Thermal conductivity of flexible Cu-Ag composite thin films by laser direct writing
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摘要:
随着柔性电子产品对高效热管理的需求不断增长，近年来制备高导电性柔性薄膜越来越受到人们的广泛关注. 以聚酰亚胺(PI)为基底，采用激光直写技术制备铜(Cu)和铜-银(Cu-Ag)薄膜，并对制备的Cu-Ag薄膜进行了物相分析和结构表征. 结果表明，铜纳米颗粒和银纳米线在激光辐照的作用下表面局部熔化，进而烧结；通过比较直写制备的铜薄膜和Cu-Ag薄膜在不同温度下7 天内电阻的变化，得出银的引入提高了复合材料整体的抗氧化性；对Cu/PI和Cu-Ag/PI两种复合材料的热扩散系数和热导率进行测试，得出银的引入提高了复合薄膜的热导率，Cu-Ag/PI薄膜表现出比Cu/PI薄膜更好的热性能. 为制备具有良好热稳定性的Cu /PI和Cu-Ag /PI复合材料提供了一种快速简便、经济节约的方法.
Abstract:With the increasing demand of flexible electronic products for efficient thermal management, the preparation of flexible thin films with high conductivity has attracted more and more attention in recent years. Cu and Cu-Ag thin films are prepared by laser direct writing technique on polyimide (PI) substrate. The phase analysis and structure characterization of the two films show that the copper nanoparticles and silver nanowires are sintered by partial melting of their surface under laser irradiation. By comparing the resistance changes of prepared copper and Cu-Ag thin films at different temperatures for 7 days, it is concluded that the introduced silver improves the overall oxidation resistance of the composites. The thermal diffusivity and thermal conductivity of the two composites are tested, and it is found that the thermal conductivity of Cu-Ag/PI is significantly improved, showing better thermal performance than Cu/PI. This work provides a quick, simple and economical method for the preparation of Cu/PI and Cu-Ag/PI composites with good thermal stability.
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Keywords:
- laser direct writing /
- Cu thin film /
- Cu-Ag thin film /
- thermal conductivity
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0. 序言
目前，国内外主要使用射线探伤和常规超声波检测对扩散连接接头进行无损检测. 当扩散连接接头缺陷的尺寸为毫米级时，利用射线探伤和常规的超声波探伤即可实现接头的无损检测[1]，然而扩散连接接头缺陷的尺寸多为微米级[2]，利用射线探伤进行检测的难度相当大；对于扩散连接接头中存在的弱结合缺陷，常规的超声波探伤也无能为力. 在扩散连接接头质量评价领域，由于还没有可靠的无损检测方法，致使扩散连接技术的应用在一定程度上受到制约[3-4].
超声成像是利用超声波获得物体可见图像的一种无损检测方法，能够以图像的形式显示扩散连接界面结合质量[5-7]，目前在扩散连接接头质量检测领域中应用最为广泛的是超声C扫描技术. 通过超声C扫描，能够显示整个扩散界面上的缺陷及其分布，超声波回波信号反射比能够与扩散连接界面强度建立联系[8-9]. 超声C扫描一般采用点聚焦探头进行水浸检测，具备较高的检测灵敏度. Debbouz等人[10]通过超声C扫描成像技术对2017铝铜合金的扩散连接接头进行了无损检测，在扩散连接界面中夹入不同尺寸的钨丝以形成不同尺寸的缺陷，利用超声C扫描最终可检测出界面中25 μm的钨丝，并且发现扩散连接接头的强度与反射波高度的平均值相关，可以据此预测扩散连接质量. Kumar等人[8]利用超声C扫描设备对不同扩散连接工艺参数下获得的接头进行超声检测，发现超声C扫描技术能够在一定程度上识别焊合区和未焊合区. 刘永军等人[11]采用超声水浸扫描成像检测系统，检测出了TC4钛合金与1Cr18Ni9Ti不锈钢超塑性扩散连接界面的焊合率状况，与用金相和界面线扫描测出的界面缺陷分布情况具有较好的一致性. 叶佳龙等人[7]运用信号处理技术对扩散连接界面的超声非线性行为进行研究，将扩散连接界面的超声非线性图像与超声C扫描图像进行比较，研究结果表明，非线性超声检测对扩散连接界面处的弱结合缺陷比较敏感，能识别超声C扫描图像无法识别的弱结合缺陷.
尽管超声检测技术用于扩散连接界面缺陷的识别可以实现，但很少工作涉及到缺陷尺寸的评价. 文中旨在研究扩散连接界面缺陷的超声响应，建立缺陷尺寸与放射波信号的定量联系，通过无损检测手段实现缺陷尺寸的预测.
1. 界面缺陷尺寸预测模型
界面缺陷尺寸小于一定阈值时，超声波波长远大于缺陷尺寸，尺寸效应本身对超声波的反射和透射行为产生影响. 针对界面缺陷的超声响应，研究人员提出弹簧模型，模型中引入了界面劲度系数(K)的概念[12-15]. 所谓界面劲度系数，是指将界面缺陷等效为一弹簧层，类比弹簧劲度系数提出. 弹簧模型的表达式为[12-15]
$$ R=\dfrac{\left(\dfrac{{Z}_{1}-{Z}_{2}}{{Z}_{1}+{Z}_{2}}\right)\left(1-\dfrac{m{\omega }^{2}}{4K}\right)+i\omega \left[\dfrac{{Z}_{1}{Z}_{2}}{\left({Z}_{1}+{Z}_{2}\right)K}-\dfrac{m}{{Z}_{1}+{Z}_{2}}\right]}{\left(1-\dfrac{m{\omega }^{2}}{4K}\right)+i\omega \left[\dfrac{{Z}_{1}{Z}_{2}}{\left({Z}_{1}+{Z}_{2}\right)K}+\dfrac{m}{{Z}_{1}+{Z}_{2}}\right]}$$ (1) 式中：R为反射系数；Z1、Z2分别为声波入射一侧和另一侧介质的声阻抗kg/(m2·s)；m为界面缺陷的等效质量；ω为角频率(rad/s)；i =
$ \sqrt{-1}$ . 对于超声波垂直界面入射情况，考虑到界面缺陷为孔洞缺陷，假设性地忽略缺陷的质量，即m = 0. 对于同种材料扩散连接界面或声学性能相近的异种材料扩散连接界面，可以假设Z1 = Z2 = Z. 相应地，式(1)简化后的反射系数为$$ \left\{ \begin{array}{l} R = \dfrac{{\dfrac{{i\omega }}{\varOmega }}}{{1 + \dfrac{{i\omega }}{\varOmega }}} = \dfrac{{{\omega ^2}}}{{{\varOmega ^2} + {\omega ^2}}}{\rm{ + }}\dfrac{{\omega \varOmega }}{{{\varOmega ^2} + {\omega ^2}}}i\\ \varOmega {\rm{ = }}\dfrac{{2K}}{Z} \end{array} \right.$$ (2) 式中：Ω为本征频率(1/s). 根据式(2)，相应的反射系数幅值表示为
$$ \left\{\begin{array}{l}\left|R\right|=\sqrt{\dfrac{{\omega }^{2}}{{\varOmega }^{2}+{\omega }^{2}}}\\ \varOmega =\dfrac{2{K}}{{Z}}\end{array}\right.$$ (3) 通常，反射系数幅值|R|可以通过超声扫描数据处理获得. 然而，实际探头检测的超声反射波信号是含有不同频率成分的. 为实现上述要求，需要通过傅里叶转变将反射波信号进行分解，进而获得不同频率所对应的幅值. 同时，对于某一特定频率，需要找到某一全反射波在该频率下的幅值作为基准，那么任一缺陷反射波在该频率下的幅值与前述基准幅值的比值，即为反射系数幅值|R|.
考虑界面劲度系数K与界面微观缺陷尺寸之间的关系，Rokhlin和Wang [16]提出界面层厚度h的概念，并指出完全焊合时劲度系数K与界面层厚度h具有反比例函数关系
$$ K=\frac{\rho \left({c}_{\rm{l}}^{2}-{c}_{\rm{s}}^{2}\right)}{h}$$ (4) 式中：ρ为界面层材料密度；cl和cs分别为界面层材料中的纵波和横波声速；h为界面层厚度.
值得注意的是，式(4)仅在界面完全焊合时成立. 对于文中所涉及的扩散缺陷界面而言，材料的属性与母材一致，但未完全焊合区的缺陷深度尺寸并不能等价地代替式(4)中的h. 因此，提出等效缺陷界面厚度hequi的概念，即hequi = h − h0，则可得到
$$ K=\dfrac{\rho \left({c}_{\rm{l}}^{2}-{c}_{\rm{s}}^{2}\right)}{{h}_{\rm{equi}}}=\dfrac{\rho \left({c}_{\rm{l}}^{2}-{c}_{\rm{s}}^{2}\right)}{h-{h}_{0}}$$ (5) 式中：h更广义地指代缺陷界面厚度；h0为基准界面厚度. 由此，根据式(3)和式(5)，即可采用K作为媒介，建立超声反射系数与界面微观缺陷之间的联系，同时超声检测中的频率f = ω/2π，由此可得
$$ {\text{π}} fZ\sqrt{\frac{1}{{\left|R\right|}^{2}}-1}=K=\frac{\rho \left({c}_{\rm{l}}^{2}-{c}_{\rm{s}}^{2}\right)}{h-{h}_{0}}$$ (6) 2. 试验结果
为定量研究缺陷超声响应，需要制备带有人工缺陷的扩散连接试样. 采用两块1 mm的Ti-6Al-4V合金板材进行扩散连接，向两块板材之间添加厚0.1 mm，宽20 mm的Ti-6Al-4V箔片，扩散连接工艺参数为900 ℃，10 MPa，15 min，最终获得的试样在箔片两侧会自然地形成厚度逐渐减小的楔形界面缺陷.
人工缺陷试样如图1所示，中央两虚线之间为添加了箔片的区域，左侧A ~ F线为微观观察位置，相应的界面缺陷如图2所示，可见各处缺陷均为预想的楔形，但缺陷长度不一. 针对人工缺陷试样的超声无损检测采用水浸聚焦超声检测系统，超声探头中心频率采用30 MHz.
传统超声C扫描图像如图3所示，据此可以判定图中红色区域为缺陷区，但无法体现缺陷的尺度. 为此，提出了超声脉冲反射法中缺陷反射信号的分析模型，模型采用界面劲度系数K作为媒介，建立超声反射系数与界面微观缺陷之间的联系. 通过人工缺陷试样超声扫描数据的后处理分析和利用破坏性试验分析特定位置的实际微观缺陷尺寸来确定模型参数，最终实现基于超声扫描的界面缺陷尺寸评估. 针对入射波为30 MHz的超声扫描数据进行分析时，首先需要在一对始波和底波之间设置闸门，对闸门区间内的超声反射波信号作离散傅里叶变换，从而获得所有扫描点频域信号在30 MHz处的幅值. 然后，需要将幅值分布转化为反射系数分布，由于试样中存在明显的缺陷，假设最大幅值点的反射系数为1，其幅值为Aref，那么对于其它幅值数据点，其反射系数为
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图 3 入射波频率为30 MHz时的超声C扫描图像Figure 3. Ultrasonic C-scan image with incident wave frequency of 30 MHz$$ {R}_{x,y}=\frac{{A}_{x,y}}{{A}_{\rm{ref}}}$$ (7) 式中：Ax,y和Rx,y分别为坐标为(x, y)的扫描点在特定入射波频率下的幅值和反射系数. 针对每一个扫描点采用式(7)进行计算，即获得反射系数在整个扫描域内的分布情况. 进一步根据式(6)计算界面劲度系数K，其中f取值30 MHz，Z取值参考钛单质的声阻，取为27.3 × 106 kg/(m2·s) = 27.3 MRayls[17]. 计算所得的扫描域内劲度系数数值分布如图4所示，由于试样内外区域K值相差多个数量级，为更好地展示数据，对K取常用对数后再作图.
通过频谱分析的方式获得了界面劲度系数的分布情况，后续需建立缺陷尺寸与界面劲度系数的联系. 为此，采用破坏性金相检测方法，对图1中C所表示的直线位置微观缺陷高度进行测量，图5显示了距离楔形缺陷端部2 000 ~ 10 000 μm区间内的缺陷高度测量结果. 相应地，从图4提取C所对应位置处相同距离区间内的界面劲度系数K的数值分布，如图6所示. 根据式(5)，通过最小二乘回归拟合方式确定待定常数h0. 其中：ρ = 4.48 × 103 kg/m3；cl = 6.1 × 103 m/s；cs = 3.1 × 103 m/s (单质钛的材料属性[17]). 根据拟合结果，h0 = −2.55 × 10−5 m.
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图 5 缺陷高度随距离的变化(楔形缺陷端部为0点)Figure 5. Dependence of defect height on the distance (the end of wedge-shaped defect was set as zero point)![]()
图 6 界面劲度系数随距离的变化(楔形缺陷端部为0点)Figure 6. Dependence of interfacial stiffness coefficient on the distance (the end of wedge-shaped defect was set as zero point)确定了模型常数后，即可获得缺陷高度尺寸在扫描域内的分布，如图7所示. 可以看到，该三维分布图非常直观地展示了缺陷的位置及其高度尺寸，这为扩散连接件界面缺陷的无损检测提供了良好的解决方案.
按图4中C所对应位置比较测量和预测的缺陷高度随距离的变化，如图8所示(预测值从图7中提取得到)，显然，两者吻合良好，表明根据数值预测模型能够实现缺陷高度的预测，也证实前述采用图7将缺陷高度可视化的可行性.
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图 8 测量和预测的缺陷高度随距离的变化对比(楔形缺陷端部为0点)Figure 8. Dependence of measured and predicted defect height on the distance (the end of wedge-shaped defect was set as zero point)3. 结论
(1)根据人工缺陷试样的超声响应，利用超声C扫描设备有效检测和识别了扩散连接缺陷，采用30 MHz入射波频率时能够识别微米级界面缺陷.
(2)提出了未焊合缺陷的超声响应模型，利用扩散连接界面劲度系数建立超声反射系数与界面微观缺陷尺寸之间的定量联系，在缺陷高度尺寸三维分布图中可直观地展示扫描域内缺陷位置及其高度尺寸，验证了界面缺陷高度可视化的可行性，为扩散连接缺陷的无损检测提供了良好的解决方案.
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图 1 激光直写制备 Cu-Ag 薄膜过程示意图
Figure 1. Process of fabricating composite thin films by laser direct writing
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图 2 Cu和Cu-Ag薄膜数码照片以及Cu-Ag薄膜光镜形貌
Figure 2. Images of Cu and Cu-Ag thin films, and OM images of Cu-Ag thin films. (a) image of Cu thin film; (b) image of Cu-Ag thin film; (c) OM images of Cu-Ag thin film
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图 3 复合薄膜的XRD图谱和XPS图
Figure 3. XRD spectra and XPS spectra of different composite thin films. (a) XRD spectra of Cu and Cu-Ag thin films; (b) Cu 2p3/2 spectra; (c) Ag 3d spectra; (d) O 1s spectra
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图 4 Cu薄膜和Cu-Ag薄膜的SEM形貌
Figure 4. SEM images of Cu and Cu-Ag thin films. (a) SEM images of Cu thin films; (b) SEM image of lasal microstructure about Cu thin films; (c) SEM images of Cu-Ag thin films
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图 6 Cu-Ag复合薄膜的TEM图
Figure 6. TEM images of Cu-Ag composite thin films: (a) interface of Cu-Cu; (b) typical single Ag nanowire; (c) TEM images of typical single Ag nanowire; (d) interface of Cu-Ag
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图 7 Cu /PI和Cu-Ag/PI复合薄膜的导热特性
Figure 7. Thermal properties of Cu /PI and Cu-Ag/PI composite thin films. (a) relative resistance changes of Cu and Cu-Ag composite film at different temperatures; (b) thermal diffusion coefficient and thermal conductivity of different materials; (c) thermal images of ceramic heater on Cu-based/PI composite films
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