04 - Effective mass and holes

04 - Effective mass and holes - EECS 320 Bandstructure...

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EECS 320 Bandstructure, Effective Mass, and Holes J. Phillips EECS 320 Electrons In A Crystal dt dv m qF 0 Force = = Free electrons in a vacuum respond to applied electric fields by the following m 0 =electron rest mass Do electrons in the conduction band of a crystal follow the same relationship? E C E V E q=charge on an electron (1.6x10 -19 C) F=electric field v=velocity (“-” sign for electron)
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J. Phillips EECS 320 Wavevector “k” λ π 2 = k From de Broglie p=momentum A convenient description of momentum is the wavevector h=Planck’s constant (6.63x10 -34 J-s) λ =wavelength λ h p = k p h = s J h × = = 34 10 06 . 1 2 π h Relation to force and energy dt dk dt dp dt dv m h = = = 0 Force m k m p E 2 2 2 2 2 h = = (Kinetic energy) J. Phillips EECS 320 Electrons In A Crystal Electron sees potential variation in crystal U x E p 0 2 2 m p E = Free electron energy-momentum relationship Does E vs p look the same as for free electron?
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J. Phillips EECS 320 Effective Mass Energy-Momentum Relations In A Semiconductor
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