6.152J3.155J CRYSTAL GROWITH 6.12J/3.155J Microelectronic pn CRYSTAL GROWTH step Crystal and questlons 1. Reactants In molten form 2. Transport to s/L Interface TAS Increases AH decreases 4 CHtcal nucleus slze 6. Impurities, defects more stable at high T how grow pure crystal 7. Segregation solld vS. quid What do we need to know pror to crystal growth? N。v.26,2003 Defects and crystal growth 6.12J/3. 155J Microelectronic processing e Defects impurities, vacancies, dislocations .. T dependence e Crystal growth techniques: float zone, Bridgman, Czochralski Segregation during growth Segregation coefficients Nov.26,2003
6.152J/3.155J 1 1 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing CRYSTAL GROWTH Si Crystal What do we need to know prior to crystal growth? 4. Critical nucleus size 5. Growth 6. Impurities, defects more stable at high T ; how grow pure crystal? 7. Segregation solid vs. liquid 1. Reactants in molten form 2. Transport to S/L interface 3. Adsorbtion: entropy decreases CRYSTAL GROWTH steps and questions DS DH -TDS increases DH decreases (exo) 2 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing Defects and crystal growth •Defects impurities, vacancies, dislocations…T dependence •Crystal growth techniques: float zone, Bridgman, Czochralski •Segregation during growth Segregation coefficients
6.152J3.155J Thermodynamics and phase diagrams 6.12J/3.155JMi Hn -h.=AH= heat of formation wAH of b from a Do all reactions that give off heat proceed? SB-SA=AS=Entropy(disorder)change s[/B from a to b Do all reactions that increase disorder proceed? Answer in Gibbs free energy = Gn -G=4G=AH. TAS G must decrease if reaction is to proceed (From equilibrium, all changes increase G N。v.26,2003 Thermodynamics and phase diagrams 6.12J/3. 155J Microelectronic processing AH= of b from a h Do all Exothermic exothermal reactions Configuration AS=from a to b B△S>0 △S<0 → ordered Does disorder al ways increase AG=AH-T4 Will not go Will not go above T=H/AS belOw T=AH/AS Examples: freezing of water melting of copper Nov.26,2003
6.152J/3.155J 2 3 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing Thermodynamics and phase diagrams HB - HA = DH = heat of formation of B from A Do all reactions that give off heat proceed? SB - SA = DS = Entropy (disorder) change from A to B Do all reactions that increase disorder proceed? ¨S A B S Configurations H A B ¨H G = H - TS GB - GA = DG = DH - TDS G must decrease if reaction is to proceed. (From equilibrium, all changes increase G). A B G Answer in Gibbs free energy: 4 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing DH = of B from A DS =from A to B ¨S < 0 B more ordered A B S Configurations H A B ¨H DG = DH - TDS Will not go above T = DH /DS A B G Exothermic Do all exothermal reactions proceed? ¨S > 0 B more disordered A B S Configurations H A B ¨H Will not go below T = DH /DS A B G Endothermic Does disorder always increase in reactions? Examples: freezing of water melting of copper Thermodynamics and phase diagrams
6.152J3.155J Under what conditions will Si melt crystallize? 6.12J/3.155J Microelectronic processing Liquid Si high s high H Crvstal Si △H=H(T)-H(r)<0 △G=△-As TAS must have smaller magnitude than 4/ for solidification: this defines solidification temp. N。v.26,2003 Note the relatively large solid solubility of As in Si 6.12J/3. 155J Microelectronic processing Atomic Portent Arsenic then decreases Arsenic solubility Whereas increases with T s As +SiA Nov.26,2003
6.152J/3.155J 3 5 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing Under what conditions will Si melt crystallize? T Tm Liquid Si T = Tm + T = Tm - Crystal Si high S high H low S low H For solidification: DS = S T- ( )final - S T+ ( )initial < 0 DH = H T- ( ) - H T + ( ) < 0 DG = DH - TmDS < 0 > 0 TDS must have smaller magnitude than DH for solidification; this defines solidification temp. 6 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing Note the relatively large solid solubility of As in Si Whereas this field is As + SiAs2 Arsenic solubility in Si increases with T ….then decreases on approaching Tmelt
6.152J3.155J 1-dimensional defects: We saw soluble impurities in Si 6.12J/3.155J Microelectronic processing T/7 020 Impurity content(cm-3) 1-dimensional defects: More point defects ○○○ Interstitial Frankel defect Self Substitutional Strain field of vacancy. interstitial 中 Strain and surface energy can be reduced ○必 Vacancy = void ○○○○ when concentration > equilibrium Nov.26,2003
6.152J/3.155J 4 7 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing 1-dimensional defects: We saw soluble impurities in Si. 1.0 T/Tm 1020 1021 Impurity content (cm-3) B As P Smix Si Impurity -TSmix Si Impurity From Phase diagram 8 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing 1-dimensional defects: More point defects Interstitial impurity Substitutional impurity Vacancy Self interstitial V-I pair = Frankel defect Strain field of vacancy… Strain and surface energy can be reduced by agglomeration: Vacancy => void, Interstitial => precipitate …when concentration > equilibrium interstitial
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.26,2003
6.152J/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 antibonding 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: