EEE 3394Electronic Materials

Chris FerekidesFall 2014Week 8

What happens when we bring two metals together ??

F(M

o) =

4.2

0 eV

Electrons

Vacuum

Fermi level

Pt MoVacuum

Fermi level

Electrons

F(Pt

) =

5 .36

eV

F(M

o) =

4.2

0 eV

Electrons

Vacuum

Fermi level

Pt MoVacuum

Fermi level

Electrons

F(Pt

) =

5 .36

eV

Fermi level

F (Pt) F (Mo) = 1.16 eV = eDV

Vacuum

Vacuum

5.36

eV

4 .20

eV

- e transfer due to difference in energy- net e-transfer leaves behind a

positive charge, while making the other metal more negative

- the result is charge separation … E-field and V! known as the Contact Potential

Metal to Metal Contacts

Net diffusion of electrons from the “hot” to the “cold” region of a metal …

- Fermi function at a higher T “spreads” more toward higher energies

- High energy e’s move to fill in lower energy states ...

- This process leaves behind a net positive charge … therefore E-field … Voltage!

- The Seebeck Coefficient or Thermoelectric Power is:

E

1

EFH

E

f(E)1

EFC

Conductor

0 0

Hot Cold

Hot Cold­­­­

++++

Temperature, DT

f(E)

Voltage, DV ­+

dTdV

S

Seebeck Effect

The electron movement is NOT always from Hot to Cold because the diffusion process depends on several parameters including the mean free path … which also depends on T!

The Seebeck coefficient can be –ve or +ve depending on which mechanism dominates …

E

1

EFH

E

f(E)1

EFC

Conductor

0 0

Hot Cold

Hot Cold­­­­

++++

Temperature, DT

f(E)

Voltage, DV ­+

dTdV

S

2

1

T

T

SdTΔV

x3eE

TkπS

FO

22

Seebeck Effect

100 °C 0 °C

Cold Hot

mVMetaltype B

Metaltype B

Metaltype A

Metal

100 °C

Cold Hot

mV Metal

Metal

0 °C

What is a thermocouple ??

Can we measure the voltage generated by the temperature difference ??

0

So how can we utilize the Thermoelectric Power ??

0

Thermocouple

The difference in Seebeck coefficients will result in a net Voltage across the two wires …

100 °C 0 °C

Cold Hot

mVMetaltype B

Metaltype B

Metaltype A

0

2

1

T

TBAAB )dTS-(SV

Thermocouple

Thermionic Emission

• Heated filament in a vacuum will emit electrons !

C ath o d e

F ila m e n t

I

V a cu u m

P la te o r A n o d e

(a )

I

V

S a tu ra tio n cu rre n t

(b)

(a) Thermionic electron emission in a vacuum tube.(b) Current-voltage characteristics of a vacuum diode.

0

T3

T2

n (E ) = g (E ) f(E )

E

T1

E lec tro n co n c en tra tio np e r u n it en erg y

E

EF +

EF

0 1 .0f(E )0

P ro b ab ility

T3

T2

T1

Free E lectron

Thermionic Emission - Rectifier

• Why does the current saturate ?• What happens when the voltage is reversed ?

C ath o d e

F ila m e n t

I

V a cu u m

P la te o r A n o d e

(a )

I

V

S a tu ra tio n c u rre n t

(b)

(a) Thermionic electron emission in a vacuum tube.(b) Current-voltage characteristics of a vacuum diode.

Thermionic Emission Equation

• Where Bo is a constant called the Richardson-Dushman constant

kT

TBJ o exp2

C ath o d e

F ila m e n t

I

V a cu u m

P la te o r A n o d e

(a )

I

V

S a tu ra tio n c u rre n t

(b)

(a) Thermionic electron emission in a vacuum tube.(b) Current-voltage characteristics of a vacuum diode.

Bonding Model:- Rem: four nearest neighbors;- covalent bonding - sharing of electrons between neighboring atoms;- each atom contributes four “shared” electrons;- each atom accepts four shared electrons from its neighbors;

Note: at room temperature some bonds are “broken” i.e. free electrons.

Silicon:- 14 electrons;- 10 are tightly bound to nucleus; (core electrons);- 4 weakly bound; valence electrons - participate in chemical reactions.(Ge similar to Si with 28 core electrons)

Silicon (Si) Bonding Model

CHARGE CARRIERS: In conductors: electrons

In semiconductors?: At 0ºK no broken bonds i.e. no free electrons. At 0ºK no electrons in conduction band, valence band completely filled- energy band

model electrons in valence band can still move but net momentum (quantized) is zero;

therefore no NET current flow. At room temperature “some” bonds are broken and there exist electrons in the

conduction band: conduction electrons. Breaking of a bond also creates a “void”; vacancy in the valence band: a HOLE is also a

charge carrier. (see figs)

TERMINOLOGY: Dopants: certain impurity atoms added to semiconductors in order to control the number

of holes/electrons. Intrinsic semiconductor: pure (undoped) semiconductor. Extrinsic semiconductor: doped semiconductor; properties determined by added

impurities.

Semiconductor Terminology

E lec tron en erg y

V a le n c e B a n d (V B )

F u ll o f e le c tr o n s a t 0 K .

Ec

Ev

0

E c+c

( c )( b )

yB

C o n d u c t io n B a n d (C B )

E m p ty o f e le c tr o n s a t 0 K .

S i cry sta l in 2 -D

Bandgap = E g

What Happens @ 0 K ?

E

g(E)

g(E) µ (E Ec)1/2

f(E)

EF

nE(E) or pE(E)

E E

Forelectrons

For holes

[1 f(E)]

nE(E)

pE(E)

Area = p

Area = ( ) ndEEEn =ò

Ec

EvEv

Ec

0

Ec+c

EF

VB

CB

-

Intrinsic means … n=p

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

V B

C B

V B

C B

x

x = 0 x = L

V (x )E le c tr o s ta t ic PE (x )

(a ) (b )

E x

E x

Hol

een

ergy

Ele

ctro

nE

nerg

y

When an electric field is applied, electrons in the CB and holes in theVB can drift and contribute to the conductivity. (a) A simplifiedillustration of drift in Ex. (b) Applied field bends the energy bandssince the electrostatic PE of the electron is -eV(x) and V(x) decreases inthe direction of Ex whereas PE increases.

REM – We are considering Si for most examples

a donor atom has 5 valence electrons; when a donor atom replaces a Si atom 4 of its 5 valence electrons will participate in the

formation of the four covalent bonds; the 5th electron is weakly bound to the donor atom;

what does weakly bound means? It takes about 1 eV to break a Si-Si bond (i.e. to free an electron in pure Si.) it takes about 0.1 eV or less to remove the extra electron from the donor atom.

Most donor and acceptor binding energies are about 1/20 Eg (Si).

(Same can be described for an acceptor atom with one less electron!).

Note: when a donor atom gives up its extra electron the net charge of the donor is +1. This

charged donor is FIXED.

Bonding Model

n-type Doping

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (©

McGraw-Hill, 2005)

A s+

e-

Arsenic doped Si crystal. The four valence electrons of As allow it tobond just like Si but the fifth electron is left orbiting the As site. Theenergy required to release to free fifth-electron into the CB is verysmall.

x

As+ As+ As+ As+

Ec

Ed

Ev

As atomsites every106 Si atoms

Distanceintocrystal

~0.03eV

CB

ElectronEnergy

p-type Doping

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (©

McGraw-Hill, 2005)

B -h +

( a ) (b )

B -

F r ee

Boron doped Si crystal. B has only three valence electrons. When itsubstitutes for a Si atom one of its bonds has an electron missing andtherefore a hole as shown in (a). The hole orbits around the B- site bythe tunneling of electrons from neighboring bonds as shown in (b).Eventually, thermally vibrating Si atoms provides enough energy tofree the hole from the B- site into the VB as shown.

x D is ta n c ein to c ry s ta l

E v

E a

B a to m s ite s ev e ry 1 0 6 S i a to m s

V B

E c

E le c tro n e n e rg y

~0.05eV

B- B- B- B-

h+

Light Effects

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (©

McGraw-Hill, 2005)

(a) A photon with an energy greater than Eg can excite an electron from the VB to the CB. (b) When a photon breaks a Si-Si bond, a free electron and a hole in the Si-Si bond is created.

e hole

C B

V B

Ec

Ev

0

E c+

Eg

F ree e h > E g

H ole

E le c tro n e n e rg y

h

(a ) (b )

Semiconductors – Bonding/Energy Band Model

Donor

Acceptor

the binding energy for a donor electron is about 1/20 Eg.

if energy equal to binding energy is supplied to the crystal the extra electron will leave the donor and end up in the conduction band.

Note:at OºK no thermal energy therefore no donor electrons can be excited to the conduction band.The creation of a free electron from a donor atom does not result in the creation of a hole (rem. Intrinsic semiconductor).

Semiconductors n & p

EQUILIBRIUM CARRIER CONCETRATIONSREM: gC(E)d(E) represents the number of available states (cm-3) in the energy interval E+dE. f(E) is the probability a state is occupied by an electron; (1-f(E) holes);

gC(E)f(E)d(E) gives the number of electrons (cm-3) in the interval E+dE;

Therefore the TOTAL number of electrons n (and holes p) in the conduction band (and in the valence band) can be obtained by

integrating the relationships:

TOP

C

E

ECo (E)f(E)dEgn

V

Botom

E

EVo f(E)]dE(E)[1gp

32c

*n

*n

c

)E(E2mm(E)g

32

v*p

*p

v

E)(E2mm(E)g