AN2386

MOS structure

9/30

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

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

Φ

Φ

s

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

appear across the oxide and the rest on the silicon surface:

Equation 20

n

i

2

N

E

g0

b

–

kT

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





N

b

1

k

-----





e

E

g0

kT

---------





=

=

N

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

E

is

E

i

–

kT

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





–

n

q

Φ

s

kT

-------

•





=

=

n

s

n

E

is

E

i

–

kT

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





–

n

q

Φ

s

kT

-------

•





=

=

Φ

s

2

Φ

F

=

V

G

V

OX

Φ

s

–

=