How should I write an appropiate email for a PhD position? I am a graduated Master's student from Asia and really want to take a PhD position in Canada, America or Germany. My English language skills are good but I don't have an IELTS degree. Some of my friends say that if I talk to a professor who I want to work with, I do not need a high grade in English exams like IELTS and I do not have any reaserch or projects or paper because it is unusual in master of pure math(which I studied) to have any of them(because it is so hard to do). On the other hand, I wrote the following email but I am so nervous of the whole structure and its content. Would you please guide me for sending a better email for a PhD position? Thank you in advance.

Dear professor “ “:
My name is Dal.OL. This year, I graduated from
Shahid Beheshti University with a master's degree in geometry with GPA
3.69. My interesting field for researching is dynamical systems in geometry and my master’s dissertation was in hyperbolic dynamical
systems which was really exciting for me and made me Curious about the
hole concepts used around it, therefore I am deciding to continue
studying in this field of Geometry. I am seeking admission to the PhD
studies in related with my master’s dissertation and I also like to
work on the manifold concepts and their extension in dynamical
systems. In the other hand I reviewed your profile and thought that it
would be wonderful if you would be willing to take me as your PhD
student.
I look forward to hearing from you.
Thanking you for your consideration. Sincerely,
Welcome to Academia.SE; I personally think that many parts of this question are clearly addressed in answers to some other questions on this site; and I think that this may be closed. Just read the existing questions which answer many of your questions about writing emails, questions on requirements, language tests, etc.
As a general hint to form your emails, you should be specific in your emails about what mutual research interests are with the potential advisor you are contacting and how your academic background may help the research team with their current and on-going projects. This may be shown by mentioning your related projects you have been involved in, parts of programming and codes you have developed which can be found over an online repository or publications, papers and reports you have had out of your research projects and masters thesis.
Moreover you may attach a complete resume and possibly a portfolio which shows your academic activities to the potential advisor and make sure you narrate your resume and edit it to contain publications and activities which are specifically related to the topics of interest of the research group you are eager to join.
Official required documents like degree reports, language tests and recommendations are sometimes required to be pressented to the admissions committee of the university you want to join. Some of these (like funding letters and language reports) are required for students visa applications which may be less of attention to the advisor and more of importance to official procedures.
Good luck with your search and hope you find a good desired PhD position.