6.152J3.155J Bonding-antibonding orbital energy separation 6.12J/3.155JMcr GpⅣ uators 2p2 A Conduction band Valence band。。。。。 Bound feet rux Band Model N。v.26,2003 Vacancy concentration: Vacancy requires breaking 4 bonds -E,门] band nm=5×102exp[26cVk门 Arrhenius E plo Ek Equilibrium vacancy concentration: 1000/k7 At RT: nac = 3.4 x 10-23/cm3(=300 km between vacancies) At1273K:na=2.6×1012/cm3(≈700 nm betwee en vacancies Nov.26,20036.152J/3.155J 5 9 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing Bonding-antibonding orbital energy separation bonding/antibonding => energy gaps in semiconductors, insulators E Gp IV atom s2p2 Gp IV atom s2p2 s-p3 anti￾bonding s-p3 bonding Semicon crystal Gap Conduction band Valence band 10 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing Vacancy concentration: Vacancy requires breaking 4 bonds nvac = n0 exp -Eg /k [ ] BT Eg = 1.12 eV Conduction band Valence band nvac = 5 ¥1022 exp -2.6 eV /k [ ] BT Empirical: ln nvac n0 Ê Ë Á ˆ ¯ ˜ = -Ea /kBT ln nvac n0 Ê Ë Á ˆ ¯ ˜ 1000 /kBT Ea Arrhenius plot At RT: nvac = 3.4 x 10-23/cm3 (§ 300 km between vacancies) At 1273 K: nvac = 2.6 x 1012/cm3 (§ 700 nm between vacancies) Vacancies abundant at high temperature Equilibrium vacancy concentration: