While it's not technically something a doctor 'prescribes', sleep is an important part of cancer recovery.
During the day, your body is busy with physical activity, digesting food, using your brain to process ever-changing data. But sleep is when your body heals itself. When you're asleep, the brain triggers hormones that encourage tissue growth and repair. A restful state allows the blood pressure to drop, giving your heart a much needed rest.
Studies show that people who get 7-8 hours of sleep per night, are 3 times less likely to catch a cold. That's important when your immune system may be compromised by your chemotherapy treatment.
Sleep is important, so give yourself permission to rest. If you are overly tired, that's probably your body telling you to take a break. Listen to your body.
But, as important as sleep is, do not let yourself worry if you find you are wakeful at night. It's natural for people to have a small stretch of time in the middle of the night when they are not in a deep sleep, or are even awake. Just allow yourself to rest, and fall back to sleep when you can. Then, if you are tired during the day, take a short nap (no longer than an hour) in the afternoon.
If you are stressing about whether you are sleeping or not, that will only make you feel worse. The important thing to remember is to get some quality sleep at some point, and get enough sleep/rest so you feel rested and healthy.
Every body is different. Find what works for you.