6 - electrical properties

8/2/2019 6 - Electrical Properties

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Structure Properties

Atomic Structure

Bond Structure

Crystal Structure

Defect Structure Energy Band structure................ELECTRICAL PROPERTIES


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ELECTRICAL PROPERTIES

AIM: to describe the current-voltagecharacteristics of materials.


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QUIZ 51. Electical properties of materials are directly related to the ________.a) Behavior of atoms in vacuum

b) Behavior of electrons in crystal latticec) Behavior of Nihat Doand) Behavior of the molecules in liquid

2. The best formulation to describe the behavior (motion) of electrons is__________.a) Quantum mechanics called wave mechanicsb) Classical physicsc) Ficks 1st lawd) Nihat Doan Model

3. Schrdinger is ____________a) The person who described the diffusion in solidsb) The person who desribed the motion of electrons by wave equation

c) The neighbor of Pascal Noumad) The person who gave the plum pudding atomic model.


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Electical properties of materials are directly related to thebehavior of electrons in crystal lattice.

The best formulation to describe the behavior (motion) ofelectrons is Quantum mechanics called wave mechanics.

Schrdinger is the person who desribed the motion ofelectrons by wave equation


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A. Energy-Band Theory

Discussed: Single atom

The energy of the bound electron is quantized

The radial probability density for the electron

Probability of finding electron at a particular distancefrom the nucleus

Electron is not localized at a given radius

Now: Extrapolate these single atom results to a CRYSTAL!

We will find that the energy states for electrons occur inbands of allowed states and are separeted by forbiddenenergy bands

An introduction to semiconductor devices Donald Neamen (p.41)


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1. Formation of Energy Bands

When two atoms get closer their valence electrons willinteract splitting of energy levels into a band of energies.


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2. The Energy Band and the Bond Model

Valence band filled highest occupied energy levels

Conduction band empty lowest unoccupied energy levels


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2. The Energy Band and the Bond Model

Breaking of a covalentbond

Generation of a negativeand positive charge withthe breaking of a covalentbond


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3. Charge Carriers

Interested in the I-V characteristics

Current is a result of the flow of charge

Charges that can move when forces are applied

ChargesCARRIERS ELECTRONS

HOLES

IONS


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ELECTRONS Negatively charged particle

We are interested in number of electrons in CB.

Net drift of electrons in CBDRIFT CURRENT

CB: Conduction Band

If a force is applied to a particle and particle moves, it must gainenergy: dE = F.dx = F.v.dt

Due to the external force, electrons can gain energy and anet momentum Drift current density due to the motionof electrons:

=1

e: electronic chargeN:# of electrons per unit volume in CBv: electron velocity

CURRENT related to HOW WELL THE ELECTRON MOVE INTHE CRYSTAL


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HOLES


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4. Effective Mass

The movement of an electron in a lattice will be different fromfree space

In addition to an externally applied force,

there are internal forces in crystal due to

positively and negatively charged ions

Protons

Other electrons

e-

vacuum

E Fielde-

E Field

- -

-+

+

+

Motion of an electron in vacuum Motion of an electron in a solid

Ftotal=Fext+Fint = m.a

Fext= m*.am*: effective mass

(particle mass and effect ofinternal forces)


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5. Metals, Insulators and Semiconductors

Each crystal has its own energy band structure

Variations in band structures wide range of electricalcharacteristics in various materials


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Metals, Insulators and Semiconductors

METALS

Partiallyfilledband

Overlappingbands

INSULATORS SEMICONDUCTORS


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6. Electrons traveling in different directions

[100]

[110]

Electrons traveling in differentdirections encounter differentpotential patterns.


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Homework

Read Chapter 19: Electrical Properties

Do the Example problems: 1, 2, 3


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About the presentationsSome examples... 15min ppt

There will be a quastion related in final

How does a ... work?

1. Metal-Oxide-Semiconductor Field-Effect Transistor

2. Bipolar Transistor

3. Junction Field-Effect Transistor

4. Solar Cells

5. Photodetectors

6. Light Emitting Diodes

7. Laser Diodes


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B. Determination of number of electronsand holes in conduction process

AIM: to describe the current-voltage characteristics of materials.

Current: result of charge flow

QUESTION: How to determine the number of electrons and

holes in the semiconductor that will be available forconduction

1. Pauli Exclusion principle: only one electron may occupy a givenquantum state.

2. Determine the density of the available energy / quantum states

3. Probability of an electron occupying a quantum state


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DENSITY OF QUANTUM STATES

Objective: To determine the density of the available energy /quantum states

Use an appropriate model

nfinite potential well model

Apply Shrdingers wave equation Allowed electronic energy states in CB and VB

=4 2 3/2

3

=4 2 3/2

3

e-


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Statistical Mechanics

Objective: To describe the probability of an electronoccupying a quantum state

Large number of particles statistical behavior of

the group as a whole In crystal electrical characteristics determinedby the statistical behavior of large number ofelectrons


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Statistical Laws that Particles Obey

Three distribution las determining the distributionof particles among available energy states:

Maxwell-Boltzman probability function

behavior of gas molecules in a container Bose-Einstein function behavior of photons

Fermi-Dirac probability functionelectrons in a

crystal


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Fermi-Dirac Distribution Function & Fermi Energy

Probability that an allowed quantum state at the energy Eis occupied by an electron (ratio of filled to total number ofquantum states N(E)/g(E))

= 11+exp(

)

EF: Fermi energy


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Fermi Energy

To understand the meaning of distribution function andFermi energy plot distribution function versus energy

at T=0

EEfexp(+) = + f(E)= 0

= 11+exp(

)

Ef E

f(E)

1

0

Meaning: at T=0K, the propbability of a quantum state being

occupied for EEf is zero.

At T=0K, all electrons are in their lowestpossible energy states.


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Metals, Insulators and Semiconductors

METALS

Partiallyfilledband

Overlappingbands

INSULATORS SEMICONDUCTORS


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Excitation

Thermal-excitation

Photo-excitation

Chemo-excitation


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Chemo-excitation

Dopant Atoms and

Energy Levels

Qualitative Description

N-type semiconductor

The pure semiconductor is calledINTRINSIC SEMICONDUCTOR

Adding controlled amounts of dopant atomsresult in EXTRINSIC SEMICONDUCTOR


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N-type semiconductor

Impurity donates an electron to the conduction band sois called DONOR IMPURITY ATOM.


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P-type semiconductor


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P-type semiconductor


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Extrinsic Semiconductors

Addition of donor or acceptor impurity atoms will changethe distribution of electrons and holes in the material.

Density of electrons > density of holes n-type

Majority carriers: electrons

Density of electrons < density of holes p-type

Majority carriers: holes


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Carrier Transport Net flow of electrons and holes will generate currents

The process by which these charged particles move iscalled TRANSPORT.

Two transport mechanisms:

Drift

Apply an electric field to semiconductor produce force onelectrons and holes a net accelation and net movement (if thereare available energy states in CB and VB)

Net movement of charge due to and electric field: DRIFT DRIFTCURRENT

Diffusion

Due to density gradient

DIFFUSION CURRENT


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Carrier Drift J= charge density x drift velocity

F=m*.a=e.E Average drift velocity v = . E

, mobility: how well a particle will move in lattice due to anelectric field.

Collisions with onized impurity atoms Thermally vibrating lattice atoms


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Semiconductor Conductivity and Resistivity

Drift current density: =e.(. + .). = .:conductivity (.cm)-1

Resistivity: = 1

A bar of semiconductor material

L

V

A

I

= =

= .

Ohms lawresistance=f(resistivity, geometry)

= .


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Semiconductor Conductivity andResistivity of an Extrinsic Semiconductor Assume complete ionization

F(concentration and mobility of the majority carrier)

Ex. For N-type: n>>pe.e.ne


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ExampleConsider a bar of Silicon uniformly doped with acceptor

impurities and having the geometry given below. For an appliedvoltage of 5V, a current of 2mA is required. The current densityis to be no larger than 100A/cm2.Find the required cross-sectional area , length and doping concentration.

A bar of semiconductor material

L

V

A

I


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EXTRA SLIDES


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The Semiconductor in Equilibrium

Last time: general behavior of electrons in single-crystallattice.

Now: apply the concepts to semiconductor material

Equilibrium: no external forces such as:

Voltages

Electric fields

Magnetic fields

Temperature gradients

acting on the semiconductor material..


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Semiconductor device characteristics

Determined by conductivity

Can be varied (good conductor good insulator) bycontrolling the concentration of specific impurities in thematerial.

Process by which these impurities are introduced into thematerial: DOPING

By diffusion process

By ion implantation process


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Charge Carriers in Semiconductors

Current: the rate of charge flow

Charge carriers: electrons and holes

Density of charge carriersnumber of electrons in CBand number of holes in VB.

The distribution of electrons (wrt energy) in CB: density ofallowed quantum states x the probability that a state isoccupied by an electron.

n(E)=gc(E). f(E)

g(E): density of quantum states in CB

f(E): Fermi-Dirac probability function


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Density of electrons and holes

Nv: effective density of states

0 = .exp(( ) ) 0 = .exp(( ) )

Intrinsic carrier concentration

2= .exp(

)

: band gap energy

6 - electrical properties

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