"MacBook Air EFI Firmware Update 2.9 (4.3MB)
This update is recommended for MacBook Air (Mid 2011) models. This update addresses an issue where systems may take longer to wake from sleep than expected and fixes a rare issue that may cause fans to run at full speed after waking from sleep.
OS X 10.9.2 and later
Update over these EFI versions only:
(Note these may actually be .B00, .B08, etc)
According to a later doc, the EFI version after this update should be MBA41.0077.B11.
(The D/L page was dated July 15th but not seen until July 21st. It was added to the List of EFI/SMC firmware updates (doc date 21st) but later removed after update was pulled.)
FYI: The MacBook Air forum has a thread where some owners reported problems with this update. Later posts/pages there include some troubleshooting. (For anyone that hasn't updated yet, if you're not having any of the problems this update was to fix (noted above) remember the golden rule on fw updates - 'it it ain't broke, don't fix it'. If I must update, I use D/L updaters run from a clean boot.)
BTW: Someone there also linked to the (old) apple doc on Firmware Restoration CDs, but there is none for this mac model that I know of. (I have a list of D/L pages for Firmware Restoration CDs here.)
Update: Reportedly Apple has identified a problem and is working on a corrected release.
Apple later posted these tips for owners that had problems applying the update. (May not fix everyone's problems but worth trying.)
Tips for 2011 MacBook Air black screen after attempt to install EFI 2.9 Update
"if your (Mid 2011) MacBook Air doesn't finish the EFI Update 2.9 firmware installation, and a black screen appears after the computer restarts, follow these steps:
Make sure MagSafe power adapter is plugged into your MacBook Air.
(i.e. not running on battery power)
Press Power key for at least 10 seconds.
Release Power key.
Press Power key again to turn on MacBook Air.
The MacBook Air may take a few minutes to power on."
Another (user) suggestion was to try Shift+Control+Fn+Power.