ECE-Elec 3 Lec1 Basic Physics of Semiconductors With Exercise

8/13/2019 ECE-Elec 3 Lec1 Basic Physics of Semiconductors With Exercise

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ECE-Elec 3 Lecture 1

ECE ELEC3-UST ECE 2013 1

Erika Escandor, ECE


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Outline

2

Introduction

ECE ELEC3-UST ECE 2013


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Introduction

ELECTRONICS vs MICROELECTRONICS

ELECTRONIC MICROELECTRONICS

Began about a century ago

Vacuum Tubes

Transistors (1940s)

Not until 1960s

Integrated Circuits (ICs)

Microchips

3ECE ELEC3-UST ECE 2013


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Introduction

Imagine:

A microprocessor containing about 100

million transistors in a chip area of approximately3 cm x 3 cm.

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uppose s were no nven e :Build the processor using 100 million

discrete transistors.



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Introduction

Using 100 million discrete

transistors:

If each device occupies a volume of3 mm x

3 mm x 3 mm

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n mum vo ume wou e m xPlus wires to connect the transistors thus

volume would increase substantially

this will be extremely SLOW since signals

would need to travel on long wires



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Introduction

Using 100 million discrete

transistors:

If each discrete transistor costs Php2.00,

the processor would be worth Php200

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If each discrete transistor would weigh 1 g

each, the processor would weight up to 100

tons



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Integrated Circuit (IC)

IC consists of interconnected electronic

components in a single piece (chip) of

semiconductor material

In 1958, ack S. Kilb (Texas

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Instruments) showed that it was possibleto fabricate a simple IC in Germanium


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In 1959, Robert Noyce (Fairchild

Semiconductor) demonstrated an IC

made in Silicon using SiO2 as the

insulator and Al for the metallic

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interconnects


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An IC that performs very complex tasks

Can be built by connecting a large number

of components, each performing simple

operations



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The degree of integration has increased

at an exponential pace over the past ~40

years



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Moores Law

Number o transistors on


ICs doubles approximatelyevery two years

Named after Intel co-

founder Gordon E.

Moore


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Outline

12

Basic Semiconductor P!sics

Semiconductors

Intrinsic Silicon

"o#ing

Carrier Concentrations

$rans#ort o% Carriers Carrier "ri%t and "i%%usionECE ELEC3-UST ECE 2013


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Semiconductor

Material which has electrical

conductivity between that of a metal and

an insulator

Remember:

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Low resistivity = conductor

High resistivity = insulator

Intermediate resistivity = semiconductor

ELE 311-UST ECE 2013


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Semiconductor

Generally crystalline in structure for

IC devices

In recent years, however, non-crystalline

semiconductors have become

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commerc a y very mportant


polycrystalline amorphous crystalline


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Structure o% Solid

Crystalline

Solid material whose constituent atoms,

molecules, or ions are arranged in an

ordered pattern extending in all three

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spat a mens ons Amorphous

Non-crystalline solid is a solid that lacksthe long-range order characteristic of a

crystal



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Structure o% Solid

Polycrystalline

Solids that are composed of many

crystallites of varying size and orientation

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Semiconductor

Has the ability to change conductivity

by addition of impurities calledDoping



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&alence e-

Remember:

-

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electronics, since this is where we can get

free electrons electrons that get

dislodged from their orbit, capable ofcarrying a charge through a conductor.

NOTE: The farther the electron is from

the nucleus, the easier it is to set it free.ELE 311-UST ECE 2013


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&alence e-

Neon

Complete outermost shell

No tendency for chemical reaction

Sodium

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One (1) valence electron

Donor of electrons

Chloride Seven (7) valence electrons

Acceptor of electronsELE 311-UST ECE 2013


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Semiconductor

Atoms having approximately four (4)

valence electrons fall somewhere

between inert gases and highly volatile

elements

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Group IV in periodic table Ex.Silicon,Germanium



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Periodic $a'le o% Elements



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Silicon

Atomic density:5 x 1022atoms/cm3

Si has four valence electrons

Thus requiring another four to complete its

outermost shell


It can form covalent bonds with four of itsnearest neighbors.


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Electron Pro#erties o% Silicon

Silicon is a semiconductor material

Pure Si has a relatively high electrical

resistivity at room temperature

There are 2 t es o mobile char e-


carriers in Si:Conduction electrons- negatively charged

Holes- positively charged


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Electron Emission

Electrons on the outermost shell were

given enough additional energy to

escape

Methods o Electron Emission


Thermionic

Photoelectric

Field Emission / Cold Cathode / Antoelectronic

Secondary Emission


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Electron Emission %or Silicon

The concentration (#/cm3) of conduction

electrons & holes in a semiconductorcan be modulated in several ways:

B


(dopants)

By applying an electric field

By changing the temperatureBy irradiation


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Silicon "uring $ermal Emission

When temperature goes up:

Electrons gain thermal energy

Thus can break away from the covalent

bond and act as free charge carrier


Free electrons now exist in theconductionband

Until they fall into another incomplete

bond


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Electron-ole Pair eneration

When a conduction electron is thermally

generated, a void or hole is also

generated

A hole is associated with a ositive


charge, and is free to move about the Sicrystal as well


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Bandga# Energ!

Denoted byEg

Amount of energy needed to remove anelectron from a covalent bond


,g= .

Unit eV (electron volt) - represents the

energy necessary to move one electron

across a potential difference of 1 V1 eV = 1.6 x 10-19J


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"ensit! or Concentration o% Electrons

Number of electrons per unit volume

Denoted byni


ere = . x

-

= Boltzmann constant

T= absolute temperature

Eg= bandgap energy

B= coefficient related to a specific

semiconductor material


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"ensit! or Concentration o% Electrons

Semiconductor Constants

MATERIAL Eg (eV) B (cm-3 K-3/2)

Silicon (Si) 1.1 5.23 x 1015


a um rsen e

(GaAs)

. . x

Germanium (Ge) 0.66 1.66 x 1015


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E*am#le +1

Determine the density of electrons in

Silicon at T = 300K (room temperature)

and T = 600 K.


,


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Intrinsic and E*trinsic Semiconductors

Intrinsic Semiconductor

Pure Silicon -> has very high resistance

Mass-Action Law


Where: n electron density

= ni

p hole density


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Intrinsic and E*trinsic Semiconductors

Extrinsic Semiconductor

Resistivity of Silicon can be modified by

replacing some of the atoms in the crystal

with atoms of another material



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"o#ing

Addition of impurities to intrinsic

semiconductor (ex. Silicon)

Silicon can be doped with other


properties


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"o#ing (, $!#e)

For example, if Si is doped with

phosphorus (P)P atom contains five (5) valence electrons


electron, so that the Si crystal has moreelectrons than holes


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"o#ing (, $!#e)

If a certain number of Phosphorus atoms

are uniformly introduced in a Siliconcrystal


equivalent to the number of P atoms

Phosphorus is adonor dopant

Silicon crystal becomes an ExtrinsicSemiconductorknown asn type


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"ensit! %or "o#ed Material

Under thermal equilibrium conditions,

the product of the conduction-electron

density and the hole density isALWAYS

e ual o he uare o n


Where:n electron density in extrinsic semiconductor

p hole density in extrinsic semiconductor

ni density in intrinsic semiconductor


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E*am#le +

A crystalline Silicon is doped uniformly

with Phosphorus atoms. The doping

density is 1016 atoms/cm3. Determine the

electron and hole densities at room


temperature.


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Carriers in an ,-t!#e Semiconductor

Electron majority carrier

Hole minority carrier



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"o#ing (P $!#e)

For example, if Si is doped with Boron

(B)

B atom contains three (3) valence electrons


,

the Si crystal has more holes thanelectrons


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"o#ing (P $!#e)

If a certain number of Boron atoms are

uniformly introduced in a Silicon crystal

The density of holes will be equivalent to

the number o B atoms


Boron is anacceptor dopant

Silicon crystal becomes an Extrinsic

Semiconductorknown asp type


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Carriers in an P-t!#e Semiconductor

Hole majority carrier

Electron minority carrier



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" C i


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"o#ant Com#ensation

An n-type semiconductor can be

converted into p-type material by

counter-doping it with acceptors such

that N > N


" C i


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"o#ant Com#ensation

A compensated semiconductor material

has both acceptors and donors

P-type material

N-type material


A> DD> A

S % C C i


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Summar! o% Carge Carriers


$ % C i


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$rans#ort o% Carriers

Movement of charge in semiconductors

DriftDiffusion



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& l it


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&elocit!

Acceleration due to the field and the

collision with the crystal counteract

leading to a constant velocity for the

carriers


Average velocity (v) is proportional to

theElectric field(E):

&elocit!


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&elocit!

where: -mobility, cm2/(Vs)

Electron Velocit


Hole Velocity

&elocit!


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&elocit!

For Silicon:

n

= 1350 cm2/ V s

p= 480 cm2/ V s


E*am#le +3


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E*am#le +3

A uniform piece of n-type Silicon that is

1 m long senses a voltage of 1 V.

Determine the velocity of the electrons.


electrons to cross a 1 m long Silicon.

Current Calculation


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Current Calculation

NOTE:

q = 1.6 x 10-19 C [charge of hole and

electron (negative for the electron)]


Current Calculation


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Current Calculation


With velocity ofv m/s

Total charge in v meters passed thecross section in 1 second

Current Calculation


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Current Calculation

Current - equal to the total charge

enclosed in v meters of the bars length


v W h represents volume

n q charge density in coulombs

negative sign is due to electrons carrying anegative charge

Current "ensit!


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Current "ensit!

Current density - current passing

through a unit cross section area

2


In the presence of electrons and holes:

E*am#le +.


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E*am#le +.

Consider an equal electron and hole

drift currents, how should the carrier

densities be chosen?


,

densities for Silicon?

Conducti/it! and 0esisti/it!


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Conducti/it! and 0esisti/it!

Conductivity

unit: mho/cm


Resistivity

unit: ohm-cm

&elocit! Saturation


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&elocit! Saturation

With this we assume that velocity rises

linearly with electric fieldIf electric field is high enough, there is


no linear relationship between v and Eanymore

Because the carriers collide with the

crystal so frequently and the time between

the collisions is so short that they cannot

accelerate much

&elocit! Saturation


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&elocit! Saturation

Velocity saturation seen in

transistors


Where: 0 low-field mobility

b proportionality factor

&elocit! Saturation


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&e oc t! Satu at o

Thus we can say that:


E*am#le +


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#

A uniform piece of semiconductor 0.2

m long sustains a voltage of 1 V. If the

low-field mobility is equal to 1350 cm2/

V s and the saturation velocit o the


carriers 107cm/s, determine the effectivemobility.

E*am#le + (cont2)


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# ( )

Also, calculate the maximum allowable

voltage such that the effective mobility is

only 10% lower than 0.


condition.

"i%%usion


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Flow from a region of high


concentrat on to reg on o ow

concentration

Even in the absence of electric field, can

carry electric current as long as non-

uniformity is sustained

"i%%usion


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The more non-uniform the

concentration, the larger the current


Where: n carrier concentration at a

given point along the x axis

dn/dx concentration gradientwith respect to x

"i%%usion


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If each carrier has charge equal toqand

given a cross-section area ofA


Where: Dn - proportionality factor called

thediffusion constant, cm2/s

"i%%usion Constant


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For intrinsic Silicon:

For electrons:


For holes:

Current "ensit! %or "i%%usion Carrier


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In the presence of electrons and holes:

Linear Concentration Pro%ile


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Constant diffusion current

Suppose the electron concentration is

equal toNat x = 0 and falls linearly to


E*am#le +


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A p-type bar of Silicon is subjected to

electron injection from the left and hole

injection from the right. Determine the

total current lowin throu h the device


if the cross-section area is equal to 1 mx 1 m.

,on-Linear Concentration Pro%ile


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Varying diffusion current


$otal Current 4lowing in a


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Semiconductor

Total current flowing in a semiconductor

is thesum of drift current and diffusion


Einstein 0elation


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and D are related as:


Summar! o% Carge $rans#ort


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Mecanisms


0e%erences


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Fundamentals of Microelectronics by

Wiley and Razavi

Microelectronics : circuit analysis and


5dditional E*ercise +1


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The intrinsic carrier concentration of

Germanium is expressed as


where Eg= 0.66 eV

Calculate ni at 300K and 600K and

compare the results with those obtained forSilicon.



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The intrinsic carrier concentration of

Germanium is expressed as


where Eg= 0.66 eV

Determine the electron and hole

concentrations if Ge is doped with P at adensity of 5 x 1016cm-3

5dditional E*ercise +


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An n-type piece of silicon experiences an

electric field equal to 0.1 V/m.

Calculate the velocity of electrons and

holes in this material.


What doping level is necessary to providea current density of 1 mA/m2 under these

conditions? Assume the hole current is

negligible.



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A n-type piece of silicon with a length of

0.1 m and a cross section area of 0.05

m x 0.05 m sustains a voltagedi erence o 1 V.


If the doping level is 1017 cm-3, calculatethe total current flowing through the device

at T = 300 K.

Calculate the total current flowing through

the device at T = 400K. Assume that

mobility does not change with temperature.

ECE-Elec 3 Lec1 Basic Physics of Semiconductors With Exercise

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Transcript of ECE-Elec 3 Lec1 Basic Physics of Semiconductors With Exercise