ee232lightwavedevices lecture3:basicsemiconductorphysics …ee232/sp17/lectures/ee232... ·...

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1 EE232 Lecture 3-1 Prof. Ming Wu EE 232 Lightwave Devices Lecture 3: Basic Semiconductor Physics and Optical Processes Instructor: Ming C. Wu University of California, Berkeley Electrical Engineering and Computer Sciences Dept. EE232 Lecture 3-2 Prof. Ming Wu Optical Properties of Semiconductors Optical transitions Absorption: exciting an electron to a higher energy level by absorbing a photon Emission: electron relaxing to a lower energy state by emitting a photon E C E V Absorption Emission Interband Transition E A ImpuritytoBand Transition Intraband Transition (FreeCarrier Absorption)

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Page 1: EE232LightwaveDevices Lecture3:BasicSemiconductorPhysics …ee232/sp17/lectures/EE232... · 2017-01-24 · 2 EE232 Lecture 3-3 Prof. Ming Wu BandMtoMBand"Transition •Since"most"electrons"and"holes"are"near"the"bandM

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EE232 Lecture 3-1 Prof. Ming Wu

EE 232 Lightwave DevicesLecture 3: Basic Semiconductor Physics

and Optical Processes

Instructor: Ming C. Wu

University of California, BerkeleyElectrical Engineering and Computer Sciences Dept.

EE232 Lecture 3-2 Prof. Ming Wu

Optical Properties of Semiconductors

• Optical transitions– Absorption: exciting an electron to a higher energy level by absorbing a photon

– Emission: electron relaxing to a lower energy state by emitting a photon

EC

EV

Absorption Emission

InterbandTransition

EA

Impurity-­to-­BandTransition

Intraband Transition(Free-­Carrier Absorption)

Page 2: EE232LightwaveDevices Lecture3:BasicSemiconductorPhysics …ee232/sp17/lectures/EE232... · 2017-01-24 · 2 EE232 Lecture 3-3 Prof. Ming Wu BandMtoMBand"Transition •Since"most"electrons"and"holes"are"near"the"bandM

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EE232 Lecture 3-3 Prof. Ming Wu

Band-­to-­Band Transition

• Since most electrons and holes are near the band-­edges, the photon energy of band-­to-­band (or interband) transition is approximately equal to the bandgap energy:

• The optical wavelength of band-­to-­band transition can be approximated by

λ =cν=hcEg

≈1.24Eg

λ : wavelength in µmEg : energy bandgap in eV

hv = Eg

EE232 Lecture 3-4 Prof. Ming Wu

Energy Band Diagram in Real Space and k-­Space

EC

VB

E

x

E

k

CB

EV

Real Space K-­Space

* 212e C eE E m v= +

* 212h V hE E m v= -

Ee = EC +!2k 2

2me*

Eh = EV −!2k 2

2mh*

Effective Mass Approximation

!k =me*ve

Momentum:

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EE232 Lecture 3-5 Prof. Ming Wu

Band-­to-­Band Transition

CB

VB

hn

CB

VB

hn

CB

VB

hn hn

Absorption SpontaneousEmission

StimulatedEmission

Photodetectors;;Solar Cells LED Optical Amplifiers;;

Semiconductor Lasers

EE232 Lecture 3-6 Prof. Ming Wu

Conservation of Energy and Momentum

• Conditions for optical absorption and emission:– Conservation of energy

– Conservation of momentum

CB

VB

hn

E2

E1

kk1

k2

E

E2 −E1 = hν

( ) ( )

2 1

2 1

2 1

2, ~

2~

~ 0.5 ~1

h

h

k k k

k ka

k

a nm m

k k

n

n

p

pll µ

- =

<<

Þ =LatticeConstant

Optical transitions are “vertical” lines

Page 4: EE232LightwaveDevices Lecture3:BasicSemiconductorPhysics …ee232/sp17/lectures/EE232... · 2017-01-24 · 2 EE232 Lecture 3-3 Prof. Ming Wu BandMtoMBand"Transition •Since"most"electrons"and"holes"are"near"the"bandM

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EE232 Lecture 3-7 Prof. Ming Wu

Direct vs Indirect Bandgaps

• Direct bandgap materials– CB minimum and VB maximum occur at the same k

– Examples• GaAs, InP, InGaAsP• (AlxGa1-­x)As, x < 0.45

• Indirect bandgap materials– CB minimum and VB maximum occur at different k

– Example• Si, Ge• (AlxGa1-­x)As, x > 0.45

– Not “optically active”

CB

VB

hn

CB

VB

hn X

Phonon

EE232 Lecture 3-8 Prof. Ming Wu

Absorption Coefficient

• Light intensity decays exponentially in semiconductor:

• Direct bandgap semiconductor has a sharp absorption edge

• Si absorbs photons with hv > Eg = 1.1 eV, but the absorption coefficient is small– Sufficient for CCD

• At higher energy (~ 3 eV), absorption coefficient of Si becomes large again, due to direct bandgap transition to higher CB

xeIxI a-= 0)(

Page 5: EE232LightwaveDevices Lecture3:BasicSemiconductorPhysics …ee232/sp17/lectures/EE232... · 2017-01-24 · 2 EE232 Lecture 3-3 Prof. Ming Wu BandMtoMBand"Transition •Since"most"electrons"and"holes"are"near"the"bandM

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EE232 Lecture 3-9 Prof. Ming Wu

Review of Semiconductor Physics

Electron and hole concentrations:

( ) ( )

( ) ( )

Fermi-Dirac distributions:1( )

1 exp

1( )1 exp

: electron quasi-Fermi level : hole quasi-Fermi l

C

V

n eE

E

p h

nn

B

pp

B

n

p

n f E E dE

p f E E dE

f EE Fk T

f EF Ek T

FF

r

r

¥

=

=

=æ ö-

+ ç ÷è ø

=-æ ö

+ ç ÷è ø

ò

ò

evel

EE232 Lecture 3-10 Prof. Ming Wu

Electron/Hole Density of States (1)

• Electron wave with wavevector k

• Periodic boundary conditions

• An electron state is defined by

• Number of electron states between k and k + Dk in k-­space per unit volume

xL

zL

yL

eik!⋅r!

eik!⋅r!

= eik!⋅ r!+Lx x!

( ) = eik!⋅ r!+Ly y!"

( ) = eik!⋅ r!+Lz z!

( )

kx ,ky ,kz( )↑↓= m 2πLx,n 2πLy,l 2πLz

#

$%%

&

'((↑↓

2 2

2

2 4 ( )2 2 2 k

x y z

k dk k dk k dkV

L L L

p rp p p p× = =

k

k k+D

xk

yk

zk

Spin Up and Down

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EE232 Lecture 3-11 Prof. Ming Wu

Electron/Hole Density of States (2)

• Number of electron states between E and E + DE per unit volume

• Likewise, hole density of states

E = EC +!2k 2

2me*⇒ dE = !

2kme*dk

k 2

π 2dk = me

*

!2π 22me

* E − EC( )!

dE = ρe (E)dE

ρe (E) =12π 2

2me*

!2!

"##

$

%&&

3/2

E − EC

ρh (E) =12π 2

2mh*

!2!

"##

$

%&&

3/2

EV − E

EE232 Lecture 3-12 Prof. Ming Wu

Electron and Hole Concentrations

n = fn (E)ρe (E)dEEC

∫ =1

1+ expE − FnkBT

!

"#

$

%&

12π 2

2me*

!2!

"##

$

%&&

2

E − EC dEEC

n = NC ⋅F1/2Fn − ECkBT

!

"##

$

%&&

NC = 2πme

*kBT2π 2!2

!

"##

$

%&&

3/2

p=NV ⋅F1/2EV − FpkBT

!

"##

$

%&&

NV = 2πmh

*kBT2π 2!2

!

"##

$

%&&

3/2

( )0

Fermi-Dirac Integral

1 ( 1) 1

Gamma Function

3( )2 2

j

j x

xF dxj e hh

p

¥

-=G + +

G =

ò

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EE232 Lecture 3-13 Prof. Ming Wu

Approximation of Electron/Hole Concentration

Fj η( ) = 1Γ( j +1)

x j

1+ ex−η0

∫ dx ≈ eη when η <<1

43η3

π

&

'(

)

*+

1/2

when η >>1

,

-..

/..

When Fn << EC (Boltzmann approximation)

n ≈ NC ⋅e−EC−FnkBT

When Fn >> EC (Degenerate)

n ≈ NC ⋅4 Fn − EC

kBT

&

'(

)

*+

3/2

3 π

Fn − ECkBT

C

nN

Boltzmann Approx

Degenerate

Quasi-­FermiLevel Cross Band Edge