Booting to Internet Recovery Mode boots directly to a netboot image provided by Apple/Akamai servers. The netboot image is a stripped down OS X version which only provides some diagnostic tools and a tool to either restore OS X or a Time Machine backup. The downloaded OS is completely loaded to RAM and nothing is written to hard disks.
After shutting down/rebooting the Mac the RAM is wiped and everything has to be downloaded again if you want to start to Recovery Mode a second time.
To create a Recovery HD on your Mac you have to install OS X (Restore OS X). While downloading and installing OS X a recovery partition will be built also.
Another option is to set up a Mac running Server.app and enable caching services. That will keep a copy of the recovery image locally in cache and speed up the download - perhaps 100x as fast if you have a gigabit speed network locally.