Control of thermo-optic coefficients and their polarization dependence in polyimide films formed on Si substrates

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Abstract
Thermo-optic coefficients dn/dT for TE- and TM-polarized lights (dnTE/dT and dnTM/dT, respectively) were measured for aromatic polyimide (PI) films formed on Si Substrates. The values of dn/dT for the average refractive index (dnav/dT) is in a range of -52 to -87 ppm/K, and amorphous PI films with large nav have large |dnav/dT|, which is well accounted by the temperature derivative of the Lorentz-Lorenz equation. On the other hand, the absolute values of dnTE/dT were significantly larger than those for dnTM/dT even for the PI films with very small polarization dependence in refractive index (Δn; in-plane/out-of-plane birefringence). This result cannot be explained by the temperature derivative of the Vuks equation, which represents that the large polarization dependence in dn/dT is caused by the large Δn. Polarization dependence in dn/dT for the PI films with small Δn is caused by the temperature dependence in large stress birefringence. Based on these results, large thermal expansion and small stress birefringence (small residual stress or small polarization anisotropy) is essential for achieving large |dnav/dT| and small polarization dependence in dn/dT. To demonstrate this assumption, dn/dT measurements were carried out for PI films derived from a fluorine-containing dianhydride and aliphatic diamines, which exhibit loose chain packing and small polarizability anisotropy. As a result, these PI films exhibit small polarization dependence in dn/dT, and relatively large dnav/dT compared to the aromatic PI films with almost the same nav.

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