Pauli Exclusion Principle
- Practical Electron Microscopy and Database -
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The valence band electrons normally originate from the electrons in the incomplete outer shell of atoms, for instance, the valence band is formed for silicon (Si) crystals as shown in Figure 3376. An isolated Si atom contains 14 electrons, which occupy 1s, 2s, 2p, 3s and 3p orbital in pairs. When atoms are far away from each other, the electrons in the out shell do not interact. As the distance between atoms is reduced to d1, there is an overlap of electron wavefunctions across adjacent atoms. This leads to a splitting of the energy levels consistent with Pauli exclusion principle, and forming energy bands. This splitting leads to 2N states in the 3s band and 6N states in the 3p band, where N is the number of Si atoms in the crystal. A further reduction of the lattice spacing causes the 3s and 3p energy bands to merge into a single band having 8N available states, and then split again into two bands containing 4N states each. At the temperature of zero Kelvin, the lower band is completely filled with electrons and named as the valence band. The upper band is empty and named as the conduction band. Note that in crystal Si (with lattice spacing d0), the core level electrons do not start yet to interact.

Detailed illustration of electronic structure of silicon as a function of distance between atoms

Figure 3376. Detailed illustration of electronic structure of silicon as a function of distance between atoms. The left red circle is a zoom-in of the right red circle.

In x-ray absorption spectroscopy (XAS), for energies below an absorption edge, the x-rays penetrate rather easily without absorption because the Pauli exclusion principle prevents excitation.




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