U of M PHYS 4201 - Semiconductor statistics (17 pages)

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Semiconductor statistics



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Semiconductor statistics

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Pages:
17
School:
University of Minnesota- Twin Cities
Course:
Phys 4201 - Statistical and Thermal Physics
Statistical and Thermal Physics Documents

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Semiconductor statistics Semiconductor a system with electron orbitals grouped into two energy bands separated by an energy gap band gap Lower band is the valence band upper band is the conduction band g c v In Si energy gap is 1 1 eV room temperature is 25 meV In a pure semiconductor at zero temperature all VB orbitals are occupied all CB orbitals are empty and semiconductor is an insulator Finite conductivity is due to occupied orbitals in CB conduction electrons or unoccupied orbitals in VB holes Two mechanisms are possible 1 Thermal excitation of electrons from VB to CB 2 Thermal ionization of impurities that provide additional orbitals and can donate donors or accept acceptors electrons Semiconductor statistics In pure intrinsic semiconductors concentration of conduction electrons is equal to the concentration of holes Electrical neutrality condition ne nh In semiconductors with impurities doped semiconductors impurities may be ionized donors become positively charged and acceptors become negatively charged n n n Net ionized donor doping concentration d a Electrical neutrality condition ne nh n nd na Electron and hole concentrations can be found from the F D distribution Ne 1 functions f e N e f e ne V exp 1 CB N 1 N h f h nh h V exp 1 VB Chemical potential Fermi level is found from electrical neutrality condition ne nh n f h 1 f e Classical regime Classical regime implies low orbital occupancies f e 1 f h 1 This happens when the Fermi level lies deep in the energy gap so that 1 1 exp c 1 exp c 1 f e exp 1 1 1 exp v 1 exp v 1 f h exp 1 Therefore c 0 and v 0 Such a semiconductor is called nondegenerate and is described by classical distribution functions f e exp f h exp Classical regime Total number of electrons in CB N e exp exp c exp c CB CB 1 4442444 3 Nc N e N c exp c Total number of holes in VB N h exp exp v exp v VB VB 1 4442444 3 N h N v exp v Nv Orbitals close to the band edge make dominant contributions orbitals deep in the bands can be ignored Nc Nv is



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