多层红外光学薄膜的热应力分析
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摘要
通常红外光学薄膜是在较高温度下制备得到的。在低温下应用时,其产生的热应力会显著影响其光谱性能和可靠性。利用传统桥梁弯曲理论和膜层间位移协调条件分析了多层膜中的水平应变、弯曲应变和热应力分布情况。在详细推导的基础上,根据膜层厚度远小于基片厚度的实际情况,得出了多层膜中热应力的简化计算公式。结合长波红外窄带滤光片实例,分析了其多层膜中热应力的数值大小和分布情况。
Infrared optical films are usually fabricated at higher temperatures.When they are used at low temperatures,the thermos elastic stress generated may significantly affect their spectral performance and reliability.According to the traditional bridge bending theory and the displacement coordination condition,the horizontal strain,bending strain and thermal stress distribution in multilayer films are analyzed.On the basis of detail derivation,the simplified calculation formulas of thermal stress in multilayer films are derived when the thickness of the film is much smaller than that of the substrate.Taking the long-wave infrared narrow-band filter as an example,the numerical value and distribution of thermal stress in multilayer films are analyzed.
Infrared optical films are usually fabricated at higher temperatures.When they are used at low temperatures,the thermos elastic stress generated may significantly affect their spectral performance and reliability.According to the traditional bridge bending theory and the displacement coordination condition,the horizontal strain,bending strain and thermal stress distribution in multilayer films are analyzed.On the basis of detail derivation,the simplified calculation formulas of thermal stress in multilayer films are derived when the thickness of the film is much smaller than that of the substrate.Taking the long-wave infrared narrow-band filter as an example,the numerical value and distribution of thermal stress in multilayer films are analyzed.
引文
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[2]Hsueh C H,Evans A G.Residual Stress in Metal/Ceramic Bonded Strips[J].Journal of the American Ceramic Society,1985,68(5):241--248.
[3]Liu H C,Murarka S P.Elastic and Viscoelastic Analysis of Stress in Thin Films[J].Journal of Applied Physics,1992,72(8):3458--3463.
[4]Freund L B.Some Elementary Connections between Curvature and Mismatch Strain in Compositionally Graded Thin Films[J].Journal of the Mechanics&Physics of Solids,1996,44(5):723--736.
[5]Hsueh C H.Modeling of Elastic Deformation of Multilayers Due to Residual Stresses and External Bending[J].Journal of Applied Physics,2002,91(12):9652--9656.
[6]Teixeira V.Mechanical Integrity in PVD Coatings Due to the Presence of Residual Stresses[J].Thin Solid Films,2001,392(2):276--281.
[7]Gao C,Zhao Z,Li X.Modeling of Thermal Stresses in Elastic Multilayer Coating Systems[J].Journal of Applied Physics,2015,117(5):R53--R80.
[8]Teixeira V,Andritschky M,Fischer W,et al.Effects of Deposition Temperature and Thermal Cycling on Residual Stress State in Zirconia-based Thermal Barrier Coatings[J].Surface&Coatings Technology,1999,120--121:103--111.
[9]Townsend P H,Barnett D M,Brunner T A.Elastic Relationships in Layered Composite Media with Approximation for the Case of Thin Film on a Thick Substrate[J].Journal of Applied Physics,1987,62(11):4438--4444.
[10]Chang K H,Kim S H.Derivation of the Centerwavelength Shift of Narrow-Bandpass Filters under Temperature Change[J].Optics Express,2004,12(23):5634.
[11]Hsueh C H.Thermal Stresses in Elastic Multilayer Systems[J].Thin Solid Films,2002,418(2):182--188.
[12]张麟,倪榕,黄春,等.中心波长14.95μm超窄带滤光片的研制[J].光学学报,2014,34(7):314--317.
[13]Houston B,Strakna R E,Belson H S.Elastic Constants,Thermal Expansion,and Debye Temperature of Lead Telluride[J].Journal of Applied Physics,1968,39(8):3913--3916.
[14]Chung D H,Buessem WMR.The Voigt-ReussHill Approximation and Elastic Moduli of Polycrystalline MgO,CaF2,ZnS,ZnSe,and CdTe[J].Journal of Applied Physics,1967,38(6):2535--2540.
[15]Moriaki W,Keiei K,Takehisa S.周海宪,程云芳,译.光学材料手册[M].北京:化学工业出版社,2010:213--218.