This guide goes over how to replace the controller's joystick.
If you are experiencing problems with the joystick, you will want to open up the device to fix the problem. A common solution associated with this problem is to take a small dry tissue or towel and clean the parts of the controller to ensure there is no debris limiting the joystick’s range of motion. If that doesn’t work, move the shaft underneath the joystick around to see how fluid it is. If the shaft is the problem, the joystick component will have to be replaced.
To complete this task you will need the indicated screwdriver and spudger. Note that you will need to solder to replace the joystick component which can be a potential danger.