Writing ads to attract female PhD candidates
It is believed that the use of "gendered" language in job ads can make ads appeal more to men or women [1]. See no reason that this should not also apply to ads for PhD students.
There are several websites that claim to test your job Ads for gender bias based on the word lists in [1].
E.g.
http://gender-decoder.katmatfield.com/
or
https://www.totaljobs.com/insidejob/gender-bias-decoder/
The other common advice is to avoid specifying requirements that are not really requirements, but actually nice-to-haves. Widely cited research [2] suggests that men are far more likely than women to apply for a job even if they don't meet all of the requirements. So for example, if you say that you require students to have taken a class in X, but when it actually comes to it you get no good applicants that have, but decide to take a student who is really good in all other ways, but does not have class X, then class X shouldn't be specified as a requirement, but a nice-to-have. Saying in your ad that applicants must have X is then biasing against women.
Mind you, I always follow all this advice (the gender checkers even rate my ads as slightly feminine bias), but I still get next to no female applicants.
[1] Gaucher, Friesen, and Kay, Journal of Personality and Social Psychology, July 2011, Vol 101(1)
[2] https://hbr.org/2014/08/why-women-dont-apply-for-jobs-unless-theyre-100-qualified
This is an indirect answer from my experience hiring software developers.
TL;DR Stop focusing on the ad itself and instead focus on where people see the ad, in particular get small groups of people to learn about the opportunity in an intimate setting.
As opposed to focussing on the language of the ad, I find it's more effective to focus on where the ad gets placed.
For example, I have posted several jobs on LinkedIn using their "easy apply" feature. Sure, it's easy to apply but applicants also generally have a picture and some personal information on their profile which can create a stigma for potential minority applicants owing to the bias of recruiters, which is unfortunately very real. The net result is that you get fewer quality minority applicants.
You may not be searching for applicants on LinkedIn but I suspect that you are in a male dominated field (like software) which itself can create the same stigma.
My suggestion is to change your recruiting tactics. During my last search for a developer I posted the ad on LinkedIn but I also reached out to local developer meet-ups and asked for referrals from current employees. The more informal and more personal recruiting effort resulted in qualified women applying to job at a rate of 2:1 compared to men despite no substantial change in the local candidate pool.
Did recruiting in this manner take more effort? Yes. Was it worth it to create a great, well balanced team? Definitely.
It may seem against some ideologies out there, but as a husband, a father, and a colleague of numerous women in academia I can approximately tell you what women considering career in academia want to see in your ad.
How family friendly is your work environment? Any benefits for parents? Not just women, their husbands too. Vacations, breaks, holidays? Available housing close to campus? Hospitals / kindergartens / schools nearby? Public commute options? Low stress, friendly work environment? Stability of employment?
If you want a more accurate opinion, ask some women what they want from an academic institution to consider a career there.
Then write your ad describing what your institution has to offer women. Specific, succinct, and solid offers. No 'maybe', 'if then maybe', etc. Then you will attract top talent. Sure, many under-qualified will apply, but you can reject them based on their CV and pick the best.
Don't present requirements as 'requirements'. The people you really want will have requirements for you. Instead, ask applicants to please include in their resume 1), 2), 3), etc. without using the word 'requirement'.
One thing that won't work for sure is making a flashy ad like for selling a vacuum cleaner. With career decision of such critical importance, there is no chance fooling anyone into it. Especially smart, young women. Age 24-30 is a good time to make a family, give birth to a child, and put a down-payment on a house. And smart women do want it good.
In fact, many people disagree with such a pragmatic view, but I honestly don't understand why. It works. The question is not about letting women to participate or not. I am assuming there are equal rights. The question is about attracting talented women.