Deadlines

Keep in mind that for a PhD position in North America (and a few programmes in the UK) you need to start planning about a year before your intended starting time, with application deadlines being typically around the end of the calendar year and some requiring you to have taken a standardised test (such at the GRE) by the time you apply. Keep in mind that some of these tests may only be offered on a few selected dates each year.

At the other extreme, for some PhD positions in Europe (particularly those that are project-based) you may be able to apply just a couple of months before the intended starting date, but most European deadlines are around spring for a start in September or October.

In any case, you should reserve some time in your third semester to carefully think about what you want to do and, if applicable, to work on your applications.