Transparent conducting oxide (TCO) films are widely used in the integrated circuits of consumer electronic products. The version with a near-zero permittivity (epsilon-near-zero, ENZ) manufactured by controlling carrier concentration has become one of the potential candidate materials in the design of on-chip integrated optical chips due to its unique linear and nonlinear optical properties.

As a member of degenerate semiconductors, the optical and electrical properties of such materials are influenced by temperature. In the terminal product applications of large-scale electro-optical integration, system warming from the encapsulation of many operating devices is unavoidable. In this study, scientists from École Polytechnique Fédérale de Lausanne (EPFL), Peking University, and Tsinghua University collaborated to systematically investigate the thermal effects on the linear and nonlinear optical properties of ENZ TCO nanolayers within three key infrared (IR) telecommunication bands (O-band, C-band, and 2-micron band). The research is conducted under the common junction temperature limit of transistors (< 100°C) through precision optical and thermal design. This study reveals that under ENZ conditions, the material exhibits significant enhancements in thermo-optic effects, dispersion, and thermo-optic nonlinearity, providing a powerful supplement to a series of previously reported enhancements of other optical properties.

Optical materials encountered in daily life typically have a refractive index greater than 1.0. However, ENZ materials can exhibit a phase refractive index less than 1.0 in certain frequency ranges without violating the principles of general relativity. This unique characteristic can trigger a series of “chain reactions”, leading to extraordinary changes or enhancements in other optical properties of such materials. In recent years, ENZ TCO materials have also been reported to exhibit great enhancement in their Kerr nonlinearity in the infrared region, inspiring numerous subsequent studies in ENZ nonlinear optics.

On the other hand, in the field of microelectronics, TCO films have been widely used in manufacturing transparent electrodes. Benefiting from this, micro-nano integrated optical chips manufactured using similar processes can also incorporate ENZ TCO devices. This enables the realization of nonlinear light-matter interactions at the nanoscale, offering broad prospects for applications in data processing, infrared optical communication, new frequency generation, and novel light sources.

In consumer microelectronics, regardless of how the performance of electronic integrated circuits confirms or even surpasses Moore's Law, their operational efficiency is consistently influenced and limited by temperature. Commercial microelectronic chip products typically operate within the limits of the highest transistor junction temperature, usually in the range of 95 to 105 degrees Celsius. As photonic chip technology and electro-optical integration techniques advance and mature, complex on-chip photonic systems (SoC) will also face similar constraints.

ENZ TCO materials, being degenerate semiconductors, have strong correlations between their optical and electrical properties. While the scientific community generally acknowledges the temperature sensitivity of these materials, existing research has been confined to the irreversible effects of high-temperature annealing processes during manufacturing on optical properties. There are no reported studies on the reversible processes under the highest transistor junction temperature. Research into this phenomenon could provide forward-looking guidance for the design of ENZ-integrated photonic chips.

This study employed a meticulously designed, highly efficient on-chip thermal control platform compatible with an ellipsometer. Complemented by other precise microelectronic and materials characterization methods, a rigorous comparison was made between samples of non-ENZ and ENZ materials processed through the same fabrication process. The research revealed that within the corresponding ENZ frequency range, conditions of near-zero dielectric constant could enhance the thermo-optic coefficient (TOC), i.e., the change in refractive index per unit temperature change, by 660% to 955%, approaching an order of magnitude. This enhanced half-width range covers an ultra-wide spectral band around 70 to 93 terahertz, centered at the ENZ frequency. This provides possibilities for broad-spectrum and multi-wavelength applications.

Linear thermo-optic effects, influenced by the heating of light or the environment, can give rise to thermo-optic nonlinear effects, wherein the refractive index varies with light intensity under the influence of temperature, akin to traditional Kerr nonlinear effects. The study found that under ENZ conditions, through the modulation of thermo-optic effects and material losses, the thermo-optic nonlinear coefficient experiences a wide-frequency enhancement ranging from 1113% to 2866%. This enhancement can be compared to reported ENZ-enhanced Kerr nonlinear effects resulting from different principles.

In typical optical materials, considering the material's thermal response (heating and cooling rates), the time threshold for thermo-optic nonlinearity is approximately in the picosecond (10^-12 seconds) range. In ENZ materials, however, due to the presence of thermo-optic enhancement, this threshold enters the “ultrafast” regime, theoretically predicted to be around 157 to 677 femtoseconds (10^-15 seconds), providing a new platform for nonlinear applications. Additionally, this research marks the first experimental observation of the ENZ ultra-high group velocity dispersion predicted by the authors in 2020. The observed dispersion is orders of magnitude higher than that of common optical materials.

This research uncovers new physical phenomena and mechanisms of ENZ materials, providing important references for the design of ENZ integrated optical devices and a deeper understanding on the ENZ nonlinear optical platform. The project is funded by the Swiss National Science Foundation (SNSF) and the Basic and Applied Basic Research Foundation of Guangdong Province.