绝缘材料

实验条件	R²	实验条件	R²
0.5 kHz	0.89	30 kHz	0.75
1.0 kHz	0.90	10 kHz-SW	0.90
10 kHz	0.95	15 kHz-SW	0.92
15 kHz	0.93	30 kHz-SW	0.93
20 kHz	0.96	—	—

实验条件	R²	实验条件	R²
0.5 kHz	0.89	30 kHz	0.75
1.0 kHz	0.90	10 kHz-SW	0.90
10 kHz	0.95	15 kHz-SW	0.92
15 kHz	0.93	30 kHz-SW	0.93
20 kHz	0.96	—	—

性能	硅凝胶
弹性模量/MPa	<10
正电子湮灭时间/ns	>3
陷阱密度(室温)/m³	～10²⁰
主要化学键	硅氧键、碳硅键

性能	硅凝胶
弹性模量/MPa	<10
正电子湮灭时间/ns	>3
陷阱密度(室温)/m³	～10²⁰
主要化学键	硅氧键、碳硅键

实验条件	R²	实验条件	R²
50 Hz-120 ns ^(a)	0.89	5 kHz ^(c)	0.89
50 Hz-90 ns ^(a)	0.99	5 kHz ^(d)	0.95
50 Hz-110 ns ^(a)	0.99	10 kHz ^(d)	0.93
11 kV ^(b)	0.88	15 kHz ^(d)	0.97
13 kV ^(b)	0.90	20 kHz ^(d)	0.98
16 kV ^(b)	0.99	45℃ ^(e)	0.91
18 kV ^(b)	0.87	70℃ ^(e)	0.90
200 Hz ^(c)	0.88	120℃ ^(e)	0.94
1 kHz ^(c)	0.92	150℃ ^(e)	0.89

实验条件	R²	实验条件	R²
50 Hz-120 ns ^(a)	0.89	5 kHz ^(c)	0.89
50 Hz-90 ns ^(a)	0.99	5 kHz ^(d)	0.95
50 Hz-110 ns ^(a)	0.99	10 kHz ^(d)	0.93
11 kV ^(b)	0.88	15 kHz ^(d)	0.97
13 kV ^(b)	0.90	20 kHz ^(d)	0.98
16 kV ^(b)	0.99	45℃ ^(e)	0.91
18 kV ^(b)	0.87	70℃ ^(e)	0.90
200 Hz ^(c)	0.88	120℃ ^(e)	0.94
1 kHz ^(c)	0.92	150℃ ^(e)	0.89

高压下低介电硅凝胶电树枝生长模型及抑制方法研究

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张闯 , 张景程 , 安若萌 , 刘子曦 , 郭凌岐 , 王诗航 , 李盛涛 ^*

绝缘材料 | 2026,59(6): 170-176

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绝缘材料 | 2026 , 59 (6) : 170 -176

高压下低介电硅凝胶电树枝生长模型及抑制方法研究

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张闯, 张景程, 安若萌, 刘子曦, 郭凌岐, 王诗航, 李盛涛^*

作者信息

西安交通大学电气工程学院，陕西　西安　710049

通讯作者:

李盛涛（1963-），男（汉族），陕西西安人，教授，主要从事电介质理论及其应用、电气功能材料及器件、极端条件下的绝缘材料和绝缘技术等方面研究。

作者简介:

张闯（1993-），男（汉族），安徽蚌埠人，助理教授，主要从事高压大功率器件封装绝缘材料开发及评估、变频绝缘失效机理与性能提升方法等方面研究

Research on growing model and suppression methods of electrical tree in silicone gel with low dielectric constant and loss

Chuang ZHANG, Jingcheng ZHANG, Ruomeng AN, Zixi LIU, Lingqi GUO, Shihang WANG, Shengtao LI^*

Affiliations

College of Electrical Engineering, Xi′an Jiaotong University, Xi′an 710049, China

出版时间: 2026-06-20 doi: 10.16790/j.cnki.1009-9239.im.2026.06.017

文章导航

摘要

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硅凝胶是高压大功率半导体器件用关键低介电低介损绝缘材料之一，极易因高频高压高温等严苛工况引发电树枝。然而，现有研究对硅凝胶电树枝生长模型和抑制方法研究不足，阻碍了高压大功率器件的进一步发展。本文基于断键-自愈理论构建了硅凝胶电树枝生长模型，并通过高频电树枝生长与抑制实验验证了上述模型的准确性。结果表明：随着加压时间增加，断键速率（R_b）和自愈速率（R_s）共同调节硅凝胶电树枝发展过程：当R_b>>R_s时，电树枝快速生长；当R_b稍大于R_s时，电树枝缓慢生长；当R_b<R_s时，电树枝停滞生长。高频正弦/方波电压下硅凝胶中电树枝呈现“阶梯状”发展特征，与本文所提述模型相符。此外，结合文献中已有数据，进一步阐释本文所提硅凝胶电树枝生长模型能普遍适用于不同电压波形、温度等驱动因素作用的情形。提出了紫外吸收剂掺杂抑制电树枝发展的方法，采用放电发光光谱和激光共聚焦荧光显微表征证实了所提方法的有效性。本研究可为高压大功率封装绝缘的进一步发展提供理论依据与实验参考。

关键词

硅凝胶 / 电树枝 / 生长模型 / 自愈 / 抑制 / 高压

Abstract

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As one of the critical insulating materials with low dielectric constant and low dielectric loss for high-voltage and high-power semiconductor devices, silicone gel is highly prone to electrical treeing degradation due to severe operating conditions of high frequency, high voltage, and elevated temperatures. However, existing researches have no enough comprehensive investigations into the growing models and suppression methods of electrical tree in silicone gel, impeding further advancement in high-voltage and high-power devices. This paper established a growing model for electrical tree in silicone gel based on the theory of bond-breaking and self-healing, and validated the accuracy of the model through electrical tree growth and inhibition experiments under high-frequency sinusoidal and bipolar square wave voltage. The results demonstrate that the bond-breaking rate (R_b) and self-healing rate (R_s) collectively regulate the development of electrical tree in silicone gel as the voltage application time increases: when R_b>>R_s, electrical tree grows rapidly; when R_b is slightly greater than R_s, electrical tree exhibits slow growth; when R_b<R_s, electrical tree propagation stagnates. It is indicated that electrical tree in silicone gel under high-frequency sinusoidal or square wave voltages exhibit a stepped propagation characteristic, which aligns with the proposed model. Furthermore, combined with existing data in literature, it is further illustrated that the proposed growth model of electrical trees in silicone gel can be universally applicable to the scenarios driven by different driving factors such as voltage waveforms and temperatures. A method of doping ultraviolet absorber into silicone gel is proposed to suppress electrical tree development. The effectiveness of this method is confirmed through discharge luminescence spectroscopy and laser confocal fluorescence microscopy characterization. This study provides theoretical foundations and experimental references for the further development of high-voltage and high-power encapsulation insulation.

Key words

silicone gel / electrical tree / growth model / self-healing / suppression / high voltage

引用本文

张闯, 张景程, 安若萌, 刘子曦, 郭凌岐, 王诗航, 李盛涛. 高压下低介电硅凝胶电树枝生长模型及抑制方法研究. 绝缘材料, 2026 , 59 (6) : 170 -176 . DOI: 10.16790/j.cnki.1009-9239.im.2026.06.017

Chuang ZHANG, Jingcheng ZHANG, Ruomeng AN, Zixi LIU, Lingqi GUO, Shihang WANG, Shengtao LI. Research on growing model and suppression methods of electrical tree in silicone gel with low dielectric constant and loss[J]. Insulating Materials, 2026 , 59 (6) : 170 -176 . DOI: 10.16790/j.cnki.1009-9239.im.2026.06.017

正文

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0　引言

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新型电力系统以新能源为供给主体，是推进能源战略安全与可持续发展的关键技术支撑，具有高比例电力电子设备、高比例新能源的“双高”特征，对其安全稳定运行至关重要^[1]。然而，诸如高压大功率半导体器件等电力电子设备绝缘需承受高压高频高温等严苛工况，极易发生绝缘劣化甚至失效^[2]。硅凝胶是高压大功率半导体器件的关键低介电低介损封装绝缘材料，其绝缘劣化特性与机理受到学术界与工业界的广泛关注^[3-5]。电树枝是硅凝胶绝缘劣化的重要形式，一旦引发电树枝，将严重威胁设备安全^[6]。国内外学者研究了脉冲^[7]、直流^[8]、工频^[9-10]、单极性方波^[11-12]、双极性方波^[13]、高频正弦^[13-15]等多种波形电压和不同温度^{[13, 16]}下硅凝胶的电树枝生长特性，得到如下共识：①硅凝胶电树枝存在自愈特性，即电树枝发展过程中同时存在通道扩展与愈合的动态特征；②硅凝胶电树枝呈现快速生长-滞长或缓慢生长的阶梯式两段生长特征；③硅凝胶电树枝存在显著的频率依赖特征，随施加电压频率的增加，电树枝发展速度加快且长度增加。

然而，现有研究尚未完全揭示硅凝胶电树枝发展的物理过程，仍未获得不同电压波形和温度下硅凝胶电树枝生长模型，不能从失效机理的角度构建提升硅凝胶耐电树枝能力的方法。因此，本文基于聚合物断键与修复的动力学模型，构建硅凝胶电树枝生长模型，通过实验验证所提模型的准确性，并进一步通过文献数据证实该模型的普适性。基于硅凝胶电树枝生长模型的断键抑制，提出了紫外吸收剂掺杂的方法来抑制硅凝胶电树枝生长。本研究可为进一步认知高压大功率封装绝缘失效机制及性能提升方法提供理论与实验基础。

1　硅凝胶电树枝生长建模与实验

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1.1　硅凝胶中电树枝生长模型的建立

T LEWIS等^[17]提出介质在垂直于电场方向的电应力作用下会产生扩展的断键通道，同时由于热力学的驱动，这些断键会有部分愈合。硅凝胶电树枝存在明显的断键和愈合现象，因此建立硅凝胶电树枝生长模型如下。

由于硅凝胶电树枝存在生长和自愈动态共存的特征（如图1所示）^[7,10]，且硅凝胶弹性模量很低，分子链运动活性很强，几乎无法存储从电场获得的大量能量，其能量释放较快。因此采用动力学模型对电树枝生长进行分析，如式（1）所示。

d m d t = R b · (M - m) - R s · m

（1）

式（1）中：m为已断裂化学键数；M为未断裂化学键数；R_b为化学键断裂速率，s^-1；R_s为化学键恢复速率，s^-1。

对上式进行变换，令n=m/M并代入式（1），可得式（2）。

d n d t = R b · (1 - n) - R s · n

（2）

将初始条件t=0、n=0代入式（2），可得式（3）。

n = R b R b + R s · {1 - e x p [- (R b + R s) · t]}

（3）

1.2　硅凝胶中电树枝生长实验与表征

1.2.1　试样制备

由于硅凝胶黏度高且质软，不易脱模，本文采用开口式模具浇注的方法制备硅凝胶电树枝试样，如图2所示。将硅凝胶固化用原材料A组分和B组分（Caster 1010）按照质量比为1∶1进行混合搅拌后抽真空15 min，然后浇注进装配好的开口透明模具内，将其置于烘箱中60℃下保温12 h即可获得电树枝试样。其中，针电极直径为0.3 mm，针尖曲率半径为3 μm，针电极到地电极距离约为2 mm。紫外吸收剂选用商用UV-1（N-(乙氧基羰基苯基)-N′-甲基-N′-苯基脒），在制作硅凝胶电树枝试样时将紫外吸收剂与A、B组分一起共混即可制得掺杂紫外吸收剂的待测。

1.2.2　实验平台与表征方法

为通过实验研究本文所提硅凝胶电树枝生长模型的准确性，建立了高频正弦/双极性方波电压作用下硅凝胶电树枝的测试平台，如图3所示，组合电源可输出电压幅值为±12 kV、频率为50 Hz～30 kHz的高频方波/正弦电压，相机可实现电树枝形貌记录与统计分析，采用所提模型对不同电压波形作用下硅凝胶电树枝长度-时间关系进行拟合。

通过光纤光谱仪研究掺杂紫外吸收剂前后硅凝胶电树枝发光光谱特征，光纤光谱仪通过光纤集束探头汇聚直径约为10 mm范围内的光谱，加压测试前先采集背景光谱，之后用测试光谱扣除背景光谱后即为因电树枝通道放电发光产生的光谱。采用激光共聚焦表征硅凝胶电树枝劣化的微观结构。

2　结果与讨论

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2.1　高频电压下硅凝胶中电树枝生长特征

图4为采用式（3）拟合本文实验中归一化电树枝长度的结果，拟合度R²如表1所示。其中，10 kHz表示频率为10 kHz的方波电压，10 kHz-SW表示频率为10 kHz的正弦电压，其他依此类推。从图4及表1可以看出，除30 kHz双极性方波电压下电树枝生长后期不符合该模型外（R²为0.75），高频正弦和宽频双极性方波电压下电树枝长度的时间依赖特征皆符合本文所提模型，拟合度均在0.89以上。这是因为30 kHz双极性方波电压下电树枝生长过程中不存在停滞过程，而是快速生长后再缓慢生长直至击穿。

放电发光测试表明硅凝胶中局部放电主要发生在电树枝主通道内，这归因于硅凝胶电树枝通道的非导电性^[13]。电树枝生长主要是膨胀应力导致的基体撕裂，电树枝尖端发光强度较弱，导致电树枝持续发展的动力下降^[13]。在快速生长阶段，R_b>>R_s，说明断键占据主导；在滞长阶段，R_b<R_s，电树枝长度不再变化，即dn/dt=0；在缓慢生长阶段，R_b稍大于R_s。

进一步分析发现，在硅凝胶电树枝快速生长阶段以后，高频（30 kHz）双极性方波电压作用下电树枝缓慢生长可能是因为在高频下局部放电更强，使得电树枝通道导电性增强，电树枝尖端场强较低频下更高，能够发生有限的局部放电。此时，R_b略大于R_s，电树枝生长过程可划分为快速生长和缓慢生长两个阶段，其中快速生长阶段时间为t₀，对应n值为n₀，由式（3）可得式（4）。

n = 12 {1 - e x p [- 2 R b · (t - t 0)]} + n 0

（4）

针对30 kHz双极性方波电压作用下电树枝生长的时间依赖特性，本文试验得到t=t₀=10 s时，n₀=0.53，此时为快速生长至缓慢生长的拐点，将这两个参数代入式（4）并对图4(a)中数据进行拟合，可得图4(b)，可见所提模型依然可与实验数据相吻合。

表2为与电树枝特性相关的硅凝胶主要性能参数。由于硅凝胶弹性模量低，电应力导致的分子链位移效应在不同电压频率间差异不明显，电树枝发展主要体现为局部放电的作用。局部放电使得电树枝通道内压强增大，聚合物基体承受膨胀应力，因此基体材料的弹性模量会影响其抵抗电树枝扩展的能力。弹性模量越低，抵抗能力越弱，产生裂纹的路径也就越多，表现为丛状电树枝的出现。

此外，正电子湮灭时间越长，聚合物内自由体积越大。由表2可知，硅凝胶的正电子湮灭时间> 3 ns，说明其自由体积较一般聚合物更大^[18-19]，因此其电子平均自由程增加，电子能量增大，碰撞电离和电荷复合强度增加^[20]，表现为放电发光光谱集中于近紫外段，其释放的光子能量更高，产生的热电子能量也更高，因而基体降解更加严重，产生的气体压强更高^[13]。硅凝胶通过膨胀撕裂使得电树枝尖端累积的能量在短时间内不断向周围耗散，造成电树枝快速发展，之后由于树枝通道内电场强度随电树枝长度增加而下降明显，无法维持持续断键，表现为快速生长后的停滞。

2.2　电树枝生长模型的进一步验证

为进一步验证本文所提模型的准确性，统计了不同文献中不同电压波形、温度下硅凝胶电树枝生长的时间依赖特征^[7,11-12,16]。统计的文献中硅凝胶电树枝生长主要呈现两类特征：一是快速生长至最大长度后维持该长度不变，依然呈现“阶梯状”生长特征；二是先快速生长至一定长度后再缓慢生长至最大值。由于硅凝胶的自愈特征，导致归一化电树枝长度存在大于1的情形，与本文实验结果类似，但不影响整体变化趋势。提取数据，采用本文所提出模型对其进行拟合，结果如图5所示，拟合度列于表3。

从表3可以看出，大部分文献实验条件下的拟合度在0.90以上，少部分文献实验条件下的R²位于0.87～0.89，这归因于硅凝胶动态生长特性和放电随机性。以上结果表明，本文所提硅凝胶电树枝生长模型适用于不同电压波形、温度等作用下硅凝胶电树枝生长的时间依赖特征，普适性较高。

2.3　基于硅凝胶断键抑制的电树枝抑制方法

由上述模型可知，硅凝胶断键过程对电树枝生长过程影响显著，即若能降低R_b，则可以显著抑制硅凝胶电树枝生长。已有研究表明，硅凝胶电树枝生长受电树枝通道内放电发光主导，而硅凝胶放电发光集中于近紫外波段^[13]。因此，本文提出通过掺杂紫外吸收剂抑制硅凝胶电树枝发展的方法。

本文掺杂的紫外吸收剂为N-(乙氧基羰基苯基)-N′-甲基-N′-苯基脒，制备了质量分数为0.3%、0.5%、0.7%、1%的4种掺杂量的硅凝胶复合电树枝试样，然后在5 kV、10 kHz双极性方波电压下进行电树枝生长实验。图6为添加不同含量紫外吸收剂后硅凝胶电树枝的激光共聚焦显微成像。

从图6可以看出，添加紫外吸收剂后电树枝生长过程受到明显抑制，表现为电树枝由枝状转变为浓密丛状，电树枝侵蚀区域减少，这源于紫外吸收剂对高能光子的吸收作用。为定量研究紫外吸收剂添加量对硅凝胶电树枝的影响，提出通过图像识别和像素点数统计的方法对激光共聚焦显微成像图片进行灰度化处理并统计电树枝劣化区域的长度/宽度，如图7所示，统计结果如图8所示。

从图8可以看出，随着紫外吸收剂含量的增加，对电树枝的抑制效果呈先上升后下降的趋势，当紫外吸收剂质量分数为0.7%时，对电树枝的抑制效果最好。这是因为较少紫外吸收剂对紫外光子的吸收作用有限，而较多的紫外吸收剂可能会导致硅凝胶交联不充分，降低耐电树枝能力。

为进一步揭示紫外吸收剂抑制硅凝胶电树枝生长的物理机制，研究了5 kV、10 kHz双极性方波电压下不同紫外吸收剂含量的硅凝胶电树枝通道发光特性，结果如图9所示。

由图9可知，添加紫外吸收剂后，硅凝胶复合试样对紫外波段（370 nm以下）的光吸收作用明显加强，尤其是当紫外吸收剂质量分数大于0.3%后，紫外波段光近乎全部吸收，表明局部放电和放电发光强度降低，由此产生的膨胀撕裂效应被抑制，因而电树枝劣化程度显著降低。

3　结论

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（1）基于断键-自愈理论构建了硅凝胶电树枝生长模型，断键速率和自愈速率的相对大小决定了硅凝胶电树枝生长特征。本文所提生长模型适用于不同电压波形、温度等实验条件下的硅凝胶电树枝发展特性。

（2）高频正弦/方波电压下硅凝胶中电树枝呈现快速生长后停滞或快速生长后缓慢生长至停滞/击穿的“阶梯状”发展特征。这主要因为硅凝胶具有较大的自由体积、较低的弹性模量和较大的电子湮灭时间等特征。

（3）本文提出了紫外吸收剂掺杂抑制硅凝胶电树枝发展的方法。结果表明，随紫外吸收剂掺杂量的增加，电树枝抑制能力先上升后下降，放电发光光谱和激光共聚焦荧光显微表征证明了上述结论。

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2026年第59卷第6期

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doi: 10.16790/j.cnki.1009-9239.im.2026.06.017

接收时间：2025-09-15
首发时间：2026-09-10
出版时间：2026-06-20

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收稿日期：2025-09-15
修回日期：2025-11-11

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西安交通大学电气工程学院，陕西　西安　710049

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2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
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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