Cu微粒，统计规律如图5所示。
从图5中可以看出，与之前理论计算的结果不同，实际中上升沿的影响并非与粒径大小呈正相关，因此针对这一情况进行了探讨。传动杆的运动将会产生两方面的效果，一方面，熔体会因挤压而从小孔处排出，在此前提下，受挤压排出的熔体体积会随时间的增加而增加，这与式（10）所呈现的相吻合；而另一方面，根据流体力学基本原理，传动杆以一定速度运动后急停，在传动杆的末端将产生压力波，压力波在熔体中传播到微孔处产生脉动压力，打破微孔处受力平衡，液滴从微孔处喷射而出。脉动压力的大小由传动杆的速度所决定，因此当电压一定，即位移大小不变时，若上升沿时间增加，也就是传动杆达到最大位移的时间增加，这会导致传动杆的运动速度减慢，此时传动杆运动所带来的脉动压力减小，熔体获得的能量也随之减小，所离散出的粒子获得的表面能减小，此时得到的微粒体积则会减小。式（10）为粒径控制提供了一定的指导意义，但由于实验结果与公式推导的理论分析结果存在部分差异，可以判断单纯使用哈根泊肃叶定律的挤压原理解释POEM液滴制备原理仍具有一定局限性，这可能是由于式（10）只是基于挤压产生微滴的原理进行推算，并未考虑传动杆运动引起的脉动压力波会在熔体中传播并对熔体进行扰动，最终离散产生微滴的情况。
与喷射启动因素、粒径控制因素所总结的依据不同，喷射稳定因素是依据实验调控过程中的实验现象得到的经验因素。理想状态下应该是持续稳定的单束直流（图6（a）），在该状态下所得到的微粒尺寸及圆球度都会更加均一；然而，在实验过程中，有时会出现图6（b）所示不稳定多束的情况，此时液滴无规地从微孔中离散出来，即使每束液滴尺寸一致，也很难保证多束液滴尺寸都一致，因此所得到的微粒尺寸差异较大。喷射的稳定性取决于过程中受力情况，而主要调节的工艺参数是杆距。当杆距不同时，传动杆引起的压力波传播到小孔附近形成的脉动压力有所不同。若杆距太大，压力波传播过程中由于损耗过大在微孔附近形成的脉动压力不足以打破此处的受力平衡，无法造成喷射；而在能够喷射时，存在稳定喷射的杆距范围，在范围域之外高于或低于单束喷射的最佳位置，都会使其出现偏差，造成喷射状态不稳定甚至不能喷射。
通过改变微孔孔径的单一变量法测试稳定喷射的杆距，如图7所示。可以看出，孔径为100 μm时，稳定喷射域为0.24~0.91 mm之间；孔径为200 μm时，其稳定喷射域为0.21~0.98 mm之间；孔径为300 μm时，其稳定喷射域为0.23~1.01 mm之间。由此可见，随着孔径的减小，其稳定喷射的杆距范围逐渐变窄，表明在小孔径下更难调控，与之相对应的，当脱离了稳定喷射域，束流会开始变得紊乱，因此，喷射过程中喷射稳定域的确定至关重要。
2.2 验证性实验分析
从以上分析及实验结果可以看出，分别通过对喷射启动影响因素、粒径控制影响因素及喷射稳定影响因素的调控，可以实现目标粒径微滴的稳定喷射。为了验证脉冲微孔喷射法对于制备目标粒径及较窄粒度分布铜微粒的可控性，在温度为1200 ℃、差压为4.5 kPa条件下，结合上述调控规律，针对铜微粒目标粒径为100 μm和200 μm的制备需求，对表1内的相关参数进一步进行选择，具体选取的实验工艺参数如表4所示。
从表4可以看出，通过对上述工艺参数的调整选择，成功制备出理想目标大小的Cu微粒，且其与目标粒径大小平均偏差不超过4 μm。图8显示了POEM制备的Cu微粒表面形貌及粒径分布，由图8（a）统计结果可得，目标粒径为100 μm的铜微粒，其平均粒径约为96.27 μm，标准偏差约为2.67 μm，球形度为0.95；由图8（c）统计结果可得，目标粒径为200 μm的铜微粒，其平均粒径约为200.69 μm，标准偏差约为2.64 μm，球形度为0.96。可以看出，所制备的Cu微粒表面光滑、圆球度高、粒径分布窄、标准偏差较小。通过调控上述参数，完全可精准控制粒径大小，实现对目标尺寸Cu微粒的稳定制备，且喷射效果良好。
3 结论
收起
（1）基于哈根泊肃叶公式，对微滴的控制因素进行了推导，其中脉冲波形和杆距对粒径的影响与POEM实际情况相吻合，但差压的作用、上升沿时间与粒径的关系与实际的实验情况存在差异，表明POEM并非单纯依靠哈根泊肃叶挤压理论喷射。
（2）Cu液滴能否顺利喷射主要受熔体温度所带来的不同表面张力、黏度以及控制熔体回流与差压大小的影响；在孔径一定时，粒径主要受驱动电压和上升沿时间以及杆距三者控制，从正交实验结果可确定，电压起主要作用，制备Cu粒子的粒径大小随电压增大而增加；喷射稳定因素主要受不同杆距引起的脉动压力影响，在杆距0.2~1.0 mm之间存在稳定喷射区。
（3）基于上述因素的影响规律，成功制备出目标尺寸的铜粒子，喷射效果良好，粒径分布较窄且均一可控，满足3D微电子封装对Cu核球的要求。
基金
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  • 国家自然科学基金项目(51571050)
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2026年第54卷第3期
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doi: 10.11868/j.issn.1001-4381.2024.000241
  • 接收时间：2024-04-02
  • 首发时间：2026-10-27
  • 出版时间：2026-03-20
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  • 收稿日期：2024-04-02
  • 录用日期：2024-05-16
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作者信息
    1.大连理工大学 材料科学与工程学院，辽宁 大连 116024
    2.陆军装甲兵学院 装备再制造技术国防科技重点实验室，北京 100072

通讯作者:

许富民（1969—），男，副教授，博士，主要从事单分散粉末制备及相关研究，联系地址：辽宁省大连市甘井子区凌工路2号大连理工大学新三束实验室208（116024），E-mail：
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2种不同金属材料的力学参数
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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