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| Energy Bands in Solids |
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| Atoms are clustered together and are overlapped in solids. Therefore, the outermost valence atoms are overlapped. |
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| No two atoms can have the same quantum state. Hence, all electrons have discrete energy states. |
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| If there are 'n' orbits, then there are 2n possible energy levels which are splitting and creating a band of energy (electrons possessing a range of energy levels). |
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| When the electrons have closely spaced energy levels, a valence band is created. |
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| Conduction bands are caused due to the higher energy levels of the electrons. |
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| Valence band and the conduction band lies in the energy gap. |
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| According to the Bohr's theory, free electrons in an isolated atom have certain definite discrete amount of energy. If large number of atoms are brought close to one another to form a crystal, they begin to influence each other. The valence electrons are attracted by the nucleus of the other atoms. This brings about a considerable modification in the case of energy levels of the electrons in the outer shells. The process of splitting of energy levels can be understood as follows: |
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a) If interatomic spacing of atoms is very large i.e., r = d>>a, there is no interatomic separation. Each atom in the crystal behaves as free atom. Take for example silicon whose electronic configuration is
1s2 2s2 2p6 3s2 3p2. If N atoms were to be considered in silicon crystal, then there will be 2N electrons filling 2N possible energy levels in 3s, 6N possible levels in 3p of which only 2N is completely filled.
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b) When the spacing is progressively decreased i.e., c<r<d, there is no visible splitting of energy levels.
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c) When r = c, the 3s and 3p electrons of neighbouring silicon atoms becomes appreciable. The energy of electrons of each atom starts changing, whereas the energies of electrons in the inner shell do not change.
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d) When r lies between b and c, the energy levels get slightly changed and instead of a single 3s or 3p levels, we get a large number of closely packed levels. This collection of closely spaced energy levels is called an energy band.
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e) When r = b>a, the gap between 3s and 3p completely disappear and the 8N energy levels are (2N of 3s and 6N of 3p sub shells) continuously distributed. In this stage 4N levels are filled and 4N levels are empty.
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f) When r = a i.e., actual spacing in the crystal the 4N filled energy levels are separated from 4N unfilled energy levels. This gap or separation is called the forbidden gap. E.g., the lower completely filled band is called valence band and upper unfilled band is called conduction band.
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