Recommend a 4 TB drive for Time Machine

I have been having a very hard time trying to find a good 4 TB external hard drive to serve as my Time Machine disk as these drives all seem to have built-in energy saving features which make the hard drive spin down constantly. The problem here is that it does this contstantly while I am working and the result is the drive continually needing to spin up which basically brings most operations of the computer to a halt as it waits 5-7 seconds for the drive to come on line. Unchecking the box for "Put hard disks to sleep when possible" under Energy Saver preferences has no effect on this behavior. I have tried both the the Western Digital Green WD40EZRX 4TB and the Seagate ST4000DM000 4TB and they both suffer from the same behavior. Is there a 4TB drive out there that either other users have had success with for use with Time Machine? Does Apple have a recommended drive list, in particular drives which actually can be controlled by the Energy Saver preferences?