Midterm Exam Question (Thermal doping review)
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Thermal Doping Review
Midterm Exam Question
You have a n-type silicon wafer that has a resistivity of 0.36 ohm-cm. You
want to use boron to form the base region in the wafer for an npn transistor.
You perform a solid-solubility limited boron “predeposition” at 900 C for 15
minutes followed by (after deglaze and clean) a 5 hour “drive-in” at 1100C.
Find the boron surface concentration , the junction potential and the dose.
(I) just after the “predeposition” step.
(II) just after the “drive in” step.
Thermal Doping Review
Midterm Exam Question
Find the boron surface concentration, the junction potential, and dose.
(I) just after the “predeposition” step.
(a) Boron surface concentration just after the “predeposition” step.
1) Get N from the solubility graph for Boron at 900 C.
0
2) Find the value for diffusion coefficient at 900 C.
For Boron, B, the model
becomes
D(1173) = D0,B e
B
900 C
[
E ,B
A
k (1173)
1173 K
]
3) Find the number of boron atoms, N ( x, t ) when x = 0 and t = 15 minutes
(900 seconds).
N(x,t) = N
0
erfc
[
x2
4D t
T
]
1/2
Thermal Doping Review
Midterm Exam Question
Find the boron surface concentration, the junction potential, and dose.
(I) just after the “predeposition” step.
(b) Boron junction depth in the original resistivity of 0.36 ohm-cm n doped wafer.
1) Determine the number of Boron atoms that correspond to the same
resisitivity. (dopant concentration vs resistivity plot)
2) Use the concentration profile model as a function of distance and time and
solve for the junction depth distance.
(c) Boron dose for this process.
1) Integrate the area under the concentration profile model for the predeposition or the “drive-in” process.
(II) just after the “drive-in” step.
(a) Boron surface concentration just after the “drive-in” step.
1) Use the concentration profile model as a function of distance and time and
solve when x = 0.
2
N(x,t) =
[p
Q
1/2
2
D
T
t
]
e
-[ 4
x
]
D t
T
Thermal Doping Review
Midterm Exam Question
Find the boron surface concentration, the junction potential, and dose.
(II) just after the “drive-in” step.
(a) Boron surface concentration just after the “drive-in” step.
1) Use the concentration profile model as a function of distance and time and
solve when x = 0.
2
N(x,t) =
[p
Q
1/2
2
D
T
t
]
e
-[ 4
x
]
D t
T
(b) Boron junction depth, just after “drive in” step, in the original resistivity of
0.36 ohm-cm n doped wafer.
1) Solve concentration profile model as a function of distance and time for
junction depth.
x j  2 Dt ln( N0 / N B )
Thermal Doping Review
Midterm Exam Question
Find the boron surface concentration, the junction potential, and dose.
(II) just after the “drive-in” step.
(a) Boron surface concentration just after the “drive-in” step.
1) Use the concentration profile model as a function of distance and time and
solve when x = 0.
2
N(x,t) =
[p
Q
1/2
2
D
T
t
]
e
-[ 4
x
]
D t
T
(b) Boron junction depth, just after “drive in” step, in the original resistivity of
0.36 ohm-cm n doped wafer.
1) Solve concentration profile model as a function of distance and time for
junction depth.
x j  2 Dt ln( N0 / N B )
Find the boron surface concentration, the junction potential, and dose.
(II) just after the “drive-in” step.
(a) Boron surface concentration just after the “drive-in” step.
1) Use the concentration profile model as a function of distance and time and
solve when x = 0.
2
N(x,t) =
[p
Q
1/2
2
D
T
t
]
e
-[ 4
x
]
D t
T
(b) Boron junction depth, just after “drive in” step, in the original resistivity of
0.36 ohm-cm n doped wafer.
1) Solve concentration profile model as a function of distance and time for
junction depth.
x j  2 Dt ln( N0 / N B )