lectures15-17 - (e) Electrons, holes, and ionization states...

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(e) Electrons, holes, and ionization states of defects The process of forming intrinsic electron-hole pairs is excitation across the bandgap + h e ' null Their concentrations can be approximated as = = kT E N N p n g c 2 exp v N c – effective conduction band density of states, ~ 10 19 cm -3 at 300K N v – effective valence band density of states, ~ 10 19 cm -3 at 300K E g – band gap n , p – electron and hole concentrations in number of electrons and holes per unit volume (when compared with mole fractions of atomic defects such as vacancy concentrations, care needs to be taken about units) Example: intrinsic ionic and electronic defect concentrations in MgO (from Physical Ceramics by Y. M. Chiang et al) Data at 1673 K: H s ~ 7.7eV; E g ~ 6.28eV, ( N c N v ) 1/2 ~ 1.3x10 20 cm -3 density = 3.58g/cm 3 , molecular weight = 40.31g/mole [] [ ] 12 2 / 1 O ' ' Mg 10 5 . 2 2 exp V V × = = kT H K s s () 3 - 10 2 1 v cm 10 6 . 4 2 exp × = = = kT E N N p n g c Vacancy concentrations in terms of per unit volume: [] [ ] 3 - 11 MgO MgO 12 O ' ' Mg cm 10 4 . 1 10 5 . 2 V V × = × × = W N o ρ
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e K np = Any unit conversion factor can be absorbed into the equilibrium constant, K e . The number of lattice sites per unit volume in MgO is about 5x10 22 /cm 3 whereas typical impurity level in MgO is on the order of ppm or hundreds of ppms. Therefore, the intrinsic ionic and electronic defect concentrations are much lower than impurity levels, and thus in MgO, defect concentrations are controlled by impurities, i.e. [ ] [ ] (1ppm) level impurity ' ' << = > = p n V V O Mg [ ] [ ] 3 - 10 ' ' cm 10 6 . 4 × = = > = p n V V O Mg Free electrons and electron holes do not themselves occupy lattice sites. However, they are tightly bound to an ion, or localized (“trapped”) at a lattice site. In this case, the bound
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lectures15-17 - (e) Electrons, holes, and ionization states...

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