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Chapter 4
Field-Effect Transistors
Microelectronic Circuit Design
Richard C. Jaeger
Travis N. Blalock
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-1
Chapter Goals
•
•
•
•
•
•
•
•
•
•
•
•
Describe operation of MOSFETs.
Define FET characteristics in operation regions of cutoff, triode and saturation.
Develop mathematical models for i-v characteristics of MOSFETs.
Introduce graphical representations for output and transfer characteristic
descriptions of electron devices.
Define and contrast characteristics of enhancement-mode and depletion-mode
FETs.
Define symbols to represent FETs in circuit schematics.
Investigate circuits that bias transistors into different operating regions.
Learn basic structure and mask layout for MOS transistors and circuits.
Explore MOS device scaling
Contrast 3 and 4 terminal device behavior.
Describe sources of capacitance in MOSFETs.
Explore FET modeling in SPICE.
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Chap 4-2
4.1 MOS Capacitor Structure
• First electrode- Gate:
Consists of low-resistivity
material such as metal or
polycrystalline silicon
• Second electrode- Substrate
or Body: n- or p-type
semiconductor
• Dielectric- Silicon dioxide:
stable high-quality
electrical insulator between
gate and substrate.
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Chap 4-3
Substrate Conditions for Different Biases
Accumulation
Depletion
Inversion
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• Accumulation
– VG << VTN
• Depletion
– VG < VTN
• Inversion
– VG > VTN
Chap 4-4
Low-frequency C-V Characteristics for MOS
Capacitor on P-type Substrate
• MOS capacitance is nonlinear function of voltage.
• Total capacitance in any
region dictated by the
separation between capacitor
plates.
• Total capacitance modeled as
series combination of fixed
oxide capacitance and
voltage-dependent depletion
layer capacitance.
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Chap 4-5
Capacitors in series
•
•
•
•
Capacitor C1 in series with Capacitor C2
Q1 = C1 * V1
Q2 = C2 * V2
Totally Q = Ceq * V = Q1= Q2, V = V1 + V2
• Ceq = Q/V = Q/(V1 + V2) = Q/(Q1/C1 +Q2/C2)
•
= 1/(1/C1 + 1/C2) = C1*C2/(C1 + C2)
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Chap 4-6
4.2 NMOS Transistor: Structure
• 4 device terminals:
Gate(G), Drain(D),
Source(S) and Body(B).
• Source and drain
regions form pn
junctions with substrate.
• vSB, vDS and vGS always
positive during normal
operation.
• vSB always < vDS and vGS
to reverse bias pn
junctions
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Chap 4-7
NMOS Transistor: Qualitative I-V
Behavior
• VGS <<VTN : Only small leakage
current flows.
• VGS <VTN: Depletion region formed
under gate merges with source and
drain depletion regions. No current
flows between source and drain.
• VGS >VTN: Channel formed between
source and drain. If vDS > 0,, finite
iD flows from drain to source.
• iB=0 and iG=0.
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Chap 4-8
NMOS Transistor: Triode Region
Characteristics
for vGS VTN vDS 0

where, Kn= Kn’ W/L
Kn’=mnCox’’ (A/V2)
Cox’’=ox / Tox
 ox= oxide




v

i  Kn v V  DS v
D
GS TN
2  DS

permittivity (F/cm)
Tox= oxide thickness (cm)
Microelectronic Circuit Design, 4E
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Chap 4-9
NMOS Transistor: Triode Region
Characteristics (contd.)
• Output characteristics
appear to be linear.
• FET behaves like a
gate-source voltagecontrolled resistor
between source and
drain with








1
iD
Ron 
v

DS
v
DS
0








Q pt

Kn'

1


W
V V V
L GS TN DS v
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DS
0
1
Kn'W V V 
L  GS TN 


Chap 4-10
MOSFET as Voltage-Controlled Resistor
Example 1: Voltage-Controlled Attenuator
vo
Ron
1




vs R R 1K RV
V
on

n  GG TN 

If Kn= 500mA/V2, VTN =1V, R = 2k and
VGG =1.5V, then,
vo
1
 0.667
vs 
mA 


1500
20001.51V


2 
V


To maintain triode region operation,
v v V
or vo VGG VTN
DS GS TN
0.667v (1.51)V
S

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or


v 0.750V
S
Chap 4-11
NMOS Transistor: Saturation Region
•
•
•
If vDS increases above triode region limit,
channel region disappears, also said to be
pinched-off.
Current saturates at constant value,
independent of vDS.
Saturation region operation mostly used for
analog amplification.
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Chap 4-12
NMOS Transistor: Saturation Region
(contd.)
K' W 
2
n
i 
V 
v
D 2 L  GS TN 
v
v V
DSAT GS TN


v v V
DS GS TN
for

is also called saturation or pinch-off
voltage
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Chap 4-13
Transconductance of a MOS Device
• Transconductance relates the change in drain current to a
change in gate-source voltage
di
gm  D
dv
GS Qpt
• Taking the derivative of the expression for the drain

current in saturation region,
2I
W
D
gm Kn' (V V )
L GS TN V V
GS TN

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Chap 4-14
Channel-Length Modulation
• As vDS increases above vDSAT,
length of depleted channel
beyond pinch-off point, DL,
increases and actual L decreases.
• iD increases slightly with vDS
instead of being constant.
K ' W 

2
n
i 
V  1 v 
v
 GS
D
TN  
DS 
2 L
channel length modulation

parameter
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Chap 4-15
Depletion-Mode MOSFETS
• NMOS transistors with VTN 0
• Ion implantation process used to form a built-in n-type
channel in device to connect source and drain by a resistive
channel
• Non-zero drain current for vGS = 0, negative vGS required to
turn device off.
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Chap 4-16
Transfer Characteristics of MOSFETS
• Plots drain current versus gate-source voltage for a fixed
drain-source voltage
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Chap 4-17
Body Effect or Substrate Sensitivity
• Non-zero vSB changes threshold
voltage, causing substrate
sensitivity modeled by




V V g v 2  2
TN TO
SB
F
F





where
VTO= zero substrate bias for VTN (V)
gbody-effect parameter 
V
2FF= surface potential parameter (V)

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Chap 4-18
NMOS Model Summary
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Chap 4-19
4.3 Enhancement-Mode PMOS
Transistors: Structure (11/14)
• P-type source and drain regions
in n-type substrate.
• vGS < 0 required to create p-type
inversion layer in channel
region
• For current flow, vGS < vTP
• To maintain reverse bias on
source-substrate and drainsubstrate junctions, vSB < 0 and
vDB < 0
• Positive bulk-source potential
causes VTP to become more
negative
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Chap 4-20
Enhancement-Mode PMOS Transistors:
Output Characteristics
• For VGS VTP , transistor is
off.

• For more negative vGS, drain
current increases in
magnitude.
• PMOS is in triode region for
small values of VDS and in
saturation for larger values.
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Chap 4-21
PMOS Model Summary
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Chap 4-22
4.4 MOSFET Circuit Symbols
• (g) and (i) are the
most commonly
used symbols in
VLSI logic design.
• MOS devices are
symmetric.
• In NMOS, n+
region at higher
voltage is the drain.
• In PMOS p+ region
at lower voltage is
the drain
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Chap 4-23
Microelectronic Circuit Design, 4E
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Chap 4-24
Microelectronic Circuit Design, 4E
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Chap 4-25
4.5 Internal Capacitances in Electronic
Devices
• Limit high-frequency performance of the electronic device
they are associated with.
• Limit switching speed of circuits in logic applications
• Limit frequency at which useful amplification can be
obtained in amplifiers.
• MOSFET capacitances depend on operation region and are
non-linear functions of voltages at device terminals.
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Chap 4-26

NMOS Transistor Capacitances: Triode
Region
C
C  GC C
W Cox"WL C
W
GS
GSO
GSO
2
2
C
C
 GC  C
W  Cox"WL  C
W
GD
GDO
GDO
2
2
Cox” = Gate-channel
capacitance per unit
area (F/m2).
CGC = Total gate channel
capacitance.
CGS = Gate-source
capacitance.
CGD = Gate-drain
capacitance.
CGSO and CGDO = overlap
capacitances (F/m).
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Chap 4-27
NMOS Transistor Capacitances: Triode
Region (contd.)
C C A C
P
SB J S JSW S


C C A C
P
DB J D JSW D
CSB = Source-bulk capacitance.
CDB = Drain-bulk capacitance.
AS and AD = Junction bottom area
capacitance of the source and
drain regions.
PS and PD = Perimeter of the
source and drain junction
regions.
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Chap 4-28
NMOS Transistor Capacitances:
Saturation Region
• Drain no longer connected to channel
C  2 C C
W
GS 3 GC GSO


C C
W
GD GDO
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Chap 4-29
NMOS Transistor Capacitances: Cutoff
Region
• Conducting channel
region completely
gone.
C C
W
GS GSO

C C
W
GD GDO
C C
W
GB GBO


CGB = Gate-bulk
capacitance
CGBO = gate-bulk
capacitance per unit
width.
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Chap 4-30
SPICE Model for NMOS Transistor
Typical default values used by SPICE:
Kn or Kp = 20 mA/V2
g=0
=0
VTO = 1 V
mn or mp = 600 cm2/V.s
2FF = 0.6 V
CGDO = CGSO = CGBO = CJSW = 0
Tox= 100 nm
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Chap 4-31
MOS Transistor Scaling
• Drain current:


Kn*  mn ox W /  mn ox W  Kn
Tox L
Tox / L /
v
v
v
v
i



W
/

GS
TN
DS
ox
DS
D


*
i  mn
*



 
D
Tox / L /  

2 

• Gate Capacitance:
ox W / CGC
*
*
*
*
C
 (Cox") W L 

GC
Tox / L /

* C
D
V
DV /  t
t* C *
 GC
 i / 
GC i *
D
D
where t is the circuit delay in a logic circuit.
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Chap 4-32
MOS Transistor Scaling (contd.)
• Circuit and Power Densities:
V
i
*i *  DD D  P
 
DD D
2
P*
P*
P / 2
P
P




A* W *L* (W / )( L / ) W L A
P* V
• Power-Delay Product:
t  PDP
PDP*  P*t *  P 
2
3
• Cutoff Frequency:
g
f  1 m  1
T 2 C
2
GC
mn 
V V 
L2 GS TN 


fT improves with square of channel length reduction
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Chap 4-33
MOS Transistor Scaling (contd.)
• High Field Limitations:
– High electric fields arise if technology is scaled down
with supply voltage constant.
– Cause reduction in mobility of MOS transistor,
breakdown of linear relationship between mobility and
electric field and carrier velocity saturation.
– Ultimately results in reduced long-term reliability and
breakdown of gate oxide or pn junction.
– Drain current in saturation region is linearised to
C "W
i  ox (v  v )v
D
GS TN SAT
2
where, vSAT is carrier
saturation velocity
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Chap 4-34
MOS Transistor Scaling (contd.)
• Sub-threshold Conduction:
– ID decreases exponentially for
VGS<VTN.
– Reciprocal of the slope in
mV/decade gives the turn off
rate for the MOSFET.
– VTN should be reduced if
dimensions are scaled down,
but curve in sub-threshold
region shifts horizontally
instead of scaling with VTN.
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Chap 4-35
Process-defining Factors
• Minimum Feature Size, F : Width of smallest line or space that
can be reliably transferred to wafer surface using given generation
of lithographic manufacturing tools
• Alignment Tolerance, T: Maximum misalignment that can occur
between two mask levels during fabrication
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Chap 4-36
Mask Sequence for a Polysilicon-Gate
Transistor
• Mask 1: Defines active area or
thin oxide region of transistor
• Mask 2: Defines polysilicon
gate of transistor, aligns to
mask 1
• Mask 3: Delineates the contact
window, aligns to mask 2.
• Mask 4: Delineates the metal
pattern, aligns to mask 3.
• Channel region of transistor
formed by intersection of first
two mask layers. Source and
Drain regions formed wherever
mask 1 is not covered by mask
2
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Chap 4-37
Basic Ground Rules for Layout
• F=2 L
• T=F/2=L,L
could be 1, 0.5,
0.25 mm, etc.
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Chap 4-38
MOSFET Biasing
• ‘Bias’ sets the DC operating point around which the device
operates.
• The ‘signal’ is actually comprised of relatively small
changes in the DC current and/or voltage bias.
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Chap 4-39
Bias Analysis Approach
• Assume an operation region (generally the saturation
region)
• Use circuit analysis to find VGS
• Use VGS to calculate ID, and ID to find VDS
• Check validity of operation region assumptions
• Change assumptions and analyze again if required.
NOTE : An enhancement-mode device with VDS = VGS is
always in saturation
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Chap 4-40
Four-Resistor and Two-Resistor Biasing
• Provide excellent bias for transistors in discrete circuits.
• Stabilize bias point with respect to device parameter and
temperature variations using negative feedback.
• Use single voltage source to supply both gate-bias voltage
and drain current.
• Generally used to bias transistors in saturation region.
• Two-resistor biasing uses lesser components that fourresistor biasing and also isolates drain and gate terminals
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Chap 4-41
Bias Analysis: Example 1 (Constant
Gate-Source Voltage Biasing)
Problem: Find Q-pt (ID, VDS , VGS)
Approach: Assume operation
region, find Q-point, check to see if
result is consistent with operation
region
Assumption: Transistor is saturated,
IG=IB=0
Analysis: Simplify circuit with
Thevenin transformation to find VEQ
and REQ for gate-bias voltage. Find
VGS and then use this to find ID. With
ID, we can then calculate VDS.
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Chap 4-42
Bias Analysis: Example 1 (Constant
Gate-Source Voltage Biasing)(contd.)
V
 I R V
DD D D DS


Since IG=0,
V  I R V V
EQ G EQ GS GS


K 
2
I  n V V 
D 2  GS TN 

6 

2510

mA



312 V2  50 mA

2
V2
V 10V (50uA)(100K)
DS
 5.00 V
Check:VDS>VGS-VTN. Hence
saturation region assumption is
correct.
Q-pt: (50.0 mA, 5.00 V) with
VGS= 3.00 V
Discussion: The Q-point of this
circuit is quite sensitive to changes
in transistor characteristics, so it is
not widely used.
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Chap 4-43
Bias Analysis: Example 2 (Load Line
Analysis)
Problem: Find Q-pt (ID, VDS , VGS)
Assumption: Transistor is saturated,
IG=IB=0
Approach: Find an equation for the
load line. Use this to find Q-pt at
Analysis: For circuit values above,
intersection of load line with device load line becomes
characteristic.
10 I 100K V
D
DS
V
 I R V
DD D D DS

Use this to find two points on the load
line.

Microelectronic Circuit Design, 4E
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Chap 4-44
Bias Analysis: Example 2 (Load Line
Analysis)(contd.)
10 I 100K V
D
DS
@VDS=0, ID=100uA

@ID=0, VDS=10V
Plotting on device characteristic yields
Q-pt at intersection with VGS = 3V
device curve.
Check: The load line approach agrees with
previous calculation.
Q-pt: (50.0 mA, 5.00 V) with VGS= 3.00 V
Discussion: Q-pt is clearly in the saturation
region. Graphical load line is good visual
aid to see device operating region.
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Chap 4-45
Bias Analysis: Example 3 (Constant Gate-Source
Voltage Biasing with Channel-Length Modulation)
Problem: Find Q-pt (ID, VDS , VGS)
of previous example, given =0.02
V-1.
Approach: Assume operation
region, find Q-point, check to see if
result is consistent with operation
region
Assumption: Transistor is saturated,
IG=IB=0
Analysis: Simplify circuit with
Thevenin transformation to find VEQ
and REQ for gate-bias voltage. Find
VGS and then use this to find ID. With
ID, we can then calculate VDS.
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Chap 4-46
Bias Analysis: Example 3 (Constant Gate-Source
Voltage Biasing with Channel-Length Modulation)
Kn 
2 

I 
V  1 V 
V
D 2  GS TN  
DS 
V V
I R
DS DD D D


(25106 )
V 10V (100K)
31210.02 V 

DS

DS 
2
 4.55 V
(25106 )
I 
312 10.02 (4.55) 54.5 mA

D
2

Check: VDS >VGS -VTN. Hence
saturation region assumption is
correct.
Q-pt: (54.5 mA, 4.55 V) with
VGS = 3.00 V
Discussion: The bias levels have
changed by about 10%. Typically,
component values will vary more
than this, so there is little value in
including  effects in most circuits.
Microelectronic Circuit Design, 4E
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Chap 4-47
Bias Analysis: Example 4 (Four-Resistor
Biasing)
Assumption: Transistor is saturated,
I G = IB = 0
Analysis: First, simplify circuit, split
VDD into two equal-valued sources and
apply Thevenin transformation to find
VEQ and REQ for gate-bias voltage
Problem: Find Q-pt (ID, VDS)
Approach: Assume operation
region, find Q-point, check to see if
result is consistent with operation
region
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Chap 4-48
Bias Analysis: Example 4 (Four-Resistor
Biasing)
V 2 0.05V  7.21 0
GS
GS

V  2.71V,  2.66V
GS
Since VGS<VTN for VGS= -2.71 V
and MOSFET will be cut-off,
Since IG = 0,
V V I R
EQ GS D S
Kn 
2
V V   V V  R
EQ GS 2  GS TN  S
4 V 
GS




25106 3.910 4 




V   2.66V and ID= 34.4 mA
GS
Also, VDD  ID(RD RS )VDS
V 6.08V
DS


2
2
V 1
GS 





VDS > VGS - VTN. Hence
saturation region assumption is
correct.
Q-pt: (34.4 mA, 6.08 V) with
VGS = 2.66 V
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-49
Bias Analysis: Example 5 (Four-Resistor
Biasing with Body Effect)
V V g ( V 2  2 )
TN TO
SB
F
F
Analysis with body effect using
same assumptions as in example 1:
V 10.5( V 0.6  0.6)
TN
SB


25106 


2


V

I '
V


D


GS
TN
2



V V
 I R  6 22,000 I
D
GS EQ D S
V  I R  22,000 I
D
SB D S
Iterative solution can be found by
following steps:
• Estimate value of ID and use it
to find VGS and VSB
• Use VSB to calculate VTN
• Find ID’ using above 2 steps
• If ID’ is not same as original ID
estimate, start again.
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-50
Bias Analysis: Example 5 (Four-Resistor
Biasing) (contd.)
The iteration sequence leads to ID= 88.0 mA, VTN = 1.41 V,
V
DS
V
DD
 I (R  R ) 10  40,000 I  6.48V
D D S
D
VDS >VGS - VTN. Hence saturation region assumption is correct.
Q-pt: (88.0 mA, 6.48 V)
Check: VDS > VGS - VTN, therefore still in active region.
Discussion: Body effect has decreased current by 12% and increased
threshold voltage by 40%.
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-51
What if Veq = +4 V +- 1 Volt, Vds = ?
An amplifier?
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-52
Bias Analysis: Example 6 (Two-Resistor
Feedback Biasing)

Kn R 
2
D V V 
V V

GS DD
2  GS TN 



2.6104 10 4 
V  3.3
GS




2





2




V 1
GS
V  0.769V,  2.00V
GS

Since VGS <VTN for VGS = -0.769 V
and MOSFET will be cut-off,
Assumption: IG = IB = 0, transistor is
saturated (since VDS= VGS)

Analysis:
V V
I R
DS DD D D

V 2.00V and ID= 130 mA
GS
VDS >VGS - VTN. Hence saturation
region assumption is correct.
Q-pt: (130 mA, 2.00 V)
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-53
Bias Analysis: Example 7 ( Biasing in
Triode Region)
Also


V
 I (R R )V
DD D D S
DS
41600I V
D DS
V 2.19V
DS
But VDS <VGS - VTN. Hence,

saturation region assumption is
incorrect. Using triode region
equation,
V
Assumption: IG = IB = 0, transistor
is saturated (since VDS = VGS)

Analysis: VGS =VDD=4 V
VDS < VGS - VTN, transistor is in triode region
I  250 mA (41)2 1.13mA
D 2 V2

4V 1600 250 mA (41 DS )V
DS
DS
2 V2
2
V  2.3V and ID=1.06 mA
DS

Q-pt: (1.06 mA, 2.3 V)
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-54
Bias Analysis: Example 8 (Two-Resistor
biasing for PMOS Transistor)
Also 15V(220k)ID VDS  0
50 mA V 22 V  0
15V(220k)

GS
2 V 2  GS 

V   0.369V,  3.45V
GS
Since VGS= -0.369 V is less than VTP= -2 V,
VGS = -3.45 V
Assumption: IG = IB = 0, transistor ID = 52.5 mA and VGS = -3.45 V
is saturated (since VDS= VGS)
V
V
V
DS GS TP
Analysis:
Hence saturation assumption is correct.
V (470k)I V  0
GS
G DS
Q-pt: (52.5 mA, -3.45 V)

Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-55
Junction Field-Effect
Transistor (JFET) Structure
• Much lower input current and
much higher input impedance than
the BJT.
• In triode region, JFET is a voltagecontrolled resistor,
RCH  r L
tW
r = resistivity of channel
• n-type semiconductor block
L = channel length
houses the channel region in nW = channel width between pn
channel JFET.
junction depletion regions
• Two pn junctions form the gate.
t = channel depth
• Current enters channel at the drain
• Inherently a depletion-mode device
and exits at source.
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-56
JFET with Gate-Source Bias
• vGS = 0, gate isolated from channel.
• VP < vGS < 0, W’ < W, and channel
resistance increases; gate-source
junction is reverse-biased, iG almost 0.
• vGS = VP < 0, channel region pinchedoff, channel resistance is infinite.
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-57
JFET Channel with Drain-Source Bias
• With constant vGS, depletion region
near drain increases with vDS.
• At vDSP = vGS - VP , channel is totally
pinched-off; iD is saturated.
• JFET also suffers from channellength modulation like MOSFET at
larger values of vDS.
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-58
N-Channel JFET
i-v Characteristics
Transfer Characteristics
Output Characteristics
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-59
N-Channel JFET
i-v Characteristics (cont.)
• For all regions : iG 0 for vGS 0
• In cutoff region: iD  0 for vGS VP VP 0

• In Triode region:

2I DSS 
v DS 2
iD 
v VP 
v for vGS VP and vGS VP VDS  0
 GS
 DS
2
VP 
2 
•  In pinch-off region:



DSS 


iD  I

1
v
2

GS  




P 
V
1 vDS 
for
vDS  vGS VP  0
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-60
P-Channel JFET
• Polarities of n- and p-type regions of the n-channel
JFET are reversed to get the p-channel JFET.
• Channel current direction and operating bias voltages
are also reversed.
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-61
JFET Circuit Symbols
• JFET structures are symmetric like MOSFETs.
• Source and drain determined by circuit voltages.
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-62
JFET n-Channel Model Summary
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-63
JFET p-Channel Model Summary
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-64
N-channel JFET Capacitances and
SPICE Modeling
• CGD and CGS are determined by depletionlayer capacitances of reverse-biased pn
junctions forming gate and are bias
dependent.
• Typical default values used by SPICE:
Vp = -2 V
= CGD = CGD = 0
Transconductance parameter BETA
BETA = IDSS/VP2 = 100 mA/V2
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-65
Biasing JFET and Depletion-Mode
MOSFET: Example
N-channel JFET
Depletion-mode MOSFET
• Assumptions: JFET is pinched-off, gate-channel junction is reverse-biased,
reverse leakage current of gate, IG = 0
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-66
Biasing JFET and Depletion-Mode
MOSFET: Example (cont.)
• Analysis:
Since I S  I D , VGS   I D RS



S


VGS   I DSS R 1


GS 


P 
V
2





 510 3 A 1000 1
V
 VGS  1.91V, 13.1V


VGS
 5V





2
Since VGS = -13.1 V is less than VP= -5 V, VGS = -1.91 V and ID = IS =
1.91 mA. Also,
VDS VDD  ID(RD  RS )12(1.91mA)(3k) 6.27V
VDS > VGS -VP. Hence pinch-off region assumption is correct and gatesource junction is reverse-biased by 1.91V.

Q-pt: (1.91 mA, 6.27 V)
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-67
End of Chapter 4
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap
Chap
3 -68
4-68
HW4
• 4.34
• 4.79
• 4.118
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-69
Coulomb’s law
• The torsion balance, also called torsion pendulum, is a
scientific apparatus for measuring very weak forces,
usually credited to Charles-Augustin de Coulomb, who
invented it in 1777, but independently invented by John
Michell sometime before 1783.
• Its most well-known uses were by Coulomb to measure the
electrostatic force between charges to establish Coulomb's
Law, and by Henry Cavendish in 1798 in the Cavendish
experiment to measure the gravitational force between two
masses to calculate the density of the Earth, leading later to
a value for the gravitational constant.
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-70
• The torsion balance consists of a bar suspended from its
middle by a thin fiber.
• The fiber acts as a very weak torsion spring.
• If an unknown force is applied at right angles to the ends
of the bar, the bar will rotate, twisting the fiber, until it
reaches an equilibrium where the twisting force or torque
of the fiber balances the applied force.
• Then the magnitude of the force is proportional to the
angle of the bar.
• The sensitivity of the instrument comes from the weak
spring constant of the fiber, so a very weak force causes a
large rotation of the bar.
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-71
• In Coulomb's experiment, the torsion balance was an insulating rod
with a metal-coated ball attached to one end, suspended by a silk
thread.
• The ball was charged with a known charge of static electricity, and a
second charged ball of the same polarity was brought near it.
• The two charged balls repelled one another, twisting the fiber through a
certain angle, which could be read from a scale on the instrument.
• By knowing how much force it took to twist the fiber through a given
angle, Coulomb was able to calculate the force between the balls.
• Determining the force for different charges and different separations
between the balls, he showed that it followed an inverse-square
proportionality law, now known as Coulomb's law.
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-72
• To measure the unknown force, the spring constant of the torsion fiber
must first be known.
• This is difficult to measure directly because of the smallness of the
force.
• Cavendish accomplished this by a method widely used since:
measuring the resonant vibration period of the balance.
• If the free balance is twisted and released, it will oscillate slowly
clockwise and counterclockwise as a harmonic oscillator, at a
frequency that depends on the moment of inertia of the beam and the
elasticity of the fiber.
• Since the inertia of the beam can be found from its mass, the spring
constant can be calculated.
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-73
• Coulomb first developed the theory of torsion fibers and
the torsion balance in his 1785 memoir, Recherches
theoriques et experimentales sur la force de torsion et sur
l'elasticite des fils de metal &c.
• This led to its use in other scientific instruments, such as
galvanometers, and the Nichols radiometer which
measured the radiation pressure of light.
• In the early 1900s gravitational torsion balances were used
in petroleum prospecting.
• Today torsion balances are still used in physics
experiments.
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-74
• In 1987, gravity researcher A.H. Cook wrote:
• The most important advance in experiments on gravitation
and other delicate measurements was the introduction of
the torsion balance by Michell and its use by Cavendish.
• It has been the basis of all the most significant experiments
on gravitation ever since.
Microelectronic Circuit Design, 4E
McGraw-Hill
Chap 4-75