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Transistor
Characteristics
EMT 251
Outline
•
•
•
•
Introduction
MOS Capacitor
nMOS I-V Characteristics (ideal)
pMOS I-V Characteristics (ideal)
Introduction
• So far, we have treated transistors as ideal
switches
• An ON transistor passes a finite amount of
current
– Depends on terminal voltages
– Derive current-voltage (I-V) relationships
• Transistor gate, source, drain all have capacitance
– I = C (DV/Dt) -> Dt = (C/I) DV
– Capacitance and current determine speed
MOS Capacitor
• Gate and body form MOS capacitor
• Operating modes
– Accumulation
– Depletion
– Inversion
polysilicon gate
silicon dioxide insulator
Vg < 0
-V
+
-
p-type body
(a)
0 < V g < Vt
V+
+
-
depletion region
(b)
V g > Vt
V++
(c)
+
-
inversion region
depletion region
Terminal Voltages
• Mode of operation depends on Vg, Vd, Vs
– Vgs = Vg – Vs
– Vgd = Vg – Vd
– Vds = Vd – Vs = Vgs - Vgd
• Three regions of operation
– Cutoff
– Linear
– Saturation
nMOS Cutoff
• No channel
• Vgs < Vt
• Ids = 0
Vgs = 0
+
-
g
+
-
s
d
n+
n+
p-type body
b
Vgd
nMOS Linear
• Channel forms
Vgs > Vt
+
-
– Vds = Vgs-Vgd
– If Vds=0 (i.e. Vgs=Vgd)
• No electrical field tending
to push current fr. d to s.
• Small positive potential Vds
• Current flows from d to s
– e- from s to d
• Ids increases with Vds
• Similar to linear resistor
g
+
-
s
d
n+
n+
Vgd = Vgs
Vds = 0
p-type body
b
Vgs > Vt
+
-
g
s
+
d
n+
n+
p-type body
b
Vgs > Vgd > Vt
Ids
0 < Vds < Vgs-Vt
nMOS Saturation
• Channel pinches off
• Ids independent of
Vds
• We say current
saturates
• Similar to current
source
Vgs > Vt
+
-
g
+
-
Vgd < Vt
d Ids
s
n+
n+
p-type body
b
Vds > Vgs-Vt
Nmos region of operation
1.
Cutoff region:
VGS < VT, any value of VDS
ID = 0
2.
Linear (or Resistive, or Triode) region:
VGS > VT, VDS < (VGS – VT)
V 

I D   VGS  VT  DS VDS
2 

W
where    nCox
L
3.
Saturation region:
VGS > VT, VDS > (VGS – VT)
I DSAT 

2
VGS  VT 2
where    n Cox
W
L
“CUTOFF” region: VG < VT
Example
• We will be using a 0.6 m process for your project
– From AMI Semiconductor
2.5
– tox = 100 Å
V =5
2
–  = 350 cm2/V*s
1.5
V =4
– Vt = 0.7 V
1
V =3
• Plot Ids vs. Vds
0.5
V =2
V =1
– Vgs = 0, 1, 2, 3, 4, 5
0
0
1
2
3
4
– Use W/L = 4/2 l
V
Ids (mA)
gs
gs
gs
gs
gs
ds
 3.9  8.85  1014   W 
W
W
2
  Cox   350 

120

A
/
V
 
8
L
100

10
L

 L 
5
pMOS I-V
• All doping and voltages are inverted for pMOS
• Mobility mp is determined by holes
– Typically 2-3x lower than that of electrons mn
– 120 cm2/V*s in AMI 0.6 mm process
• Thus pMOS must be wider to provide same
current
– In this class, assume mn / mp = 2
– *** plot I-V
Transistor Operation
• Current depends on region of
transistor behavior
• For what Vin and Vout are nMOS and
pMOS in
– Cutoff?
– Linear?
– Saturation?
Schematic of CMOS
inverter
nMOS Operation
Cutoff
Vgsn < Vtn
Vin < Vtn
Linear
Vgsn > Vtn
Vin > Vtn
Vdsn < Vgsn – Vtn
Vout < Vin - Vtn
Vgsn = Vin
Saturated
Vgsn > Vtn
Vin > Vtn
Vdsn > Vgsn – Vtn
Vout > Vin - Vtn
VDD
Vdsn = Vout
Vin
Idsp
Idsn
Vout
pMOS Operation
Cutoff
Vgsp > Vtp
Vin > VDD + Vtp
Vgsp = Vin - VDD
Vdsp = Vout - VDD
Linear
Vgsp < Vtp
Vin < VDD + Vtp
Vdsp > Vgsp – Vtp
Vout > Vin - Vtp
Saturated
Vgsp < Vtp
Vin < VDD + Vtp
Vdsp < Vgsp – Vtp
Vout < Vin - Vtp
VDD
Vtp < 0
Vin
Idsp
Idsn
Vout
Calculation of VIL
When the input voltage is Vin = VIL, the slope of
the VTC is equal to [-1](dVout/dVin). At this point
B, nMOS transistor operates in saturation while
the pMOS transistor operates in the linear
region. Using KCL at output node:
[Id,n(saturation)= Id,p(linear)]
Calculation of VIH
At point D, input voltage is equal to VIH,
the nMOS transistor operates in the
linear region and pMOS transistor
operates in saturation. By applying KCL
at the output node:
[ Id,n(linear) = Id,p(saturation)]
Calculation of Vth
Threshold voltage is defined as
Vth=Vin=Vout. For Vin=Vout, both transistor
operate in saturation region, refer point
C. By applying KCL at output node:
[ Idn(saturation)=Idp(saturation) ]
Exercise 1
Consider a CMOS inverter circuit with
the following parameters, calculate the
(W/L) ratios of the nMOS and pMOS
transistors if the switching voltage is
Vth = 1.5 V.
VDD = 3.3 V
VT,n = 0.6 V
VT,p = -0.7V
µncox = 80 µA/V2
µpcox = 30 µA/V2
Exercise 2
Consider a CMOS inverter circuit with
the following parameters, calculate the
Switching voltage (Vth) of the circuit.
VDD = 3.3 V
VT,n = 0.6 V
VT,p = -0.7V
µncox = 80 µA/V2
µpcox = 30 µA/V2
(W/L)n = 8
(W/L)p = 12
Voltage transfer characteristic
Inverter with n-Type MOSFET load
Depletion-Load nMOS Inverter
Calculation of VOH
When the input voltage Vin is smaller than
the driver threshold voltage VTO, the
driver transistor is turned off and thus
not conduct any drain current. ID,load = 0,
VOH = VDD  ID,load = 0
Calculation of VOL
Assume Vin = VOH = VDD. Driver transistor
operate in linear region and load
transistor operate in saturation. By
using KCL.
Id,driver(linear) = Id,load(saturation)
Calculation of VIL
When Vin = VIL the slope of the VTC is
equal to (-1),(dVout/dVin). Driver
transistor operate in saturation region
and load transistor operate in linear
region. KCL
Id,driver(saturation) = Id,load(linear)
Calculation of VIH
Driver transistor operate in linear region
and load transistor operate in
saturation region.
Id,driver(linear) = Id,load(saturation)
Operating Regions
(Summary)
nMOS
pMOS
2.5
A
Cutoff
Linear
2
B
Saturation
Linear
1.5
C
Saturation
Saturation
D
Linear
Saturation
E
Linear
Cutoff
NMOS off
PMOS res
NMOS s at
PMOS res
NMOS sat
PMOS sat
NMOS res
PMOS sat
0.5
Region
1
Vout
0.5
1
1.5
2
NMOS res
PMOS off
2.5
Vin
Exercise 3
VDD = 3.3 V
Threshold voltage nMOS (VT,n) = 0.6 V
Threshold voltage pMOS (VT,p) = -0.7V
Kn = 200 µA/V2
Kp = 80 µA/V2
Based on the inverter circuit and parameter in figure above,
what is the value of:
i) Switching Voltage, VTH
ii) Input Voltage High, VIH
THE END