3.155J/6.152J Lecture 6:
IC Lab Testing
Prof,Martin A,Schmidt
Massachusetts Institute of Technology
9/24/2003
Outline
Review of Process
Structures to be Tested
Sheet Resistance
MOS Capacitor
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 2
Our Process
Polysilicon Gate (n-type) MOS Capacitor
n-type substrate
250nm n-type polysilicon gate
50nm gate oxide
Various size capacitors
Polysilicon sheet resistivity monitor
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 3
Resistance
W
L
t
R = ρ L/A = (ρ/t) (L/W)
Resistivity
Process
Mask
-cm
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 4
Concept of Sheet Resistivity
R = ρ L/A = (ρ/t) (L/W)
Sheet Resistivity (R
S
)
# of Squares
/sq
L = W
R = R
S
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 5
Number of Squares
R = 2R
S
R = R
S
/2
R = R
S
/3
R = 8R
S
R = 6.5R
S
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 6
Measurement of Sheet Resistance
+
V
DC
A
B
CD
I
AB
A
B
CD
+
-
V
DA
I
CB
R’ = V
DC
/ I
AB
R’’ = V
DA
/ I
CB
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 7
Van der Pauw
R
S
= (π/ln2)? (R’+R’’) f(R’/R’’)
f(R’/R’’)
Correction Factor
1
Assumptions:
Uniform thickness
Continuous (no holes)
0.2
1 10 100 1000
R’/R’’
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 8
Van der Pauw
Implement a
symmetric structure
R’ = R’’
f(R’/R’’) = 1
R
S
= 4.53 R
ave
R
ave
=? (R’+R’’)
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 9
N Square Resistor
L = L
mask
+?L
W = W
mask
+?W
N = L
mask
/W
mask
>>1
R = R
S
(L/W) = R
S
[L
mask
/(W
mask
+?W)]
Used to determine the process ‘bias’ (?W)
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 10
4-Point Probe
I
I
+ -
V
Eliminates the effect of contact resistance
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 11
Analysis of Resistivity
Semiconductor Resistivity(ρ)/Conductivity(σ)
1/ρ = σ = q(μ
n
n+ μ
p
p)
N-type
n >> p
σ = qμ
n
n
Single Crystal Silicon
n=N (doping density)
μ
Si
= f(N)
Polysilicon
<< μ
Si
μ
poly
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 12
MOS Capacitor
A
t
C = ε A/t = ε
r
ε
o
A/t
C
*
= C / A
ε
r
(SiO
2
) = 3.9 ε
o
= 8.85 x 10
-14
F/cm
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 17
MOS Capacitance Measurement
+
V
GB
v
ac
i
ac
Ref,A,Akinwande
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 18
MOS Capacitor
+ - + - + - +
- + - + - + -
+ - + - + - +
- + - + - + -
+ - + - + - +
- + - + - + -
+ - + - + - +
+ - + - + - +
- + - + - + -
+ - + - + - +
- + - + - + -
+ - + - + - +
- + - + - + -
+ - + - + - +
-
+
-
+
-
+
-
Poly
Oxide
t
ox
n-Si
C
*
= C / A
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 19
MOS Capacitor in Accumulation
+ + + + + + + +
- - - - - - - -
C
*
= C
ox
= ε
ox
/ t
ox
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 20
---------------
MOS Capacitor in Depletion
C
ox
C
s
x
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
s
Depletion
Layer
Function
of V
GB
C
*
= C
ox
C
s
/(C
ox
+ C
s
) C
s
= ε
Si
/ x
s
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 21
-- ------ -------- ------
C
MOS Capacitor in Inversion
C
ox
s,max
- - - -
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ + + + + + +
+ + + + + + + +
x
Depletion
s,max
Layer
Function
of V
GB
C
*
min
= C
ox
C
s,max
/(C
ox
+ C
s,max
)
C = ε
Si
/ x
ss,max
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 22
Depletion Layer Thickness
x
s,max
V
GB
Inversion Accumulation
Flatband
Rapid V
GB
Change
V
FB
V
T
x
s
Depletion
C
s
= ε
Si
/ x
s
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 23
Effect of Oxide Charge
+ + + + + + + +
+ + + +
- - - - - - -- - - - -
A net shift in C-V curve:
Need to add more negative charge (voltage) to invert surface
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 25
MOS Capacitance Measurement
Three measurements
C
ox
C
min
V
FB
Produce
t
ox
N
D
Q
f
Ref,A,Akinwande
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 26
C-V Analysis,Inversion
Can extract N
D
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 27
C-V Analysis,Flatband
Can extract Q
f
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 28
Summary
Measurements - Extraction
Substrate Resistivity - Substrate Doping
Oxide Thickness
Poly Thickness
Poly Sheet Resistivity – Poly Doping,Effective Mobility
C-V (multiple areas) – Oxide Thickness,Substrate Doping,
Flatband Voltage (Fixed Charge)
Comparisons/Discussion
Oxide Thickness – Theory,C-V
Substrate Doping – Resistivity,C-V
Poly mobility – Expectations (relative to single crystal)
Flatband(Fixed Charge) – Expectations (sign and magnitude)
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 29
IC Lab Testing
Prof,Martin A,Schmidt
Massachusetts Institute of Technology
9/24/2003
Outline
Review of Process
Structures to be Tested
Sheet Resistance
MOS Capacitor
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 2
Our Process
Polysilicon Gate (n-type) MOS Capacitor
n-type substrate
250nm n-type polysilicon gate
50nm gate oxide
Various size capacitors
Polysilicon sheet resistivity monitor
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 3
Resistance
W
L
t
R = ρ L/A = (ρ/t) (L/W)
Resistivity
Process
Mask
-cm
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 4
Concept of Sheet Resistivity
R = ρ L/A = (ρ/t) (L/W)
Sheet Resistivity (R
S
)
# of Squares
/sq
L = W
R = R
S
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 5
Number of Squares
R = 2R
S
R = R
S
/2
R = R
S
/3
R = 8R
S
R = 6.5R
S
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 6
Measurement of Sheet Resistance
+
V
DC
A
B
CD
I
AB
A
B
CD
+
-
V
DA
I
CB
R’ = V
DC
/ I
AB
R’’ = V
DA
/ I
CB
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 7
Van der Pauw
R
S
= (π/ln2)? (R’+R’’) f(R’/R’’)
f(R’/R’’)
Correction Factor
1
Assumptions:
Uniform thickness
Continuous (no holes)
0.2
1 10 100 1000
R’/R’’
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 8
Van der Pauw
Implement a
symmetric structure
R’ = R’’
f(R’/R’’) = 1
R
S
= 4.53 R
ave
R
ave
=? (R’+R’’)
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 9
N Square Resistor
L = L
mask
+?L
W = W
mask
+?W
N = L
mask
/W
mask
>>1
R = R
S
(L/W) = R
S
[L
mask
/(W
mask
+?W)]
Used to determine the process ‘bias’ (?W)
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 10
4-Point Probe
I
I
+ -
V
Eliminates the effect of contact resistance
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 11
Analysis of Resistivity
Semiconductor Resistivity(ρ)/Conductivity(σ)
1/ρ = σ = q(μ
n
n+ μ
p
p)
N-type
n >> p
σ = qμ
n
n
Single Crystal Silicon
n=N (doping density)
μ
Si
= f(N)
Polysilicon
<< μ
Si
μ
poly
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 12
MOS Capacitor
A
t
C = ε A/t = ε
r
ε
o
A/t
C
*
= C / A
ε
r
(SiO
2
) = 3.9 ε
o
= 8.85 x 10
-14
F/cm
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 17
MOS Capacitance Measurement
+
V
GB
v
ac
i
ac
Ref,A,Akinwande
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 18
MOS Capacitor
+ - + - + - +
- + - + - + -
+ - + - + - +
- + - + - + -
+ - + - + - +
- + - + - + -
+ - + - + - +
+ - + - + - +
- + - + - + -
+ - + - + - +
- + - + - + -
+ - + - + - +
- + - + - + -
+ - + - + - +
-
+
-
+
-
+
-
Poly
Oxide
t
ox
n-Si
C
*
= C / A
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 19
MOS Capacitor in Accumulation
+ + + + + + + +
- - - - - - - -
C
*
= C
ox
= ε
ox
/ t
ox
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 20
---------------
MOS Capacitor in Depletion
C
ox
C
s
x
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
s
Depletion
Layer
Function
of V
GB
C
*
= C
ox
C
s
/(C
ox
+ C
s
) C
s
= ε
Si
/ x
s
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 21
-- ------ -------- ------
C
MOS Capacitor in Inversion
C
ox
s,max
- - - -
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ + + + + + +
+ + + + + + + +
x
Depletion
s,max
Layer
Function
of V
GB
C
*
min
= C
ox
C
s,max
/(C
ox
+ C
s,max
)
C = ε
Si
/ x
ss,max
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 22
Depletion Layer Thickness
x
s,max
V
GB
Inversion Accumulation
Flatband
Rapid V
GB
Change
V
FB
V
T
x
s
Depletion
C
s
= ε
Si
/ x
s
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 23
Effect of Oxide Charge
+ + + + + + + +
+ + + +
- - - - - - -- - - - -
A net shift in C-V curve:
Need to add more negative charge (voltage) to invert surface
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 25
MOS Capacitance Measurement
Three measurements
C
ox
C
min
V
FB
Produce
t
ox
N
D
Q
f
Ref,A,Akinwande
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 26
C-V Analysis,Inversion
Can extract N
D
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 27
C-V Analysis,Flatband
Can extract Q
f
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 28
Summary
Measurements - Extraction
Substrate Resistivity - Substrate Doping
Oxide Thickness
Poly Thickness
Poly Sheet Resistivity – Poly Doping,Effective Mobility
C-V (multiple areas) – Oxide Thickness,Substrate Doping,
Flatband Voltage (Fixed Charge)
Comparisons/Discussion
Oxide Thickness – Theory,C-V
Substrate Doping – Resistivity,C-V
Poly mobility – Expectations (relative to single crystal)
Flatband(Fixed Charge) – Expectations (sign and magnitude)
Fall 2003 – M.A,Schmidt 3.155J/6.152J – Lecture 6 – Slide 29