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AN2386 Datasheet(PDF) 9 Page - STMicroelectronics

Part # AN2386
Description  How to achieve the threshold voltage thermal coefficient
PDF  30 Pages
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Manufacturer  STMICROELECTRONICS [STMicroelectronics]
Direct Link  http://www.st.com
Logo STMICROELECTRONICS - STMicroelectronics

AN2386 Datasheet(HTML) 9 Page - STMicroelectronics

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AN2386
MOS structure
9/30
where b1 is equal to 4.76 x 10-23J/K.
Eg0 is equal to 1.21eV and it is the extrapolate value of the band-gap at 0°K while b1 is the
rate of energy gap shift with temperature. Now, (Equation 9) can be rewritten as:
Equation 13
Considering that for the silicon:
Equation 14
and that:
Equation 15
ni becomes:
Equation 16
In the interface layer oxide-semiconductor, the electron and hole concentrations depend on
the gate voltage and can be written as:
Equation 17
Equation 18
When
Φ
s is equal to
Φ
F the semiconductor surface becomes intrinsic. Instead, increasing
Φ
s
again, the layer becomes n-type. When ns equals to p0 a "strong inversion" occurs and the
minority carriers at the surface become the same of the majority carriers in the bulk. The
potential condition for the strong inversion occurs when:
Equation 19
As explained above, when VG is applied on the MOS structure, VOX (a part of VG) will
appear across the oxide and the rest on the silicon surface:
Equation 20
n
i
2
N
cNVe
E
g0
b
1 T
–
kT
-------------------------


N
cNve
b
1
k
-----


e
E
g0
kT
---------


=
=
N
cNVe
b
1
k
-----


3.88
10
16
•
T
3
2
---
cm
3
–
[]
=
E
g0
k
---------
14047 K
[]
=
n
i
3.88
10
16
•
T
3
2
---
e
E
g0
2kT
----------


–
3.88
10
16
–
•
T
3
2
---
e
7023
T
-------------


–
cm
3
–
[]
=
=
n
s
n
0e
E
is
E
i
–
kT
------------------


–
n
0e
q
Φ
s
kT
-------
•


=
=
n
s
n
0e
E
is
E
i
–
kT
------------------


–
n
0e
q
Φ
s
kT
-------
•


=
=
Φ
s
2
Φ
F
=
V
G
V
OX
Φ
s
–
=



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