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MOS Field-Effect Transistors (MOSFETs)
Page 1
EDB 2034
Analogue Electronics (Jan 2016 Semester)MOS Field-Effect Transistors (MOSFET)Intro & Biasing
Lecturer: Saiful Azrin bin Mohd ZulkifliPhone: 05-368 7852
Email: [email protected]
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MOS Field-Effect Transistors (MOSFETs)
Coverage :
Introduction to MOSFETs
Derivation of iDv
DSRelationship
MOSFET Current-Voltage Characteristics
Summary of MOSFET Current-VoltageCharacteristics
MOSFET Circuit at DC
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MOS Field-Effect Transistors (MOSFETs)
Introduction
Three-terminal devices (Gate, Drain, Source). Most widely used electronic devices as ICs. Current flow in longitudinal direction S to D. Fabricated on a single silicon chip. Symmetrical device (S D) Small in sizes compared to BJT.
Focusing on Enhancement-typeof MOSFET. TWO types: n-channel & p-channel. For n-channel MOSFET :
Fabricated on p-type substrate Two heavily doped n+created namely source
and drain Thin insulator (SiO2) between Gate to
substrate (tox250 nm) 4 Metal contacts deposited for
connection (G, S, D, B) Polysilicon contact is now used
as gate electrode
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MOS Field-Effect Transistors (MOSFETs)
Introduction : MOSFET Operations
No Gate Voltage :
With no bias voltage to the gate, two back toback diodes exist in series between drain andsource. Prevent current conduction from drain to
source when vDSis applied.
n-channel MOSFET
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MOS Field-Effect Transistors (MOSFETs)
Creating a Channel For Current Flow:
S and D are grounded. Positive voltage applied to the Gate, vGS. Positive gate voltage causes:
Free holes (positively charged) repelled from
the region underneath the G (pushed towardsubstrate). Leave behind a carrier-depletion (populated
negative charge) region. Positive gate also attract electrons from n+
source and drain. (abundance in the channel). Sufficient electrons create nregion between S
and D. If voltage is applied between D to S, current
will flow in the channel. The value of vGSwhich allow for mobile
electrons to accumulate and form conductingchannel is called the Threshold voltage, VT.
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MOS Field-Effect Transistors (MOSFETs)
Applying a Small vDS:
Consider vdsis small (i.e. 50 mV or so) whenvGS> VT.Voltage vDScauses iDto flow through the
induced nchannel.
Current is carried by free electrons travellingfrom S to D. By convention Ifrom D to S. iDdepends on density of electrons in the
channel, which depends on magnitude of vGS. iDversus vDSshows a linear resistance
relationship as vDSis increased and controlled
by vGS. The resistance is infinite for vGSVT.
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MOS Field-Effect Transistors (MOSFETs)
Operation as vDSis Increased :
Let vGSbe held constant greater than VT.As vDSis increased, it appears as a voltage
drop across the channel.Voltage measured relative to source increases
from 0 to vDS.Voltage between G and points along the
channel decreases from vGSat S to vGS - vDSatD end. Since channel depth depends on thisvoltage, channel is therefore has non-uniformdepth (Deepest at S while shallowest at D).
Thus, iD - vDScurve no longer straight butbends. (Picture next slide)
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MOS Field-Effect Transistors (MOSFETs)
When vDSis increased to the value that reduces the voltage between gate andchannel at the D end to VT(or vGSvDS= VT), the channel depth at the D enddecreases to almost ZERO. Channel is said to be pinched-off. Increasing vDSbeyond this value has little effect of iD. iDbecomes constant
(saturate). The voltage v
DSat which saturation occurs is denoted as v
Dsat= v
GS-V
T
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MOS Field-Effect Transistors (MOSFETs)
Derivation of the iDvDSRelationship
Objective to derive the iDv
DSrelationship at Triode and Saturation region of
operations.Assume that vGS> VTto induce a channel.Voltage vDSis applied between D to S. Consider operation in Triode region:
vDS< vGS- VT
Since the gate and the channel form a parallel platecapacitor denoted by Coxtherefore, the capacitance perunit gate area Cox is given by
oxox
ox
C
t
Where oxis the permittivity of the SiO2,ox= 3.45 x 10
-11F/m
[F/m2]
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MOS Field-Effect Transistors (MOSFETs)
Consider the infinitesimal strip of thegate at distance xfrom the source:
The capacitance of the strip is givenby
oxC Wdx
The electron charge dqin theinfinitesimal portion of the channel atpointxis given by
Q CV
( )ox GS T
dq C Wdx v v x V
Effective voltage
Negative charge
The electric field produced by vDSin the negative xdirection can be written as
[F]
dv x
E x
dx
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MOS Field-Effect Transistors (MOSFETs)
The electric field produced causes the electron charge dqto drift toward the drainwith velocity of
n n
dv xdxE x
dt dx
n- Mobility of electrons
Finally the resulting drift current, i can be obtained as follows:
dq dq dxi
dt dx dt
( )n ox GS T dv x
i C W v v x V dx
The drain-to-source current, iDcan therefore be written as
( )D n ox GS Tdv x
i i C W v v x V dx
( )D n ox GS Ti dx C W v v x V dv x
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MOS Field-Effect Transistors (MOSFETs)
Integrating both sides from x= 0 tox= L, corresponding to v(0) = 0 to v(L) = vDSyield
0 0
( )DS
vL
D n ox GS Ti dx C W v v x V dv x
21
2D n ox GS T DS DSi L C W v V v v
21
2D n ox GS T DS DS
Wi C v V v v
L
iDTriode region
To obtain current in the saturation region, we substitute vDS= vGSVTinto aboveequation which yield
21
2D n ox GS T
Wi C v V
L
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MOS Field-Effect Transistors (MOSFETs)
The term nCoxis known as the process transconductance parameter an normallysubstitute as kn
'n n oxk C
Therefore iDvDScan be rewritten as
' 21
2D n GS T DS DS
Wi k v V v v
L
2'1
2D n GS T
Wi k v V
L
(Triode region)
(Saturation region)
Aspect ratio
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MOS Field-Effect Transistors (MOSFETs)
Example:
Consider a process technology for which Lmin= 0.4 m, tox= 8 nm, n= 450 cm2/V.s,and VT= 0.7 V.
a) Find Coxand kn.b) For a MOSFET with W/L = 8 m/0.8 m, calculate the values of VGSand VDSmin
needed to operate the transistor in the saturation region with a dc current ID= 100
A.c) For the device in (b), find the value of VGSrequired to cause the device to operate
as a 1000 resistor for very small vDS.
Solution:
a) 11
3 2
9
3.45 104.32 10 /
8 10
oxox
ox
C F mt
' 2 3 2 6450 / . 4.32 10 / 194 10 / .n n oxk C cm V s F m F V s
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MOS Field-Effect Transistors (MOSFETs)
b) For operation in the saturation region,
2'1
2D n GS T
Wi k v V
L
26 61 8100 10 194 10 0.72 0.8
GSv
0.32 0.7 1.02GSv V min 1.02 0.7 0.32DS GS Tv v V V
c) For operation in the triode region,
' 21
2D n GS T DS DS
Wi k v V v v
L
For very small vDS, equation above can be reduced to
'D n GS T DSW
i k v V vL
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MOS Field-Effect Transistors (MOSFETs)
From which the drain-to-source resistance rDS
can be found as
'
1
n GS T W
k v VL
_DS
DSDS
D small v
vr
i
611000
194 10 10 0.7GSv
1.22GSv V
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MOS Field-Effect Transistors (MOSFETs)
MOSFET Current-Voltage Characteristics
The iD-vDSCharacteristics:
- Figure shows a std biasing ofn-channel MOSFET.
- The circuit can be used to measureiDvDS characteristics family of
curves at a constant vGS.- The characteristics show 3 regions
of operation : cutoff, triode, &saturation.
- Saturation region Amplifier- Cutoff & triode Switching
- CUTOFF:
- TRIODE:
GS Tv V
GS Tv V
(Induced Channel)
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MOS Field-Effect Transistors (MOSFETs)
GD Tv V (To maintain continuous Channel)
In terms of vDS,
GD GS SD GS DS v v v v v
Which yieldGS DS T v v V
Rearranging above equation will result in
DS GS Tv v V (To maintain continuous Channel)
In Triode region, the iDvGScharacteristic can be described as
' 21
2D n GS T DS DS
Wi k v V v v
L
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MOS Field-Effect Transistors (MOSFETs)
If vDS
is sufficiently small then the previous equation will become
'D n GS T DSW
i k v V vL
Specifically, for a value of vGS, rDSis given by
1'
_DS
DSDS n GS T
D small v
v Wr k v V
i L
It is also useful to express above equation in terms of gate-to-sourceoverdrive voltage given by
OV GS T V V V
Which will lead to
1'
DS n OVW
r k VL
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MOS Field-Effect Transistors (MOSFETs)
- SATURATION:
GS Tv V (Induced Channel)
The pinched off at drain end occurs by raising vDSto a value that results the gate-to-drain voltage, VGDfalling below VT,
GD Tv V (Pinched-off Channel)In terms of vDS,
GD GS DS v v v
GS DS T v v V DS GS T v v V (Pinched-off Channel)
The boundary between the triode and the saturation region is given by
DS GS Tv v V (Boundary)
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MOS Field-Effect Transistors (MOSFETs)
In Saturation region, the iDvGScharacteristic can be described as
2'1
2D n GS T
Wi k v V
L
The large-signal equivalent-circuit model that represents the MOSFET operation in
Saturation region is given by:
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MOS Field-Effect Transistors (MOSFETs)
Channel-Length Modulation:
- Previously we assume that increase of vDSbeyond vDSsathas no effect on channelsshape.
- In reality, as vDSis increased beyond VDSsat, the channel pinch-off point is movedslightly away from the drain, toward the source.
- This is due to the additional voltage applied beyond vDSsatwhich accelerates theelectrons that reach the drain end of the channel and sweeps them across thedepletion region into the drain.
- With depletion-layer widening, thechannel length effect is reducedfrom L to L - L.
- This phenomenon is known aschannel-length modulation.
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MOS Field-Effect Transistors (MOSFETs)
From previous equation and by including the channel-length modulation effect weget
2'1
2D n GS T
Wi k v V
L L
2'1 1
2 1D n GS T
W
i k v V LLL
2'1
12
D n GS TW L
i k v V L L
1LLPreviously assumed
and
' DSL v
Where is a process technology parameter (m/V).
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MOS Field-Effect Transistors (MOSFETs)
Inserting into previous equation yield
2'1 '
12
D n DS GS TW
i k v v V L L
Usually, /L is denoted as , therefore
2'1 1
2D n DS GS T
Wi k v v V L
A typical set of iD-vDScharacteristics showing the effectof channel-length modulation is as follows:
From the plot, when the straight-line are extrapolated,they intercept at the point vDS= -VA (Early Voltage).
Due to VA, the output resistance, rocan be derived as
A
o D
Vr
I
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MOS Field-Effect Transistors (MOSFETs)
Finally the large-signal equivalent circuit model by including the channel-lengthmodulation is given by
OS i ld ff i ( OS )
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MOS Field-Effect Transistors (MOSFETs)
Summary of the MOSFET Current-Voltage Characteristics
NMOS Transistor:Operation in the Triode region:
Conditions:
(1)
(2)
GS Tv V
GD Tv V DS GS T v V V
i-v Characteristics:
21
2
D n ox GS T DS DSW
i C v V v v
L
For vDS
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MOS Field-Effect Transistors (MOSFETs)
Operation in the Saturation region:
Conditions:
(1)
(2)
i-v Characteristics:
GS Tv V
GD Tv V DS GS T v V V
2'1 1
2D n DS GS T
Wi k v v V
L
2'1
2D n GS T
Wi k v V
L
(With Channel-Length Modulation effect)
MOS Fi ld Eff t T i t (MOSFET )
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MOS Field-Effect Transistors (MOSFETs)
MOSFET Circuit at DC: Example 1
Analysis of MOSFET circuit at dc. Neglect channel-length modulation unless specified (= 0).
Design the circuit of the circuit below so that the transistoroperates at ID= 0.4 mA and VD= 0.5 V. The NMOS transistor hasVT= 0.7 V, nCox= 100 A/V
2, L = 1 m, and W = 32 m.
Since,
0 0.5 0.5 0.7GD G D T v V V V
NMOS transistor is operating in Saturation region.
2 2' '1 1
2 2D n GS T n OV
W Wi k v V k V
L L
21 32
0.4 1002 1
OVm V
0.5OVV V ; 1.2OV GS T GS OV T V V V V V V V
MOS Fi ld Eff t T i t (MOSFET )
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MOS Field-Effect Transistors (MOSFETs)
Since the Gate is grounded,
0 1.2 ; 1.2GS G S S S V V V V V V V
From the G to S loop,
1.2 2.53.25
0.4
S SSS
D
V VR k
I m
From D region,
2.5 0.55
0.4
DD DD
D
V VR k
I m
MOS Fi ld Eff t T i t (MOSFET )
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MOS Field-Effect Transistors (MOSFETs)
Example 2
Design the circuit of the circuit below so that the transistoroperates at ID= 80 A. Find the value required for R and find thedc voltage VD. Let the NMOS transistor has VT= 0.6 V, nCox=200 A/V2, L = 0.8 m, and W = 4 m.
From the circuit,
0 0.6GD D D T v V V V V G D
v V
NMOS transistor is operating in Saturation region.
2 2' '1 1
2 2D n GS T n OV
W Wi k v V k V
L L
21 4
80 2002 0.8
OVV
0.4OVV V ; 1.0OV GS T GS OV T GV V V V V V V V
MOS Fi ld Eff t T i t (MOSFET )
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MOS Field-Effect Transistors (MOSFETs)
Since the S is grounded,
0 1.0GS G S G G DV V V V V V V
From D region,
3 1
2580
DD DD
D
V V
R kI
MOS Fi ld Eff t T i t (MOSFET )
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MOS Field-Effect Transistors (MOSFETs)
Example 3
Design the circuit of the circuit below to establish a drain voltage of 0.1 V. Whatis the effective resistance between drain and source at this operating point?. LetVT= 1 V, and kn(W/L) = 1 mA/V
2.
5 0.1 4.9 1GD G D T v V V V V V
MOSFET is operating in Triode region.
21
2D n ox GS T DS DS
Wi C v V v v
L
21
1 5 1 0.1 0.1 0.3952
Di m mA
The required value for RDcan bedetermined by
5 0.112.4
0.395
DD DD
D
V VR k
I m
The effective drain-to-source resistanceis calculated as
0.1253
0.395
DSDS
D
Vr
I m
MOS Field Effect Transistors (MOSFETs)
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MOS Field-Effect Transistors (MOSFETs)
Example 4
Analyze the circuit shown below to determine the voltages at all nodes and thecurrent through all branches. Let VT= 1 V, and kn(W/L) = 1 mA/V
2.
Since the gate current, IGis zero, the voltage at thegate is simply given by the voltage divider
22 1
1010 510 10
GG DDG G
R MV V V V R R M M
Assuming that the MOSFET is operating insaturation region,
5 6GS DV I k
Using
22'1 1
1 5 6 12 2
D n GS T DW
i k v V m I k L
2
18 25 8 0D DI I 0.89 ; 0.5
D DI mA I mA
MOS Field Effect Transistors (MOSFETs)
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MOS Field-Effect Transistors (MOSFETs)
Since we have two solution for ID, check the first solution yield 6 0.89 6 5.34S DV I k m k V
S GV V Doesnt make sense (NMOS is OFF).
Check the second solution yield
6 0.5 6 3S DV I k m k V
5 3 2GS G S V V V V
10 10 0.5 6 7D D DV I R m k V
Since VD> VG - VT, the transistor is indeed operating in saturation region.