MOSFETs - An Introduction
Sung June Kim
kimsj@snu.ac.kr
http://helios.snu.ac.kr
Chapter 17.
CONTENTS
• Qualitative Theory of Operation
• Quantitative I
D - V
D Relationships
• Subthreshold Swing
• ac Response
Qualitative Theory of Operation
• Assumption
– Ideal Structure
– Long Channel Enhancement-Mode
– MOSFET=MOS-Capacitor + 2 pn junctions
– n - channel (p-type substrate)
V D = 0 Case
• When V
G £ V
T , very few electrons in the channel.
an open circuit between the n+ region
• When V
G > V
T ,
– Inversion layer is formed
– The conducting channel (induced “n-type” region, inversion layer) connects the D & S
– V
G the pile up of electrons conductance
\ V
Gdetermines the maximum conductance – Thermal equilibrium prevails, and I
D
=0
• The V
D is increased in small steps starting from V
= 0 D
– The channel acts like a simple resistor – I
Dµ V
– The reverse bias junction current is negligible
D– voltage drop from the drain to the source starts to negate the inverting effect of the gate
– V
D Depletion of the channel # of carriers¯ conductance¯ slope-
over in the IV
• Pinch - off (V
D = V
Dsat )
– Disappearance of the channel adjacent to the drain
• The slope of the I
D
-V
D
becomes approximately zero(Point B)
• Post-pinch-off (V
D > V
Dsat )
– The pinched-off portion widens from just a point into a depleted channel section
D L
– The pinched-off section absorbs most of the voltage drop in excess of V
Dsat
– For D L << L, the shape of the conducting region and the potential across the region do not change Constant I
D
– For D L ~ L, I
D
will increase with V
D
> V
Dsat
• General form of the I
D - V
D ( D L << L )
– For V
G
£ V
T
, I
D
» 0 – For V
G
>V
T
, transistor action: I
D
is modulated by V
G
– V
D> V
Dsat
: saturation region – V
D< V
Dsat
: linear(triode) region
I D - V
D Characteristics
The slope increases with
V
GV
Dsatincreases with V
GQuantitative I
D - V
D Relationships
• Effective Mobility
: Impurity Scattering
+ Lattice Scattering
+ Surface Scattering
• Effective Mobility
( )
ò ò
(y) x
y x
n
n
cc
n(x,y)dx
)dx (x,y)n(x,y
=
0
0 m
m
¯
®
® surface scattering m
nG
®
– V more carriers closer to the interface higher
electric field
dy V d
V C
W
E WQ
I V
V C
Q
T G
o n
n N
D T
G o
N
f f m
m f
) (
(y) (y)
) (
(y)
- -
= -
=
® -
- -
@
• Square - Law Theory
– VD < V
• A drift current is dominant
DsatAt an arbitrary point y
) ( G T
o N
N semi
gate
V V
C Q
Q Q
Q
- -
@
-
@ -
=
Integrating
ú û ù ê
ë
é - -
=
® ( ) 2
2 D D
T G
o n D
V V V
L V C I W m
f f
m ò - -
ò 0 L I D dy = W n C o 0 V
D( V G V T ) d
– V
D³ V
Dsat
• I D is approximately constant
( ) 2
2
2
0 )
( )
(
) 2 (
T G
o n Dsat
T G
Dsat
Dsat T
G o
N
Dsat Dsat
T G
o n Dsat
V L V
C I W
V V
V
V V
V C
L Q
V V V
L V C I W
-
=
-
=
= -
- -
=
ú û ù ê
ë
é - -
=
m
m
• Subthreshold transfer characteristics
– At weak inversion, diffusion current dominates
– In long channel MOSFETS the subthreshold current varies exponentially with V
G
and is independent of V
D
provided V
D
> a few kT/q
G
S
V
Q is exponentia l function of
where
exp
where
) exp(
1
÷ ø ç ö
è æ
ú û ù ê ë
é - -
µ µ
»
kT - qV
=Q Q
kT qV L
Q L
-Q I Q
I
D S
D
D S
D S diff
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 10
-1210
-1110
-1010
-910
-810
-710
-6D ra in C u rr e n t [A ]
Gate Voltage [V]
Subthreshold swing
[ ]
D G
G t D
I V
mV/dec dV
I S d
in change
decade a
for
in change
=
= log 1
S
tslope 1
=
17.3 a.c. Response(skip)
• C
gs(C
gd
): The interaction between G and the channel charge near S(D)
• C
gsp,C
gdp
: parasitic or overlap capacitances
• Small-signal equivalent circuit
G S
D S
in MOSFET out
G
S
D
S v
d+
- v
g+
-
g
mv
gsg
dG
S
D
S v
d+
- v
g+
-
g
mv
gsg
dC
gdC
gs•A capacitor behaves like an open circuit at low frequencies.
• I
D(V
D,V
G) + i
d= I
D(V
D+ v
d, V
G+v
g)
• i
d= I
D(V
D+ v
d, V
G+v
g) - I
D(V
D,V
G)
( ) ( )
g G V
D d
D V D d
g G V
D d
D V D G
D D g
G d D
D
V v v I
V i I
V v v I
V V I
V I v
V v V
I
D G
D G
¶ + ¶
¶
= ¶
\
¶ + ¶
¶ + ¶
= +
+ , ,
ce conduc
mutual or
ce c
transcondu V
g I
ce conduc
channel or
drain V the
g I
t cons G V
D m
t cons D V
D d
D G
tan tan
tan
tan tan
L L
=
=
¶
= ¶
¶
= ¶
g m d
d
d g v g v
i = +
\
G
S
D
S v
d+
- v
g+
-
g
mv
gsg
di
d• Table 17.1
) (
G T DO n
d
V V V
L C
g = Z m - -
Below pinch-off (V
D≤V
Dsat) Above pinch-off (V
D>V
Dsat)
0
d
= g
D O n
m
V
L C g Z m
=
m n O( V
GV
T)
L C
g = Z m -
• At the higher operational frequencies encountered in practical applications, the circuit must be modified to take into account capacitive coupling between the device terminals.
• The overlap capacitance is minimized by forming a thicker oxide in the overlap region or preferably through the use of self aligned gate procedures. è C
gdis typically negligible.
G
S
D
S v
d+
- v
g+
-
g
mv
gsg
dC
gdC
gs• 17.3.2. Cutoff Frequency
The f
Tbe defined as the frequency where the MOSFET is no longer amplifying the input signal under optimum conditions.
à Value of the output current to input current ratio is unity
Dsat D
D n o
m T
in out
g m out
g o g
gd gs
in
V V
L if V C
f g i i
v g i
v C f
j v
C C
jw i
£
=
=
\
=
»
@ +
=
2 2
2 1
) 2
( )
(
p m p
p
Small Signal Characteristics
• g d vs. V
G (V
D =0)
– Extrapolating the linear portion of the g
d
- V
Gcharacteristics into the V
Gaxis and equating the voltage intercept to V
T
– Deduce the effective mobility from the slope
)
= ) (V -V
L (V C
= W
g d m n o G T D 0
– Diagnostic purposes in much the same manner as the MOS-C C-V
G