INTEGRATED CIRCUITSDr. Esam Yosry

Lec. #8

VLSI

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Introduction

Resistor Design

Capacitor Design

Inductor Design

MOSFETs (CMOS)

BJTs

BiCMOS

Intro

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ion

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Cycle

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Resistor Design

• Assume we have a sheet of material of thickness t and width W, then A = W t

• Next assume that L = W; which means that we have a square, then the resistance becomes the sheet resistance per square (Ω/).

𝑅=𝜌 𝐿𝐴

𝑅=𝜌𝑡

Material technological parameters

Resistor Design

• The fabrication house supplies the designer with the values of the sheet resistance R.

• R resistance of one square of the fabricated silicon layer.

• The engineer designs for the number of squares to be put in series or in parallel to get the needed resistance.

Resistor Design

Sheet ResistanceCounting SquaresEnd ContactsBends (Corners)

R

3R

R/3

End contact =0.3 to 0.4 (0.35 is typical)

Corner =0.65

CC=dxd

2dx2d

Resistor Design• Example• If R = 100 Ω/, and the resistance needed is

200 Ω, then two squares are added in series.• If the resistance needed is 50 Ω, then two

squares must be put in parallel.

• n squares in series R= n R

• n squares in parallel R= R/n

• The sheet resistance of the diffused layer from 10 to 200 Ω (100kΩ?!)

Equivalent Resistance of End Contacts

R= body resistance (nR) + end contacts resistance (2x0.35R) + corners resistance (ncx0.65R) + metal/Si contact resistance RC (usually very low)

End contact =0.35

CC=dxd

2dx2d

Resistor’s Accuracy

Absolute Accuracy

Matching Accuracy *Resistors are usually made from polysilicon

* Inaccuracy comes frompoly line edge-shift duringprocessing (PR dimensionalchange, lateral etching, UVdiffraction,…etc)

*As inaccuracy is almost the same in the two resistors matchingaccuracy is very high

Absolute Accuracy

Rnominal = n R =(nL/L) R

= (length/width) R

Include line-edge shift of LR = (length L / L L) R

(length / L L) R

= (length/L)(1+ L/L) R

= (length/width) R )(1+ L/L) = Rnominal (1+ L/L) L/L = 1 to 5 %

R= nR

n squares

L

Length>>width

Matching Accuracy

R1 = R1nominal (1+ L/L)

R2 = R2nominal (1+ L/L)

R1 / R2 = R1nominal / R2nominal

Accurate VLSI designs should depend on resistance ratio

rather than on absolute resistance

n2 squares

R1= n1R

n1 squares

R2=n2 R

Matching resistorsis feasible in ICs butaccurate resistors arehard to obtain

How to Increase Absolute Accuracy ?

Use rounded corners(since errors on corner squares are high)

Use straight lines with metallic interconnects(to eliminate any corner effect)

Use dummy features(to reduce over etching - see explaination)

Rounded Corners

Current density is more uniformly distributed in rounded corners than in square corners

Perfectly roundedshapes are sometimesnot supported by Sifoundries

45o are acceptedby most layouttools and Sifoundries

Straight Poly Lines with Metallic Interconnects

End contacts should have the lowest contact

resistance

Color Code for Masks:Red: PolysiliconBlue: Metalic interconnectBlack: Contact cut

Dummy Poly Features

• The dummy shapesaround the main body of the resistor makes the lateral etching equal allover the poly edges.

• Knowing the etching rate, the etching time is optimized to etch just the necessary volume of poly.

Without dummyfeatures

Withdummyfeatures

How to Increase Matching Accuracy?

Use pairs with common centroid

(to reduce the effect of technological parameter spread also

called gradient)

R1

R1

R2

R2

dummy dummy

Comparison of the Chip Area required for Serpentine Resistor Geometries

Versus Multiple Straight Resistors

Capacitors

Between two polys

Cnominal = A / Tox

Poly I

Poly II

Oxidedielectricconst.,r = 4

Upper poly IIarea

Oxidethicknessbetweenpoly I andPoly II

Capacitor’s Accuracy

Absolute AccuracyMatching Accuracy

* Inaccuracy comes frompoly line edge-shift duringprocessing (PR dimensionalchange, lateral etching, UVdiffraction,…etc)

*As inaccuracy is almost the same in the two caps matchingaccuracy is very high if of the sameperimeter-to-area ratio

Absolute Accuracy

Anominal = axb (dashed line)

A = Anominal - xP is the edge-shiftP is the nominal perimeter =2(a + b)

Absolute Cap Error = C/C= A/A=- xP/A (A is nominal)

Error is proportional to the perimeter-to-area ratioNever use large perimeter features (like zigzags)

a

b

Matching Accuracy

Cap ratio Error = C1/ C2 = [C1xxP1/A1]/ [C2xxP2/A2]

For matched caps C1=C2 (nominal and real values)

P1/A1 = P2/A2 makes C1= C2 for matched real values

On Chip Inductors

Square (hollow) Octagonal (hollow) Series resistance Rs

Parasitic cap Cs

Substrate Conductivity Losses Rp

Q=3 to 10 at 1 GHz

Equivalent Circuit

Equivalent Circuit Elements

Cs= cap to substrate

Substrate eddycurrent loss

Substrate displacementcurrent loss

Rp

Rs= seriesresistance

Substrate Resistivity Effect

• No substrate current loss• Low cap (series caps) • High self resonance frequency

• No substrate current loss• Large cap • Low inductance

Multi-Layer Inductors

Series resistance increases linearly with number of turnswhile L increases quadratically, hence Q is improved

L up to 60 nH

Bond Wire Inductors1 nH / mm

• L = 3 to 4 nH, Q = 40 to 50 but poor reproducibility• High pad and pin caps reduces the self-resonance frequency• Not suitable for mass production

3-D Inductors

• High L (up to 15 nH).• High Q (30 - 50)• Good reproducibility• Large pad caps

Thanks

Many thanks to Prof. Hany Fikry and Prof Wael Fikry for their useful materials that help me to prepare this presentation.