1. Device EE4271 VLSI Design Dr. Shiyan Hu Office: EERC 731
Device
Adapted and modified from Digital Integrated Circuits: A Design Perspective
by Jan M. Rabaey, Anantha Chandrakasan, and Borivoje Nikolic.

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Goal of this chapter
Present intuitive understanding of device operation
Introduction of basic device equations

3. MOS Transistor Types and Symbols
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MOS Transistor Types and Symbols D G S
NMOS D G S
PMOS

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Circuit Under Design

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Circuit on the Chip
A transistor

6. The MOS (Metal-Oxide-Semiconductor) Transistor
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The MOS (Metal-Oxide-Semiconductor) Transistor
Polysilicon
Aluminum

7. Simple View of A Transistor
A Switch! |V GS |
An MOS Transistor

8. Silicon Basics Transistors are built on a silicon substrate
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Silicon Basics
Transistors are built on a silicon substrate
Silicon forms crystal lattice with bonds to four neighbors 8

9. Doped Silicon n-type p-type Silicon is a semiconductor
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Doped Silicon
Silicon is a semiconductor
Pure silicon has no free carriers and conducts poorly
Adding dopants increases the conductivity
extra electrons (doped Borons) – n-type
missing electrons (doped Arsenic/Phosphorus) more holes) – p-type
n-type
p-type 9

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NMOS Transistor
Diffusion

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NMOS - II
Refer to gate, source, drain and bulk voltages as Vg,Vs,Vd,Vb, respectively.
Vab=Va-Vb
Device is symmetric. Drain and source are distinguished electrically, i.e., Vd>Vs.
P regions have acceptor (Boron) impurities, i.e., many holes.
N regions have donor (Arsenic/Phosphorus) impurities, i.e., many electrons.
N+ and P+ are heavily doped N and P regions, respectively.

12. NMOS - III Gate oxide are insulators, usually, silicon dioxide.
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NMOS - III
Gate oxide are insulators, usually, silicon dioxide.
Gate voltage modulates current between drain and source, how?

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Enhancement NMOS

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Enhancement NMOS - II
Does not conduct when Vgs=0, except that there is leakage current.
When Vgs is sufficiently large, electrons are induced in the channel, i.e., the device conducts. This Vgs is called threshold voltage.

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Enhancement NMOS III
Positively Changed
Negatively Changed

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Enhancement NMOS - IV
When Vgs is large enough, the upper part of the channel changes to N-type due to enhancement of electrons in it. This is refereed to as inversion, and the channel is called n-channel.
The voltage at which inversion occurs is called the Threshold Voltage (Vt).
A p-depletion layer have more holes than p-substrate since its electrons have been pushed into the inversion layer.
Does not conduct when Vgs<Vt (Cut-off).

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Enhancement NMOS V

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Enhancement NMOS - VI
When Vgs>Vt, the inversion layer (n channel) becomes thicker.
The horizontal electrical field due to Vds moves electrons from the source to the drain through the channel.
If Vds=0, the channel is formed but not conduct.

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Case when Vds=0

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Linear Region

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Linear Region - II
When Vgs>Vt and Vgd>Vt, the inversion layer increases in thickness and conduction increases.
The reason is that there are non-zero inversion layer at both source and drain (our previous analysis works for both Vgs and Vgd).This is called linear region.
Vgd>Vt means that Vgd=Vgs-Vds>=Vt, i.e., Vds<=Vgs-Vt
Ids depends on Vg, Vgs and Vds.

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Saturation Region

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Saturation Region - II
When Vgs>Vt and Vgd<Vt, we have non-zero inversion layer at source but zero inversion layer at drain.
Inversion layer is said to be pinched off. This is called the saturation region.
Vgd<Vt means that Vgs-Vds<Vt, i.e., Vds>Vgs-Vt.
Electrons leaves the channel and moves to drain terminal through depletion region.

24. Saturation Region - III
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Saturation Region - III
In saturation region, the voltage difference over the channel remains at Vgs-Vt. This is because if Vds=Vgs-Vt, the inversion layer is barely pinched off at the drain. If Vds>Vgs-Vt, the channel is pinched off somewhere between the drain and source ends. Thus, the voltage applied across the channel is Vgs-Vt.
As a result, Ids depends on Vgs alone in this region, so we cannot keep raising Vds to get better conduction.

25. Summary Three regions of conduction Cut-off: 0<Vgs<Vt
Linear: 0<Vds<Vgs-Vt
Saturation: 0<Vgs-Vt<Vds
Vt depends on gate and insulator materials, thickness of insulators and so forth – process dependant factors, and Vsb and temperature – operational factors.

26. Analysis (for linear region)
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Analysis (for linear region)

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Analysis - II
Denote by V(x) the voltage at a point x along the channel. The gate-to-channel voltage is Vgs-V(x). Since it needs to be > Vt for every point along the channel, the charge per unit area at x is
Cox is the capacitance per unit, which is
where is a constant called the permittivity of the gate oxide and tox is the thickness of gate oxide.

28. Analysis - III Gate width W, so the total charge is QW.1 W Q I
Analysis - III
Gate width W, so the total charge is QW.
I=QW/t=QWv, v being velocity of carrier.
Given surface mobility u of electrons, which depends on process, an empirical formula for v is
We have
Integrate x from 0 to L, we have
For saturation region, replace Vds by Vgs-Vt, we have It does not depend on Vds.

29. Effective Channel Length/Width
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Effective Channel Length/Width
is due to lateral diffusion of the source and drain junctions under the gate

30. Channel Length Modulation
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Channel Length Modulation
In saturation region, current is actually weakly depends on Vds. This is because that increasing Vds makes the pinch-off earlier (closer to source). Since electrons flow through depletion layer to move to drain in saturation region, this means a long trip. The current value is actually
is empirically determined. Usually it is <0.02/Vds.

31. Summary - II Three regions of conduction Cut-off: 0<Vgs<Vt, I=0
Linear: 0<Vds<Vgs-Vt,
Saturation: 0<Vgs-Vt<Vds

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PMOS

33. PMOS - II Dual of NMOS Three regions of conduction
Cut-off: 0>Vgs>Vt
Linear: 0>Vds>Vgs-Vt
Saturation: 0>Vgs-Vt>Vds
Current computation is the same as NMOS except that the polarities of all voltages and currents are reversed.
Mobility of holes u in PMOS is usually half of the mobility of electronics in NMOS due to process technology.

34. I-V characteristics (different Vt)
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I-V characteristics (different Vt)

35. I-V Characteristics II
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I-V Characteristics II

36. Threshold Voltage and Body Effect
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Threshold Voltage and Body Effect
Since gate and substrate form the plates of a capacitor, a strong enough inversion layer needs sufficient amount of voltage difference, i.e., Vgs=Vt.
The amount of positive charge = the amount of negative charge on both plates.
If we decrease the bulk/substrate voltage Vb, more charge is needed on the lower plate to counteract it.
Vgs >Vt in order to form the same inversion layer as before
Make the circuit run slower.
It is called Body Effect. Try to avoid it.
where is called the body-effect coefficient and Vt0 is the threshold voltage when Vsb=0.

37. Threshold Voltage and Body Effect
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Threshold Voltage and Body Effect

38. Short Channel Effects is true for long channel.
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Short Channel Effects
is true for long channel.
The depletion layer/electron move under the gate is assumed to be caused entirely by vertical field, i.e.,
Near source and drain, there is also depleted region due to horizontal electrical field (Vd,Vs). So the region below gate is already partially depleted.
Device actually conducts with smaller Vt.
OK for far-apart drain and source. If the channel is very short, effect is significant, which make the device hard to control.
In practice, L>= Lmin.

39. Short Channel Effect - II
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Short Channel Effect - II

40. Sub-threshold conduction (Leakage)
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Sub-threshold conduction (Leakage)
0.5 1
1.5 2
2.5 10
-12
-10 -8 -6 -4 -2 V GS
(V) I D
(A) VT
Linear
Exponential
Quadratic (in Vds)
Saturation Region
Linear/Triode/Resistive region
Sub-threshold region

41. Sub-threshold conduction (Leakage) - II
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Sub-threshold conduction (Leakage) - II
Vgs<Vt, cut-off and I=0. Not true.
In practice, for Vgs<Vt,
I is exponentially dependent on Vgs. Id0 and n are experimentally determined, k is Boltzmann’s constant and T is temperature.
Source of standby power consumption in portable devices.
Some extremely low-power circuits use sub-threshold conduction, e.g., digital watch.

42. Transistor Equivalent Resistance
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Transistor Equivalent Resistance
In linear region, R=V/I, so
In saturation region, the voltage applied across the channel is Vgs-Vt. Thus,
Roughly speaking, channel resistance inversely depends on W since

43. Transistor Resistance - II
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Transistor Resistance - II
Larger gate width (larger gate area) -> smaller resistance -> device runs faster
This means that power/area increases with delay decreases. A lot of power-delay tradeoff like this.

44. Transistor Resistance - III
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Transistor Resistance - III

45. Transistor Capacitance
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Transistor Capacitance
Gate Capacitance = Channel Capacitance + Overlap Capacitance

46. Overlap Capacitance Overlap capacitance=2Cox Xd W x L Polysilicon gate
Top view
Source n +
Drain W t ox n +
Cross section L
Gate oxide
Overlap capacitance=2Cox Xd W

47. Channel Capacitance Larger gate width -> Larger capacitance Cut-off
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Channel Capacitance
Cut-off
Resistive
Saturation
Larger gate width -> Larger capacitance

48. Gate Capacitance Capacitance as a function of VGS
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Gate Capacitance
Capacitance as a function of VGS
(with VDS = 0)
Capacitance as a function of the degree of saturation

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Measuring the Gate Cap
I=CdV/dt, so C=idt/dV

50. In Standard Cell Library
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In Standard Cell Library
A gate type has multiple gate sizes (widths)
Larger gate width means larger gate capacitance and smaller driving resistance.
Thus, for a gate type, we have a variety of transistors with different capacitance and resistance tradeoff.
Larger width means larger capacitance and thus larger power due to charging and uncharging the capacitance.
Usually, larger width transistor has smaller delay.

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Technology Scaling
Devices scale to smaller dimensions with advancing technology.
A scaling factor S describes the ratio of dimension between the old technology and the new technology. In practice, S=

52. Technology Scaling - II
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Technology Scaling - II
In practice, it is not feasible to scale voltage since different ICs in the system may have different Vdd. This may require extremely complex additional circuits. We can only allow very few different levels of Vdd.
In technology scaling, we often have fixed voltage scaling model.
W,L,tox scales down by 1/S
Vdd, Vt unchanged
Area scales down by 1/S2
Cox scales up by S due to tox
Gate capacitance = CoxWL scales down by 1/S
scales up by S
Linear and saturation region current scales up by S
Current density scales up by S3
P=Vdd*I, power density scales up by S3
Power consumption is a major design issue

53. Summary NMOS PMOS is the dual device of NMOS
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Summary
NMOS
Cut-Off, Linear and Saturation Regions
How to compute I
Channel length modulation, short channel effect, sub-threshold conduction
PMOS is the dual device of NMOS
I-V characteristics of MOS transistors
Resistance
Capacitance