Integrated Circuit Fabrication, Exercises of Analysis and Design of Digital Integrated Circuits

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Practice Problems in Oxidation

Practice Problems in Oxidation 3.1 How long does it take to grow 100 nm of oxide in wet oxygen at 1000 °C (assume 100 sil- icon)? In dry oxygen? Which process would be preferred? 3.2 A 1.2-m silicon dioxide film is grown on a <100> silicon wafer in wet oxygen at 1100 °C. How long does it take to grow the first 0.4 um? The second 0.4m? The final 0.4 un’? 3.3 Derive Eq. (3.8) by solving differential Eq. (3.7). J = DN,/(X, + Dik,). (3.6) aX./dt = J/M = (DNofM)/(X, + D/k.)- (3.7) t= X2/B + X,/(B/A)—7, (3.8) where A =2D/k., B=2DN,/ M, and += X//B + X;/(B/A). 3.4 A 3-um silicon dioxide film is grawn on a <100> silicon wafer in wet oxygen at 1150 C. How long does it take to grow the initial 1 pm oxide? The second micron? The final micron? 3.5 The gate oxide for a CMOS process on <100> silicon is to have a thickness of 10 nm (200 A). Calculate the time required to grow this oxide at 850° C in wet oxygen using Eq. 3.8. Repeat for 1600° C. (Be careful!) Do either of these possible processes seem to be controllable? If so, which one. 3.6 A 2-pm SiO, film is necded as the initial oxide on a <100> silicon wafer. (a) Find the growth time in wet oxygen at 1150° C using Fig, 3.6. (b) Use Eq. (3.8) to calculate the growth time. 3.7 A 1-m SiO, film is needed as the initial oxide on a <100> silicon wafer. {a) Find the growth time in wet oxygen at 1050° C using Fig. 3.6. (b) Repeat the calculation for dry oxygen. (c) Use Eq. (3.8) to calculate the growth times. TABLE 3.1 Values for Coefficient D, and Activation Energy £, for Wet and Dry Oxygen‘ Wet O,(X; = Onm) Dry 0,(X, = 25nm) Dy E, Dy Ey <100> Silicon Linear (B/A) 9.70 X 10” wmv 2.05 eV 3.71 X 108 pm/hr 2.00eV Parabolic (B) 386 wm’shr 0.78 eV 772 pmo"/ar 1.23 eV <111> Silicon Linear (B/A) 1.63 X LO ym/nr 2.05 eV 6.23 x 10° wovbr 2.00 eV Parabolic (B) 386 ym*/hr 0.78 eV 772 um? fat 1.23 eV 3.8 A dry-wet-dry oxidation cycle of 30 min.120 min/30 min. is performed at 1100° C. (a) What is the final oxide thickness for a <100> silicon wafer? Use Eq. 3.8. (b) What is the final oxide thickness for a <111> silicon wafer? 3.9 An one-hour dry oxidation at 1000° C is followed by a 5-hour wet oxidation at 1100° C. (a) Calculate the oxide thickness after cach step for a <100> wafer. (b) Find the final oxide thickness graphically.