On Doctoral level, no tuition fees are charged, but you will need to cover your living expenses. If you are admitted as a Doctoral student, contact your Finnish university department for advice on research funding options. The universities may have Doctoral funding schemes of their own, and they can also direct you to potential grant-awarding foundations in your field of scientific research.
Also check out the national EDUFI scholarship programmes available for Doctoral level studies and research in Finland:
If you have questions regarding the EDUFI scholarships, please contact the scholarships admins directly. You can find their contact details on the web pages listed above.
For general information on scientific research in Finland, also see the Academy of Finland website.