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 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 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:
6.152J3.155J Oxygen impurities in Si: Observed to follow Arrhenius Cm=2×102cxp[-1.03eV/n7 Want about 10-30 ppm(7 x 1017/cm) which occurs at T 1250C Anneal - denuded zone deeper than deepest feature Oxygen E. Vacancy Interstitial Activation energies(ev): 1.03 1.12 2.6 4.5 Dopants, impurities(substitutional, interstitial) 6.12J/3.155J Microelectronic processing At rt number of intrinsic carriers n=(nnh)12=eXp(-E/2kB7)=>n=2X1010cm3 5x1022 (5x102/cm3) ,A 5x1016/ Very small doping concentration =>large increase in carrier concentration What do dopants do? nI E
6.152J/3.155J 6 11 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing Oxygen impurities in Si: Observed to follow Arrhenius Coxy = 2 ¥1022 exp -1.03eV /k [ ] BT Want about 10 - 30 ppm (7 x 1017/cm3)… which occurs at T § 12500C Activation energies (eV): 1.03 1.12 2.6 4.5 Oxygen Eg Vacancy Interstitial 40 Coxy (ppm) 20 0 Agglomeration => warpage, stress, dislocations No agglomeration (many isolated O2- ions) Optimal 1414 T (0C) 1200 High Coxy 3 hr anneal => 15 ppm Anneal => denuded zone deeper than deepest feature Agglomeration Oxygen § 25 microns 12 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing Dopants, impurities (substitutional, interstitial) At RT number of intrinsic carriers: ni = (nenh)1/2 = n0exp(-Eg/2kBT) => ni = 2 x 1010/cm3 5 x 1022 J =sE = ne m = v E = s ne = et m * s = ne2 t m * What do dopants do? Very small doping concentration => large increase in carrier concentration So doping at 1 ppm => 10-6 = nD,A/(5 x 1022/cm3 ) nD,A = 5 x 1016/cm3
6.152J3.155J CRYSTAL GROWTH 6.12J/3.155J Microelectronic processing COnfined CZ Meniscus controlle Zone Pull from freezing solution horizontal 00● vertical 团B2O3 N。v.26,2003
6.152J/3.155J 7 13 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing CRYSTAL GROWTH 1 Confined Normal freezing (Bridgman) Crystal horizontal vertical Crystal B2O3 Si 2 CZ Meniscus controlled LEC Pull from solution Crystal Crystal Floating zone feed rod high-purity crystal 3 Zone melting poly poly
6.152J3.155J 1)Reactants: first need high-purity Si 6.12J/3.155J Microelectronic processing Making high-purity Si: distill I SO2ban·Si+py, SiHCI(D1100C“ Si +hcl MGS-98%6 pure EGS 9 9s pure (Electronic grade S) nAC 二---#1500°c Nov.26,2003
6.152J/3.155J 8 16 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing 1) Reactants: first need high-purity Si 1500°C seed tang VAC crystal SiO2 Si + CO(g) SiHCl3(l) Si + HCl C boat HCl + H2 distill H2 1100°C poly Making high-purity Si: MGS -98% pure (Metallurgical grade Si) EGS 9 9s pure (Electronic grade Si)
6.152J3.155J Growth rate∝G.-G,≡AG 6.12J/3.155J Microelectronic processing Crystal AG=0→ Equilibrium at T△S △S=△H/T -A -T △H<0 interfax Must decrease solidification (latent) heat 1)Pulling crystal from melt seed stal 500°C At S-L interface: ksA=kL Thermal k,=1.5W/cm-C) 0 if growth velocity solid If 7a)too large (Typical v- 1 mm thermal stress Nov.26,2003
6.152J/3.155J 9 17 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing Growth rate µGs -GL > DG DG = 0 fi DH = TDS, DS = DH /Teq. Equilibrium at \Tinterface < Teq DH < 0 Hs - HL larger (latent) heat content Crystal DG = DH Teq -T Teq È Î Í Í ˘ ˚ ˙ ˙ Must decrease for solidification to occur DG = DH - TDS 18 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing 1) Pulling crystal from melt At S-L interface: kSA ,T ,z ˆ ¯ S = kL A ,T ,z ˆ ¯L + L ,m ,t ,m ,t = vAr m Heat of fusion Liquid ÆSolid L ª 340 cal mole Thermal conductivities ks ª1.5 W /(cm- °C) T z Q If growth velocity too large, solid cannot dissipate heat (Typical v = 1 mm / min.) vmax = ks Lr m ,T ,z ˘ ˚solid If too large fi thermal stress T z( )¢ S 0 1500°C seed tang VAC crystal
6.152J3.155J Czochralski growth of single crystals: stress, dislocations 6.12J/3.155J Microelectronic processing Dead boundary layer For large temperature gradients, e.g. dT/a w 1000C/cm and given a=2.6 x 10-6/C, then AV- aAT=> strains of 0.6%6 which exceeds the yield stress of Si,-> dislocations N。v.26,2003 Line defects: dislocations Dislocations originate in shear strains, mostly induced by thermal gradients during growt A couple of dislocations/wafer is typical Why so few? 1)"Tang"(neck at beginning of xtl allows dislocations to move to surface 2)Large number of atoms are involved in a dislocation = high energy, U Dislocation has low entropy(most atoms are in unique place = TS is very positive larg small Nov.26,2003
6.152J/3.155J 10 19 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing dT/dx § 1000C/cm Seed Melt Dead boundary layer Czochralski growth of single crystals: stress, dislocations For large temperature gradients, e.g. dT/dx § 1000C/cm., and given a = 2.6 x 10-6/0C, then Dl/l = aDT => strains of 0.6%, which exceeds the yield stress of Si, => dislocations 20 Nov.26 , 2003 6.12J / 3.155J Microelectronic processing Dislocations originate in shear strains, mostly induced by thermal gradients during growth. Line defects: dislocations A couple of dislocations/wafer is typical. Why so few? 1) “Tang” (neck at beginning of xtl) allows dislocations to move to surface 2) Large number of atoms are involved in a dislocation, => high energy, U Dislocation has low entropy (most atoms are in unique place) G = H - TS is very positive large small
