Energy Bands in Semiconductors Overlap of energy bands
Energy Bands in Semiconductors Overlap of energy bands – presence of mixed states s 2+p 6 = = 2 x (s 1+p 3) 2 (s+p)-Bands In the ground state at 0 K: valence band is completely filled, conduction band is empty 1
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Undoped (intrinsic) semiconductors (e- in the CB) 3
Fermi Energy in Semiconductors Fermi energy: Temperature T > 0 K Energy T = 0 K The Fermi energy (Fermi level) of semiconductors at 0 K is located in the middle of the energy gap 4
Electrons and Holes EC 5
Electrons in the Conduction Band Fermi function: 6
Number of Electrons in Conduction Band 7
Electrons in the Conduction Band Number of electrons in the conduction band: Fermi energy: Effective mass: Number of electrons in the conduction band (per unit of volume): 8
Number of Charge Carriers and Electrical Conductivity 9
Electrical conductivity Mobility of electrons and holes Density of the charge carriers 10
Electrical Properties of some Semiconductors Effective mass The mobility of electrons (in conduction band) is always larger than the mobility of holes (electrons in valence band), because the concentrations of the respective charge carriers are different. The effective charge carriers are always electrons, which are “few” in the conduction band, but still “many” in the valence band. 11
Table 14. 6. gap energy, mobility of electrons and holes and the effective mass of conduction electrons Lattice parameter (Å) 3. 5670 4. 3585 Diamond 5. 4300 5. 6568 5. 6533 6. 0954 6. 056 6. 4867 12
Correlation between the lattice parameter and the gap size For the same (or similar) crystal structure type, the lattice parameter defines the distances between neighboring atoms, which affect the gap size. Short atomic distances make the gap size larger, large atomic distances make the gap size smaller. 13
Energy Transition of Electrons between Valence Band Conduction Band* Thermal excitation Photon Electron Optical transition Phonon Cutoff frequency of absorption: * Quantum jump 14
- Slides: 14