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The scientific concept which most closely matches your description of "brain fog" is sleep inertia.

Any theories on why this may happen?

First, a brief detour. Sleep is divided up into 5 stages (stages 1, 2, 3, 4, and REM). Since 2007, NREM sleep has been reclassified into stages N1, N2, N3, with N3 being a combination of the former stages 3 and 4; however, most scientific papers are still using the old system, so I'll refer to them by the old stage names. Below, you can see a typical hypnogram, where sleep stage is plotted versus time for one night's sleep. Cycles through the night tend to progress from 1→2→3→2→REM, but can change unexpectedly if the subject is awakened.

(image from Wikipedia)

While sleep inertia has been well researched since the late 70s, its definition relies on changes in responses to behavioral measures rather than any specific anatomical structures that might be involved. In other words, it is difficult to "diagnose" someone with sleep inertia without seeing their performance on a demanding cognitive task.

It is known that waking up results from a signal that travels between the reticular system of the thalamus to the thalamus itself, and from the thalamus onto the cortex. Many studies have used fMRI as a means to catch the brain as it falls asleep, but there don't seem to be too many which capture that moment of awakening.

Sleep staging (how levels of sleep are scored, as seen above) relies on EEG measures, so it is natural that after a subject wakes up from a study, their EEG signals can continue to be measured. This gives researchers an opportunity to see into the dynamics of the cortex, but anatomical resolution and involvement of subcortical structures (like the thalamus) is not measurable. It would be nice to have a functional picture of subcortical activity to gauge the progression of waking.

A recent EEG study by Marzano (2011) found that the waking brain had a higher degree of delta activity in occipito-parietal (more posterior) areas, and a lower degree of delta activity in the frontal areas. They found increases in beta activity in the frontal areas, which tended to be stronger after awakening from stage 2 sleep than from REM sleep. This study did not attempt to localize any anatomical structures, but in general indicates that more posterior portions of the brain (perhaps associated with vision and posture) tended to mimic the activity found in slow-wave sleep for a time after awakening.

Sleep inertia has been found to depend on

prior sleep duration

sleep stage prior to being awake

time of day of awakening

and last between 30 minutes and 3-4 hours depending on prior sleep deprivation and other factors.

However, the effects of it seem to vary greatly based on the task that the brain is asked to attend to during that time.

Is anyone familiar with any research regarding less brain fog with less sleep?

On the extreme timescale of a short nap, this has been shown to be true, but the results can be extrapolated to longer time scales. Tassi (2000) reported on a study in which the subjects took 20, 50, and 80 minute naps. The 50 minute nap-takers were found to have more intense sleep inertia, most likely due to the chance to lapse into a higher percentage of slow wave sleep during that time (stages 3 + 4 under the old system, and stage N3 in the new one) and potentially not return to stage 1 or 2 before awakening. The 80 minute nappers, which one might think would have worse sleep inertia upon waking, were able to get into REM sleep, and so experienced less sleep inertia (this is a slight contradiction to Marzano's result above, but I think Tassi's assertion is more widespread in the literature). However, Tassi also reported a study where decrements in performance were reported in REM sleep with a higher density of eye movements.

Sleep deprivation tends to increase the amount of deeper sleep once the person has the opportunity to rest. In that case, regardless of stage upon awakening, the sleep inertia tends to be worse.

Matchock (2010) has reevaluated some of the experimental evidence in light of circadian influences. He added ultradian phase (the marker of one's progress through the circadian day) and whether awakenings were forced or self-imposed to Tassi's list of factors above. Levels of cognition and performance, both hindered in sleep inertia situations, are found not to be uniform throughout the 24 hour day. Matchock reported on studies where late afternoon naps were more restorative and hindered cognitive function less (less sleep inertia). Other findings in his review found a relationship between both drops in core body temperature and body temperature of the extremities (both factors known to vary over the day) tended to increase sleep inertia.