Section 4: Multi-frequency capacitance-voltage unit
Model 4200A-SCS Parameter Analyzer Reference Manual
4-62
4200A-901-01 Rev. C / February 2017
Where:
•
W
M
= metal work function (V)
•
W
S
= substrate material work function (electron affinity) (V)
•
E
G
= substrate material bandgap (V)
•
φ
B
= bulk potential (V)
In tests, the values for W
M
, W
S
, and E
G
are listed in the Formulator as constants. You can change the
values depending on the type of materials.
For silicon, silicon dioxide, and aluminum:
Where:
•
k = Boltzmann’s constant (1.3807 x 10
-23
J/K)
•
T = Test temperature (K)
•
q = Electron charge (1.60219 x 10
-19
C)
•
N
BULK
= Bulk doping (cm
-3
)
•
DopeType = is +1 for p-type materials and -1 for n-type materials; the value for DopeType is
changed in the Constants area of the Formulator
For example, for a MOS capacitor with an aluminum gate and p-type silicon
(N
BULK
= 10
16
cm
-3
), W
MS
=
−
0.95 V.
For the same gate and n-type silicon
(N
BULK
= 10
16
cm
-3
), W
MS
=
−
0.27 V.
Because the supply voltage of modern CMOS devices is decreasing and since aluminum reacts with
silicon dioxide, heavily doped polysilicon is often used as the gate material. The goal is to achieve a
minimal work-function difference between the gate and the semiconductor, while maintaining the
conductive properties of the gate.
Effective and total bulk oxide charge
The effective oxide charge,
Q
EFF
, represents the sum of oxide fixed charge (
Q
F
), mobile ionic charge
(
Q
M
), and oxide trapped charge (
Q
OT
):
Q
EFF
= Q
F
+ Q
M
+ Q
OT
