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Lecture Notes_3-4_Carriers_Ef_2014

Therefore the momentum p is an integral multiple of

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Unformatted text preview: use the (Maxwell- )Boltzmann Approximation, which is an exponential form. D. In quantum mechanics, particles can behave like waves, and waves can behave like a particle. Electrons in a crystal with infinite potential barriers at the sides have wavefunctions only in the crystal, that is, the wavefunction is zero at the crystal boundary (side). The crystal length (L) then is an integral number of half wavelength (lamda/2). From de Broglie’s relation in quantum mechanics, lamda equals Plank’s constant h divided by momentum p. Therefore, the momentum p is an integral multiple of h/2L. Since L is macroscopic (mm or cm in size), the quantum of p is very small. Energy E is (px2 + py2 + pz2)/2m*, which describes a sphere in (kx, ky, kz) space, where px = 2πkx and kx is called wave vector. The density of states is the number of states (in uni...
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