Professors: what makes you respond to unsolicited PhD applications?

Hi everyone,

I’m currently considering applying for PhD positions and would love some advice,especially from people who have been through the process or professors who receive such inquiries.

My idea is to first carefully review specific papers and ongoing research from potential supervisors (and their PhD students) and then see how my own background and interests align with their work. The part I’m struggling with is how best to approach a professor when no official position is posted.

From what I’ve seen, there are generally two ways:

1. Cold emailing with a CV writing a concise email explaining my interest in their work, how my experience aligns, why I want to work with them, and then asking if they’d be open to a conversation.
2. Calling briefly introducing myself, asking if they consider open applications at all, and only then following up with documents if they’re open to it.

Of course, if a position is already posted, I wouldn’t send an open application I’d just apply through the formal channel.

About me:

• Bachelor’s (good grade)
• Master’s (very good grade)
• 6 months of research assistant experience at university during my studies
• No publications yet

My questions:

• What’s the most appropriate and effective way to reach out to a professor with an open application?
• As a professor (or someone experienced), what makes you more likely to respond positively to such an email?
• Are there things I definitely should or should not do in this first contact?

Thanks a lot in advance, I’d really appreciate your perspectives!