1. MOSFET Transistor Basics
AVLSI Workgroup
Paul Hasler

2. Diffusion of Charge over BarrierEc
qDV Ec E0 Ec Ef
Case I: P(E) ~ exp( - E0 /kT)
Case II: P(E) ~ exp( - ( E0 - qDV)/kT)
Ratio of Case II to Case I = 1
P(E) =
~ e-(E-Ef)/kT
1 + e-(E-Ef)/kT
exp( DV / UT )
UT = kT/q

3. P-N Junctions Depletion Layer or Region N-type ND P-type NA qND Charge
Density
-qNA
Band
Diagram

4. P-N Junctions --- Diodes
N-type ND
P-type NA
First-Principles Model

5. A MOSFET Transistor
Source
Drain
Gate
Drain
Gate
Source
Substrate

6. 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

7. CMOS Process Cross Section
(n-well)
CMOS Process =
nFETs and pFETs are available
all p-n junction must
be reversed bias

8. MOS Transistor Operation
Use subthreshold operation as the fundamental case
Sub-VT operation simplifies this 2D problem to 2 1D problems
Allows intuition across sub-VT and above-VT operation

9. Water Analogy of a MOSFET

10. Channel Current Dependence on Gate Voltage
In linear scale, we
have a quadratic
dependence
In log-scale, we
have an exponential
dependence

11. MOSFET Channel Picture

12. MOS Capacitor Picture

13. MOSFET Channel Picture

14. Calculation of Drain Current

15. ( ) I = I e - e ( ) ( ) d n Dn = dx No recombination Dn = Ax + B l dn2 n
No recombination Dn =
Dn = Ax + B dx 2 dn d D n 2 = D + G - R dt n dx 2 l
y varies as kVG dn n - n
(qDn / l) (e-(Y - Vs)/UT - e-(Y - Vd)/UT) J = qD = qD
source
drain = n dx n l ( ) ( ) ( ) k V - V / u k V - V / u I = I e - g S T e g d T

16. MOSFET Current-Voltage Curves( ) e I u V T d g S - = / k ( ) I = I e KV / u e - V / u - e - V / u G T S T D T DS ( ) ( ) k ( ) = V - V / u - - I e 1 - e V V / u g S T d S T ( ) = I e ( KV - V ) / u 1 - e - V / u G S T dS T = I e ( KV - V ) / u G S T

17. Channel Current Dependence on Gate Voltage
In linear scale, we
have a quadratic
dependence
In log-scale, we
have an exponential
dependence

18. 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
0.9 10
-11
-10 -9 -8 -7 -6
Gate voltage (V)
Drain current (A)
k =
Io = fA
In linear scale, we
have a quadratic
dependence
In log-scale, we
have an exponential
dependence

19. Determination of Threshold Voltage
0.4
0.5
0.6
0.7
0.8
0.9 1
0.1
0.2
0.3
1.1
Gate voltage (V)
Drain current / subthreshold fit
VT = 0.86

20. Drain Current --- Source Voltage
0.6
0.65
0.7
0.75
0.8
0.85
0.9 10
-12
-11
-10 -9 -8 -7
Gate voltage (V)
Drain current (A)
UT = 25.84mV
k = 0.545

21. Origin of Drain Dependencies
Increasing Vd effects
the drain-to-channel
region:
increases barrier
height
increases depletion
width

22. Cause of DIBL

23. Drain Characteristics

24. Current versus Drain Voltage

25. Current versus Drain Voltage

26. Current versus Drain Voltage
Not flat due to Early effect
(channel length modulation)

27. Current versus Drain Voltage
Not flat due to Early effect
(channel length modulation)
In BJTs --- Base Modulation Effects

28. 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

29. Drain Induced Barrier Lowering
Data taken from a popular
1.2mm MOSIS process
Data taken from a popular
2.0mm MOSIS process

30. MOSFET Operating Regions
Qs = e
(Y - Vs)/UT
Y = ln( 1 + e )
(k(Vg - VT) - Vs)/UT
(EKV modeling)
Below Threshold
Above Threshold
End on mobile
charges in channel
End on fixed
ions in bulk
Field Lines from
gate charges
Charge boundary
condition at source
Set by Fermi
Distribution
Cox(k(Vg-VT)-Vs)
Approximate
surface potential
kVg
ln(Qs)
Channel
current flows
Diffusion
Drift

31. MOS-Capacitor Regions
Surface potential
moving from depletion
to inversion
Qs = e
(Y - Vs)/UT
Qs = ln( 1 + e )
(k(Vg - VT) - Vs)/UT
Depletion (k(Vg - VT) - Vs < 0)
Qs = e
(k(Vg - VT) - Vs)/UT
Inversion (k(Vg - VT) - Vs > 0)
Qs = (k(Vg - VT) - Vs)/UT

32. Band-Diagram MOSFET Picture
picture moving
from subthreshold to
above-threshold
Conduction band bends due to electrostatic force
of the electrons moving through the channel

33. Physics Based Models: Channels
What if Hodgkin and Huxley had known /
understood MOSFET transistors when
developing the original modeling….. E K Na C V me m M N a - - + - V + + - - + + - - + + - + + + - - - + - - + + -
Outside -
Inside + + - - + +
Gate
Source
Drain n + n + De pl e ti o n L ay e r
l = Channel Length
p-substrate Y E c V d s E c
Utilizing the physics of physical medium (Si)
to efficiently implement computation
[Farquhar and Hasler, 2004]