Lecture 3 Given [Compatibility Mode]

7/31/2019 Lecture 3 Given [Compatibility Mode]

1/23

EL 511

VLSI Design

Instructor:

Mazad S. Zaveri

Faculty Block 4, Room 4206

ma : maza _zaver a c .ac. nhttp://intranet.daiict.ac.in/~mazad_zaveri/

EL 511 VLSI Design

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2/23

We will have a Quiz-1 today. (10 minutes)

Homework-1 has been posted

Gate-length 45 nm 32 nm =

45*0.7 nm

22 nm =

45*0.7*0.7 nm

Year 2009 2011 2013

Generation x Next after x next after (next after x)

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3/23

-1. A software has 500 lines of code. Of

, ,

100 lines can run only sequentially.

a s e max mum spee -up max

How many processors are needed to- . max

2. What is the reason behind using high-k

ga e-ox e n newer genera on o n eprocessors? Briefly explain, atleast two

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reasons.


4/23

Conceptual Energy Band ModelElectron

Ec

Energy (E)

Ev

When silicon atoms come

New electron energy band modelis created

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of the band model


5/23

E = Conduction Band

Electron

Energy (E)

(starting) level Ev = Valence Band

Ec

Ev

Conduction Band

Band Gap

en ng eve

EG = Energy band gap

Valence Band

No Allowed states

EG = Ec Ev

E= Electron energy Unit is electron-volt (eV)

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6/23

Types of Carriers- Electron & HoleWhen no bonds in the (lattice) or bondingmodel are broken, there are no carriers

(In terms of energy band model) No carriers

are present Valence band is completely filled

When Si-Si bond breaks, the associated electron

with electrons; and Conduction band is devoid

of any electrons

s ree o wan er n e a ce, e re ease

electron is a carrier

(In terms of energy band model) Excitation of

carrier Electrons in conduction band are carriers

When Si-Si bond breaks, in addition to electron

release we have a missin bond void in the

lattice). Nearby electrons may jump to fill this

bond, creating a void in a new place. This void is

called Hole

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(In terms of energy band model) Flow of void in

the valence band, due to motion of electrons inthe valence band


7/23

Material Classification based on Band Gap

Insulator

Bad conductor large energy band gap (EG)

Semiconductor on uc s on y w en exc a on energy s prov e s G

between the EG of metal and insulator Metal Good conductor Very narrow EG

Electron-volt (eV) is an unit of

energy equal to 1.6 x 10-19joules

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electron = 1.6 x 10-19 coulomb


8/23

Carrier numbers in Intrinsic Semiconductor

Intrinsic semiconductor

Extremely pure semiconductor

Without any externally added impurity (dopants)

n= number of electrons/cm3

p= number of holes/cm

In intrinsic semiconductor, Underequilibrium conditions

Electron concentration = hole concentration

n= = n

For silicon (at room temp), ni = 1 x 1010 / cm3

Holes and electrons are created only in pairs in intrinsic

semiconductors

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9/23

Doping manipulation of carrier numbers

Doping Means the addition of controlled amounts of specific

Why? Purpose of increasing either the electron or the hole

concentration

How? Replace some Si atoms with some dopant atoms

Density of Si atoms in the Si crystal is 5 x 1022 / cm3

ope sem con uc or s ca e x r ns csemiconductor

To increase electron concentration

Use Donors (Column V elements in periodic table) P (Phosphorus), As (Arsenic), Sb (Antimony)

To increase hole concentration

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se ccep ors o umn e emen s n per o c a e B (Boron), Ga (Gallium), In (Indium)


10/23

Donor (n-type material) Column V elements

Have five valence electrons

,

Si atom with a donor atom Four out of five electrons of the donor

are use n orm ng our on s sotightly bound

Fifth electron is loosely bound to

Can be easily released at roomtemperature acts as a carrier

If released from the donor site leaves

P+

behind a +ve charged donor ion Donor ion cannot move around in the

crystal

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11/23

Acceptor (p-type material) Column III elements

Have 3 valence electrons

Inside a silicon crystal, we replace Sia om w an accep or a om Three electrons of the acceptor will form three

out of four bonds

Electron from other nearby Si-Si bond, will be

taken or accpeted and the incomplete bond

will be completed ,

will now have a missing bond, and will act as ahole

The acceptor atom, accepted an electron so will

Holes can be easily formed at room temperature acts as a carrier

Acceptor ion cannot move around in the crystal -

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-


12/23

Donor and Acceptor

Visualization in terms of energy band model Donor

Weekly bound electrons are in a donor site

Need only about 0.05 to 0.1eV to excite and jump to conduction band

Donor

A new electronic level (EA )is introduced in the forbidden gap, above Ev Electrons from valence band will excite/jump to this new level, creating holes

Acce tor

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13/23

Fermi Function 1= erm unc on

Specifies, under equilibrium

( ) /1 F

E E kTe +

,

an available state at an EnergyE will be occupied by an

EF = Fermi Level or Fermi energy

k= Boltzmann constant

k= 8.617 x 10-5 eV/K

T= Temperature in Kelvin (K)

Indicates the relative

concentration of electrons in

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14/23

Semiconductor classification based on Fermi-level

Intrinsic Fermi level Lies in the middle of ener band a

Ei = (Ec + Ev )/2 and Ei = EF

N-type semiconductor F > i

P-type semiconductor E < E

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15/23

Carrier distributions

N-type

conduction band

( ) ( )c

g E f E

Intrinsic

Distribution of holes

(unfilled states) in valence

band

( ) 1 ( )vg E f E

P-type

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16/23

n= number of electrons/cm3

p= number of holes/cm3

In intrinsic semiconductor n= p= ni

Ei EF and np ni

Use these equations to find the electron and holeconcen ra ons

Valid only under equilibrium conditions of the semiconductor

( ) /F iE E kT

in n e= ( ) /i FE E kTip n e

=2

inp n=

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17/23

Intrinsic carrier concentration

As temperature increases, thenumber of intrinsic carriers increase

But for intrinsic carriers n= p= ni

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18/23

Charged entities in an extrinsic semiconductor

Electron (n) and +ve charged donor ions (ND)

Holes (p) and ve charged acceptor ions (NA)

For an extrinsic semiconductor Assuming both type of dopants (donor and acceptors)

Uniformly doped semiconductor

Assuming equilibrium conditions No electric fields (built-in or external)

This semiconductor is charge-neutral

0D A

p n N N+ + =

Only some dopant atoms are ionized

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D A Valid forT> room temp

When all dopant atoms are ionized


19/23

The eneral case

Assume both types of dopants in the semiconductor For simplicity, assume that all dopant atoms are

on ze room emp

1/ 22

2

1/ 2

2 2

D A D Ai

n n

= + +

2

2 2

i A D A Di

n N N N N p nn

= = + +

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20/23

Electron-Hole concentration from doping

concen ra ons

D A

D i

N N

N n

2

D

inpN

=

use

When

A DN N Ap Nuse

A iN n2

i

A

nn

N=

When

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21/23

Electron-Hole concentration from doping

concen ra onsuse

When n N N

The above condition can also occur with increasing temperature.

in the intrinsic carrier concentration. At sufficiently high temperatures niwill

eventually equal and then exceed net doping concentration

All semiconductors become intrinsic at sufficientl hi h tem eratures

1/ 2

useWheni A Dn N N

2

1/ 222

2 2D A D A

iN N N Nn n

n N N N N

= + +

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2 2i

p nn

= = + +


22/23

Position of Fermi-level from do in concentration

useWhen DN =D A

N NF i

i

n

D iN n

Whenln Ai F

i

E E kTn

=

A D

A iN n

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23/23

Temperature dependence of carrier concentrations

Plot is for phosphorus ND = 1015/cm3

ambient temperature, causes

monotonic increase in the

intrinsic carrier concentration. At

sufficiently high temperatures ni

will eventually equal and thenexceed net doping concentration

All semiconductors become

intrinsic at sufficiently high

temperatures

-123C 0C27C

C = K - 273

EL 511 VLSI Design

23(= -273C)

Lecture 3 Given [Compatibility Mode]

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