How about the energy of crystal in a direct transition?

  1. When a photon is absorbed by an electron through a direct transition in a crystal, the crystal momentum of electron would not approximately change. Therefore momentum change of electron would neutralize momentum change of crystal. In other words, the crystal would gain momentum as well as electron. But why we don't consider the energy of crystal in this process (we consider all the absorbed energy only as energy of electron transition)?
     
  2. jcsd
  3. DrDu

    DrDu 4,101
    Science Advisor

    How big is the energy change of a crystal of mass ##M \to \infty## if its momentum changes by ##\Delta P##?
     
  4. Suppose conduction and valence bands are parabolic with the same curvature. If we were to consider the conservation of kinetic energy before and after absorption, the photon energy must be equal to " change of electron's kinetic energy + change of crystal's kinetic energy). According to our supposition electron velocity and hence it's kinetic energy doesn't change so the change of crystal's kinetic energy is equal to the photon energy. Therefore all the photon energy is transfered into kinetic energy of crystal! Could you please help me?
     
  5. DrDu

    DrDu 4,101
    Science Advisor

    No, what I mean is that the crystal's momentum changes from 0 to P and its energy from 0 to ##E=P^2/2M##. If P is finite, E becomes 0 in the limit of infinite mass of the crystal.
    So the crystal takes care of the conservation of true momentum, but is irrelevant for energy conservation.
     
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