Improved model and experimental study of laser-induced damage in multilayer dielectric films
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摘要:目的
多层介质薄膜的结构会调制光场，因此在研究激光诱导损伤特性时，有必要考虑薄膜体系内部的能量分布以及由此引起的材料光学性质变化。
方法以 HfO2/SiO2多层介质薄膜结构为例，基于激光诱导电离/电子倍增过程，在光场计算中引入Drude模型，将膜层折射率由静态常数扩展为由自由电子密度驱动的动态复折射率。在此基础上耦合热传导（及热应力）模型，计算纳秒脉冲激光作用下薄膜内部的热效应演化，并求得相应的损伤阈值为13.65 J/cm2，同时开展实验研究其损伤特性。
结果验证实验观察到HfO2/SiO2多层介质薄膜的损伤形貌为圆孔状，属于典型的热熔融型损伤，测得的损伤阈值13.75 J/cm2略高于理论分析结果，与理论模型结论吻合。
结论本文建立的改进模型有助于从理论层面进一步分析强激光与多层介质薄膜的相互作用，并更好地研究光学薄膜的抗损伤能力。
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关键词:
- HfO2/SiO2多层介质膜 /
- 场致效应 /
- Drude模型 /
- 热力耦合 /
- 损伤阈值
Abstract:ObjectiveThe structure of multilayer dielectric film will modulate the optical field, thus in the study of laser-induced damage characteristics, it is necessary to consider the energy distribution within the film system and the resulting changes in material optical properties.
MethodTaking the HfO2/SiO2 multilayer dielectric film structure as an example, and based on the laser-induced ionization/electron multiplication process, the Drude model is introduced into the optical field calculation, extending the film layer refractive index from a static constant to a dynamic complex refractive index driven by the free electron density. Based on this, a thermal conduction (and thermal stress) model is coupled to calculate the evolution of thermal effects inside the thin film under nanosecond pulsed laser irradiation, and the corresponding damage threshold is determined to be 13.65 J/cm2, and the damage characteristics of the film are studied experimentally.
ResultThe verification experiment observed that the damage appearance of the HfO2/SiO2 multilayer dielectric film is a round hole type, which is a typical thermal melting damage, and is consistent with the conclusion of the theoretical model. The measured damage threshold is 13.75 J/cm2, which is only higher than the theoretical analysis result.
ConclusionThe improved model established is helpful to further analyse the interaction between strong laser and multilayer dielectric film from the theoretical level, and to better study the damage resistance of optical thin film.
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Key words:
- multilayer dielectric films /
- field effect /
- Drude model /
- thermal-stress coupling /
- damage threshold
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图 1 激光辐照下多层介质膜的理论模型
Figure 1. Theoretical model of multilayer dielectric films under laser irradiation
图 2 波长
1064 nm激光辐照下膜内的光场强度分布Figure 2. Optical field intensity distribution inside the film under
1064 nm laser irradiation
图 3 波长
1064 nm激光辐照下膜内各参数变化趋势。(a) 电场沿深度分布；(b) 自由电子数密度沿深度分布；(c) 折射率实部沿深度分布；(d) 折射率虚部沿深度分布；(e) 电场随时间变化；(f) 自由电子数密度随时间变化Figure 3. Variation of film parameters under
1064 nm laser irradiation. (a) Electric field distribution along depth; (b) Free electron density distribution along depth; (c) Real refractive index distribution along depth; (d) Imaginary refractive index distribution along depth; (e) Electric field variation over time; (f) Free electron density variation over time.
图 4 波长355 nm激光辐照下膜内电场沿深度分布
Figure 4. Optical field intensity under 355 nm laser irradiation (Drude-Improved vs. Initial)
图 5 脉宽7 ns的纳秒激光辐照下薄膜内的温度变化曲线。(a) 薄膜中心处轴向温度变化曲线；(b)温度最高点随时间的变化曲线
Figure 5. Temperature variation curves within the film under 7ns laser irradiation. (a) Axial temperature variation curve at the center of the film; (b) Temperature peak variation curve over time.
图 6 纳秒激光脉冲辐照下膜内热应力场分布。(a)径向应力；(b)环向应力；(c)轴向应力
Figure 6. Thermal stress distribution within the film under laser pulse irradiation. (a) Radial stress; (b) Hoop stress; (c) Axial stress
图 7 纳秒激光脉冲辐照下膜层的最大热应力场分布 (a) HfO2膜层 (b) SiO2膜层
Figure 7. Maximum thermal stress distribution within the film irradiated by laser pulses (a) HfO2 (b) SiO2
图 9 不同激光能量辐照后膜层的损伤形貌。(a)激光能量密度12.5 J/cm2；(b)激光能量密度14.5 J/cm2；(c)激光能量密度20.0 J/cm2；(d)激光能量密度5.0 J/cm2；(e)激光能量密度30.0 J/cm2
Figure 9. Damage morphology within the film after irradiation with different laser energies (a) Laser energy density 12.5 J/cm2; (b) Laser energy density 14.5 J/cm2; (c) Laser energy density 20.0 J/cm2; (d) Laser energy density 5.0 J/cm2; (e) Laser energy density 30.0 J/cm2
Parameter Symbol HfO2 SiO2 Band gap $ {E}_{g}/({\mathrm{eV}}) $ 5.5 7.8 Effective electron mass $ m/({10}^{-31}{\mathrm{kg}}) $ 0.39×9.11 0.50×9.11 Electron saturated drift velocity $ {v}_{s}/({10}^{5}\;{\mathrm{m}}\cdot {{\mathrm{s}}}^{-1}) $ 2.0 2.0 Refractive index $ {n}_{0} $ 1.97 1.45 Heat capacity*Density $ \rho c/({10}^{6}\;{\mathrm{J}}\cdot {{\mathrm{m}}}^{-3}\cdot {{\mathrm{K}}}^{-1}) $ 4.65 2.10 Thermal conductivity $ K/({\mathrm{W}}\cdot {{\mathrm{m}}}^{-1}\cdot {{\mathrm{K}}}^{-1}) $ 2.0 1.19 Melting point $ T/({\mathrm{K}}) $ 3073 1997 Young’s modulus $ \gamma /({10}^{10}\;{\mathrm{Pa}}) $ 24.0 8.7 Thermal coefficient of expansion $ \beta /({10}^{-6}\;{{\mathrm{K}}}^{-1}) $ 5.6 0.5 Poisson’s ratio $ \nu $ 0.27 0.17 
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