mosfet transistor basics avlsi workgroup paul hasler
TRANSCRIPT
MOSFET Transistor Basics
AVLSI Workgroup
Paul Hasler
Diffusion of Charge over Barrier
Ec
Ec
Ef
Ec
A B
P(E) =
~ e-(E-Ef)/kT
1
1 + e-(E-Ef)/kT
10-4
10-3
10-2
10-1
100
-2
-1
0
1
2
3
4
5
6
7
8
Probability
Ene
rgy
(eV
)
Case I: P(E) ~ exp( - E0 /kT)
qV
E0
Case II: P(E) ~ exp( - ( E0 - qV)/kT)
Ratio of Case II to Case I = exp( V / UT )
UT = kT/q
P-N Junctions
N-typeN
D
P-typeN
A
Depletion Layer or Region
ChargeDensity
qND
-qNA
BandDiagram
P-N Junctions --- Diodes
N-typeN
D
P-typeN
A
First-Principles Model
A MOSFET Transistor
Gate
Source
Drain
Source
Substrate
Gate
Drain
Self-Aligned Process
How do we make a basic transistor element?
We create a silicon-oxide “stencil” (or mask)
We get highly repeatable gates because the gate acts as a stencil as well
CMOS Process Cross Section
n nn pp
(n-well)
all p-n junction must be reversed bias
p
CMOS Process = nFETs and pFETs are available
MOS Transistor Operation
• Use subthreshold operation as the fundamental case
• Allows intuition across sub-VT and above-VT operation
• Sub-VT operation simplifies this 2D problem to 2 1D problems
Water Analogy of a MOSFET
Channel Current Dependence on Gate Voltage
In linear scale, we have a quadraticdependence
In log-scale, wehave an exponentialdependence
MOSFET Channel Picture
MOS Capacitor Picture
MOSFET Channel Picture
Calculation of Drain Current
No recombination 02
2
dx
ndDn
ndx
dnqDJ
l
nnqD drainsource
n
ddC
SSC
V
V
0 l varies as VG
TSC usource en /
TdC udrain en /
n = Ax + B
RGdx
ndD
dt
dnn
2
20 0 0
(qDn / l) (e-( - Vs)/UT - e-( - Vd)/UT)
eeIIuVVuVV TdgTSg / /
0
MOSFET Current-Voltage Curves
1
/)(0
//)(0
///0
TSG
TdSTSG
TDTSTG
uVKV
uVuVKV
uVuVuKVDS
eI
eeI
eeeII
Saturation
4 TdS uV
eeIIuVVuVV TdgTSg //
0
1 //0
TSdTSg uVVuVVeeI
Channel Current Dependence on Gate Voltage
In linear scale, we have a quadraticdependence
In log-scale, wehave an exponentialdependence
Channel Current Dependence on Gate Voltage
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.910
-11
10-10
10-9
10-8
10-7
10-6
Gate voltage (V)
Dra
in c
urr
en
t (A
)
= 0.58680 Io = 1.2104fA
In linear scale, we have a quadraticdependence
In log-scale, wehave an exponentialdependence
Determination of Threshold Voltage
0.4 0.5 0.6 0.7 0.8 0.9 10.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Gate voltage (V)
Dra
in c
urre
nt /
sub
thre
shol
d fit
VT = 0.86
Drain Current --- Source Voltage
0.6 0.65 0.7 0.75 0.8 0.85 0.9
10-12
10-11
10-10
10-9
10-8
10-7
Gate voltage (V)
Dra
in c
urre
nt (
A)
UT = 25.84mV
= 0.545
Origin of Drain Dependencies
Increasing Vd effects the drain-to-channel region:
• increases depletion width
• increases barrier height
Cause of DIBL
Drain Characteristics
Current versus Drain Voltage
Current versus Drain Voltage
Current versus Drain Voltage
Not flat due to Early effect (channel length modulation)
Current versus Drain Voltage
Not flat due to Early effect (channel length modulation)
In BJTs --- Base Modulation Effects
Current versus Drain Voltage
Not flat due to Early effect (channel length modulation)
Id = Id(sat) (1 + (Vd/VA) )
or
Id = Id(sat) eVd/VA
In BJTs --- Base Modulation Effects
Drain Induced Barrier Lowering
Data taken from a popular 1.2m MOSIS process
Data taken from a popular 2.0m MOSIS process
MOSFET Operating Regions
End on mobilecharges in channel
End on fixedions in bulk
Field Lines fromgate charges
Below Threshold Above Threshold
Channelcurrent flows Diffusion Drift
Charge boundarycondition at source
Set by FermiDistribution
Cox((Vg-VT)-Vs)
= ln( 1 + e )((Vg - VT) - Vs)/UT
Qs = e( - Vs)/UT
Approximatesurface potential Vg ln(Qs)
(EKV modeling)
MOS-Capacitor Regions
Qs = ln( 1 + e )((Vg - VT) - Vs)/UTQs = e
( - Vs)/UT
Depletion ((Vg - VT) - Vs < 0)
Qs = e ((Vg - VT) - Vs)/UT
Inversion ((Vg - VT) - Vs > 0)
Qs = ((Vg - VT) - Vs)/UT
Surface potentialmoving from depletionto inversion
Band-Diagram MOSFET Picture
Band-diagrampicture moving from subthreshold toabove-threshold
Conduction band bends due to electrostatic force of the electrons moving through the channel
Physics Based Models: Channels
Utilizing the physics of physical medium (Si) to efficiently implement computation
n +
p-substrate
n +
l = Channel LengthDe pl e tion Lay er
Vds
Ec
Ec
What if Hodgkin and Huxley had known / understood MOSFET transistors when developing the original modeling…..
+ -
V
Out
side
Insi
de
+
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
+
+ +
+ +
+ +++
+ +
+ +
+ +
GateDrainSource
E K
E Na
C
Vme m
M Na
M K
[Farquhar and Hasler, 2004]