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 N
2
molecules.
c) Calculate the flux of N
2
molecules,J (molecules/(cm
2
-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:
SiH
4
(g) ′ SiH
2
(g) + H
2
(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￥ 10
9
(Torr) exp[-1.8 eV/(k
B
T)],find
the partial pressure of each gas assuming p(SH
2
) p(Si H
2
).
4,Assume a CVD process based on the reaction,2AB(g) ′ 2A(s) + B
2
(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.
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:
SiH
4
(g) ′ Si (s) + 2H
2
(g)
2PH
3
(g) ′ 2P (s) + 3H
2
(g).
Deposition occurs at 1000 C,N
Si
=5￥ 10
22
cm
-3
,the Si deposition is reaction limited
(c
g
=10
18
cm
-3
,k
o
=6￥ 10
5
(cm/s),DG = 1.0 eV,and the deposition of the P is
transport limited (c
g
= 10
18
cm
-3
,D
g
= 10
-5
￥ T
3/2
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?
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 N
2
molecules.
c) Calculate the flux of N
2
molecules,J (molecules/(cm
2
-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:
SiH
4
(g) ′ SiH
2
(g) + H
2
(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￥ 10
9
(Torr) exp[-1.8 eV/(k
B
T)],find
the partial pressure of each gas assuming p(SH
2
) p(Si H
2
).
4,Assume a CVD process based on the reaction,2AB(g) ′ 2A(s) + B
2
(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.
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:
SiH
4
(g) ′ Si (s) + 2H
2
(g)
2PH
3
(g) ′ 2P (s) + 3H
2
(g).
Deposition occurs at 1000 C,N
Si
=5￥ 10
22
cm
-3
,the Si deposition is reaction limited
(c
g
=10
18
cm
-3
,k
o
=6￥ 10
5
(cm/s),DG = 1.0 eV,and the deposition of the P is
transport limited (c
g
= 10
18
cm
-3
,D
g
= 10
-5
￥ T
3/2
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?
