Device

© Digital Integrated Circuits2nd Devices

DeviceDevice

Dr. Shiyan HuOffice: EERC [email protected]

Adapted and modified from Digital Integrated Circuits: A Design Perspective by Jan M. Rabaey, Anantha Chandrakasan, and Borivoje Nikolic.

EE5900 Advanced EE5900 Advanced Algorithms for Algorithms for Robust VLSI CADRobust VLSI CAD


Goal of this chapterGoal of this chapter

Present intuitive understanding of device operation

Introduction of basic device equations


MOS Transistor Types and SymbolsMOS Transistor Types and SymbolsD

S

G

G

S

D

NMOS

PMOS

© Digital Integrated Circuits2nd Devices4

Circuit Under DesignCircuit Under Design

VDD VDD

VinVout

M1

M2

M3

M4

Vout2


Circuit on the ChipCircuit on the ChipA transistor


The MOS (Metal-Oxide-Semiconductor) The MOS (Metal-Oxide-Semiconductor) TransistorTransistor

Polysilicon Aluminum


Simple View of A TransistorSimple View of A Transistor

VGS VT

RonS D

A Switch!

|VGS|

An MOS Transistor


Silicon BasicsSilicon Basics Transistors are built on a silicon substrate Silicon forms crystal lattice with bonds to

four neighbors


Doped SiliconDoped 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


NMOS TransistorNMOS Transistor

Diffusion


NMOS - IINMOS - 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.


NMOS - IIINMOS - III Gate oxide are insulators, usually, silicon

dioxide. Gate voltage modulates current between

drain and source, how?


Enhancement NMOSEnhancement NMOS


Enhancement NMOS - IIEnhancement 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.


Enhancement NMOS IIIEnhancement NMOS III

Positively Changed

Negatively Changed


Enhancement NMOS - IVEnhancement 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).


Enhancement NMOS VEnhancement NMOS V


Enhancement NMOS - VIEnhancement 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 does not conduct.


Case when Vds=0Case when Vds=0


Linear RegionLinear Region


Linear Region - IILinear 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.


Saturation RegionSaturation Region


Saturation Region - IISaturation 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.


Saturation Region - IIISaturation 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.


SummarySummary 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.


Analysis (for linear region)Analysis (for linear region)

n+n+

p-substrate

D

SG

B

VGS

xL

V(x) +–

VDS

ID

MOS transistor and its bias conditions


Analysis - IIAnalysis - 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.


Analysis - IIIAnalysis - 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.

1

W1

QI


Summary - IISummary - II

Three regions of conduction Cut-off: 0<Vgs<Vt, I=0 Linear: 0<Vds<Vgs-Vt,

Saturation: 0<Vgs-Vt<Vds


PMOSPMOS


PMOS - IIPMOS - 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.


Sub-threshold conduction (Leakage)Sub-threshold conduction (Leakage)

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.


Transistor Equivalent ResistanceTransistor 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


Transistor Resistance - IITransistor 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.


Overlap CapacitanceOverlap Capacitance

tox

n+ n+

Cross section

L

Gate oxide

xd xd

L d

Polysilicon gate

Top view

Source

n+

Drain

n+W

Overlap capacitance=2Cox Xd W


Channel CapacitanceChannel Capacitance

S D

G

CGCS D

G

CGCS D

G

CGC

Cut-off Resistive Saturation

Larger gate width -> Larger capacitance


In Standard Cell LibraryIn 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.


Technology ScalingTechnology 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=1.2-1.5.


Technology Scaling - IITechnology 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


SummarySummary NMOS

Cut-Off, Linear and Saturation Regions How to compute I

PMOS is the dual device of NMOS I-V characteristics of MOS transistors

Resistance Capacitance

Device

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