Quality of sleep is more important than duration of sleep. The easiest way to get good quality sleep is to get in tune with your body clock. Interestingly, our bodies do different things at different times during our sleep cycles: REM sleep is linked to learning and memory, whereas growth hormones are released during deep sleep.
So if you want to exact all the benefits of sleep, understand the different sleep phases and ensure you get adequate of each.
If you are always groggy when your alarm goes off, invest in a bodyclock alarm clock or app that will wake you at the end of a sleep cycle, as close to your desired get up time as possible.