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AN2386 Datasheet(PDF) 8 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) 8 Page - STMicroelectronics

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MOS structure
AN2386
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Equation 4
ni is the intrinsic electron concentration; Ei is the intrinsic Fermi level; EF is the Fermi level; k
is the Boltzmann constant and it is equal to 1.38x10-23J/K;
ΦF is the Fermi potential.
Considering that the semiconductor is doped of Na acceptor, (Equation 4) becomes:
Equation 5
Now, it is possible achieve
Φ
F as:
Equation 6
For an intrinsic semiconductor ni can be written in two different ways as:
Equation 7
Equation 8
Multiplying (Equation 7) and (Equation 8) it is possible obtain:
Equation 9
NC and NV are the effective density of states at the conduction and valence edges
respectively and Eg is the energy band-gap. NC and NV can be achieved by the electron and
hole distribution functions and they are equal to:
Equation 10
Equation 11
me* and mh* are the electron and hole density of the states effective masses and h is the
Planck constant. The energy band gap depends on the temperature and it can be written as:
Equation 12
p
0
n
ie
E
F
E
i
–
kT
------------------


n
ie
q
φ
F
kT
-------
•


=
=
N
a
n
ie
E
F
E
i
–
kT
------------------


–
n
ie
q
φ
F
kT
-------
•


=
=
Φ
F
kT
q
-------
N
a
n
i
-------


ln
=
n
i
N
ce
E
c
E
F
–
kT
-------------------


–
=
n
i
N
Ve
E
c
E
F
–
kT
-------------------


–
=
n
i
2
N
cNVe
E
c
E
v
–
kT
------------------


N
cNve
E
g T
()
kT
---------------
=
=
N
c
2
2
πm
e
kT
•
h
2
----------------------------



3
2
---


=
N
v
2
2
πm
h
kT
•
h
2
----------------------------



3
2
---
=
E
g
E
g0
b
1T
–
=



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