Chapter42Chapter42

Conduction of Electricity Conduction of Electricity in Solidsin Solids

42-2 The Electrical Properties of Solids42-2 The Electrical Properties of Solids

silicon and diamond

Classify solids electrically according to three basic properties:

1. resistivity

2. Temperature coefficient of resistivity

3. Number density of charge carriers n

Use measurements of , and n to divide into three categories:metalssemiconductors

insulators

42-3 Energy Levels in a Crystalline Solid42-3 Energy Levels in a Crystalline Solid

According to Pauli exclusion principle

42-4 Insulators42-4 InsulatorsAs (a) shows,in an insulator the highest band containing any electrons is fully occupied,and the Pauli exclusion principle keeps electrons from moving to occupied levels.The electrons in the filled band have no place to go,they are in gridlock,no one can move.

Sample Problem 42-1Sample Problem 42-1kTEEx xe

N

N /)(

0

0 213)300)(/1062.8(

5.55

KKeV

eV

kT

Eg

93213)/(

0

103 eeN

NP kTEx g

42-5 Metals42-5 Metals

As Fig.42-4b shows,the highest occupied energy level falls somewhere near the middle of an energy band.There are plenty of vacant levels at nearby higher energies into which electrons can jump. Electrons in its highest occupied band can easily move into higher energy levels within that band.

The total number of conduction electrons:

atomper electrons

valenceofnumber

samplein

atoms ofnumber

samplein electrons

conduction ofnumber

The number density n of conduction electrons in a sample:

V volumesample

samplein electrons conduction ofnumber n

The number of atoms in a sample:

AN/)M massmolar (

)V volumesample)(density smaterial'(

M)/N mass(molar

M mass sample

mass atomic

M mass sample

samplein

atoms ofnumber

A

samsam

How Many Conduction Electrons Are There?How Many Conduction Electrons Are There?

Sample Problem 42-2Sample Problem 42-2

M massmolar

)V volumesample)(density smaterial'(

samplein

atoms of

number AN

molkg

molmmkg

/100926.2

)1002.6)(1000.2)(/10738.1(21

1233633

223

21

1061.8/10312.24

/100926.2

samplein

atoms ofnumber

molkg

molkg

electrons1072.1)atom

electrons2)(atoms1061.8(

samplein

electrons conduction

ofnumber 2322

Conductivity at T>0Conductivity at T>0The quantity Kt,may be give to a conduction electron by the random thermal motions of the lattice.Only some few conduction electrons whose energies are close to the Fermi energy are likely to jump to higher energy levels due to thermal agitation.

How Many Quantum States Are There?How Many Quantum States Are There?

The density of states N(E)

2/13

2/328)( E

h

mEN

Sample Problem 42-3Sample Problem 42-3(a)

sample of

volumeV

eV 7at N(E)

states ofdensity

7eVat eVper

states ofnumber

119391328 104)102)(102(7eVat eVper

states ofnumber

eVmeVm

(b)

)E rangeenergy (eV 7at eVper

states ofnumber

7eVat E rangein

N states ofnumber

or1717119 101102.1)003.0)(104( eVeVN

The Occupancy Probability P(E)The Occupancy Probability P(E)

1

1)( /)( kTEE Fe

EP

T=0For ,the exponential term in Eq.42-6 is ,or zero.so P(E)=1

For ,the exponential term in Eq.42-6 is ,so P(E)=0

Fig.42-6b is a plot of P(E) for T=1000K. Note that if E=EF (no matter what the temperature T), the exponential term in Eq.42-6 is and P(E)=0.5

The Fermi energy of a given material is the energy of a quantum state that has the probability 0.5 of being occupied by an electron.

Sample Problem 42-4Sample Problem 42-4

45.1)800)(/1062.8(

10.05

KKeV

eV

kT

EE F

%19 19.01

1)(

45.1or

eEP

%81 81.01

1)(

45.1or

eEP

(a)

(b)

How Many Occupied States Are There?How Many Occupied States Are There?

)()()(0 EPENEN

Eenergy at P(E)

yprobabilitoccupancy

Eenergy at N(E)

states ofdensity

Eenergy at (E)N

states occupied ofdensity

o

Sample Problem 42-5Sample Problem 42-5

1328

1328

0

101

)50.0)(102(

)()()(

eVm

eVm

EPENEN

sample of

V volume

eV 7at (E)N states

occupied ofdensity

eV 7at eVper states

occupied ofnumber

0

11939328 102)102)(101(eV 7at eVper states

occupied ofnumber

eVmeVm

Calculating the Fermi EnergyCalculating the Fermi EnergyIn Fig.42-7a at all energies between E=0 and E=EF:

FE

dEENn0

0 )(

In Fig.42-7a Because P(E)=1 ,we substitute Eq.42-5 into Eq.42-8, we find that

3

22828 2/3

3

2/3

0

2/13

2/3F

EE

h

mdEE

h

mn

F

3/22

3/22

3/2 121.0)

216

3( n

m

hn

m

hEF

42-6 Semiconductors42-6 SemiconductorsThe semiconductor has a much smaller energy gap Eg between the valence band and conduction band.There is a real possibility that thermal agitation at room temperature will cause electrons to jump the gap from the valence band to the conduction band.

Number Density of Charge Carriers nNumber Density of Charge Carriers nBoth the elections in the conduction band and the holes in the valence band serve as charge carriers.The electrons in the valence band,being negatively charged.In effect,the holes behave like moving particles of charge +e.

The resistivity of a material is . From the metal,this vast difference can be accounted for by the vast difference in n.

Temperature Coefficient of Resistivity Temperature Coefficient of Resistivity

dT

d

1

The resistivity of metal increases with temperature, is positive for metal.The resistivity of semiconductor decreases with temperature, is negative for semiconductor.

ResistivityResistivity

42-7 Doped Semiconductors42-7 Doped Semiconductors

p-Type Semiconductorsp-Type SemiconductorsSemiconductors doped with acceptor atoms are called p-type semiconductors;the p stands for positive to imply that the holes introduced into the valence band,which behave like positive charge carriers,greatly outnumber the electrons in the conduction band.In p-type semiconductors,holes are the majority carriers and electrons are the minority carriers.

Semiconductors doped with donor atoms are called n-type semiconductors;the n stands for negative,to imply that the negative charge carriers introduced into the conduction band greatly outnumber the positive charge carries,which are the holes in the valence band.In n-type semiconductors,the electrons are called the majority carriers,and the holes the minority carriers.

n-Type Semiconductorsn-Type Semiconductors

pnnn 00610

6328

322

105

1

105

10

m

m

n

n

si

p

3223660

600

6 10)10)(10(1010 mmnnnnp

Asi )/NM massmolar (silicon

)V volumesample)(densitysilicon (

samplein

atoms ofnumber

si

Asi M

Nn

)densitysilicon (

3281233

105/0281.0

)1002.6)(/2330(

mmolkg

molmkgnsi

Sample Problem 42-6Sample Problem 42-6

42-8 The p-n Junction42-8 The p-n Junction

A p-n junction (Fig.42-11a) is a single semiconductor crystal that has been selectively doped so that one region is n-type material and the adjacent region is p-type material.Such junctions are at the heart of essentially all semiconductor devices.The transition from one region to the other is perfectly sharp,occurring at a single junction plane.

Motions of the Majority CarriersMotions of the Majority CarriersElectrons on the n side of Fig.42-11a that are close to the junction plane tend to diffuse across it and into the p side,where there are very few free electrons. Similarly,holes on the p side that are close to the junction plane tend to diffuse across that plane and into the n side,where there are very few holes.The motions of both the electrons and the holes contribute to a diffusion current Idiff.Electrons diffusing through the junction plane from right to left in Fig.42-11a result in a buildup of space charge on each side of the junction plane,as indicated in Fig.42-11b. Holes diffusing through the junction

plane from left to right have exactly the same effect. The motions of both majority carriers —electrons and holes — contribute to the buildup of these two space charge regions,one positive and one negative. These two regions form a depletion zone.The buildup of space charge generates an associated contact potential difference V0 across the depletion zone,as Fig.42-11c shows.This potential difference limits further diffusion of electrons and holes across the junction plane.

Motions of the Minority CarriersMotions of the Minority CarriersThese few holes and electrons are the minority carriers in the corresponding materials. Both types of carriers are swept across the junction plane by the contact potential difference and,together, constitute a drift current Idrift across the junction plane from right to left, as Fig.42-11d indicates. An isolated p-n junction is in an equilibrium state in which a contact potential difference V0 exists between its ends.At equilibrium,the average diffusion current Idi

ff that moves through the junction plane from the p side to the n side is just balanced by an average drift current Idrift that moves in the opposite direction.These two currents cancel because the net current through the junction plane must be zero;otherwise charge would be transferred without limit from one end of the junction to the other.

42-9 The Junction Rectifier42-9 The Junction RectifierLook now at Fig.42-12.It shows that,if we place a potential difference across a p-n junction in one direction(here labeled + and “Forward bias”),there will be a current through the junction.However,if we reverse the direction of the potential difference,there will be approximately zero current through the junction.

A p-n junction connected as a junction rectifier.The action of the circuit in (b) is to pass the positive half of the input wave form (a) but to suppress the negative half.The average potential of the input wave form is zero;that of the output wave form (c) has a positive value Vavg.

(a) The forward-bias connection of a p-n junction, showing the narrowed depletion zone and the large forward current IF .

(b) the back-bias connection, showing the widened depletion zone and the small back current IB.

42-10 The Light-Emitting Diode (LED)42-10 The Light-Emitting Diode (LED)

The energy can be emitted as a photon of energy hf at wavelength

gg E

hc

hE

c

f

c

/

Fig.42-15

Fig.42-16

Sample Problem 42-7Sample Problem 42-7

nmm

eVJeV

smSJ

E

hc

g

650105.6

)/1060.1)(9.1(

)/1000.3)(1063.6(

7

19

834

42-11 The Transistor42-11 The Transistor

REVIEW & SUMMARYREVIEW & SUMMARY

Metals Metals

The total number of conduction electrons:

atomper electrons

valenceofnumber

samplein

atoms ofnumber

samplein electrons

conduction ofnumber

The number of atoms in a sample:

AN/)M massmolar (

)V volumesample)(density smaterial'(

M)/N mass(molar

M mass sample

mass atomic

M mass sample

samplein

atoms ofnumber

A

samsam

The number density n of conduction electrons in a sample:

V volumesample

samplein electrons conduction ofnumber n

The density of states N(E)

2/13

2/328)( E

h

mEN

1

1)( /)( kTEE Fe

EP

The occupancy probability P(E)

)()()(0 EPENEN The density of occupied states N0(E)

3/22

3/22

3/2 121.0)

216

3( n

m

hn

m

hEF

Semiconductors n-type semiconductorp-type semiconductorThe p-n JunctionApplications of the p-n Junction

The energy can be emitted as a photon of energy hf at wavelength

gg E

hc

hE

c

f

c

/