Charge transport 2011-lec

MSE462 (Prof. Z.H. Lu) : Charge Transport Phenomena

Transport in metallic systemsTransport in amorphous systemsTransport in semiconductors and heterojunctionsTransport in conjugated molecular systems



Classical Theory of Electrical Conduction in Materials (Drude Model)--- charge carrier density


Classical Theory of Electrical Conduction in Materials (Drude Model)--- charge carrier mobility

Nq

EENqvNqj

1

)(

densitycurrent




The history of electricity goes back more than two thousand years, to the time the Ancient Greeks discovered that rubbing fur on amber caused an attraction between the two. By the 17th century, many electricity-related discoveries had been made, such as the invention of an early electrostatic generator, the differentiation between positive and negative currents, and the classification of materials as conductors or insulators. In the year 1600, English physician William Gilbert conned the term electric, from the Greek elektron, to identify the force that certain substances exert when rubbed against each other. While many believe Benjamin Franklin to be the father of electricity, current findings seem to show otherwise. In 1752, Franklin is said to have performed the famous experiment of flying a kite during a thunderstorm, which led to the discovery that lightning and electricity were somehow related. Modern scientists know this to be something of a tall tale, since being hit by lightning would have been fatal. It's likely that Franklin was actually insulated, away from the path of lightning. The kite experiment helped Franklin establish a relationship between lightning and electricity, which led to the invention of the lightning rod. Benjamin Franklin went on to observe other phenomena related to electricity, but many believe that he didn't actually discover its true nature. In 1800, Italian-born physicist Alessandro Volta constructed the voltaic pile, later known as the electric battery, the first device to produce a steady electric current. It was Volta, not Franklin, who discovered that certain chemical reactions could produce electricity. Volta also created the first transmission of electricity by linking positively-charged and negatively-charged connectors and driving an electrical charge, or voltage, through them. It wasn't until 1831 that electricity became viable for use in technology. English scientist Michael Faraday created the electric dynamo, a crude precursor of modern power generators. This invention opened the door to the new era of electricity. A few decades later, in 1879, Thomas Alva Edison invented the light bulb. Source:www.wisegeek.com


Classical Theory of Electrical Conduction in Materials (Drude Model)--- temperature effect

a

u

Electron

S = a2

=u


n

T

T

0

0

Fig. 2.6: The resistivity of various metals as a function of temperatureabove 0 °C. Tin melts at 505 K whereas nickel and iron go through amagnetic to non-magnetic (Curie) transformations at about 627 K and

1043 K respectively. The theoretical behavior (~ T) is shown forreference.[Data selectively extracted from various sources including sections inMetals Handbook, 10th Edition, Volumes 2 and 3 (ASM, MetalsPark, Ohio, 1991)]

T

Tungsten

Silver

Copper

Iron

Nickel

Platinum

NiCr Heating Wire

Tin

Monel-400

Inconel-825

10

100

1000

2000

100 1000 10000

Temperature (K)R

esis

tivi

ty (

n

m)

From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)

http://Materials.Usask.Ca


120 V

40 W

0.333 A

Fig. 2.9: Power radiated from a light bulb at 2408 °C is

equal to the electrical power dissipated in the filament.


Classical Theory of Electrical Conduction in Materials --- impurity effects


Matthiesen’s rule

Temperature (K)

0

20

40

60

0 100 200 300

T

I

CW

100%Cu (Annealed)100%Cu (Deformed)

Cu-1.12%Ni

Cu-1.12%Ni (Deformed)

Cu-2.16%Ni

Cu-3.32%Ni

Fig. 2.8: Typical temperature dependence of the resistivity ofannealed and cold worked (deformed) copper containing variousamount of Ni in atomic percentage (data adapted from J.O. Linde,Ann. Pkysik, 5, 219 (1932)).



Resis

tivit

y (

n

m)

defimpth


Linde’s rule of metal’s resistivity


mass. atomic M,density; , constant; Avogadro ,N0

0

M

NNN a

Nq

EENqvNqj

1

)(

densitycurrent


Quantum Mechanical Consideration


Quantum Mechanical Consideration





10610310010-310-610-910-1210-1510-18 109

Semiconductors Conductors

1012

Conductivity (m)-1

AgGraphite NiCrTeIntrinsic Si

Degenerately

Doped Si

Insulators

Diamond

SiO2

Superconductors

PETPVDF

Amorphous

As2Se

3

Mica

Alumina

Borosilicate Pure SnO2

Inorganic Glasses

Alloys

Intrinsic GaAs

Soda silica glass

Many ceramics

Metals

Polypropylene

Figure 2.24: Range of conductivites exhibited by various materials






Anderson Localization Theory (PW Anderson, Phys. Rev. 109, 1492 (1958)


Conduction through hopping


Conduction through hopping


Modified hopping conduction by Efros and Shklovskii

T

T

c

c

e

ΔE

P

E

eR

ΔEΔE

ΔE

ReΔE

0

0

2

2

0

energy hopping optimum find to

4

0

transporthoppingfor requiredenergy The

4/

behindleft “holes” its andelectron hopping a

betweenenergy n interactio Coulomb The




Conduction in semiconductors vs metals

Fig. 5.20: Temperature dependence of electrical conductivityfor a doped (n-type) semiconductor.

log(n)

Intrinsic

Extrinsic

Ionization

log()

log()

T 3/2 T 3/2

Lattice

scattering

Impurity

scattering

1/TLow TemperatureHigh Temperature

T

Metal

Semiconductor

Logari

thm

ic S

cale



Resi

stiv

ity

hhee eNeN


Conduction through tunneling



L

R

L

R

L

dEETh

eI

dEETEfEfh

eIII

dEETEfh

eI

dEETEfh

eI

URLRL

URR

ULL

)(2

function. step ~ is function Fermiature,low temperAt

)()),(),((2

currentnet The

)(),(2

left right to from tunnelingelectronby causedcurrent The

)(),(2

right left to from tunnelingelectronby causedcurrent The

?

MSE462 (Prof. Z.H. Lu) : Charge Transport PhenomenaConduction through tunneling----P-N Junction Esaki Diode



----P-N Junction Esaki Diode


Quantum tunneling semiconductor devicesRTD


Quantum tunneling semiconductor devicesRTD


Quantum tunneling semiconductor devices-RTD (S.M. Sze, Modern Semiconductor Device Physics)




Cathode

Anode

Substrate

Al

q

Photo source: Samsung

http://web.kaist.ac.kr/~ioel/EMB00000ce07cb2.jpg


WHY and How Molecule Conduct Charge?


WHY and How Molecule Conduct Charge?


WHY and How Molecule Conduct Charge?Injection and Transport

Transporting molecule

Hopping conduction

electric field


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