What is happening physically when I get sleepy and when I wake up?
During sleep the cerebrospinal fluid clears out the waste products of brains cells. Sleep fragmentation or sleep deprivation can prevent this process, or reduce its efficiency. So I think the accumulation of waste products cause that you have to sleep more after sleep deprivation and extreme sleep deprivation (e.g. by fatal insomnia) can cause death. Low quality sleep and sleep deprivation can cause or worsen both neural (e.g. Alzheimer's disease),  and metabolic diseases (e.g. diabetes mellitus, etc...), so you should avoid it, if you can (I cannot :D).

Daily sleep is regulated by the circadian clock. Many hormones can affect that clock, e.g. melatonin (dependent on blue light), insulin, etc...  


  The conservation of sleep across all animal species suggests that
  sleep serves a vital function. We here report that sleep has a
  critical function in ensuring metabolic homeostasis. Using real-time
  assessments of tetramethylammonium diffusion and two-photon imaging in
  live mice, we show that natural sleep or anesthesia are associated
  with a 60% increase in the interstitial space, resulting in a striking
  increase in convective exchange of cerebrospinal fluid with
  interstitial fluid. In turn, convective fluxes of interstitial fluid
  increased the rate of β-amyloid clearance during sleep. Thus, the
  restorative function of sleep may be a consequence of the enhanced
  removal of potentially neurotoxic waste products that accumulate in
  the awake central nervous system.



2013 - Sleep Drives Metabolite Clearance from the Adult Brain
2013 - Sleep Facilitates Clearance of Metabolites from the Brain: Glymphatic Function in Aging and Neurodegenerative Diseases 



  According to the traditional understanding of cerebrospinal fluid
  (CSF) physiology, the majority of CSF is produced by the choroid
  plexus, circulates through the ventricles, the cisterns, and the
  subarachnoid space to be absorbed into the blood by the arachnoid
  villi. This review surveys key developments leading to the traditional
  concept. Challenging this concept are novel insights utilizing
  molecular and cellular biology as well as neuroimaging, which indicate
  that CSF physiology may be much more complex than previously believed.
  The CSF circulation comprises not only a directed flow of CSF, but in
  addition a pulsatile to and fro movement throughout the entire brain
  with local fluid exchange between blood, interstitial fluid, and CSF.
  Astrocytes, aquaporins, and other membrane transporters are key
  elements in brain water and CSF homeostasis. A continuous
  bidirectional fluid exchange at the blood brain barrier produces flow
  rates, which exceed the choroidal CSF production rate by far. The CSF
  circulation around blood vessels penetrating from the subarachnoid
  space into the Virchow Robin spaces provides both a drainage pathway
  for the clearance of waste molecules from the brain and a site for the
  interaction of the systemic immune system with that of the brain.
  Important physiological functions, for example the regeneration of the
  brain during sleep, may depend on CSF circulation.



2014 - A new look at cerebrospinal fluid circulation



  Sleep fragmentation is present in numerous sleep pathologies and
  constitutes a major feature of patients with obstructive sleep apnea.
  A prevalence of metabolic syndrome, diabetes and obesity has been
  shown to be associated to obstructive sleep apnea. While sleep
  fragmentation has been shown to impact sleep homeostasis, its specific
  effects on metabolic variables are only beginning to emerge. In this
  context, it is important to develop realistic animal models that would
  account for chronic metabolic effects of sleep fragmentation. We
  developed a 14-day model of instrumental sleep fragmentation in mice,
  and show an impact on both brain-specific and general metabolism. We
  first report that sleep fragmentation increases food intake without
  affecting body weight. This imbalance was accompanied by the inability
  to adequately decrease brain temperature during fragmented sleep. In
  addition, we report that sleep-fragmented mice develop glucose
  intolerance. We also observe that sleep fragmentation slightly
  increases the circadian peak level of glucocorticoids, a factor that
  may be involved in the observed metabolic effects. Our results confirm
  that poor-quality sleep with sustained sleep fragmentation has similar
  effects on general metabolism as actual sleep loss. Altogether, these
  results strongly suggest that sleep fragmentation is an aggravating
  factor for the development of metabolic dysfunctions that may be
  relevant for sleep disorders such as obstructive sleep apnea.



2012 - Sustained sleep fragmentation affects brain temperature, food intake and glucose tolerance in mice
2014 - Sirtuin 3: A Molecular Pathway Linking Sleep Deprivation to Neurological Diseases



  Inadequate sleep simultaneously modulates the levels of multiple
  hormones that govern metabolism, In general, with sleep deprivation,
  the following hormones are decreased: insulin, growth hormone (GH),
  growth hormone releasing hormone (GHRH), and leptin levels. In
  contrast, ghrelin and somatostatin are increased. Essentially,
  hormones that signal that the body has plenty of energy are decreased,
  while those that signal energy need are increased. Experiments
  utilizing knockout animals as well as pharmacological agonists,
  antagonists, and immunodepletion of the proteins, illustrate that
  these hormones affect sleep regulation. Diabetic rats have decreased
  sleep time and consolidation while replacement of insulin increases
  increases slow-wave sleep.



2013 - The Genetic Basis of Sleep and Sleep Disorders (book)



  In humans, melatonin is produced by the pineal gland, a small
  endocrine gland[26] located in the center of the brain but outside the
  blood–brain barrier. The melatonin signal forms part of the system
  that regulates the sleep–wake cycle by chemically causing drowsiness
  and lowering the body temperature, but it is the central nervous
  system (specifically the suprachiasmatic nuclei, or SCN)[26] that
  controls the daily cycle in most components of the paracrine and
  endocrine systems[27][28] rather than the melatonin signal (as was
  once postulated).



wikipedia - melatonin