Staying in Europe is not anymore a dead-end for your scientific career. Finland is certainly not on the top of the list when looking for potential European destinations. However, especially among students, Finland gained a reputation as an insider's tip for exchange periods abroad. Among these, German students form the biggest group, followed by French, Spanish, Dutch, and Italian students. Most of these come via the European Union-sponsored Erasmus exchange program. I recently wrote a guest blog on Claudia's Helsinki about coming to Finland as a scientist. The blog post is in German, but its bottom line can be summarized in one sentence:
There are several scientific areas, where Finland does world-class research.
And Finnish universities are increasingly offering international study programs (mostly MSc and PhD programs). These study programs have a tuition fee, but if you come from an EU country (or the degree you apply with is from an EU country) you are exempt from the tuition fee. If you come from outside the EU, you can pay the tuition fee or you can apply for a scholarship. However, the number of available scholarships is in my opinion not large enough. Besides, you really need to have an excellent study record to stand any chances. However, the tuition fees are a bargain compared to most other Top100 universities: Most study MSc programs ask 15,000 per year. A few programs ask 13000 or 18000 (you find this information on the respective web pages of the respective study program). See what MSc and PhD programs are offered at the University of Helsinki:
BSc: /en/admissions/degree-programmes/science-bachelors-programme
MSc: https://www.helsinki.fi/en/admissions/explore-our-international-masters…
PhD: https://www.helsinki.fi/en/research/doctoral-education/doctoral-schools…