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.26,20036.152J/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