AN2386

MOS structure

11/30

Equation 28

and it can be written as:

Equation 29

Up to now, the ideal MOS structure was considered. In the real MOS structure, when no

voltage is applied on the gate, a difference between metal and semiconductor work function

exists, as well as charges in the oxide. In this paper, the charges inside the oxide will be

neglected and also the metal-semiconductor difference work function

The charges inside the oxide are related to the real process flow and they involve a small

threshold voltage shift. In order to consider the effect of

following formula must be taken into account:

Equation 30

charges inside the oxide are neglected.

For metal gate,

Equation 31

Instead, for polysilicon gate (the real case usually) of n-type and the semiconductor is of p-

type,

Equation 32

TVTC can be, thus, achieved deriving (Equation 30) against the temperature:

Equation 33

and also:

V

G

2

ε

C

OX

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

Φ

s

+

=

V

TH

4

ε

C

OX

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

2

Φ

F

+

=

V

TH

V

FB

t

OX

4

ε

ε

OX

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

2

Φ

F

Φ

ms

Q

OX

C

OX

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

t

OX

4

ε

ε

OX

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

•

2

Φ

F

++

+

=

++

=

Φ

ms

Φ

m

χ

E

()

2q

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

Φ

F

±

+





–

=

Φ

ms

kT

q

-------

N

g

N

a

•

ni

2

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







ln

–

=

∂V

TH

∂T

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

∂Φ

ms

∂T

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

t

OX

4

ε

ε

OX

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

•

∂Φ

F

∂T

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

•

2

∂Φ

F

∂T

---------

•

++

=