Investigation of local strain distribution and linear electro-optic effect in strained silicon waveguides

Abstract

We present detailed investigations of the local strain distribution and the induced second-order optical nonlinearity within strained silicon waveguides cladded with a Si₃N₄ strain layer. Micro-Raman Spectroscopy mappings and electro-optic characterization of waveguides with varying width w(WG) show that strain gradients in the waveguide core and the effective second-order susceptibility χ(2)(yyz) increase with reduced w(WG). For 300 nm wide waveguides a mean effective χ(2)(yyz) of 190 pm/V is achieved, which is the highest value reported for silicon so far. To gain more insight into the origin of the extraordinary large optical second-order nonlinearity of strained silicon waveguides numerical simulations of edge induced strain gradients in these structures are presented and discussed.

High-frequency electro-optic measurement of strained silicon racetrack resonators

“…This demonstrates that plasma carrier dispersion is responsible for the observed electro-optic effect. After normalizing out free carrier effects, our results set an upper limit of 8 pm/V to the induced high-speed χ (2) eff,zzz tensor element at an applied stress of −0.5 GP a. This upper limit is about one order of magnitude lower than the previously reported values for static electro-optic measurements.…”

“…In the last years, a lot of effort was spent investigating the strain induced second order nonlinearity (χ (2) effect) in Silicon by investigating the induced Pockels effect [1][2][3][4][5]. Strain induced χ (2) could be instrumental to make ultrafast and energy efficient electro-optic modulators for the Silicon photonics platform which would replace present electro-optic modulators based on the plasma dispersion effect [6][7][8][9].…”

“…Strain induced χ (2) could be instrumental to make ultrafast and energy efficient electro-optic modulators for the Silicon photonics platform which would replace present electro-optic modulators based on the plasma dispersion effect [6][7][8][9]. More generally, the presence of an appreciable χ (2) in Silicon would validate the Silicon-on-Insulator (SOI) platform as an alternative to Lithium Niobate for second order nonlinear optics [10,11]. In most of these works, the centro-symmetry of Silicon is broken by a stressing film of Silicon Nitride which induces strain in the underlying Silicon waveguide and enables a χ (2) = 0 -at least from a first principle point of view [12].…”

“…More generally, the presence of an appreciable χ (2) in Silicon would validate the Silicon-on-Insulator (SOI) platform as an alternative to Lithium Niobate for second order nonlinear optics [10,11]. In most of these works, the centro-symmetry of Silicon is broken by a stressing film of Silicon Nitride which induces strain in the underlying Silicon waveguide and enables a χ (2) = 0 -at least from a first principle point of view [12]. With the exception of refs.…”

“…[10,11], the Pockels effect was investigated by using an integrated imbalanced Mach-Zehnder interferometer in which one or both interferometer arms are driven by a DC or a low frequency (≈ kHz) AC electric field [1][2][3][4][5]. Then, an effective χ (2) mat value is extracted from the measured shift of the interference fringes by taking into account the system geometry and the magnitude of the applied static electric field. As expected from theory, the relation between the effective index change and the applied static electric field is found to be linear.…”