I don't know about your school, but the engineering physics at my prospective schools ( SFU and UBC) have options.
SFU is more microelectronics, semiconductor, and some programming
UBC has an electrical option, mechanical, and mechatronics option.
it really depends on how your school's curriculum is layed out. Different schools have different strengths.
Also, after talking to a department chair about double majoring in engineering(i also wanted to do that), he advised me *not* to.
He told me it would be much wiser to major in engineering physics then a masters in mechatronics(that was my two choices) because he said i may find that after my first degree, undergraduate courses is not the most efficient way of learning because with a solid background in engineering physics, i can pick up mechatronics at the graduate level with the help of suitable textbooks and a good faculty supervisor.
Which makes sense since university after all, teaches you to be efficient in learning by yourself.