Chap. 41: Chap. 41: Conduction of electricity Conduction of electricity
in solidsin solids
Hyun-Woo LeeHyun-Woo Lee
41-1 What Is Physics?41-1 What Is Physics?
Q: Why certain materials conduct electricitQ: Why certain materials conduct electricity?y?
Q: Why certain materials do NOT conduct Q: Why certain materials do NOT conduct electricity?electricity?
Solid materialSolid material Many many electrons and atomsMany many electrons and atoms
Solid state physicsSolid state physics Application of quantum physics to solidsApplication of quantum physics to solids
41-2 Electrical Properties of 41-2 Electrical Properties of SolidsSolids
Crystalline solidsCrystalline solids Lattice structureLattice structure
• Repetition of unit cellsRepetition of unit cells
Classification criteriaClassification criteria Resistivity Resistivity at room temperature ( at room temperature (m)m) Temperature coefficient of resistivity Temperature coefficient of resistivity (K (K-1-1))
Number density of charge carriers Number density of charge carriers nn (m (m-3-3))• Can be found from Hall effect measurementCan be found from Hall effect measurement
Metals, semiconductors, insulatorsMetals, semiconductors, insulators
)/)(/1( dTd
Insulators, semiconductors Insulators, semiconductors & metals& metals
InsulatorsInsulators Extremely large Extremely large Ex: Diamond Ex: Diamond diamonddiamond//coppercopper~10~102424
Semiconductors vs MetalsSemiconductors vs Metals insulatorinsulator >> >> semiconductorsemiconductor >> >> metalmetal
siliconsilicon==3310103 3 m, m, coppercopper=2=21010-8 -8 mm
semiconductorsemiconductor <0, <0, metalmetal>0>0siliconsilicon= -70 = -70 1010-3 -3 KK-1-1, , CopperCopper= +4= +41010-3-3 K K-1-1
nnsemiconductorsemiconductor << << nnmetalmetal
• nnsiliconsilicon=1=110101616 m m-3-3, , n ncoppercopper=9=910102828 m m-3-3
41-3 Energy Levels 41-3 Energy Levels in a Crystalline Solidsin a Crystalline Solids Single atom (Ex: Cu Single atom (Ex: Cu ZZ=29)=29)
11ss22 2 2ss22 2 2pp66 3 3ss22 3 3pp66 3 3dd1010 4 4ss11
Two atomsTwo atoms Tunneling between two atomsTunneling between two atoms
Three atomsThree atoms More tunnelingMore tunneling
Tunneling effectsTunneling effects
Two wellsTwo wells
Level splitting into two levelsLevel splitting into two levels
Tunneling effects inTunneling effects in solidssolids
NN(() wells) wells Energy level splitting into Energy level splitting into NN levels levels Energy bands & energy gapsEnergy bands & energy gaps
41-4 Insulators41-4 Insulators
No partially filled bandsNo partially filled bands
For a current to exist,For a current to exist, Kinetic energy must increaseKinetic energy must increase
Electrons must move to higher-energy levelsElectrons must move to higher-energy levels Pauli exclusion principlePauli exclusion principle
• Transition to filled state is prohibitedTransition to filled state is prohibited
Energy gap (Ex: Energy gap (Ex: EEgg=5.5 eV in diamond)=5.5 eV in diamond) Large energy supply neededLarge energy supply needed
Current flow strongly suppressedCurrent flow strongly suppressed
Thermal fluctuation effectsThermal fluctuation effects
Thermal excitationsThermal excitations Finite probability to jump Finite probability to jump EEgg
Probability Probability PP for the jump for the jump For For EEgg=5.5 eV, =5.5 eV, TT=300K=300K
• cf: # of electron in 1 cmcf: # of electron in 1 cm33 ~ 10 ~ 102323
93213 103)/exp(~ ekTEP g
41-5 Metals41-5 Metals
Partially filled bandsPartially filled bands Easy to induce energy “jump”Easy to induce energy “jump”
Fermi level Fermi level EEFF
Highest occupied level at Highest occupied level at TT=0K=0K Ex: Ex: EEFF=7.0 eV for copper=7.0 eV for copper
Fermi speed Fermi speed vvFF
Electron speed at Electron speed at EEFF
Ex: Ex: vvFF=1.6=1.6101066 m/s for copper m/s for copper
No relaxation of No relaxation of vvFF due to Pauli exclusion princip due to Pauli exclusion princip
lele
How Many Conduction How Many Conduction Electrons Are There?Electrons Are There?
Number density Number density nn
Ex: Magnesium w/ volume 2.00Ex: Magnesium w/ volume 2.001010-6-6 m m33
BivalentBivalent
atomper electrons
valenceofnumber
samplein
atoms ofnumber
samplein electrons
conduction ofnumber
Vn
volumesample
samplein electrons conduction ofnumber
221061.8samplein
atoms ofnumber
231072.1samplein electrons
conduction ofnumber
Conductivity Above Absolutely Conductivity Above Absolutely ZeroZero
Ex: Ex: TT=1000 K=1000 K kTkT=0.086 eV=0.086 eV cf: cf: EEFF=7.0 eV in copper=7.0 eV in copper
# of charge carriers extremely insensitiv# of charge carriers extremely insensitive to e to TT
41-6 Semiconductors41-6 Semiconductors
No partially filled bandsNo partially filled bands But small energy gapBut small energy gap
Ex: Ex: EEgg=1.1 eV for silicon=1.1 eV for silicon
cf: cf: EEgg=5.5 eV for diamond=5.5 eV for diamond
Valence bandValence band Highest filled bandHighest filled band
Conduction bandConduction band Lowest vacant bandLowest vacant band
Number Density of Charge Number Density of Charge CarriersCarriers
Probability Probability PP for jump for jump
Charge carriersCharge carriers ElectronsElectrons
• Conduction bandConduction band HolesHoles
• Valence bandValence band # of charge carriers extremely sensitive to # of charge carriers extremely sensitive to TT
196.42 104)/exp(~ ekTEP g
Motion of charge Motion of charge carrierscarriers
Electrons in conduction bandElectrons in conduction band
Holes in valence bandHoles in valence band
Efficient description in terms of holesEfficient description in terms of holes Effective charge of hole: +Effective charge of hole: +ee
E
E
Resistivity Resistivity siliconsilicon / / coppercopper = 1.5 = 1.510101111
Classical estimationClassical estimation
Difference between Difference between siliconsilicon and and coppercopper mainly mainly
from carrier density from carrier density nn
nem 2/
Temperature Coefficient of ResistiviTemperature Coefficient of Resistivity ty
::
Temperature dependenceTemperature dependence Classical estimationClassical estimation
Semiconductor (Ex: silicon)Semiconductor (Ex: silicon) nn increases as increases as TT increases increases < 0 < 0
Metal (Ex: copper)Metal (Ex: copper) decreases as decreases as T T increases increases > 0 > 0
dT
d
1
nem 2/
More about metalsMore about metals
How Many Quantum States Are How Many Quantum States Are There?There?
Too many states to list all statesToo many states to list all states Density of states Density of states NN((EE))
NN((EE))dEdE : # of states between : # of states between EE and and EE++dEdE per v per volumeolume
Near lower edge of partially filled bandNear lower edge of partially filled band
)Jm(28
)( 1-3-2/13
2/3
Eh
mEN
How Many Quantum States Are How Many Quantum States Are There ? There ? (continued)(continued)
Ex: Metal w/ Ex: Metal w/ VV=2=21010-9-9 m m33 at at EE=7 eV=7 eV
1-19 eV104eV 7at eVper
states of #
17101eV 7at eV 0.003 rangein
states of #
N
The Occupancy The Occupancy Probability Probability PP((EE))
Maxwell distributionMaxwell distribution Not applicable due to Pauli exclusion principleNot applicable due to Pauli exclusion principle
Fermi-Dirac statisticsFermi-Dirac statistics
At At EE==EEFF PP((EE)=1/2 regardless of )=1/2 regardless of TT Useful way to define Useful way to define EEFF at at TT>0>0
1
1)( /)( kTEE Fe
EP
How Many Occupied States Are How Many Occupied States Are There?There?
Density of occupied states Density of occupied states NN00((EE)) NN00((EE)=)=NN((EE))PP((EE))
Calculating the Fermi EnergyCalculating the Fermi Energy
At At TT=0,=0, Due to Pauli exclusion principleDue to Pauli exclusion principle
With With NN((EE) ) EE1/21/2
F
0
)(E
dEENn
3
228 2/3F
3
2/3 E
h
mn
3/22
3/223/2
F
121.0
216
3n
m
hn
m
hE
More about semiconductorsMore about semiconductors
41-7 Doped 41-7 Doped SemiconductorsSemiconductors
DopingDoping Introducing a small number of replacement Introducing a small number of replacement
atoms (impurities) into semiconductor latticeatoms (impurities) into semiconductor lattice
~ 1 out of 10~ 1 out of 1077 atoms replaced atoms replaced
nn-Type Semiconductors-Type Semiconductors Pure silicon: Si (Pure silicon: Si (ZZ=14) 1=14) 1ss22 2 2ss22 3 3pp66 3 3ss22 3 3pp22
Valence number: 4Valence number: 4
Doping by P (Doping by P (ZZ=15, valence=5)=15, valence=5) One extra el.One extra el. nn(egative)(egative)-type-type 5th el. in the “conduction band”5th el. in the “conduction band”
Extra electron & protonExtra electron & proton w/o extra protonw/o extra proton
w/ extra protonw/ extra proton
Weakly bound donor levels Weakly bound donor levels
At room temperatureAt room temperature
Thermal excitationsThermal excitations EEdd =0.045 eV for phosphorous doping =0.045 eV for phosphorous doping
cf: cf: EEgg=1.1 eV=1.1 eV Excitations from donor levels to conduction Excitations from donor levels to conduction
band much easierband much easier
Majority carriersMajority carriers Electrons in conduction bandElectrons in conduction band
Minority carriersMinority carriers Holes in valence bandHoles in valence band
Doping levelDoping level
Pure siliconPure silicon # density of conduction el. at room temp# density of conduction el. at room temp
• ((nn00))no-dopingno-doping ~ 10 ~ 101616 m m-3-3
Q: Doping for (Q: Doping for (nn00))dopingdoping=10=1066 ((nn00))no-dopingno-doping
((nn00))dopingdoping= = ((nn00))no-doping no-doping + + nnPP
nnP P 10 102222 m m-3-3
cf: cf: nnSi Si 5 510102828 m m-3-3
6Si
P
105
1
n
n
pp-Type Semiconductors-Type Semiconductors Doping by Al (Doping by Al (ZZ=13)=13)
One missing el One missing el pp(ositive)-type(ositive)-type Missing el in “valence band”Missing el in “valence band”
w/ missing protonw/ missing proton Weakly bound acceptor levelsWeakly bound acceptor levels
At room temperatureAt room temperature
Thermal excitationsThermal excitations EEdd =0.067 eV for aluminium doping =0.067 eV for aluminium doping
cf: cf: EEgg=1.1 eV=1.1 eV Excitations from valence band to acceptor lExcitations from valence band to acceptor l
evels much easierevels much easier
Majority carriersMajority carriers Holes in valence bandHoles in valence band
Minority carriersMinority carriers Electrons in conduction bandElectrons in conduction band
41-8 The 41-8 The pp--nn Junction Junction Junction of Junction of pp-type and -type and nn-type semicond.-type semicond.
Upon contact, …(no bias yet)Upon contact, …(no bias yet)
Junction planeJunction plane
Motions of the Majority Motions of the Majority CarriersCarriers
DiffusionDiffusion Diffusion current Diffusion current IIdiffdiff
Space chargeSpace charge
-e
+eDepletion Depletion zonezoneContact potential Contact potential difference difference VV00
Idiff
Idiff = 0
Motions of the Minority CarriersMotions of the Minority Carriers
Minority carriersMinority carriers Drift current Drift current IIdriftdrift
Space charge somewhat relaxedSpace charge somewhat relaxed
Majority & minority carriersMajority & minority carriers Balance of Balance of IIdiffdiff & & IIdriftdrift
Idrift
41-9 The Junction Rectifier41-9 The Junction Rectifier II vs. vs. VV
pp--nn junction as a rectifier junction as a rectifier AC AC DC conversion DC conversion
Forward biasForward bias
Reduce Reduce VV00
Reduce V0
Narrower depletion zone
Backward biasBackward bias
Enhance Enhance VV00
Enhance V0
Wider depletion zone
41-10 The Light-Emitting Diode (LED)41-10 The Light-Emitting Diode (LED) LEDLED
Light emission from Light emission from pp--nn junction junction
Photon or lattice vibration Forward bias
pp--nn junction as LED junction as LED Forward biased Forward biased pp--nn junction junction
Photon wavelengthPhoton wavelength
Commercial LEDsCommercial LEDs in visible rangein visible range Ex: Gallium (valence 3) doped with arsenic (valEx: Gallium (valence 3) doped with arsenic (val
ence 5, 60%) and phosphorous (valence 5, 4ence 5, 60%) and phosphorous (valence 5, 40%) atoms0%) atoms
• EEgg=1.8 eV (red color)=1.8 eV (red color)
gg E
hc
hE
c
f
c
/
The Photo-DiodeThe Photo-Diode Photo-diode = (LED)Photo-diode = (LED)-1-1
Photon Photon Current Current
Ex: TV remote controlEx: TV remote control• Remote control : LEDRemote control : LED
Generate a certain sequence of infrared photonsGenerate a certain sequence of infrared photons
• TV : Photo-diodeTV : Photo-diode Photon detection Photon detection Electric signal Electric signal
Photon-induced transition
The Junction LaserThe Junction Laser
Stimulated emission inStimulated emission in p p--nn junction junction
Junction laserJunction laser• Ex: Laser head in compact disc (CD) playersEx: Laser head in compact disc (CD) players
MirrorMirror
41-11 The Transistor41-11 The Transistor
TransistorTransistor Intentional control of on-offIntentional control of on-off Application: AmplifierApplication: Amplifier
FET (Field Effect Transistor)FET (Field Effect Transistor) Integrated circuitsIntegrated circuits
TransistorsTransistors CapacitorsCapacitors Resistors etc.Resistors etc.
Intel Pentium chip (w/ ~7 million transistors)
MOSFETMOSFET(Metal-Oxide-Semiconductor-FET)(Metal-Oxide-Semiconductor-FET)
MOSFETMOSFET High speed on-offHigh speed on-off ~500 nm in length~500 nm in length
Gate voltage Gate voltage VVGSGS
Negatively charge gateNegatively charge gate Repel el. in Repel el. in nn-channel down into substrate-channel down into substrate Wider depletion zone between Wider depletion zone between pp and and nn nn-channel width reduced -channel width reduced Larger resistance (off realized)Larger resistance (off realized)
The EndThe End