Here I am giving you information about courses offered by Indian institutes of technology after passing GATE Electronics Exam below :

M tech courses offered in following subjects :
VLSI & Embeded systems
Robotics.
Radio communication
Nano technology
Power electronics
Advance communication.

Or you can apply for PHD in Electronics engineering program offered by IIT colleges.

Top IIT colleges are :

Indian Institute of Technology, Delhi

Indian Institute of Technology, Kharagpur

Indian Institute of Technology, Bombay

Indian Institute of Technology, Kanpur

Indian Institute of Technology, Madras

Indian Institute of Technology (BHU), Varanasi

Indian Institute of Technology, Guwahati

Indian Institute of Technology, Bhubaneswar