《Microelectronics Process》Gas kinetics, vacuum tehcnology

3.155J6.152J Microelectronic Processing Technology Fall term. 2003 Bob handley Martin schmidt Homework set 1 out:Sept.8、2003 Due: Sept. 17. 2003 Gas kinetics, vacuum tehcnology Reading Assignment: Kinetics, Vac. Tech: Campbell, 10.1-1. 4(or Ohring Ch 2) 1. Consider a vacuum system at room temperature that has been pumped down to a 10 m-Torr with mostly nitrogen as determined from the residual gas analyzer. Make an intelligent estimate of the diameter of a nitrogen molec a)Calculate the mean free path, 2, of the nitrogen molecules at this pressure b) Calculate the volume density of N, molecules c) Calculate the flux of N2 molecules, J(molecules/(cm-s)impinging an a surface In the chamber d) Calculate the average molecular speed in this case 2. Assume a cryo-pump operates at 100 K and 1 mT(milli-Torr) with a pump speed of 100 sccm. What is the pump speed in L/s(liters per second)? Read: Plummer Secs. 9.1, 9.21-9.22. Campbell, Ch. 10, Secs. 1-3, all of Ch. 13 CVD 3. Assume chemical equilibrium is established in a Cvd reactor according to the qua SiH (g) 2A(S)+b(g) a) Sketch and briefly describe the individual steps that control the reaction b) How would you distinguish between I)the reaction-limited and ii) a transpo limited c)Sketch the variation of the log of the Cvd growth rate as functions of the square root of the gas flow velocity and as a function of 1/T

1 3.155J/6.152J Microelectronic Processing Technology Fall Term, 2003 Bob O'Handley Martin Schmidt Homework Set 1 Out: Sept. 8, 2003 Due: Sept. 17, 2003 Gas kinetics, vacuum tehcnology Reading Assignment: Kinetics, Vac. Tech.: Campbell, 10.1 – 1.4 (or Ohring Ch. 2) . 1. Consider a vacuum system at room temperature that has been pumped down to a pressure of 10 m-Torr with mostly nitrogen remaining as determined from the residual gas analyzer. (Make an intelligent estimate of the diameter of a nitrogen molecule.) a) Calculate the mean free path, l, of the nitrogen molecules at this pressure. b) Calculate the volume density of N2 molecules. c) Calculate the flux of N2 molecules, J (molecules/(cm2 -s)) impinging an a surface in the chamber. d) Calculate the average molecular speed in this case. 2. Assume a cryo-pump operates at 100 K and 1 mT (milli-Torr) with a pump speed of 100 sccm. What is the pump speed in L/s (liters per second)? Read: Plummer Secs. 9.1, 9.21 - 9.22. Campbell, Ch. 10, Secs. 1 - 3, all of Ch. 13. CVD 3. Assume chemical equilibrium is established in a CVD reactor according to the equation: SiH4 (g) ´ SiH2 (g) + H2 (g) The temperature is maintained at 650 C and the pressure at 0.1 atm. If the equilibrium constant for the reaction is K(T)=2 ¥ 109 (Torr) exp[-1.8 eV/(kBT)], find the partial pressure of each gas assuming p(SH2) p(Si H2). 4. Assume a CVD process based on the reaction: 2AB(g) ´ 2A(s) + B2(g). a) Sketch and briefly describe the individual steps that control the reaction. b) How would you distinguish between I) the reaction-limited and ii) a transport￾limited cases? c) Sketch the variation of the log of the CVD growth rate as functions of the square root of the gas flow velocity and as a function of 1/T

d)If you wanted to increase the growth rate of a transport-limited CVd process what processing variables would be most effective? (List them in decreasing rder of efficacy. 5.Phosphorus-doped polysilicon is produced by CVD based on the following reactions: Siha (g) e Si(s)+ 2H,(g) 2PH,(g) 2P(s)+3H2(g) Deposition occurs at 1000 C, Ns=5x 102 3, the Si deposition is reaction limited (c2=108cm3,k。=6×10°cm/s),△G=10eV, and the deposition of the P is transport limited(ce=10,D2 =10-x T cm/s, and(pu/n)o.=0.01 cm) a) What range of P concentration in the poly-silicon might you expect across a 30 cm diameter wafer? Explain the assumptions you must make to answer this question b) If the temperature at the far end of the wafer is constrained to be 10 C hotter than that at the near end of the reactor, how does this affect your answer?

2 d) If you wanted to increase the growth rate of a transport-limited CVD process, what processing variables would be most effective? (List them in decreasing order of efficacy.) 5. Phosphorus-doped polysilicon is produced by CVD based on the following reactions: SiH4 (g) ´ Si (s) + 2H2 (g) 2PH3 (g) ´ 2P (s) + 3H2 (g). Deposition occurs at 1000 C, NSi = 5 ¥ 1022 cm-3, the Si deposition is reaction limited (cg = 1018 cm-3, ko = 6 ¥ 105 (cm/s), DG = 1.0 eV, and the deposition of the P is transport limited (cg = 1018 cm-3, Dg = 10-5 ¥ T3/2 cm/s, and (ru/h) 0.5 = 0.01 cm-0.5). a) What range of P concentration in the poly-silicon might you expect across a 30 cm diameter wafer? Explain the assumptions you must make to answer this question. b) If the temperature at the far end of the wafer is constrained to be 10 C hotter than that at the near end of the reactor, how does this affect your answer?