Winnie N. Ye, Rong Sun, Jurgen Michel, Lionel C. Kimerling
Temperature stability is extremely important in device operation, especially for devices in materials with large thermo-optic coefficient such as silicon. There has been an enormous amount of research in reducing the device temperature sensitivity. The most common method introduces heaters/coolers for temperature control. However such method demands higher cost and power budget. In addition, special polymers with negative thermo-optic coefficient have been studied for compensating the thermal effects. This approach is constrained by the availability of the resources and technology. In the current study we propose the use of stress engineering to achieve athemal device performance.
The thermo-optic effect defines the temperature dependency in material refractive index (n); that is,
Δn = BΔT (1)
where ΔT is temperature change and B is the thermo-optic coefficient which depends on the index, wavelength, and temperature. The thermo-optic coefficient of silicon is on the order of 10e-4/K, while that of silica is ~10e-5/K. A 100K temperature fluctuation will cause a 10e-2 increase in the refractive index of silicon by the thermo-optic effect alone. Thus it is necessary to find an efficient way to reduce or compensate the drastic change. Recently, stress engineering has shown promising potential in controlling the refractive index in optical devices via photoelastic effect[2-5], which relates the stress distribution to the effective index; that is,
Δn = CΔσ (2)
where C is the photoelastic constant which depends on the material type and wavelength, and Δσ is the change in stress distribution. Stress (Δσ) is a result of the mismatch in the thermal expansion coefficients between the substrate and its coating film. The temperature dependence in device performance could be effectively compensated by choosing materials with a high photoelastic and a low thermo-optic constant, as can be seen from Eqs. (1) and (2).
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