Research Assistant Position/Research Internship Question

Hello,

I am currently trying to get an internship at a lab, and I wanted to know if it’s a good idea to include some of my current project proposals in the email. While I’m not necessarily trying to find a mentor (right now I’d just like to find an internship) I’m thinking that adding my project proposals could help show my background in their fields of research.

Does anyone think this is a good idea or have any suggestions for showing scientists my background in science and research in internship emails?

Thanks