MOS structure

AN2386

12/30

Equation 34

At the beginning, the thermal coefficient of

Deriving (Equation 32), it is possible achieve:

Equation 35

and, thus:

Equation 36

Considering (Equation 16) and deriving it versus T is possible obtain:

Equation 37

and also:

Equation 38

Replacing (Equation 38) in (Equation 36) it is possible obtain:

Equation 39

Now, the thermal coefficient of the Fermi voltage is studied. In fact, deriving (Equation 6) it is

possible achieve:

Equation 40

Replacing (Equation 38) in (Equation 40), the following equation can be achieved:

Equation 41

Replacing (Equation 41) and (Equation 39) in (Equation 34), TVTC can be rewritten as:

Equation 42

∂V

TH

∂T

-------------

∂Φ

ms

∂T

-------------

t

OX

ε

ε

OX

Φ

F

---------------------

•

∂Φ

F

∂T

---------

•

2

∂Φ

F

∂T

---------

•

++

=

∂Φ

ms

∂T

-------------

k

q

---

N

g

N

a

•

ni

2

--------------------





 2kT

qni

----------

∂ni

∂T

--------

•

+

ln

–

=

∂Φ

ms

∂T

-------------

Φ

ms

T

----------

2kT

qni

----------

∂ni

∂T

--------

•

+

=

∂n

i

∂T

-------

3

2

---

3.88

10

16

•

•

T

1

2

---

e

E

g0

2KT

-----------





3.88

10

16

•

T

3

2

---

e

E

g0

2KT

-----------





E

g0

2KT

2

--------------

•

+

=

∂n

i

∂T

-------

n

i

2T

-------

3

E

g0

KT

---------

+

•

=

∂Φ

ms

∂T

-------------

Φ

ms

T

----------

3

K

q

----

E

g0

qT

---------

++

=

∂Φ

F

∂T

---------

K

q

----

N

a

n

i

-------



 KT

qn

i

--------

∂n

i

∂T

-------

•

–

ln

=

∂Φ

F

∂T

---------

Φ

F

T

------

3

2

---

K

q

----

•

–

E

go

2qT

-----------

–

=

∂V

TH

∂T

-------------

Φ

ms

T

----------

2

Φ

F

T

------

•

t

OX

ε

ε

OX

Φ

F

---------------------

•

∂Φ

F

∂T

---------

•

++

=