Reminds me of the old saying, 'the hours you sleep before midnight are more important than the hours after midnight.'
Not a study, but a Q&A with the "sleep director the Sleep and Neuroimaging Lab at Beth Israel Deaconess Medical Center and Assistant Professor of Psychology at Harvard Medical School."
http://www.pbs.org/wgbh/nova/body/walker-sleep.html
"There is nothing particularly special about the clock time of midnight for sleep. Upon falling asleep, there is a general propensity to go through a 90-minute cycle of non-REM sleep followed by REM sleep. However, as mentioned above, the ratio of non-REM-to-REM sleep within these 90-minute cycles changes across the night, such that early in the night (e.g., 11p.m.-3a.m.), the majority of those cycles are comprised of deep non-REM sleep (stages 3 and 4) and very little REM sleep. As we push through to the second half of the night (e.g. 3a.m.-7a.m.), this balance changes, such that the 90-minute cycles are comprised of more REM sleep (the stage commonly associated with dreaming), together with a lighter form of non-REM sleep (stage 2).
But there is a subtle twist to this story that rises above these 90-minute laws: the earlier in the night, the greater the propensity for deep non-REM sleep, and the later in the morning, the greater the propensity for REM. Therefore, someone who sleeps from 9p.m. to 5a.m. (8 hours total) will have a different overall composition of sleep - biased towards more non-REM - than someone who sleeps from 3a.m. to 11a.m. (also 8 hours total), who is likely to experience more REM. Indeed, if you afford yourself the luxury of sleeping in later during the weekends, you'll experience this phenomenon, with a greater likelihood of having more dreams due to the increased proportion of REM sleep."