What is the ideal way of following up with Micron after completing the initial internship application process?

Do you know your hiring manager or recruiter's email by any chance? If so, I would suggest sending an email saying you applied an internship on when, and how and why you are great fit in the role attached with some related research paper, activity or project. If not, I would wait any update. I am sure recruiter is taking time to see all resume from everyone so it might take some time to get response but be patience.
Good luck!

Thank you for taking the time to respond! We had a few people come from Micron to visit the University I attend. I didn't have a specific recruiter assigned to me. I was just advised to apply through the website. Is there a way to find the specific recrutier or hiring manager for the internships in which I applied for? I didn't see them listed on the application page.

Thank you so much!

I see, I feel that you are worried about your application process. I was on same page when I was student.
I believe what you can do now is to read again the job description of internship position you applied and prepare for interview till you receive an email from micron regrading if you will be moved on to next step.