3.155J/6.152J Homework set 3,fall 2003
1
3.155J/6.152J
Microelectronic Processing
Fall Term,2003
Bob O'Handley
Martin Schmidt
Problem set 3 Out Sept,29,2003 Due Oct,8,2003
Diffusion,Read Plummer Chap,7,sections 7.1-7.4,7.5.2,7.5.3,7.5.8
1,Show that c(z,t) =
Q
pDt
exp - z/ a( )
2
[ ]
,with a = 2 Dt,is a solution to Fick's second
law of diffusion,
dc(z,t)
dt
= D
d
2
c(z,t)
dz
2
.
2,a) What is the intrinsic carrier concentration in Si at 1100 C?
b) Calculate the effective diffusivity (including first-order,charged-vacancy
corrections) for As impurities in Si at 1100 C for two cases,i) C
As
= 10
15
cm
-3
and ii)
C
As
= 10
19
cm
-3
,(Use Table 7.5 in Plummer.)
c) What is the diffusion length in each case for t = 1 hr.
3,You start with a uniformly doped (N
A
= 10
17
cm
-3
),p-type silicon wafer,Then a
predeposition of phosphorus is made at 1000
o
C to a concentration equal to its
solubility limit (see class notes,Diff I figure),This process takes 2 min.
a) What is the surface dose,Q,of phosphorus?
After the deposition,the surface of the Si was sealed and a "drive-in" anneal was
made at 1100
o
C.
b) For how long must the "drive-in" anneal be carried out to put the n-p junction 0.4
microns beneath the surface? (Here you have to make a sensible approximation about
the role of t).
a) What is the surface concentration,C
s
(0,t),after "drive-in"?
Ion implantation,Read Plummer Chap,8,sections 8.1-8.4,and 8.5.1-8.5.6
Or Campbell 5.1-5.6
4,Calculate and plot the concentration of boron atoms as a function of x (one dimension
into the Si wafer) following ion implantation,The boron atoms are incident to the
surface with energy 40KeV and the dose was 5 x 10
15
cm
-2
,The sample is then
subjected to an anneal for 37 minutes at 950 °C; plot the dopant concentration after
the anneal,If the silicon substrate has a background concentration of 2 x 10
15
cm
-3
,at
what depth is the pn junction?
3.155J/6.152J Homework set 3,fall 2003
2
5,A 30-keV implant of B
11
is done into bare silicon,The dose is 10
12
cm
-2
.
a) What is the depth of the peak of the implanted profile?
b) What is the concentration at this depth?
c) What is the concentration at a depth of 3000 A (0.3 mm)
d) The measured concentration at 0.3 mm is found to be an order of magnitude larger
than the value predicted in part (c),although the profile agrees with answers (a)
and (b),Give a possible explanation,assuming that the measured value is correct.
6,A particular silicon device needs to have an implant of boron with a peak at a depth
of 0.3 mm (3000 A) and a peak concentration of 10
17
cm
-3
,Determine the implant
energy and dose that should be used for this process,Find the as-implanted junction
depth if the substrate is n-type with a concentration of 10
15
cm
-3
.
1
3.155J/6.152J
Microelectronic Processing
Fall Term,2003
Bob O'Handley
Martin Schmidt
Problem set 3 Out Sept,29,2003 Due Oct,8,2003
Diffusion,Read Plummer Chap,7,sections 7.1-7.4,7.5.2,7.5.3,7.5.8
1,Show that c(z,t) =
Q
pDt
exp - z/ a( )
2
[ ]
,with a = 2 Dt,is a solution to Fick's second
law of diffusion,
dc(z,t)
dt
= D
d
2
c(z,t)
dz
2
.
2,a) What is the intrinsic carrier concentration in Si at 1100 C?
b) Calculate the effective diffusivity (including first-order,charged-vacancy
corrections) for As impurities in Si at 1100 C for two cases,i) C
As
= 10
15
cm
-3
and ii)
C
As
= 10
19
cm
-3
,(Use Table 7.5 in Plummer.)
c) What is the diffusion length in each case for t = 1 hr.
3,You start with a uniformly doped (N
A
= 10
17
cm
-3
),p-type silicon wafer,Then a
predeposition of phosphorus is made at 1000
o
C to a concentration equal to its
solubility limit (see class notes,Diff I figure),This process takes 2 min.
a) What is the surface dose,Q,of phosphorus?
After the deposition,the surface of the Si was sealed and a "drive-in" anneal was
made at 1100
o
C.
b) For how long must the "drive-in" anneal be carried out to put the n-p junction 0.4
microns beneath the surface? (Here you have to make a sensible approximation about
the role of t).
a) What is the surface concentration,C
s
(0,t),after "drive-in"?
Ion implantation,Read Plummer Chap,8,sections 8.1-8.4,and 8.5.1-8.5.6
Or Campbell 5.1-5.6
4,Calculate and plot the concentration of boron atoms as a function of x (one dimension
into the Si wafer) following ion implantation,The boron atoms are incident to the
surface with energy 40KeV and the dose was 5 x 10
15
cm
-2
,The sample is then
subjected to an anneal for 37 minutes at 950 °C; plot the dopant concentration after
the anneal,If the silicon substrate has a background concentration of 2 x 10
15
cm
-3
,at
what depth is the pn junction?
3.155J/6.152J Homework set 3,fall 2003
2
5,A 30-keV implant of B
11
is done into bare silicon,The dose is 10
12
cm
-2
.
a) What is the depth of the peak of the implanted profile?
b) What is the concentration at this depth?
c) What is the concentration at a depth of 3000 A (0.3 mm)
d) The measured concentration at 0.3 mm is found to be an order of magnitude larger
than the value predicted in part (c),although the profile agrees with answers (a)
and (b),Give a possible explanation,assuming that the measured value is correct.
6,A particular silicon device needs to have an implant of boron with a peak at a depth
of 0.3 mm (3000 A) and a peak concentration of 10
17
cm
-3
,Determine the implant
energy and dose that should be used for this process,Find the as-implanted junction
depth if the substrate is n-type with a concentration of 10
15
cm
-3
.
