I am recently working as a software engineer intern at a startup company. My company helps clients achieve their financial goals. The job is quite remote and mostly I am working with my direct supervisor via emails, who is responsible for sending me any tasks that he needs my help (my supervisor is not the CEO of the company, and the CEO is not familiarized with IT and works directly with clients I suppose).
The tasks I've got from my supervisor is very little so far. Usually, I get one task weekly and depends on the difficulty of the task I may finish in 1~3 days and then it takes me about 5 days to receive any feedback from my supervisor. I am not sure if my current work is such "comfy" because the company is small and there are not too many clients and tasks recently. Another possibility I thought of is my supervisor doesn't value me much becasue I am just an intern at the moment. But I think it would be dangerous if my CEO doesn't know what I have done to the company and is not good if I am gonna ask for a full time offer later this year. I am thinking about writing an email to the CEO and shows that I am able and willing to do more tasks, however, I am not sure how I should phrase in my email. Can anyone offer any help?