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ssp_20 - 6 Semiconductors Semiconductor Eg small enough for...

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6-1 6. Semiconductors Semiconductor: E g small enough for thermal excitation of electrons into conduction band. Fig. 6.1 Energy level diagram of a semiconductor. Doping : very small fraction of impurities changes electrical conductivity by orders of magnitude. Solid state electronics. Formation of a band gap in Si (Ge from 4 s 2 , 4 p 2 ) Fig.6.2 Foundation of a band gaps in Si by splitting of atomic levels into bonding and antibonding levels (cf. Chp. 1). Diamond (2 s 2 ,2 p 2 ): E g = 5.4 eV Isolator
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6-2 Temperature dependence of the energy gap Table 6.1 Temperature dependence of the energy gap Temperature 0K 300K Si E g = 1.17 eV E g = 1.12 eV Ge E g = 0.75 eV E g = 0.67 eV At 300K linear T-dependence Reason for T dependence: expansion reduced overlap of wave functions reduced energy splitting
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6-3 Band structures Indirect semiconductor : Maximum of valence band at Γ , i.e. k = (0,0,0) minimum of conduction band: Si: k along [100] Ge: k along [111] Spin-orbit splitting taken into account in calculation for Ge. Fig. 6.2 Calculated bandstructures of silicon and germanium. For germanium the spin-orbit splitting is also taken into account. Both semiconductors are so-called indirect semiconductors, i.e. the maximum of the valence band and the minimum of the conduction band are at different positions in the Brillouin zone. The minimum of the conduction band of silicon lies along the ΓΧ = [100] direction and that of germanium along the Γ L = [111] direction.
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