Why date is not taking 13/09/2016

I am checking condition for 12/09/2016 to 13/09/2016 but it is not showing me data for 13/09/2016 and giving error

The conversion of a char data type to a datetime data type resulted in an out-of-range datetime value.

Here is my query

SELECT DISTINCT  
   b.mkey ,  a.N_UserMkey, cuser_id,isnull(a.N_UserMkey,cuser_id) aa,
   ISNULL(b.first_name + ' ', '')  
   + ISNULL(b.last_name, '') NAME, convert(varchar,a.U_datetime,103) Action_Date
  FROM      inward_doc_tracking_trl a  
   INNER JOIN user_mst b ON isnull(a.N_UserMkey,cuser_id) = b.mkey  
  WHERE 
  convert(datetime,a.U_datetime,103) 
    BETWEEN convert(varchar,'12/09/2016',103)
  AND convert(varchar,'13/09/2016',103)
   and b.mkey=2357