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<img src='content_image/300397.jpg'>

thickness of the silicon nitride waveguide core must be increased substantially from the values that are typically used ( < 200 nm). To obtain the dispersion of the waveguides we simulated the effective refractive index n for various wavelengths using a finite element solver (COMSOL Multiphysics) that takes both the dispersion of the materials and, as well, the dispersion induced by the geometry of the waveguide core into account. From this the dispersion parameter, D = − l c · d $^{2}$n d$_{l}$ 2 [16], can be calculated, where l is the vacuum wavelength of the light and c the speed of light. This is shown in Fig.1, where we plot D as a function of the wavelength for waveguides with a fixed width w = 0.8 $_{m}$m and three different heights ranging from 0.8 to 1.2 $_{m}$m. As a comparison, the dispersion parameter for bulk Si$_{3}$N$_{4}$ is shown as well. While bulk Si$_{3}$N$_{4}$ does not have a ZDW in the wavelength range from 1000 to 2000 nm, the ZDW for the waveguides is calculated to range from 1200 nm ( d = 0 . 8 $_{m}$m, red) to 1560 nm ( d = 1 . 2 $_{m}$m, green) by changing the thickness d and, hence, providing phase matching for wavelengths around 1550 nm. 

However, realizing Si$_{3}$N$_{4}$ waveguides with sufficient thickness is problematic. Typi- cally, a Si$_{3}$N$_{4}$ layer is deposited on a thermally oxidized silicon substrate via LPCVD, and waveguide cores are etched from this Si$_{3}$N$_{4}$ layer. This layer has a limited thickness due to the increasing tensile stress that develops during the deposition of the Si$_{3}$N$_{4}$ 

