COMSATS Institute of Information Technology
Virtual campus
Islamabad
Dr. Nasim Zafar
Electronics 1 - EEE 231
Fall Semester – 2012
Current -Voltage Characteristics
I-V Characteristics
Lecture No. 29
 Contents:
 Qualitative theory of operation
 Quantitative ID-versus-VDS characteristics
 Large-signal equivalent circuits.
2
Lecture No. 29
Current-Voltage Characteristics
Reference:
Chapter-4.2
Microelectronic Circuits
Adel S. Sedra and Kenneth C. Smith.
Nasim Zafar.
3
Circuit Symbol (NMOS)
Enhancement-Type:
D
ID= IS
G
B
IG= 0
IS
S
G-Gate
D-Drain
S-Source
B-Substrate or Body
4
Circuit Symbol (NMOS)
Enhancement-Type
 The spacing between the two vertical lines that represent the
gate and the channel, indicates the fact the gate electrode is
insulated from the body of the device.
 The drain is always positive relative to the source in an nchannel FET.
5
Qualitative Theory of Operation
Modes of MOSFET Operation
6
Modes of MOSFET Operation
MOSFET can be categorized into three modes of operation,
depending on VGS:
VGS < Vt: The cut-off Mode
VGS > Vt and VDS < (VGS − Vt): The Linear Region
VGS > Vt and VDS > VGS − Vt: The Saturation Mode
Nasim Zafar.
7
MOSFET-Structure
Enhancement Type-NMOSFET
Body
(bulk or
B
substrate)
Source
S
y
Gate: metal or heavily doped poly-Si
G
Drain
IG=0
D
ID=IS
IS
metal
oxide
n+
p
n+
x
L
W
8
VGS<0
n+p n+ Structure  ID ~ 0
body
B
Source
S
Gate
G
- +
Drain
D
VD=Vs
n++
n+
oxide
p
L
n+
W
9
VGS < Vt
The Cut-off Mode:
n+-depletion-n+ structure  ID ~ 0
body
B
source
S
gate
G
- +
drain
D
VD=Vs
+++
n++
oxide
n+
p
L
n+
W
10
VGS > VT
The Linear Mode of Operation:
n+-n-n+ structure  inversion
body
B
source
S
VGS > VT
n+
gate
G
- +
+++
+++
+++
n++
oxide
----p
L
drain
D
VD=Vs
n+
W
11
Quantitative ID-versus-VDS Relationships
12
Quantitative ID-VDS Relationships
S
G (VG)
D (VDS)
QN = inversion layer charge
V  VD
For VG < VT, Inversion layer charge is zero (Slide11).
For VG > VT, Qn(y) =  QG =  Cox (VG  V VT) (Slide12)
13
Quantitative ID-VDS Relationships
 In the MOSFET, the gate and the channel region form a
parallel-plate capacitor for which the oxide layer serves as
a dielectric.
 If the capacitance per unit gate area is denoted Cox and
the thickness of the oxide layer is tox, then
 Cox=εox/ tox (4.2)
Where εox is the permittivity of the silicon oxide
 ε= 3.9 ε0= 3.9×8.854×10-12= 3.45×10-11F/m
Nasim Zafar.
14
Quantitative ID-VDS Relationships
 Current and Current Density:
 In general, Jn= q n n E , for the drift current
 Here, current ID is the same everywhere, but Jn (current
density) can vary from position to position.
d
d
E
(
y
)


J n  J ny  qn nE   qn n
since
dy
dy
Let “ ” be the potential along the channel
15
Quantitative ID-VDS Relationships
Current and Current Density:
To find current, we have to multiply the above with area, but Jny,
n, etc. are functions of x and z. Hence,
d
I D    J ny dx dz  Z  J ny dx   Z n
qn dx

dy
d
  Z n
Qn ( y )
Qn ( y )  charge / unit area
dy
Integrating the above equation, and noting that ID is constant, we get
Z
I D   n
L
VDS
0
Qn ( y ) d
Since we know expression for Qn(y) in
terms of , we can integrate this to get ID
16
Quantitative ID-VDS Relationships
Current and Current Density:
Z n
ID 
Cox
L
2 

VDS
; VG  VT
VG  VT  VDS 
 0  VDS  VDS, sat
2 

ID will increase as VDS is increased, but when VG – VDS = VT, pinchoff of channel occurs, and current saturates when VDS is increased
further. This value of VDS is called VDS,sat. i.e., VDS,sat = VG – VT and
the current when VDS= VDS,sat is called IDS,sat.
I D, sat 
Z  Cox
VG  VT 2
2L
VD  VDS, sat ; VG  VT
Here, Cox is the oxide capacitance per unit area, Cox = ox / xox
17
Current-Voltage Characteristics
18
Current-Voltage Characteristics
IDS
B
C
D
A
VDS
The iD-VDS Characteristics
 Figure 4.11(a) shows an n-channel enhancement-type
MOSFET with voltages VGS and VDS applied and with the
normal directions of current flow indicated.
Fig. 4.11 (a): An n-channel enhancement type MOSFET
20
The iD-VDS Characteristics
 Figure 4.11 (b) shows a typical set of iD-VDS Characteristics.
The iD–vDS Characteristics for a MOSFET Device with k’n(W/L) = 1.0 mA/V2.
21
The iD-VDS Characteristics
 Current-Voltage characteristics of Fig. 4.11 (b) show that
there are three distinct regions of operation:
 The Cutoff Region,
 The Triode Region, and
 The Saturation Region.
22
The iD-VDS Characteristics
The iD–vDS Characteristics for a MOSFET Device.
The iD-VDS Characteristics
 Saturation Region:
 The saturation region is used if the MOSFET is to operate as
an amplifier.
 Cutoff and Triode Regions:
 For operation as a switch, the cut-off and triode regions are
utilized.
24
Operation in the Triode Region
 To operate the MOSFET in the triode region we must first
induce a channel:
 VGS≧Vt
(Induced channel)
 VDS＜VGS – Vt (Continuous Channel)
 The n-channel enhancement-type MOSFET operates in the
triode region when VGS is greater than Vt and the drain voltage
is lower than the gate voltage by at least Vt volts.
25
The iD-VDS Characteristics
 The Triode Mode:
In the triode region, the iD-VDS characteristics can be described
by the following equation:
ID = kn’(W/L)[(VGS-VT)VDS - 1/2VDS2]
(4.11)
 Where kn’= μnCox is the process transcondctance parameter,
its value is determined by the fabrication technology
26
The iD-VDS Characteristics
 The Triode Mode:
• If VDS is sufficiently small
• ID = kn’(W/L)[(VGS-VT)VDS]
(4.12)
 This linear relationship represents the operation of the
MOSFET as a linear resistance rDS whose value is controlled
by VGS.
27
Operation in the Saturation Region
 To operate the MOSFET in the Saturation Region we must first induce a
channel.
 vGS≧ Vt
 vGD≦ Vt
 vDS≧ vGS-Vt
(Induced channel)
(4.16)
(Pinched-off channel)
(4.17)
(Pinched-off channel)
(4.18)
 The n-channel enhancement-type MOSFET operates in the saturation
region when vGS is greater than Vt and the drain voltage does not fall below
the gate voltage by more than Vt.
 The boundary between the triode region and the saturation region is
characterized by
 vDS= vGS-Vt (Boundary)
(4.19)
28
The iD-VDS Relationship
 Saturation Mode
In the Saturation region, the iD-VDS characteristics can be
described by eq. (4. 20):
Nasim Zafar.
29
The iD–vGS characteristic
The iD–vGS Characteristic for an NMOS Transistor in Saturation
30
Summary: MOSFET I-V Equations
 The Cut-off Region: VGS< VT
ID = IS = 0
 The Triode Region: VGS>VT and VDS < VGS-VT
ID = kn’(W/L)[(VGS-VT)VDS - 1/2VDS2]
 The Saturation Region: VGS>VT and VDS > VGS-VT
ID = 1/2kn’(W/L)(VGS-VT)2
Output Characteristics of MOSFET
32
Large-Signal Equivalent-Circuit Model
 In saturate mode, MOSFET provides a drain current whose
value is independent of the drain-voltage VDS and is
determined by the gate-voltage VGS
 Thus, the Saturated MOSFET behaves as an ideal current
source whose value is controlled by VGS according to the
nonlinear relationship in Eq. (4.20).
 Figure 4.13 shows a circuit representation of this view of
MOSFET operation in the saturation region. Note that this is a
large-signal equivalent-circuit model.
33
Large-signal equivalent-circuit model of an n-channel MOSFET operating in
the saturation region.
MOSFET Summary
35
I-V Characteristics of MOSFET
36
MOSFET: Summary
 A majority-carrier device: fast switching speed
 Typical switching frequencies: tens and hundreds of kHz
 On-resistance increases rapidly with rated blocking voltage
 The device of choice for blocking voltages less than 500V
 1000V devices are available, but are useful only at low power
levels (100W)
MOSFET Summary
Importance for LSI/VLSI
– Low fabrication cost
– Small size
– Low power consumption
 Applications
– Microprocessors
– Memories
– Power Devices
 Basic Properties
– Unipolar device
– Very high input impedance
– Capable of power gain
– 3/4 terminal device, G, S, D, B
– Two possible channel types: n-channel; p-channel
38
MOSFET: Merits/ Demerits
 Advantages
•
•
•
•
Voltage controlled device
Low gate losses
Parameters are less sensitive to junction temperature
No need for negative voltage during turnoff
 Limitations
• One disadvantage of MOSFET devices is their extreme sensitivity to
electrostatic discharge (ESD) due to their insulated gate-source regions.
• The SiO2 insulating layer is extremely thin and can be easily punctured by
an electrostatic discharge.
• High-on-state drop as high as 10V
• Lower off-state voltage capability
• Unipolar voltage device.
39