How to create a search bar without casesensitive

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i have create a search list which shows the student details i need to find the student name with both upper case and lower case

Eg
student 1 name = arun
student 2 name = Aravid

if i enter the letter (a) in searchbar both arun and aravid should to be displayed

And i need to avoid the same name repeatation

If any one can correct my code please help me to figure it out

What I have tried:

private void search_box_TextChanged_1(object sender, TextChangedEventArgs e)
     {

         List<StudentItem> student= new List<StudentItem>();
         var prefix = search_box.Text;


         bool found = false;

         List<StudentItem> searchlist = DataAccess.getallstudent(empdetails);

         for (int i = 0; i < searchlist.Count; i++)
         {
             foreach (StudentItem item in searchlist)
             {
                 if (item.LastName.StartsWith(prefix))
                 {
                     found = true;


                     var eL_item = new StudentItem();
                     eL_item.FirstName = item.FirstName;
                     eL_item.LastName = item.LastName;
                     eL_item.TImageName = item.TImageName;

                     student.Add(eL_item);


                     studentlist.ItemsSource = empylast;

                 }


             }

         }

     }