Dear Fatemah, I believe that the researcher /author is the one who knows best the contribution of a paper to the current research. The research of a PhD student should contribute something tangible, although it may not be easy to measure.
For example, in my PhD research, I proposed how my study on music preferences of teenagers provides the way in which the five objectives of music education in Malaysian schools may be achieved, and depicted it diagrammatically. The reader who is aware of the extent of the current research will be able to know the contribution of the paper. Thanks.
Article Music preferences of Malaysian students and KBSM curriculum ...
Conference Paper MUSIC PREFERENCES OF TEENAGE STUDENTS IN RELATION TO LISTENE...
At the moment, I didn't discover "any method or website measuring the percentage of the contribution a research paper to the current research". Maybe I'm just a bad looking and no found this site. In my opinion, I fear that such a site could not exist because the vast majority of researchers would not be interested in the existence of this site. Any paper is a correlation between the ENTITY (p) and the VISIBILITY (q) , p + q = 100%. Problem is to measure the actual Percentage of ENTITY (p). I don't think that can be created any method (in Foreseeable Future) to measure actual "p" for traditional papers in text formats. Why do I think so? In my opinion, the most of researchers interested to demonstrate (only) their qualification without any science contibubution in order to get PhD degree for the sake of future careers.
8. and a paper "Excellence by Nonsense: The Competition for Publications in Modern Science" on the link http://link.springer.com/chapter/10.1007/978-3-319-00026-8_3/fulltext.html
Using this opportunity, I would want to offer alternate method of measuring the percentage of the Research Contribution at least in one area of science, namely in the field of Computer Science. My proposal is the following: A TRADITIONAL PAPER (in .pdf format) MUST BE CONVERTED TO A FUNCTIONAL SITE to be accepted from a server for all people (academicans, scientists, reserchers, students, practitioners, and just ordinary users without any special knowledge) in order to use this site for solving their tasks. In my understanding, in the 21st century a "better and more realistic metric" should become USER STATISTICS of application a FUNCTIONAL SITE in the Internet. Such statistics could be the best tool to measure the percentage of the Research Contribution.
More detailed information about my proposal (in Russian) can be seen from a discussion on the link https://www.researchgate.net/post/Dear_Russian_speaking_colleagues_Will_you_please_vote_on_the_portal_rosnaukaru_on_two_of_my_initiatives .