electrical properties of materials notes part 1

1/60 IC_Implication.pdf (#16)2012-08-05 20:47:42

Moore’s LawIntel P4 (2000)

Transistor count: 42,000,000

Intel i7 (2008)Intel i7 (2008)

Transistor count: 731 000 000

Department of Electrical EngineeringDwight Look College of EngineeringJun Zou

Transistor count: 731,000,000

2/60 IC_Implication.pdf (2/6)2012-08-05 20:47:42

MOS Transistor• Metal-Oxide-Semiconductor (MOS)

transistor is the fundamental building blocks for modern ICsGate building blocks for modern ICs.

• ISD = f (VGS, VSD). The channel conductance (ISD/ VSD) can be

Source Drain

Gate

controlled by VGS.

• The gate (silicon) oxide provides electrical insulation between GateSilicon oxide

Channel

electrical insulation between Gate and Substrate.

• Any current flows between Gate and substrate is called gate leakage

Silicon oxide

Silicon

Metalsubstrate is called gate leakage current, which will interfere with ISDand is detrimental to the functioning of the transistor.



Shrinking the Size of MOS Transistorsg• Device scaling (down) is the key to

achieve more powerful and cheaper computer chips

Source Drain

Gate

computer chips.– More transistors in the same amount

area.– Faster operation speed.– Lower power consumption of eachChannel Lower power consumption of each

transistor (longer battery life).– Lower voltage operation (can be

powered by a single battery).

• Device scaling need to be done in 3D.

– Reduce the x/y dimension of gate, source, drain and channel ,(length/width).

– Reduce the thickness of the silicon oxide.



Fundamental Challenge in Down-Scalingg g

)2(2

)2(0

2

2

)(16 dk

dk

i

i

eEVEeTT

�

�

�

Source Drain

Gate

Electron t li 2

2

eV

Channel

tunneling

d

V2)(2 2 EVm

k�

• When the thickness of the silicon oxide is reduced to 1 nm, significant tunneling leakage will occur. This sets a fundamental limit of device

!2k i

scaling.

• Use high-dielectric-constant insulator (high-k dielectric)– HfO, CeO.HfO, CeO.– A reasonable thickness of the insulator with even higher V2 can still be used in

downscaled MOS transistors.


7/60 STM.pdf (#15)2012-08-05 20:47:43

Scanning Tunneling Microscopeg g p)2(

02 dk ieTT � !

)(2 22

EVmk i

�

)()2(00

0

2 dfeTI

TIIdk

tunnel

i

�

d

• Tiny surface features caused d and thus Itunnel to change. How?• Why only working on conductor surface?• Why working best at very low temperature?• Why using a sharp probe tip?

STM image of Ni (100) surface STM image of Pt (111) surface


SOURCE: Courtesy of IBM SOURCE: Courtesy of IBM

8/60 Tunneling.pdf (#14)2012-08-05 20:47:43

Conduction between two copper wirespp

FACT 1: Copper is inevitably oxidized in the airFACT 1: Copper is inevitably oxidized in the air.

FACT 2: Copper oxide is a good insulator.

Question 1: Why is it still conducting when we touch two copper wires?

Question 2: Why is it not conducting when the copper wires are heavily corroded?

Copper Copper

Copper oxide


Copper oxide

9/60 Tunneling.pdf (2/2)2012-08-05 20:47:43

Electron tunneling indicated by solution of SEsolution of SE

• Solving SE at two-interface and three-layer boundary condition.

Metal 1 Metal 2

• When E>V, 0<T<1.• When E<V, 0<T<1

(tunneling effect).


Metal 1 Metal 2

10/60 Lecture #6 (#13)2012-08-05 20:47:43

Today's topics:

1) electron tunneling2) scanning tunneling microscope3) electron tunneling issues in ICs4) Quiz #1 review

11/60 Lecture #6 (2/3)2012-08-05 20:47:44

12/60 Lecture #6 (3/3)2012-08-05 20:47:44

13/60 PWD.pdf (#12)2012-08-05 20:47:44

Quantum Well Laser DeviceMolecular Beam EpitaxyM1 M1 M2 M1M2 M2

M1 M2 M1

• Electrical current pumping to put electrons from Ei to Ej.

• The “relaxation” of electron

M1

M1

The relaxation of electron from Ej to Ei will create an output photon with energy equals to Ej-Ei.

• Changing the thickness of M2 can tune the wavelength of

M1

M1

M1

2,1L

chhfEEE ijji v � 'O

light emission.• For optical communication


2, Ljj O

14/60 PWD.pdf (2/4)2012-08-05 20:47:44

Quantum Dots

• Quantum dots are semicondutor

UV light

nanoparticles.

• They form (3D) quantum potential wells for the electrons.

• Photon energy: hf (hc/O).

• The frequency of light increases from• The frequency of light increases from red to violet, so does the energy of the photon.

• Infrared: lower energy and longer wavelength (~1µm).Magic of size ! longer wavelength ( 1µm).

• Ultraviolet: higher energy and shorter wavelength (~.3 µm).

Magic of size !


15/60 PWD.pdf (3/4)2012-08-05 20:47:44

Quantum DotsEj

L Ej

Ei

2,1L

E ji v' L

Ei

i

UV absorption (pumping) UV absorption (pumping)L

Ej

Ei

Ej

Ei

Red light emission (Relaxation) Blue light emission (Relaxation)

Relaxation Relaxation

Ej

EiOchE ji ' ,


16/60 PWD.pdf (4/4)2012-08-05 20:47:44

Quantum Dots ApplicationppBiomarkers for Cancer Imaging High-efficiency and Wide-spectrum Solar Cell

Different size of quantum dots

Different ¨Ei,j

Absorb light of different O

Utilize most energy in the

sunlight


17/60 e_PW.pdf (#11)2012-08-05 20:47:45

Discrete Energy Level in Potential Wellgy

• When E>V, _\(x)|2 can be non-zero at any CONTINOUS E value (level).• When E<V, _\(x)|2 can be non-zero ONLY at a series of DISCRETE (single) E values (levels)


When E V, _\(x)| can be non zero ONLY at a series of DISCRETE (single) E values (levels) (E1, E2, E3…).

18/60 e_PW.pdf (2/2)2012-08-05 20:47:45

Discrete Energy Level in Potential Wellgy• Discrete (integer: 1, 2, 3, 4…), Continuous (decimal: 1.0, 1.01, 1.011….)

• When the energy of an electron (E) is smaller than the height of the potential well (V2)

• The electron current transmission coefficient T = 0. The electron is “confined” in the well.

• E is discrete and can only take a value among a list of “allowable” energy levels (E1, E2, E3…)

• If the energy of an electron is Ei, we say “the electron stays at (occupy) the ith energy level.

• Each “allowable” energy has it own maximum capacity (number of states). Once it is fully “occupied”, no more electron can stay at this energy level.

• An electron can lose or gain its energy to stay at other energy levels (as long as they are not full).

• Normally, more electrons stay at lower energy levels.

E3 (5 5eV)

(Level: 3, Height: 20 ft)

(Level: 4, Height: 30 ft) Elevator breaks down. Help!!!

V2 (7eV)

E3 (5.5eV)

E2 (2.2eV)


2 ( )

E1 (1.0eV)



19/60 Lecture #5 (#10)2012-08-05 20:47:45

1)Electrons in potential well

2)Potential well with rigidwalls

3) electron/photoninteraction in potential well

4) quantum well devices

When we have a small width wascan see the discrete energyjumps, but when L is big, thechange will look so small that theenergy looks almost continuous.

20/60 Lecture #5 (2/3)2012-08-05 20:47:45

21/60 Lecture #5 (3/3)2012-08-05 20:47:46

22/60 Hw #1 (#9)2012-08-05 20:47:46

23/60 Hw #1 (2/6)2012-08-05 20:47:46

24/60 Hw #1 (3/6)2012-08-05 20:47:46

25/60 Hw #1 (4/6)2012-08-05 20:47:46

26/60 Hw #1 (5/6)2012-08-05 20:47:47

27/60 Hw #1 (6/6)2012-08-05 20:47:47

28/60 Lecture 4 (#8)2012-08-05 20:47:47

Electron existence at certain location is altered bythe potential energy there.

29/60 Lecture 4 (2/7)2012-08-05 20:47:47

30/60 Lecture 4 (3/7)2012-08-05 20:47:47

31/60 Lecture 4 (4/7)2012-08-05 20:47:48

32/60 Lecture 4 (5/7)2012-08-05 20:47:48

Probability of electrons being reflected at the interface.

Probability of electron transmission/emmision

33/60 Lecture 4 (6/7)2012-08-05 20:47:48

34/60 Lecture 4 (7/7)2012-08-05 20:47:48

35/60 HallApplication.pdf (#7)2012-08-05 20:47:49

Hall Probes for Magnetic Field MeasurementMeasurement

Iz

y Bias Voltage

Voltage meter

Ix

Uyx

z

+

-

Hall element

t

I

meterBz

+

t

Hall element

zx

Hy BtIRU y

xHyz U

IRtUB D

– By setting up the bias current (Ix) flowing into the Hall element and monitoring the traverse Hall voltage output (Uy), the input magnetic field (Bz) can be “sensed” (figured out backwards).

Hall probe and Gauss meters


can be sensed (figured out backwards).

36/60 HallApplication.pdf (2/3)2012-08-05 20:47:49

Non-contact or Wireless position sensing by measuring field strengthsensing by measuring field strength

– When a tooth of the magnetic gear moves closely to the Hall sensor, it gives out higher output voltage (Uy) due to increased

zx

Hy BtIRU zy BU D

, g g p g ( y)magnetic field (Bz).

t– By carefully designing the pitch and width of the teeth, a very

specific waveform of Uy can be created to trace the rotation speed and angle of the gear and shaft.

Magnetic gear Uy

B

Hall sensor

Bz


Hall sensor

37/60 HallApplication.pdf (3/3)2012-08-05 20:47:49

Digital Compassg p

Bz

Uy

IxHoneywell� at digikey.com

– Hall sensor is most sensitive to the magnetic field perpendicular to the plane containing the bias current and Hall voltage terminals.

– Using two or three Hall sensors allows 2-axis or 3-axis detection of the magnetic field direction.


– Hall sensor can be readily integrated with microelectronics.

38/60 HallEffect.pdf (#6)2012-08-05 20:47:49

Lorentz Force• Moving electron interacting with static magnetic

field

z

x v

FLorentzPointing into the board

Bz

Bz

FLorentz

y

x-e

vx

+q vx

T

Lorentz

BvqFLorentz&&&

u� Tsin�� BvqFLorentz

The direction follows the “right hand” rule of V cross B

BveFLorentz&&&

u�� hand” rule of V cross B. Lorentz


39/60 HallEffect.pdf (2/4)2012-08-05 20:47:49

Hall Effect • Flow of electron in solids is deflected by external magnetic

field due to the Lorentz force.

Bz

Uyt

Uy=0

z

x

Uy

w

tl

FLorentzy

Ix time


40/60 HallEffect.pdf (3/4)2012-08-05 20:47:49

Hall Effect • A built-in voltage drop (Hall voltage) is created as the result of

electron accumulation when FLorentz > FE .

Uy

Bz

Uyt

EFE

z

xw

tl

UH=Ew

FLorentzy

Ixtime

FLorentz > FE


41/60 HallEffect.pdf (4/4)2012-08-05 20:47:49

Hall Effect • At “steady state”, FE = FLorentz and the electrons are not

deflected any more. • The built in electrical field and the Hall voltage start to• The built-in electrical field and the Hall voltage start to

saturate.

BzUy

FE

Bz

tl

zx

ey B

tI

eNU 1

UH=EwEFLorentz

Ix1

timew

t: dimension in the direction of the magnetic field (Bz)

eH eNR 1

FLorentz = FE


Lorentz E

42/60 Lecture #3 (#5)2012-08-05 20:47:49

Topics covered:

1) hall effect2) hall effect application3) de broglie's hypothesis4) scanning electron microscope5) calculation example

When a piece of current carrying conductor is placed ina magnetic field, a transverse voltage will be generated.

43/60 Lecture #3 (2/5)2012-08-05 20:47:50

44/60 Lecture #3 (3/5)2012-08-05 20:47:50

45/60 Lecture #3 (4/5)2012-08-05 20:47:50

46/60 Lecture #3 (5/5)2012-08-05 20:47:50

47/60 ElectronMotion.pdf (#4)2012-08-05 20:47:50

Motion of Electrons in Solids

• The motion of electrons is hardly a “smooth” process. The electrons repeatedly collide into much larger and “vibrating” atomic centers.

Stop slow down or change direction– Stop, slow down or change direction.

• The magnitude and frequency of collision is affected by– Atomic structure (material)– Crystal lattice arrangement (material)


Crystal lattice arrangement (material)– Vibration of atomic centers (temperature)

Electrons will collide into atoms andother electrons, which cause a a delayand affects the current of the electronsin the material

Atomic structure matters

How they're arranged in space

Vibration of their atomic centers

So many things affect its mobility.

48/60 ElectronMotion.pdf (2/2)2012-08-05 20:47:50

Drift of Electrons under Electrical Field

• In the presence of an electrical field, all electrons start to accelerate d d ift i th it di ti f th fi ld A lt th iand drift in the opposite direction of the field. As a result, there is a

net current flow in the same direction of the field. • However, the acceleration can only last a short while between two

collisions This “stop-n-go” process is repeated again and againcollisions. This stop-n-go process is repeated again and again.• Statistically, there is an average time interval and distance, in which

electrons can be driven by the electric field and move freely (without collisions). These are so called mean free time (W) and mean free


path.

49/60 Conductivity.pdf (#3)2012-08-05 20:47:51

Conductor (Metal) ( )

U

E

I

U

• Lots of “free” electrons (1023/cm3) to form “electron gas”.• Electron gas serves as “glue” to bond the atomic centers (ions)

E

g g ( )through attractive electrostatic forces (metallic bond).

• The free electrons can move (drift) when an external electrical field is applied.

– In opposite direction.


pp– Form a strong current flow in the same direction of the electrical field.

50/60 Conductivity.pdf (2/6)2012-08-05 20:47:51

Insulator (NaCl) ( )

• All electrons are tightly confined to their atomic masters (Na and Clions)

E

ions).• The positively charged Na ions and the negatively charged Cl ions

directly bond to each other through attractive electrostatic forces (ionic bond).N f l t• No free electrons.

– No current flow when an external electrical field is applied.

• Nacl water solution is a good conductor?


g– The dissociated Na+ and Cl- ions contribute to the conduction.


Insulator (SiO2) ( 2)O O O

Si OO Si O Si O

O O O

E• Adjacent silicon and oxygen atoms share electrons (covalent

bond). • The covalent electrons are tightly confined to their masters.• No free electrons.

– No current flow when an external electrical field is applied.



Semiconductor (Silicon) ( )

Si Si SiSi Si

Si Si Si

Si Si Si

Si

Si

Si

Si

S S S

Si Si Si

S

Si

S

Si

• Adjacent silicon atoms share electrons (covalent bond). • The covalent electrons are not tightly confined to their masters.




Si Si SiSi Si

Si Si SiSi Si I

Si Si SiSi Si

I

• When some electrons obtained enough energy, they can “escape”.f ( ( ))

E

– Form a free electron and leave a hole behind (electron hole pair (EHP)).– Limited number of electrons and holes (1010/cm3) .– There is limited current flow when an external electrical field is applied.– Semiconductor.




Si Si SiSi Si

Si Si Si

Si Si Si

Si

Si

Si

Si

Si Si Si

Si Si Si

Si

Si

Si

Si

• When an electron loses its energy, it can recombine with a hole to

E

neutralize each other.• The tunability in the number of electrons forms the foundation of

many solid-state devices (e.g., solar cells and LEDs).


55/60 Lecture 2 (#2)2012-08-05 20:47:52

Two main questions.

-how many free electrons are there?

-how free is the mobility of the electrons in the picof material?

Mass of electron "felt"by the electrostaticdriving force. Theeffective mass is alsorelated to the materialproperties.

56/60 Lecture 2 (2/3)2012-08-05 20:47:52

Determines the operation speed ofthings such as computer parts. Themobility is important in all aspectsand describes how fast processorscan operate. Certain materials, thusare wanted for faster parts and so theprice if that material will be muchmore expensive.

Electrical conductivity

57/60 Lecture 2 (3/3)2012-08-05 20:47:52

58/60 Lecture #1 (#1)2012-08-05 20:47:52

www.ece.tamu.edu/~junzou/370/index.htm

Fundamental SI units

Length: Meter

Time: Second

Energy: Joule

Mass: Kg

For an electron:

M = 9.1 x 10^-31 kg

e= 1.6x10^-19 C

59/60 Lecture #1 (2/3)2012-08-05 20:47:53

# of charges inunit length,area, volume

60/60 Lecture #1 (3/3)2012-08-05 20:47:53

Ratio of electricfield overcurrent density

electrical properties of materials notes part 1

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