silicon nitride and sCO2
Each of these materials is largely inert and there is no reason to expect that they would react with each other. Regarding supercritical $\ce{CO2}$, this Wikipedia article states the following:  


  Supercritical $\ce{CO2}$ is becoming an important commercial and industrial solvent due to its role in chemical extraction in addition to its low toxicity and environmental impact. The relatively low temperature of the process and the stability of $\ce{CO2}$ also allows most compounds to be extracted with little damage or denaturing.  


And regarding silicon nitride:  


  Silicon nitride is a chemical compound of the elements silicon and nitrogen, with the formula $\ce{Si3N4}$. It is a white, high-melting-point solid that is relatively chemically inert, being attacked by dilute $\ce{HF}$ and hot $\ce{H2SO4}$. It is very hard (8.5 on the mohs scale). It is the most thermodynamically stable of the silicon nitrides. Hence, $\ce{Si3N4}$ is the most commercially important of the silicon nitrides and is generally understood as what is being referred to where the term "silicon nitride" is used.  


Additionally, silicone nitride is used in the most critical, high temperature, high stress of applications, such as the bearings for NASA's (now defunct) Space Shuttle engine bearings.