The temperature is 300K with
V
T
=
kT/q
=26mV, while the semiconductor is silicon with
E
gap
= 1.1eV, and
the intrinsic concentration
n
i
= 10
10
cm
3
.
np = n
i
2
can be used to estimate the minority concentration.
For a semiconductor resistor with length
l
and cross section
A
, the resistance can be estimated as
(
29
p
n
qp
qn
A
l
A
l
R
μ
ρ
+
=
=
, where
n
and
p
are the electron and hole concentrations,
n
= 1000cm
2
/Vs
and
p
= 400cm
2
/Vs are the electron and hole mobility.
The minority diffusion length as:
n
n
n
D
L
τ
=
, where
D
n=
n
kT/q
is the diffusivity and
n
=
p
=1
s
is the
minority recombination lifetime.
Diode equations:
W
d
= x
n
+ x
p
bi
D
A
si
V
N
N
q
+
=
1
1
2
0
ε
, N
A
x
p
= N
D
x
n
,
=
2
ln
i
D
A
T
bi
n
N
N
V
V
0
=8.85
×
10
14
F/cm,
si
=11.7 is the relative dielectric constant of silicon,
ox
=3.9, q
=1.6
×
10
19
coul is the
elemental charge,
k
the Boltzmann constant, and
T
the temperature.
For a longbase bipolar junction diode,
I
D
= I
0
(exp(qV
D
/kT) – 1)
, with
+
=
D
i
p
p
A
i
n
n
N
n
L
D
N
n
L
D
qA
I
2
2
0
.
The
minority injection level at the edge of the depletion region can be approximated by
p
n
= p
n0
×
exp(
qV
D
/kT
), which is valid for both forward and reverse biases. Notice that the above equation
needs to replace
L
n
and
L
p
with the geometrical length in the shortbase case.
For nMOSFET with the threshold voltage
V
th
, the drain current
I
D
in the linear and saturation regions
above threshold (
V
GS
> V
th
) are: (notice that
C
ox
ch
= k
n
’
and
λ
=1/V
A
.
(
29
(
29
saturation
)
1
(
2
linear
2
2
2
th
GS
Dsat
DS
DS
th
GS
ch
ox
D
th
GS
Dsat
DS
DS
DS
th
GS
ch
ox
D
V
V
V
V
V
λ
V
V
μ
C
L
W
I
V
V
V
V
V
V
V
V
μ
C
L
W
I

=
≥
+

=

=
<


=
For nMOSFET below the threshold voltage,
T
ox
si
GS
T
DS
V
C
C
V
V
V
n
p
D
e
e
L
D
qWn
I
)
1
/(
/
0
)
1
(
+



=
and
ox
si
C
C
m
+
2245
≡
1
1
κ
Smallsignal parameters
R
in
g
m
R
out
BJT forward active (E at ground)
r
π
=
β
/g
m
= V
T
/I
B
I
C
/V
T
r
o
=V
A
/I
C
MOSFET aboveVth saturation (S at ground)
∞
2I
D
/V
OV
r
o
=V
A
/I
D
g
mn
v
GS
NMOSFET large/small
signal model for the
saturation region.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '07
 SPENCER
 Microelectronics, pts, DVD region code, Regional lockout, nMOSFET

Click to edit the document details