EE40 Lecture 31 Prof. Chang-Hasnain 11/19/07 Reading ...inst.eecs.berkeley.edu/~ee40/fa07/lectures/cch-LectureF07... · EE40 Fall 2007 Slide 9 Prof. Chang-Hasnain If the lower floor

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Slide 1EE40 Fall 2007 Prof. Chang-Hasnain

EE40Lecture 31

Prof. Chang-Hasnain

11/19/07

Reading: Supplementary Reader


Week 13

• OUTLINE

– Basic Semiconductor Materials

– n and p doping

– Bandgap

– Gauss’s Law

– Poisson Equation

– Depletion approximation

– Diode I-V characteristics

– Lasers and LEDs

– Solar Cells

• Reading

– Supplementary Notes Chap 3

2


Conductors, Insulators and Semiconductors

• Solids with “free electrons” – that is electrons notdirectly involved in the inter-atomic bonding- arethe familiar metals (Cu, Al, Fe, Au, etc).

• Solids with no free electrons are the familiarinsulators (glass, quartz crystals, ceramics, etc.)

• Silicon is an insulator, but at highertemperatures some of the bonding electrons canget free and make it a little conducting – hencethe term “semiconductor”

• Pure silicon is a poor conductor (and a poorinsulator). It has 4 valence electrons, all ofwhich are needed to bond with nearestneighbors. No free electrons.


The Periodic Table

III IV V

3


Unit Cell of Crystalline Silicon

• Si (1s2 2s2 2p6 3s2

3p2 )

22 3

3 8 3

0

1 18 6 4# 88 2 5.00 10(5.43 10 )

Atomscm

Volume a cm

!

!

" + " +

= = = ""


Electronic Bonds in Silicon

2-D picture of perfect crystal of pure silicon; double line is a Si-Sibond with each line representing an electron

Two electrons in each bond

Si ion(charge+4 q)

Actual structure is 3-dimensional tetrahedral- just like carbonbonding in organic and inorganic materials.

Essentially no free electrons, and no conduction - insulator

4


Bandgap

• Electrons are mobile in the conduction band, while holesare mobile in the lower energy valence band.

• The excited electrons move from the valence band intothe conduction band, leaving holes in the valence band– when the crystal is illuminated with photons whose energy is

larger than the bandgap energy

– or when the crystal is sufficiently heated.

Valence Band

E

Conduction Band

Band gap, E g

e-

Ef


Bandgap for Insulator and Metal

• Insulators have alarge band gap,usually 3.5 electron-volts (eV) or greater,preventing substantialamounts of chargecarriers from flowing.

• Metals are goodconductors, withelectrons filling upinto the conductionband.

Conduction Band

E Small band

gap, Eg

E

f

Valence Band

Electrons fill into

conduction

band

Large bandgap, Eg

Valence Band

E

Conduction Band

E

f

5


If the lower floor is full and top one is empty, no traffic ispossible. Analog of an insulator. All electrons arelocked up.

Shockley’s Parking Garage Analogy for Conduction in Si

Two-story parking garage on a hill:


If one car is moved upstairs, it can move AND THE HOLEON THE LOWER FLOOR CAN MOVE. Conduction ispossible. Analog to warmed-up semiconductor. Someelectrons get free (and leave “holes” behind).



6


If an extra car is “donated” to the upper floor, it can move.Conduction is possible. Analog to N-type semiconductor.

(An electron donor is added to the crystal, creating freeelectrons).




If a car is removed from the lower floor, it leaves a HOLEwhich can move. Conduction is possible. Analog to P-type

semiconductor. (Acceptors are added to the crystal,“consuming” bonding electrons,creating free holes).



7


Fermi-Dirac Distribution

• Fermi-Dirac function provides the probability that anenergy level is occupied by a fermion which is underthermal equilibrium. Electrons as well as holes areFermions and hence obey Fermi-Dirac statistics.

Fig. 5. Fermi function plots at absolute zero, mid-range, and high temperature.


Electron and Hole Densities

, ,

( )

( )

( ) ( ) ( )

1

( )/1

11

( )/1

f c

v f

f i c v f i gv c

E E kT

c cf

c

E E kT

v vf

v

E E kT E E kT E kTE E kT

c v c v c v

n N N eE E kT

e

p N N eE E kT

e

np N e N e N N e N N e

!

!

! ! !!

=!

+

" #= !$ %!$ %+& '

= = =

!

!

2

g

i i

i i i

E kT

i c v

n p

n p n

n N N e!

=

=

=

For instrinsic (i.e.

undoped Si),

8


How to get conduction in Si?

For the first approach controlled impurities, “dopants”, are added toSi:

or

We must either:

1) Chemically modify the Si to produce free carriers (permanent) or

2) Electrically “induce” them by the field effect (switchable)

(Extra electrons produce “free electrons” for conduction.)

Add group V elements (5 bonding electrons vs four for Si),such as phosphorus or arsenic

Deficiency of electrons results in “free holes”

Add group III elements (3 bonding electrons), such as boron


Doping Silicon with Donors (n-type)

Donors donate mobile electrons (and thus “n-type” silicon)

Example: add arsenic (As) to the silicon crystal:

Immobile (stuck) positively charged arsenic ion after 5th electron left

As

Mobile electrondonated by As ion

The extra electron with As, “breaks free” and becomes a freeelectron for conduction

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Doping with Acceptors (p-type)

B

Mobile hole con-tributed by B ionand later path

Immobile (stuck) negative boron ion after accepting electron from neighboring bond

Group III element (boron, typically) is added to the crystal

The “hole” which is a missing bonding electron, breaks free fromthe B acceptor and becomes a roaming positive charge, free tocarry current in the semiconductor. It is positively charged.


Doping

• Typical doping densities:1016~1019 cm-3

• Atomic density for Si: 5 x1022 atoms/cm3

• 1018 cm-3 is 1 in 50,000

– two persons in entireBerkeley wearing a greenhat

• P-n junction effect is like

10


EE40Lecture 32

Prof. Chang-Hasnain

11/21/07



Electron and Hole Densities in Doped Si

( )

2

v fE E kT

a v

i a

p N N e

p n N

!

= =

=

• Instrinsic (undoped) Si

• N-doped Si– Assume each dopant contribute to one electron

• p-doped Si– Assume each dopant contribute to one hole

( )

2

f cE E kT

d c

i d

n N N e

p n N

!

= =

=

2

i

i

n p n

np n

= =

=

11


Summary of n- and p-type silicon

Pure silicon is an insulator. At high temperatures it conductsweakly.

If we add an impurity with extra electrons (e.g. arsenic,phosphorus) these extra electrons are set free and we have apretty good conductor (n-type silicon).

If we add an impurity with a deficit of electrons (e.g. boron) thenbonding electrons are missing (holes), and the resulting holescan move around … again a pretty good conductor (p-typesilicon)

Now what is really interesting is when we join n-type and p-typesilicon, that is make a pn junction. It has interesting electricalproperties.


Junctions of n- and p-type Regions

A silicon chip may have 108 to 109 p-n junctions today.

p-n junctions form the essential basis of all semiconductor devices.

How do they behave*? What happens to the electrons and holes?What is the electrical circuit model for such junctions?

n and p regions are brought into contact :

n p

aluminum aluminum

wire

?

*Note that the textbook has a very good explanation.

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The pn Junction Diode

Schematic diagram

p-type n-typeID

+ VD –

Circuit symbol

Physical structure:(an example)

p-type Si

n-type Si

SiO2SiO2

metal

metal

ID+

VD

–

net donor

concentration ND

net acceptor

concentration NA

For simplicity, assume that

the doping profile changes

abruptly at the junction.

cross-sectional area AD


• When the junction is first formed, mobile carriers diffuseacross the junction (due to the concentration gradients)

– Holes diffuse from the p side to the n side,leaving behind negatively charged immobile acceptorions

– Electrons diffuse from the n side to the p side,leaving behind positively charged immobile donor ions

!A region depleted of mobile carriers is formed at the junction.

• The space charge due to immobile ions in the depletion regionestablishes an electric field that opposes carrier diffusion.

Depletion Region Approximation

+++++

––

–––

p n

acceptor ions donor ions

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Summary: pn-Junction Diode I-V

• Under forward bias, the potential barrier is reduced, sothat carriers flow (by diffusion) across the junction– Current increases exponentially with increasing forward bias

– The carriers become minority carriers once they cross thejunction; as they diffuse in the quasi-neutral regions, theyrecombine with majority carriers (supplied by the metal contacts)

“injection” of minority carriers

• Under reverse bias, the potential barrier is increased, sothat negligible carriers flow across the junction– If a minority carrier enters the depletion region (by thermal

generation or diffusion from the quasi-neutral regions), it will beswept across the junction by the built-in electric field

“collection” of minority carriers ! reverse current ID (A)

VD (V)


quasi-neutral p region

Charge Density Distribution

+++++

––

–––

p n

acceptor ions donor ions

depletion region quasi-neutral n region

charge density (C/cm3)

distance

Charge is stored in the depletion region.

14


Two Governing Laws

2

2

( ) ( ) ( )d x dE x x

dx dx

! "

#= $ = $

00

1( ) ( ) ( )

x

x

E x E x x dx!"

# = $dE

dx

!

"=

1 encl

S V

QE dA dV!

" "# = # =$ $!!

" "

Gauss’s Law describes the relationship of charge (density) andelectric field.

Poisson’s Equation describes the relationship between electricfield distribution and electric potential

00( ) ( ) ( )

x

x

x x E x dx! !" = "#


Depletion Approximation 1

0 ( ) ( ) ( 0)a

po po

s

qNE x x x x x

!

"= + " < <

( )( )( )

( ) ( )000

0

0

0 , 0 and 0

0 np

nd

paxxxxx

xxqN

xxqNx >!<=

"#$

%%

%%!!& ''

xno x

x

-xpo

_o(x)

-qNa

qNd

xno x

x

-xpo

E0(x)

s

nod

s

poa xqNxqNE

!!

"=

"=)0(0

00 0

0

( )( ) ( ) ( ) 0

( ) ( )

(0 )

nox dno no

xs s

dno

s

no

x qNE x dx E x x x

qNE x x x

x x

!" "

"

#= # = # #

= #

< <

$Gauss’s Law

p n

p n

15



p n

P=1018

n=104

n=1017

p=105

x

E0(x)

s

nod

s

poa xqNxqNE

!!

"=

"=)0(0

xno-xpo

22

22 pos

a

nos

dx

qNx

qN

!!+

#0(x)

xxno-xpo

Poisson’s Equation


EE40Lecture 33

Prof. Chang-Hasnain

11/26/07


16



0 0 0( ) ( ) ( ) ( ) 0po po

po po

x xa

po pox x

s

x xa

pox x

s

qNx E x dx x x x dx

qNxdx x dx

! !"

"

# #

# #

= # + # = + +

$ %= +& '

( )

* *

* *

2

0 ( ) ( ) ( 0)2

a

po po

s

qNx x x x x!

"= + # < <

( )

2

0 0 00 0

2

0 0

( ) ( ) (0) ( ) (0 )2

2

x xd a

no po

s s

x xd a

no po

s s

qN qNx E x dx x x dx x

qN qNxdx x dx x

! !" "

" "

= # + = # # + +

= # + +

$ $

$ $

2 2

0 ( ) (2 ) (0 )2 2

d ano po no

s s

qN qNx x x x x x x!

" "= # + < <


Effect of Applied Voltage

• The quasi-neutral p and n regions have low resistivity,whereas the depletion region has high resistivity. Thus,when an external voltage VD is applied across thediode, almost all of this voltage is dropped acrossthe depletion region. (Think of a voltage dividercircuit.)

• If VD > 0 (forward bias), the potential barrier to carrierdiffusion is reduced by the applied voltage.

• If VD < 0 (reverse bias), the potential barrier to carrierdiffusion is increased by the applied voltage.

p n

+++++

––

–––

VD

17


Depletion Approx. – with VD<0 reverse bias

p n

P=1018n=1017

x

E0(x)

s

nod

s

poa xqNxqNE

!!

"=

"=)0(0

xno-xpo

22

22 pos

a

nos

dx

qNx

qN

!!+

#0(x)

xxno-xpo

#bi

Built-in potential #bi=

-xp xn

-xp xn

#bi-qVD

Higher barrier and few holes in n-type lead to little current! p=105

n=104


Depletion Approx. – with VD>0 forward bias

Poisson’s Equation

p n

n=104

n=1017

p=105

x

E0(x)

s

nod

s

poa xqNxqNE

!!

"=

"=)0(0

xno-xpo

22

22 pos

a

nos

dx

qNx

qN

!!+

#0(x)

xxno-xpo

#bi

Built-in potential #bi=

-xp xn

#bi-qVD

Lower barrier and large hole (electron) densityat the right places lead to large current!

-xp xn

P=1018

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Forward Bias

• As VD increases, the potential barrier to carrierdiffusion across the junction decreases*, andcurrent increases exponentially.

ID (Amperes)

VD (Volts)

* Hence, the width of the depletion region decreases.

p n

+++++

––

–––

VD > 0The carriers that diffuse across the

junction become minority carriers in

the quasi-neutral regions; they then

recombine with majority carriers,

“dying out” with distance.

D( 1)qV kT

D SI I e= !


Reverse Bias

• As |VD| increases, the potential barrier to carrierdiffusion across the junction increases*; thus, nocarriers diffuse across the junction.

ID (Amperes)

VD (Volts)

* Hence, the width of the depletion region increases.

p n

+++++

––

–––

VD < 0A very small amount of reverse

current (ID < 0) does flow, due to

minority carriers diffusing from the

quasi-neutral regions into the depletion

region and drifting across the junction.

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• Light incident on a pn junction generates electron-hole pairs

• Carriers are generated in the depletion region as well as n-doped and p-doped quasi-neutral regions.

• The carriers that are generated in the quasi-neutral regionsdiffuse into the depletion region, together with the carriersgenerated in the depletion region, are swept across thejunction by the electric field

• This results in an additional component of current flowing inthe diode:

where Ioptical is proportional to the intensity of the light

optical

kTVq

SD IeII !!= )1( D

Optoelectronic Diodes


Example: Photodiode

• An intrinsic region is placedbetween the p-type and n-typeregions

$ Wj % Wi-region, so that most of theelectron-hole pairs are generatedin the depletion region

! faster response time (~10 GHz operation)

ID (A)

VD (V)

with incident light

in the dark

operating point

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Planck Constant

• Planck’s constant h = 6.625·10-34 J·s• E=h&=hc/'=1.24 eV-µm/'(µm)• C is speed of light and h& is photon energy• The first type of quantum effect is the quantization of

certain physical quantities.• Quantization first arose in the mathematical formulae of

Max Planck in 1900. Max Planck was analyzing how theradiation emitted from a body was related to itstemperature, in other words, he was analyzing theenergy of a wave.

• The energy of a wave could not be infinite, so Planckused the property of the wave we designate as thefrequency to define energy. Max Planck discovered aconstant that when multiplied by the frequency of anywave gives the energy of the wave. This constant isreferred to by the letter h in mathematical formulae. It isa cornerstone of physics.


Bandgap Versus Lattice Constant

Si

21


Solar cell: Example of simple PN junction

• What is a solar cell?– Device that converts

sunlight into electricity

• How does it work?– In simple configuration, it is a

diode made of PN junction

– Incident light is absorbed bymaterial

– Creates electron-hole pairs thattransport through the materialthrough

• Diffusion (concentration gradient)

• Drift (due to electric field)PN Junction Diode


optical

kTVq

SD IeII !!= )1( D

Photovoltaic (Solar) Cell

ID (A)

VD (V)

with incident light

in the dark

Operating pointThe load line a simple resistor.

22


I-V characteristics of the device

• I-V characteristics of a PNjunction is given by

where Is is the saturation intensity

depending on band gap and dopingof the material and IL is thephotocurrent generated due to light

• Efficiency is defined as

Voc

Isc

(Vm, Im)

LSI

kT

eVII !"#

$%&

'!= 1)exp(

IntensityLight

IVFF

IntensityLight

VI scocmm **.==!

Voc - Open circuit voltage

Isc - Short circuit current

Imp , Vmp- Current and voltage

at maximum powerFF is the Fill Factor


Architecture and PV

Isofotón: aUPM spin-off

IES-UPM

23


A technology for solidarity...and a goodbusiness

Total MWp 9.51

Individual investors 752

Cost 7 kWp !53000


Space

• Efficiency &Reliability critical

• Multi-junction – 80%market

• Two players– Emcore –

125kW/year

– Spectrolab (Boeing)– 600kW/year

• Up to $40/W

• $30M/year market

Boeing 702Sojourner 16W

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Portable Electronics

• US PP $7.6b in 2004

• PV? Power!– Rechargeable (LiIon)

– Fuel cells (2013)

• TI’s Voltage Booster– Efficient sub 0.3V

step-up converter

• ULP & Low PowerElectronics?


Transportation

MIT

Venturi – AstrolabTBR Jan. 2008$120k

Pathfinder

MW-Line$560kAtlantic

Pathfinder, 75% wing cover, 8kW

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Off-Grid Small Scale

Telecommunicationtower in Australia

Railroad crossingin Georgia

Most off-shore oil rigs

Arizona, 500W

Austria

•Lighting•Communications•16% market

(PV 2010)


Electrifying the Unelectrified

Subsahara – power for light and water pumps

Panels in French Polynesia

Los Uros, Peru Southern India

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Solarizing the Electrified

Residential (grid) – 40% market

• Fastest growth (33% US)

• Typical Cost– Non-battery $6-8/W-DC

– Battery $8–12/W-DC

California $6.5/W after rebatesor $20,000 for 2,500ft2

home

Installations (2006)

1) Germany – 960MWp

2) Japan – 300MWp

3) US – 140MWp

Total World 1744MWp

Modules on apartment complexrooftops (Bremen, Germany)

Marketbuzz 2007


Utility Scale

• US Total Power Plant Capacity 600GW(28% of world) and will grow 30% by2030

• Largest PV– Gut Erlasee Solar Park(12MWp)

• PV cells - $0.25-0.39/kWhr• Coal plant - $0.06/kWhr• PV < $0.10/kWhr to be competitive!

EIA, DOE

Tucson, AZ, 4.6 MWp

NUON rooftop, Netherlands, 2.3MWp

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Example 2: Photodiode

• An intrinsic region is placedbetween the p-type and n-typeregions

$ Wj % Wi-region, so that most of theelectron-hole pairs are generatedin the depletion region

! faster response time (~10 GHz operation)

ID (A)

VD (V)

with incident light

in the dark

operating point


Photodetector Circuit Using Load Line

I

V

load line

VTh

VTh/RTh

operatingpoints underdifferent lightconditions.

As light shines on the photodiode, carriersare generated by absorption. These excesscarriers are swept by the electric field at thejunction creating drift current, which is samedirection as the reverse bias current andhence negative current. The current isproportional to light intensity and hence canprovide a direct measurement of lightintensity ! photodetector.

- What happens when Rth is too large?- Why use Vth?

VTh

+" +

V

–

RThI

As lightintensityincreases.Why?

Documents

EE40 Lecture 31 Prof. Chang-Hasnain 11/19/07 Reading ...inst.eecs.berkeley.edu/~ee40/fa07/lectures/cch-LectureF07... · EE40 Fall 2007 Slide 9 Prof. Chang-Hasnain If the lower floor