Microelectronics Devices & Circuits

8/14/2019 Microelectronics Devices & Circuits

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Administrativia

Make-up Lecture tomorrow Fr at 3:30pm (streamed)

Another Make-up Lecture Monday at 4pm (streamed)

NO LECTURE ON TUESDAY

Labs start next TU MAKE SURE TO ATTEND

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Some other reading material

Sedra and Smith, Microelectronic Circuits, Fifth Edition,Oxford University Press

Donald Neamen, Microelectronics Circuit Analysis and

Design, Third Edition, McGraw Hill

R. F. Pierret, Semiconductor Device Fundamentals,Addison Wesley, 1996. (130 Text Book)

R. S. Muller and T. I. Kamins with Mansun Chan, Device

Electronics for Integrated Circuits, 3rd Edition; Wileyand Sons, Publisher.


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Resistivity

Bulk silicon: uniform doping concentration, away from surfaces

n-type example: in equilibrium, no = Nd

When we apply an electric field, n =Nd

ENqnEqJ dnnn ==

Resistivity

Conductivity )(, adneffdnn NNqNq ==

effdnn

nNq ,

11

== cm

6

Ohms Law

( ) R

V

VL

Wt

L

V

WtEWttWJJAI =

=====

W

L

tW

L

tR

==

1

effdnn

nNq ,

11

==with


4/19

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Sheet Resistance (Rs)

IC resistors have a specified thickness not underthe control of the circuitdesigner

Eliminate tby absorbing it into a new parameter: the

sheet resistance (Rs)

=

==

W

LR

W

L

tWt

LR sq

Number of Squares

8

Using Sheet Resistance (Rs

)

Ion-implanted (or diffused) IC resistor


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Idealizations

Why does current density Jnturn?

What is the thickness of the resistor?

What is the effect of the contact regions?

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Diffusion

Diffusion occurs when there exists a concentrationgradient

In the figure below, imagine that we fill the left chamberwith a gas at temperate T

If we suddenly remove the divider, what happens?

The gas will fill the entire volume of the new chamber.How does this occur?


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Diffusion (cont)

The net motion of gas molecules to the right chamberwas due to the concentration gradient

If each particle moves on average left or right then

eventually half will be in the right chamber

If the molecules were charged (or electrons), then therewould be a net current flow

The diffusion current flows from high concentration to

low concentration:

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Diffusion Equations

Assume that the mean free path is

Find flux of carriers crossing x=0 plane

)(n)0(n

)( n

0

thvn )(2

1 th

vn )(2

1

( ))()(2

1 nnvF th =

+

=

dx

dnn

dx

dnnvF th )0()0(

2

1

dxdnvF th=

dx

dnqvqFJ th==


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Einstein Relation

The thermal velocity is given by kT

kTvm thn 212*

21 =

cthv =Mean Free Time

dx

dnqD

dx

dn

q

kTq

dx

dnqvJ nnth =

==

th

n

n Vq

kTD=

=

**

2

n

c

n

ccthth

m

q

q

kT

mkTvv

===

Mobility

Diffusion Coefficient

Einstein Relation

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Total Current

When both drift and diffusion are present, the totalcurrent is given by the sum:

dx

dnqDnEqJJJ nndiffdrift +=+=


8/19

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oxidation

opticalmask

processstep

photoresist coatingphotoresistremoval (ashing)

spin, rinse, dryacid etch

photoresist

stepper exposure

development

Typical operations in a single

photolithographic cycle (from [Fullman]).

IC Fabrication: Photo-Lithographic Process

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IC Fabrication: Si Substrate

Pure Si crystal is starting material (wafer)

The Si wafer is extremely pure (~1 part in a billion

impurities)

Why so pure?

Si density is about 5 1022 atoms/cm3

Desire intentional doping from 1014 1018

Want unintentional dopants to be about 1-2 orders of magnitude

less dense ~ 1012

Si wafers are polished to about 700 m thick (mirrorfinish)

The Si forms the substrate for the IC


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IC Fabrication: Oxide

Si has a native oxide: SiO2

SiO2 (glass) is extremely stable and very convenient for

fabrication

Its an insulator

SiO2 windows are etched using photolithography

These openings allow ion implantation into selectedregions

SiO2 can block ion implantation in other areas

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IC Fabrication: Patterning of SiO2

Si-substrate

Si-substrate Si-substrate

(a) Silicon base material

(b) After oxidation and depositionof negative photoresist

(c) Stepper exposure

Photoresist

SiO2

UV-light

Patternedoptical mask

Exposed resist

SiO2

Si-substrate

Si-substrate

Si-substrate

SiO2

SiO2

(d) After development and etching of resist,chemical or plasma etch of SiO

2

(e) After etching

(f) Final result after removal of resist

Hardened resist

Hardened resist

Chemical or plasmaetch


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Diffusion Resistor

Using ion implantation/diffusion, the thickness anddopant concentration of resistor is set by process

E.g. 100/ (unsilicided), 10/ (silicided)

Shape of the resistor is set by design (layout) Metal contacts are connected to ends of the resistor

Resistor is capacitively isolation from substrate

Reverse-biased PN Junction!

P-type Si Substrate

N-type Diffusion RegionOxide

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Using Sheet Resistance (Rs

)

Ion-implanted (or diffused) IC resistor


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Poly Film Resistor

To lower the capacitive parasitics, we should build theresistor further away from substrate

We can deposit a thin film of poly Si (heavily doped)

material on top of the oxide E.g. 10-100/ (unsilicided), 1/ (silicided) Bad absolute tolerance, very good relative tolerance

Polysilicon Film (N+ or P+ type) Oxide

P-type Si Substrate

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CMOS Process at a Glance

Define active areasEtch and fill trenches

Implant well regions

Deposit and patternpolysilicon layer

Implant source and drainregions and substrate contacts

Create contact and via windowsDeposit and pattern metal layers


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Electrostatics: a Tool for Device Modeling

E( ) =

E =

( )( ) 2 = =

Gausss Law

Potential Def.

Poissons Eqn.

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One-Dimensional Electrostatics

Gausss Law

Potential Def.

Poissons Eqn.

)()(2

2 x

dx

xd=

==

dx

dEE

dx

dE

=


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Electrostatics Review (1)

Electric field go from positive charge to negative charge(by convention)

In words, if the electric field changes magnitude, therehas to be charge involved!

Result: In a charge-free region, the electric field mustbe constant!

+++++++++++++++++++++

= E

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Electrostatics Review (2)

Gauss Law equivalently says that if there is a netelectric field leaving a region, there has to be positive

charge in that region:

+++++++++++++++++++++

Electric Fields are Leaving This Box!

= QdSE


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Electrostatics in 1D

Everything simplifies in 1-D

Consider a uniform charge distribution

==

dx

dEE dxdE

=

')'(

)()(

0

0 dxx

xExE

x

x

+=

)(x

x

xdxx

xE

x

0

0

')'(

)( ==

Zero fieldboundary

condition

1x

0

1x

)(xE

1

0

x

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Electrostatic Potential

The electric field (force) is related to the potential(energy):

Negative sign says that field lines go from highpotential points to lower potential points (negativeslope)

Note: An electron should float to a high potentialpoint:

dx

dE

=

dx

deqEFe

==

1

2

dx

deFe

=

e


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More Potential

Integrating this basic relation, we have that the potentialis the integral of the field:

In 1D, this is a simple integral:

Going the other way, we have Poissons equation in 1D:

= C ldExxr

)()( 0

)(x

)( 0xE

ldr

=x

xdxxExx

0

')'()()( 0

)()(2

2 x

dx

xd=

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Boundary Conditions

Potential must be a continuous function. If not, thefields (forces) would be infinite

Electric fields need not be continuous. We have already

seen that the electric fields diverge on charges. In fact,across an interface we have:

)( 11 E

)( 22 E

=+= insideQSESEdSE 2211 x

00

xinside

Q

02211 =+ SESE

1

2

2

1

=

E

ES


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IC MIM Capacitor

By forming a thin oxide and metal (or polysilicon) plates, acapacitor is formed

Contacts are made to top and bottom plate

Parasitic capacitance exists between bottom plate and substrate

Top PlateBottom Plate Bottom Plate

Contacts

CVQ =

Thin Oxide

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Review of Capacitors

For an ideal metal, all charge must be at surface

Gauss law: Surface integral of electric field overclosed surface equals charge inside volume

+++++++++++++++++++++

+

Vs

= Q

dSE

= Q

dSE

sox VtEdlE == 0ox

s

t

VE =0

== Q

AEdSE 0

QA

t

V

ox

s =

sCVQ =

oxt

AC

=


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Capacitor Q-V Relation

Totalcharge is linearly related to voltage Charge density is a delta function at surface (for

perfect metals)

sCVQ =

sV

Q

y

)(yQ

y+++++++++++++++++++++

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A Non-Linear Capacitor

Well soon meet capacitors that have a non-linear Q-Vrelationship

If plates are not ideal metal, the charge density can penetrate intosurface

)( sVfQ =

sV

Q

y

)(yQ

y+++++++++++++++++++++


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Whats the Capacitance?

For a non-linear capacitor, we have

We cant identify a capacitance

Imagine we apply a small signal on top of a bias

voltage:

The incremental charge is therefore:

ss CVVfQ = )(

s

VV

sss vdV

VdfVfvVfQ

s=

++=)(

)()(

Constant charge

s

VV

s vdV

VdfVfqQQ

s=

++=)(

)(0

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Small Signal Capacitance

Break the equation for total charge into two terms:

s

VV

s vdV

VdfVfqQQ

s=

++=)(

)(0

Constant

Charge

IncrementalCharge

ss

VVvCvdV

Vdfq

s

===

)(

sVVdV

VdfC

=

)(


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Example of Non-Linear Capacitor

Next lecture well see that for a PN junction, the chargeis a function of the reverse bias:

Small signal capacitance:

b

paj

VxqNVQ

= 1)(

ConstantsCharge At N Side of Junction

Voltage Across NPJunction

b

j

b

b

paj

jV

C

V

xqN

dV

dQVC

=

==

11

1

2)(

0

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