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Optoelectronic Devices & Communication Networks

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Optoelectronic Devices for Communication Networks

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Optoelectronic Devices for Communication Networks

• Requirements to understand the concepts of Optoelectronic Devices:

1. We need to study concepts of light properties

2. Some concepts of solid state materials in particular semiconductors.

3. Light + Solid State Materials

Light Properties

• Wave/Particle Duality Nature of Light

• Reflection • Snell’s Law and Total Internal Reflection (TIR) • Reflection & Transmission Coefficients • Fresnel’s Equations • Intensity, Reflectance and Transmittance

• Refraction • - Refractive Index

• Interference • - Multiple Interference and Optical Resonators

• Diffraction • Fraunhofer Diffraction • Diffraction Grating

Light Properties

• Dispersion

• Polarization of Light

• Elliptical and Circular Polarization

• Birefringent Optical Devices

• Electro-Optic Effects

• Magneto-Optic Effects

Some Concepts of Solid State Materials

Contents

The Semiconductors in Equilibrium Nonequilibrium Condition

Generation-Recombination Generation-Recombination rates

Photoluminescence & Electroluminescence Photon Absorption

Photon Emission in Semiconductors Basic Transitions

Radiative Nonradiative

Spontaneous Emission Stimulated Emission

Luminescence Efficiency Internal Quantum Efficiency External Quantum Efficiency

Photon Absorption Fresnel Loss

Critical Angle Loss Energy Band Structures of Semiconductors

PN junctions Homojunctions, Heterojunctions

Materials

III-V semiconductors Ternary Semiconductors

Quaternary Semiconductors II-VI Semiconductors IV-VI Semiconductors

Light

• The nature of light

Wave/Particle Duality Nature of Light

--Particle nature of light (photon) is used to explain the concepts of solid state optical sources (LASER, LED), optical detectors, amplifiers,…

--The wave nature of light is used to explain refraction, diffraction, polarization,… used to explain the concepts of light transmission in fiber optics, WDM, add/drop/ modulators,…

hpmcE

chhE 2

The wave nature of Light


• Polarization • Reflection • Refraction • Diffraction • Interference

To explain these concepts light can be treated as

rays (geometrical optics) or as an electromagnetic wave (wave optics, studies related to Maxwell Equations).

An electromagnetic wave consist of two fields: • Electric Field • Magnetic Field

Ex

z

Direction of Propagation

By

z

x

y

k

An electromagnetic wave is a travelling wave which has timevarying electric and magnetic fields which are perpendicular to eachother and the direction of propagation, z.

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

An electromagnetic wave consist of two components; electrical

field and magnetic field components.

k is the wave vector, and its magnitude is 2π/λ

Light can treated as an EM wave, Ex and By are propagating

through space in such a way that they are always perpendicular to

each other and to the direction of propagation z.


We can treat light as an EM wave with time varying electric and magnetic fields.

Ex and BY which are propagating through space in such a way that they are always perpendicular to each other and to the direction of propagation z.

Traveling wave (sinusoidal):

00 .cos),( rktEtrE

z

Ex = E

osin(t–kz)

Ex

z

Propagation

E

B

k

E and B have constant phase

in this xy plane; a wavefront

E

A plane EM wave travelling along z, has the same Ex (or By) at any point in a

given xy plane. All electric field vectors in a given xy plane are therefore in phase.The xy planes are of infinite extent in the x and y directions.



y

z

k

Direction of propagation

r

O

E(r,t)r

A travelling plane EM wave along a direction k.


00 cos, krtEtrE

tconskzt tan0

kdt

dz

t

zV 2Phase velocity:

]Re[),( )(

00 kztjj

x eeEtzE

During a time interval Δt, a constant phase moves a distance Δz,

zzk

2Phase difference:

k

Wave fronts

r

E

k

Wave fronts(constant phase surfaces)

z

Wave fronts

PO

P

A perfect spherical waveA perfect plane wave A divergent beam

(a) (b) (c)

Examples of possible EM waves


krtr

AE cos Spherical wave

00 cos, krtEtrEPlane wave

t

EE

2

22

Maxwell’s Wave Equations

Electric field component of

EM wave:

These are the solutions of Maxwell’s equation

Optical Divergence

y

x

Wave fronts

z Beam axis

r

Intensity

(a)

(b)

(c)

2wo

O

Gaussian

2w

(a) Wavefronts of a Gaussian light beam. (b) Light intensity across beam crosssection. (c) Light irradiance (intensity) vs. radial distance r from beam axis (z).


Wo is called waist radius and 2Wo is called spot size

)2(

42

0w

Is called beam divergence

Gaussian Beams

Refractive Index

cV 00

1

0

1

V

0 r

rv

cn

Phase velocity

Speed of light

k(medium) = nk

λ(medium)= λ/n

Isotropic and anisotropic materials?; Optically isotropic/anisotropic?

n and εr are both depend on

The frequency of light (EM wave)

If the light is traveling in dielectric medium, assuming nonmagnetic

and isotropic we can use Maxwell’s equations to solve for electric

field propagation, however we need to define a new phase velocity.

What is εr ??

+

–

kEmaxEmax

Wave packet

Two slightly different wavelength waves travelling in the samedirection result in a wave packet that has an amplitude variationwhich travels at the group velocity.


dz/dt = δω/δk or Vg = dω/dk group velocity

Refractive index n and the group index Ng of pureSiO2 (silica) glass as a function of wavelength.

Ng

n

500 700 900 1100 1300 1500 1700 1900

1.44

1.45

1.46

1.47

1.48

1.49

Wavelength (nm)


g

gN

c

d

dnn

c

dk

dmediumv

)(

What is dispersion?; dispersive

medium?

2

)(n

cvk

In vacuum group velocity

Is the same as phase velocity.

z

Propagation direction

E

B

k

Area A

vt

A plane EM wave travelling along k crosses an area A at right angles to the

direction of propagation. In time t, the energy in the cylindrical volume Avt(shown dashed) flows through A .


In EM wave a magnetic field is always accompanying electric field,

Faraday’s Law. In an isotropic dielectric medium Ex = vBy = c/n (By),

where v is the phase velocity and n is index of refraction of the

medium.

n

y

n2 n

1

Cladding

Core z

y

r

Fiber axis

The step index optical fiber. The central region, the core, has greater refractiveindex than the outer region, the cladding. The fiber has cylindrical symmetry. Weuse the coordinates r, , z to represent any point in the fiber. Cladding isnormally much thicker than shown.


Structure of Fiber Optics

n2

n2

z2a

y

A

1

2 1

B

A

B

C

k1

Ex

n1

Two arbitrary waves 1 and 2 that are initially in phase must remain in phaseafter reflections. Otherwise the two will interfere destructively and cancel eachother.


n2

z

ay

A

1

2

A

C

kE

x

y

ay

Guide center

Interference of waves such as 1 and 2 leads to a standing wave pattern along the y-direc tion which propagates along z.


n2

Light

n2

n1

y

E(y)

E(y,z,t) = E(y)cos(t – 0z)

m = 0

Field of evanescent wave

(exponential decay)

Field of guided wave

The electric field pattern of the lowest mode traveling wave along theguide. This mode has m = 0 and the lowest . It is often referred to as theglazing incidence ray. It has the highest phase velocity along the guide.


ztyEtzyE mm cos)(2,,1

mmmmm ykztykEtzyE

2

1cos

2

1cos2,, 01

y

E(y)m = 0 m = 1 m = 2

Cladding

Cladding

Core 2an

1

n2

n2

The electric field patterns of the first three modes (m = 0, 1, 2)traveling wave along the guide. Notice different extents of fieldpenetration into the cladding.


Low order modeHigh order mode

Cladding

Core

Ligh t pulse

t0 t

Spread,

Broadened

light pulse

IntensityIntensity

Axial

Schematic illustration of light propagation in a slab dielectric waveguide. Light pulseentering the waveguide breaks up into various modes whic h then propagate at differentgroup velocities down the guide. At the end of the guide, the modes combine toconstitute the output light pulse which is broader than the input light pulse.

© 1999 S.O. Kasap , Optoelectronics (Prentice Hall)

n2

z

y

O

i

n1

Ai

ri

Incident Light BiAr

Br

t t

t

Refracted Light

Reflected Light

kt

At

Bt

BA

B

A

A

r

ki

kr

A light wave travelling in a medium with a greater refractive index ( n1 > n2) suffers

reflection and refraction at the boundary.


Snell’s Law and Total Internal Reflection (TIR)

1

2

sin

sin

n

n

V

V

t

i

t

i

1

1

sin

sin

n

n

V

V

r

i

r

i

Vi = Vr , therefore θi = θr

When θt reaches 90 degree, θi = θc called critical angle

1

2sinn

nc , We have total internal reflection (TIR)

n2

i

n1 > n

2

i

Incident

light

t

Transmitted

(refract ed) light

Reflected

light

kt

i>

c

c

TIR

c

Evanescent wave

ki

kr

(a) (b) (c)

Light wave travelling in a more dense medium strikes a less dense medium. Depending onthe incidence angle with respect to c, which is determined by the ratio of the refractive

indices , the wave may be transmitted (refracted) or reflected. (a) i < c (b) i = c (c) i

> c and total internal reflection (TIR).


00

1

r

v r

v

cn

Isotropic and

anisotropic materials

zktjEezyxE izi

y

t

exp,, 0,

2

2

1

2

2

2

122 1sin

2

i

n

nn

α2 is the attenuation coefficient and 1/ α2 is called penetration depth

x

y

z

Ey

Ex

yEy

^

xEx

^

(a) (b) (c)

E

Plane of polarization

x^

y^

E

(a) A linearly polarized wave has its electric field oscillations defined along a lineperpendicular to the direction of propagation, z. The field vector E and z define a plane o fpolariza tion. (b) The E-field os cillations are contained in the p lane of polarization. (c) Alinearly polarized light at any instant can be represented by the superposition of two fields Ex

and Ey with the right magnitude and phase.

E


k i

n2

n1 > n 2

t=90°Evanescent wave

Reflected

waveIncident

wave

i r

Er,/ /

Er,

Ei,

Ei,//

Et,

(b) i > c then the incident wave

suffers total internal reflection.However, there is an evanescentwave at the surface of the medium.

z

y

x into paperi r

Incident

wave

t

T ransmitt ed wave

Ei,//

Ei,Er,/ /

Et,

Et,

Er,

Reflected

wave

k t

k r

Light wave travelling in a more dense medium s trikes a less dense medium. The plane ofincidence is the plane of the paper and is perpendicular to the flat interface between thetwo media. The electric field is normal to the direction of propagation . It can be resolvedinto perpendicular () and parallel (//) components

(a) i < c then some of the wave

is transmitted into the less densemedium. Some of the wave isreflected.

Ei,


Transverse electric field (TE)

Transverse magnetic Field (TM)

).(

0

rktj

iiieEE

).(

0

rktj

rrreEE

).(

0

rktj

ttteEE

zktjEezyxE izi

y

t

exp,, 0,

2

Fresnel’s Equations:

using Snell’s law, and applying boundary conditions:

21

22

2

122

,0

,0

sincos

sincos

ii

ii

i

r

n

n

E

Er

21

22,0

,0

sincos

cos2

ii

i

i

t

nE

Et

ii

ii

i

r

nn

nn

E

Er

cossin

cossin

22

122

22

122

//,0

//,0

//

2

1222//,0

//,0

//

sincos

cos2

ii

i

i

t

nn

n

E

Et

n = n2/n1

Internal reflection: (a) Magnitude of the reflection coefficients r// and rvs. angle of incidence i for n1 = 1.44 and n2 = 1.00. The critical angle is

44°. (b) The corresponding phase changes // and vs. incidence angle.

//

(b)

60

120

180

Incidence angle, i

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60 70 80 90

| r// |

| r |

c

p

Incidence angle, i

(a)

Magnitude of reflection coefficients Phase changes in degrees

0 10 20 30 40 50 60 70 80 90

c

p

TIR

0

60

20

80


Polarization angle

i

i n

cos

sin

2

1tan

2

122

i

i

n

n

cos

sin

2

1

2

1tan

2

2

122

//

and

r‖ = r┴ = (n1 – n2)/(n1+ n2)

For incident angle close to zero:

The reflection coefficients r// and r vs. angle

of incidence i for n1 = 1.00 and n2 = 1.44.

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60 70 80 90

p r//

r

Incidence angle, i

External reflection


2

02

1or EVI

2

2

,0

2

,0

rE

ER

i

r2

//2

//,0

2

//,0

// rE

ER

i

r

2

21

21//

nn

nnRRR

2

1

2

2

,0

2

,02

t

n

n

E

EnT

i

t2

//

1

2

2

//,0

2

//,02

// tn

n

E

EnT

i

t

2

21

21//

4

nn

nnTTT

Light intensity

Reflectance

for normal incident

Transmittance

d

Semiconductor ofphotovoltaic device

Antireflectioncoating

Surface

Illustration of how an antireflection coating reduces thereflected light intensity

n1 n2 n3

AB


n1 n2

AB

n1 n2

C

Schematic illus tration of the principle of the dielectric mirror with many low and highrefractive index layers and its reflectance.

Reflectance

(nm)

330 550 770

1 2 21

o

1/4 2/4

© 1999 S.O. Kasap, Optoelectronics (Prent ice Hall)

Light

n2

A planar dielectric waveguide has a central rectangular region ofhigher refractive index n1 than the surrounding region which hasa refractive index n2. It is assumed that the waveguide isinfinitely wide and the central region is of thickness 2 a. It isilluminated at one end by a monochromatic light source.

n2

n1 > n2

Light

LightLight


n2

n2

d = 2a

k1

Light

A

B

C

E

n

1

A light ray travelling in the guide must interfere constructively with itself topropagate successfully. Otherwise destructive interference will destroy thewave.


z

y

x

m

anmm

cos

22 1

mmm

nk

sin

2sin 1

1

mmm

nkk

cos

2cos 1

1

ΔΦ (AC) = k1(AB + BC) - 2Φ = m(2π), k1 = kn1 = 2πn1/λ

m=0, 1, 2, …

Waveguide condition

n2

Light

n2

n1

y

E(y)

E(y,z,t) = E(y)cos(t – 0z)

m = 0

Field of evanescent wave

(exponential decay)

Field of guided wave

The electric field pattern of the lowest mode traveling wave along theguide. This mode has m = 0 and the lowest . It is often referred to as theglazing incidence ray. It has the highest phase velocity along the guide.


ztyEtzyE mm cos)(2,,1

mmmmm ykztykEtzyE

2

1cos

2

1cos2,, 01

y

E(y)m = 0 m = 1 m = 2

Cladding

Cladding

Core 2an

1

n2

n2

The electric field patterns of the first three modes (m = 0, 1, 2)traveling wave along the guide. Notice different extents of fieldpenetration into the cladding.



Cladding

Core

Ligh t pulse

t0 t

Spread,

Broadened

light pulse

IntensityIntensity

Axial

Schematic illustration of light propagation in a slab dielectric waveguide. Light pulseentering the waveguide breaks up into various modes whic h then propagate at differentgroup velocities down the guide. At the end of the guide, the modes combine toconstitute the output light pulse which is broader than the input light pulse.


Ey (m) is the field distribution along y axis and constitute a mode of propagation.

m is called mode number. Defines the number of modes traveling along the waveguide. For every value

of m we have an angle θm satisfying the waveguide condition provided to satisfy the TIR as well.

Considering these condition one can show that the number of modes should satisfy:

m = ≤ (2V – Φ)/π

V is called V-number 21

2

2

2

1

2nn

aV

For V ≤ π/2, m= 0, it is the lowest mode of propagation referred to single mode waveguides.

The cut-off wavelength (frequency) is a free space wavelength for v = π/2

E

By

Bz

z

y

O

B

E// Ey

Ez

(b) TM mode(a) TE mode

B//

x (into paper)

Possible modes can be classified in terms of (a) transelectric field (TE)and (b) transmagnetic field (TM). Plane of incidence is the paper.


y

E(y)

Cladding

Cladding

Core

2 > 11 > c

2 < 11 < cut-off

vg1

y

vg2 > vg1

The electric field of TE0 mode extends more into thecladding as the wavelength increases. As more of the fieldis carried by the cladding, the group velocity increases.


i

n2

n1 > n

2

Incident

light

Reflected

light

r

z

Virtual reflecting plane

Penetration depth,

z

y

The reflected light beam in total internal reflection appears to have been laterally shifted byan amount z at the interface.

A

B


Goos-Hanchen shift

i

n2

n1 > n

2

Incident

light

Reflected

light

r

When medium B is thin (thickness d is small), the field penetrates tothe BC interface and gives rise to an attenuated wave in medium C.The effect is the tunnelling of the incident beam in A through B to C.

z

y

d

n1

A

B

C

© 1999 S.O. Kasap, Optoelectronics (Prent ice Hall)

Optical Tunneling

Incident

light

Reflected

light

i > c

TIR

(a)

Glass prism

i > c

FTIR

(b)

n1

n1n

2 n1

B = Low refractive index

transparent film ( n2)

ACA

Reflected

Transmitted

(a) A light incident at the long face of a glass prism suffers TIR; the prism deflects thelight.(b) Two prisms separated by a thin low refractive index film forming a beam-splitter cube.The incident beam is split into two beams by FTIR.

Incident

light


n

y

n2 n

1

Cladding

Core z

y

r

Fiber axis

The step index optical fiber. The central region, the core, has greater refractiveindex than the outer region, the cladding. The fiber has cylindrical symmetry. Weuse the coordinates r, , z to represent any point in the fiber. Cladding isnormally much thicker than shown.


For the step index optical fiber Δ = (n1 – n2)/n1

is called normalized index difference

Fiber axis

12

34

5

Skew ray1

3

2

4

5

Fiber axis

1

2

3

Meridional ray

1, 3

2

(a) A meridionalray alwayscrosses the fiberaxis.

(b) A skew raydoes not haveto cross thefiber axis. Itzigzags aroundthe fiber axis.

Illustration of the difference between a meridional ray and a skew ray.Numbers represent reflections of the ray.

Along the fiber

Ray path projectedon to a plane normalto fiber axis

Ray path along the fiber


E

r

E01

Core

Cladding

The electric field distribution of the fundamental modein the transverse plane to the fiber axis z. The lightintensity is greatest at the center of the fiber. Intensitypatterns in LP01, LP11 and LP21 modes.

(a) The electric fieldof the fundamentalmode

(b) The intensity inthe fundamentalmode LP01

(c) The intensityin LP11

(d) The intensityin LP21


ztjrEE lmlmLP exp.

LPs (linearly polarized waves)

propagating along the fiber

have either TE or TM type

represented by the propagation

of an electric field distribution

Elm(r,Φ) along z.

ELP is the field of the LP mode and βlm is its propagation

constant along z.

V-number

2

2VM

21

12

12

2

2

1 222

nna

nna

V

405.22

2

12

2

2

1 nna

Vc

offcut

2

1

2

2

2

1121 2// nnnnnn

Normalized index difference

For V = 2.405, the fiber is called single mode (only the

fundamental mode propagate along the fiber). For V >

2.405 the number of mode increases according to

approximately Most SM fibers designed

with 1.5<V<2.4

For weakly guided

fiber Δ=0.01, 0.005,..

0 2 4 61 3 5

V

b

1

0

0.8

0.6

0.4

0.2

LP01

LP11

LP21

LP02

2.405

Normalized propagation constant b vs. V-numberfor a step index fiber for various LP modes.


2

2

2

1

2

2

2/

nn

nkb

kn2 <β<kn1 Propagation condition

b changes between 0 and 1

Cladding

Core max

A

B

< c

A

B

> c

max

n0

n1

n2

Lost

Propagates

Maximum acceptance angle

max is that which just gives

total internal reflection at the

core-cladding interface, i.e.

when = max then = c.

Rays with > max (e.g. ray

B) become refracted and

penetrate the cladding and are

eventually lost.

Fiber axis


0

2

12

2

2

1maxsin

n

nn

2/12

2

2

1 )( nnNA

0

maxsinn

NA

NAa

V

2

Example values for n1=1.48, n2=1.47;

very close numbers

Typical values of NA = 0.07…,0.25

Numerical Aperture---Maximum Acceptance Angle

Optical waveguides display 3 types of

dispersion:

These are the main sources of dispersion in

the fibers.

• Material dispersion, different

wavelength of light travel at

different velocities within a given

medium.

Due to the variation of n1 of the core wrt

wavelength of the light.

•Waveguide dispersion, β depends

on the wavelength, so even within

a single mode different

wavelengths will propagate at

slightly different speeds.

Due to the variation of group velocity wrt V-

number

t

Spread, ²

t0

Spectrum, ²

12o

Intensity Intensity Intensity

Cladding

CoreEmitter

Very short

light pulse

vg(

2)

vg(

1)

Input

Output

All excitation sources are inherently non-monochromatic and emit within aspectrum, ², of wavelengths. Waves in the guide with different free spacewavelengths travel at different group velocities due to the wavelength dependenceof n1. The waves arrive at the end of the fiber at different times and hence result in

a broadened output pulse.


DL

• Modal dispersion, in waveguides with more than one propagating mode. Modes travel with different group velocities.

Due to the number of modes traveling

along the fiber with different group velocity and different path.


Cladding

Core

Ligh t pulse

t0 t

Spread,

Broadened

light pulse

IntensityIntensity

Axial

Schematic illustration of light propagation in a slab dielectric waveguide. Light pulseentering the waveguide breaks up into various modes which then propagate at differentgroup velocities down the guide. At the end of the guide, the modes combine toconstitute the output light pulse which is broader than the input light pulse.


0

1.2 1.3 1.4 1.5 1.61.1

-30

20

30

10

-20

-10

(m)

Dm

Dm + Dw

Dw0

Dispersion coefficient (ps km-1 nm-1)

Material dispersion coefficient (Dm) for the core material (taken asSiO2), waveguide dispersion coefficient (Dw) (a = 4.2 m) and thetotal or chromatic dispersion coefficient Dch (= Dm + Dw) as a

function of free space wavelength,


mDL

2

2

d

nd

cDm

DL

2

2

2

2

22

984.1

cna

ND

g

PDL

pm DDDL

Material

Dispersion

Coefficient

Waveguide

Dispersion

Coefficient

Dp is called profile

dispersion; group velocity

depends on Δ

Core

z

n1 x

// x

n1 y

// y

Ey

Ex

Ex

Ey

E

= Pulse spread

Input light p ulse

Out put light pulse

t

t

Intensity

Suppose that the core refractive index has different values along two orthogonaldirections corresponding to electric f ield oscillation direc tion (polarizations). We cantake x and y axes along these directions. An input light w ill travel along the f iber w ith Ex

and Ey polarizations having different group velocities and hence arrive at the output at

different times


Polarization Dispersion

Material and waveguide dispersion coefficients in anoptical fiber with a core SiO2-13.5%GeO2 for a = 2.5

to 4 m.

0

–10

10

20

1.2 1.3 1.4 1.5 1.6

–20

(m)

Dm

Dw

SiO2-13.5%GeO2

2.5

3.03.54.0a (m)



e.g.

For λ =1.5, and 2a = 8μm

Dm=10 ps/km.nm and

Dw=-6 ps/km.nm

20

-10

-20

-30

10

1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

30

(m)

Dm

Dw

Dch = Dm + Dw

1


2

n

r

Thin layer of cladding

with a depressed index

Dispersion flattened fiber example. The material dispersion coefficient ( Dm) for the

core material and waveguide dispersion coefficient (Dw) for the doubly clad fiber

result in a flattened small chromatic dispersion between 1 and 2.


t0

Emitter

Very short

light pulses

Input Output

Fiber

Photodetector

Digital signal

Information Information

t0

~2²

T

t

Output IntensityInput Intensity

²

An optical fiber link for transmitting digital information and the effect ofdispersion in the fiber on the output pulses.


n1

n2

21

3

nO

n1

21

3

n

n2

OO' O''

n2

(a) Multimode stepindex fiber. Ray pathsare different so thatrays arrive at differenttimes.

(b) Graded index fiber.Ray paths are differentbut so are the velocitiesalong the paths so thatall the rays arrive at thesame time.

23


0.5P

O'O

(a)

0.25P

O

(b)

0.23P

O

(c)

Graded index (GRIN) rod lenses of different pitches. (a) Point O is on the rod facecenter and the lens focuses the rays onto O' on to the center of the opposite face. (b)The rays from O on the rod face center are collimated out. (c) O is slightly away fromthe rod face and the rays are collimated out.


z

A solid with ions

Light direction

k

Ex

Lattice absorption through a crystal. The field in the waveoscillates the ions which consequently generate "mechanical"waves in the crystal; energy is thereby transferred from the waveto lattice vibrations.


Sources of Loss and Attenuation in Fibers

Absorption depends on

materials, amount of

materials, wavelength, and

the impurities in the

substances.

It is cumulative and depends

on the amount of materials,

e.g. length of the fiber optics.

d)1(

α is the absorption per unit length and d

is the distance that light travels

Scattered waves

Incident waveThrough wave

A dielectric particle smaller than wavelength

Rayleigh scattering involves the polarization of a small dielectricparticle or a region that is much smaller than the light wavelength.The field forces dipole oscillations in the particle (by polarizing it)which leads to the emission of EM waves in "many" directions sothat a portion of the light energy is directed away from the incidentbeam.© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Escaping wave

c

Microbending

R

Cladding

Core

Field distribution

Sharp bends change the local waveguide geometry that can lead to wavesescaping. The zigzagging ray suddenly finds itself with an incidenceangle that gives rise to either a transmitted wave, or to a greatercladding penetration; the field reaches the outside medium and some lightenergy is lost.


Attenuation in Optical Fiber

)10(

)log(101

10/L

inout

out

indB

PP

P

P

L

G. Keiser (Ref. 1)

34.4dB

Some Concepts of Solid State Materials

Contents

The Semiconductors in Equilibrium Nonequilibrium Condition

Generation-Recombination Generation-Recombination rates

Photoluminescence & Electroluminescence Photon Absorption

Photon Emission in Semiconductors Basic Transitions

Radiative Nonradiative

Spontaneous Emission Stimulated Emission

Luminescence Efficiency Internal Quantum Efficiency External Quantum Efficiency

Photon Absorption Fresnel Loss

Critical Angle Loss Energy Band Structures of Semiconductors

PN junctions Homojunctions, Heterojunctions

Materials

III-V semiconductors Ternary Semiconductors

Quaternary Semiconductors II-VI Semiconductors IV-VI Semiconductors

Classification of Devices

• Combination of Electrics and Mechanics form Micro/Nano-Electro-Mechanical Systems (MEMS/NEMS)

• Combination of Optics, Electrics and Mechanics form Micro/Nano-Opto-Electro-Mechanical Systems (MOEMS/NOEMS)

Optical Electronics

Mechanical

MEMS

MOEMS

Schematic illustration of the the structure of a double heterojunction stripecontact laser diode

Oxide insulator

Stripe electrode

SubstrateElectrode

Active region where J > Jth.

(Emission region)

p-GaAs (Contacting layer)

n-GaAs (Substrate)

p-GaAs (Active layer)

Current

paths

L

W

Cleaved reflecting surfaceElliptical

laser

beam

p-AlxGa

1-xAs (Confining layer)

n-AlxGa


12 3

Cleaved reflecting surface

Substrate


Solid State Optoelectronic Devices

Optical Sources; Laser,

LED

Switches

Photodiodes

Photodetectors

Solar Cells

Type of Semiconductors

• Simple Semiconductors

• Compound Semiconductors • Direct Band gap Semiconductors

• Indirect Band gap Semiconductors

Some Properties of Some Important Semiconductors

Compound Eg Gap(eV) Transition λ(nm) Bandgap Diamond 5.4 230 indirect

ZnS 3.75 331 direct

ZnO 3.3 376 indirect

TiO2 3 413 indirect

CdS 2.5 496 direct

CdSe 1.8 689 direct

CdTe 1.55 800 direct

GaAs 1.5 827 direct

InP 1.4 886 direct

Si 1.2 1033 indirect

AgCl 0.32 3875 indirect

PbS 0.3 4133 direct

AgI 0.28 4429 direct

PbTe 0.25 4960 indirect

Common Planes

• {100} Plane

• {110} Plane

• {111} Plane

a

a

a – Lattice Constant

For Silicon

a = 5.34 A o

Two Interpenetrating Face-Centered Cubic Lattices

Diamond or Zinc Blend Structure

Energy Band Structure of Semiconductors

Concept of positive charges in solids (holes)

Doped Semiconductors

+5

As

+4

Si +4

Si

+4

Si

+4

Si

+4

Si

+4

Si

+4

Si

+4

Si

Eg

Ec

Ev

Ef

Ed

Conduction

electron

N - Type

Doped Semiconductors

+3

Al

+4

Si +4

Si

+4

Si

+4

Si

+4

Si

+4

Si

+4

Si +4

Si

Eg

Ec

Ev

Ef

Valence

hole

Ea

P-type

The Semiconductors in Equilibrium

• The thermal equilibrium concentration of carriers is independent of time.

• The random generation-recombination of electrons-holes occur continuously due to the thermal excitation.

• In direct band-to-band generation-recombination, the electrons and holes are created-annihilated in pairs:

• Gn0 = Gp0 , Rn0 = Rp0

• -The carriers concentrations are independent of time therefore:

• Gn0 = Gp0 = Rn0 = Rp0

Nonequilibrium Conditions in Semiconductors

• When current exist in a semiconductor device, the semiconductor is

operating under nonequilibrium conditions. In these conditions excess electrons in conduction band and excess holes in the valance band exist, due to the external excitation (thermal, electrical, optical…) in addition to thermal equilibrium concentrations.

n(t) = no + n(t), p(t) = po + p(t)

• The behavior of the excess carriers in semiconductors (diffusion, drift, recombination, …) which is the fundamental to the operation of semiconductors (electronic, optoelectronic, ..) is described by the ambipolar transport or Continuity equations.

Continuity Equations

t

nng

x

En

x

nE

x

nD

t

ppg

x

Ep

x

pE

x

pD

n

nnn

p

ppp

)(

)(

2

2

2

2

Nonequilibrium Conditions in Semiconductors Generation-Recombination Rates

• The recombination rate is proportional to electron and hole concentrations.

is the thermal equilibrium generation rate.

dt

tnd

dt

tnndtptnn

dt

tdni

)())(()]()([

)( 02

)()( 0 tnntn )()( 0 tpptp

2

in

Generation-Recombination Rates

• Electron and holes are created and recombined in pairs, therefore,

• n(t) = p(t) and no and po are independent of time.

)]())[(()]())((([

))((0000

2 tnpntntpptnnndt

tndi

Considering a p-type material under low-injection condition,

)())((

0 tnpdt

tnd

00 )0()0()( n

t

tpenentn

no = (po)-1 is the minority carrier electrons lifetime, constant for low-injections.


• The recombination rate ( a positive quantity) of excess minority carriers (electrons-holes) for p-type materials is:

0

'' )(

n

pn

tnRR

Similarly, the recombination rate of excess minority carriers for n-type material is:

0

'' )(

p

pn

tpRR

• where po is the minority carrier holes lifetime.


so,

no = (p)-1 and po = (n)-1

[For high injections which is in the case of LASER and LED

operations, n >> no and p >> po ]

• During recombination process if photons are emitted (usually in direct bandgap semiconductors), the process is called radiative (important for the operation of optical devices), otherwise is called nonradiative recombination (takes place via surface or bulk defects and traps).


• In any carrier-decay process the total lifetime can be expressed as

nrr

111

where r and nr are the radiative and nonradiative lifetimes

respectively.

The total recombination rate is given by

Where Rr and Rnr are radiative and nonradiative recombination rates

per unit volume respectively and Rsp is called the spontaneous

recombination rate.

spnrrtotal RRRR

pn Junction

The entire semiconductor is a single-

crystal material:

-- p region doped with acceptor

impurity atoms

--n region doped with donor

atoms

--the n and p region are separated

by the metallurgical junction.

eNa

eNd

x

B

h+

p n

M

As+

e

W

Neutral n-regionNeutral p-region

Space charge region

Metallurgical Junction(a)

(b)

xp

xn(c)

E

E (x)

eVbi

e x)

x

x0

Eo

M

xn

xn

xp

xp

(e)

(f)

(d)

(x)

Hole PE(x)

Electron PE(x)

- the potential barrier :

- keeps the large concentration

of electrons from flowing from

the n region into the p region;

- keeps the large concentration

of holes from flowing from the

p region into the n region;

=> The potential barrier maintains thermal equilibrium.

- the potential of the n region is positive with

respect to the p region => the Fermi energy in

the n region – lower than the Fermi energy in

the p region;

- the total potential barrier – larger than in the

zero-bias case;

- still essentially no charge flow and hence

essentially no current;

-a positive voltage is applied to the p region

with respect to the n region;

- the Fermi energy level – lower in the p

region than in the n region;

- the total potential barrier – reduced => the

electric field in the depletion region – reduced;

diffusion of holes from the p region across

the depletion region into the n region;

diffusion of electrons from the n region

across the depletion region into the p region;

- diffusion of carriers => diffusion currents;

2ln

i

datbi

n

NNVV

-in thermal equilibrium :

- the n region contains many

more electrons in the

conduction band than the p

region;

- the built-in potential barrier

prevents the large density of

electrons from flowing into the

p region;

- the built-in potential barrier

maintains equilibrium between

the carrier distribution on either

side of the junction;

kT

qVnn bi

np exp00

- the electric field Eapp induced by Va – in

opposite direction to the electric field in

depletion region for the thermal equilibrium;

- the net electric field in the depletion region is

reduced below the equilibrium value;

- majority carrier electrons from the n side ->

injected across the depletion region into the p

region;

- majority carrier holes from the p region ->

injected across the depletion region into the n

region;

- Va applied => injection of carriers across the

depletion regions-> a current is created in the

pn junction;

2/1

max

2/1

max

2/1

2

)(2)(2

)(2

da

da

s

R

biR

Rbi

da

da

s

Rbi

da

daRbispn

NN

NNeVE

VV

W

VV

NN

NNVVeE

NN

NN

e

VVxxW

212

da

dabisnp

NN

NN

e

VxxW

For zero bias

For reverse biased

W

VE bi2

max

For reverse

biased

For zero bias

When there is no voltage applied across the pn junction the

junction is in thermal equilibrium => the Fermi energy level –

constant throughout the entire system.

FpFnbiV

p

n

n

p

i

dabi

n

n

e

kT

p

p

e

kT

n

NN

e

kTV lnln

2

i

d

i

aFiFnFpFinpbi

n

N

e

kT

n

N

e

kTeEEeEEV lnln/)(/)(

dx

xdEx

dx

xd

EquationsPoisson

s

)()()(

'

2

2

px

+

_

ρ(C/cm³)

deN

aeN

nx

E

x =0

x

xs p

dxxxE )(1

)(

nn

s

d

pp

s

a

xxxxeN

E

xxxxeN

E

0),(

0),(

cmFSiFor rs /)1085.8)(7.11( 140

ndpa xNxN

Charge neutrality:

The peak electric field Is at x = 0

s

pa

s

ndxeNxeN

E

max

nxpx

Emax

n

pn

p

np

sL

nqD

L

pqDJ

00

1exp

kT

qVJJ a

s - ideal-diode equation;

The bipolar transistor:

- tree separately doped regions

- two pn junctions;

The width of the base region – small compared to the minority carrier diffusion length;

The emitter – largest doping concentration;

The collector – smallest doping concentration;

- the bipolar semiconductor – not a

symmetrical device;

-the transistor – may contain two n

regions or two p regions -> the

impurity doping concentrations in the

emitter and collector = different;

-- the geometry of the two regions –

can be vastly different;

Electromagnetic Spectrum

• Three basic bands; infrared (wavelengths above 0.7m), visible

(wavelengths between 0.4-0.7m), and ultraviolet light (wavelengths below 0.4m).

• E = h = hc/ ; c = (μm) =1.24 /E(eV)

• An emitted light from a semiconductor optical device has a wavelength proportional to the semiconductor band-gap.

• Longer wavelengths for communication systems; Eg 1m. (lower Fiber loss).

• Shorter wavelengths for printers, image processing,… Eg > 1m.

• Semiconductor materials used to fabricate optical devices depend on the wavelengths required for the operating systems.

Photoluminescence & Electroluminescence

• The recombination of excess carries in direct bandgap semiconductors may result in the emission of photon. This property is generally referred to as luminescence.

• If the excess electrons and holes are created by photon absorption, then the photon emission from the recombination process is called photoluminescence.

• If the excess carries are generated by an electric current, then the photon emission from the recombination process is called electroluminescence.

Photoluminescence Optical Absorption

Consider a two-level energy states of E1 and E2. Also consider that E1 is populated with N1 electron density, and E2 with N2 electron density.

E1; N1

E2; N2

Absorption

• dN1 states are raised from E1 to E2 i.e dN1 photons are absorbed.

Electrons are created in conduction band and holes in valence band.

• When photons with an intensity of I (x) are traveling through a semiconductor, going from x position to x + dx position (in 1-D system), the energy absorbed by semiconductor per unit of time is given by

I (x)dx, where is the absorption coefficient; the relative number of

photons absorbed per unit distance (cm-1).

dxxIdxdx

xdIxIdxxI )(.

)()()(

)()(

xIdx

xdI

xeIxI

0)(

where I(0) = I0

Absorption

• Intensity of the photon flux decreases exponentially with distance. • The absorption coefficient in semiconductor is strong function of photon

energy and band gap energy. • The absorption coefficient for h < Eg is very small, so the semiconductor

appears transparent to photons in this energy range.

Photoluminescence Optical Absorption

• When semiconductors are illuminated with light, the photons

may be absorbed (for Eph = hEg= E2 – E1)or they may propagate through the semiconductors (for EphEg).

• There is a finite probability that electrons in the lower level absorb energy from incoming electromagnetic field (light) with frequency of (E2 – E1)/h and jump to the upper level.

• B12 is proportionality constant, = 2 - 1 and = I is the

photon density in the frequency range of .

1121 )( NB

dt

dN

ab

Photon Emission in Semiconductors

• When electrons in semiconductors fall from the conduction band to the

valence band, called recombination process, release their energy in form of light (photon), and/or heat (lattice vibration, phonon).

• N1 and N2 are the concentrations of occupied states in level 1 (E1) and level 2 (E2) respectively.

Basic Transitions

Radiative

Intrinsic emission

Energetic carriers

Nonradiative

Impurities and defect center involvement

Auger process


Spontaneous Emission

Einstein Relationship

Einstein Relationship

These are the two fundamental conditions for lasing.

Wave attenuation

Internal Quantum Efficiency

Materials

• Almost all optoelectronic light source depend upon epitaxial crystal growth techniques where a thin film (a few microns) of semiconductor alloys are grown on single-crystal substrate; the film should have roughly the same crystalline quality. It is necessary to make strain-free heterojunction with good-quality substrate. The requirement of minimizing strain effects arises from a desire to avoid interface states and to encourage long-term device reliability, and this imposes a lattice-matching condition on the materials used.


Oxide insulator

Stripe electrode

SubstrateElectrode


(Emission region)


n-GaAs (Substrate)


Current

paths

L

W


laser

beam

p-AlxGa


n-AlxGa


12 3


Substrate


Solid State Optoelectronic Devices

Optical Sources; Laser,

LED

Switches

Photodiodes

Photodetectors

Solar Cells

Materials

• The constraints of bandgap and lattice match force that more complex compound must be chosen. These compounds include ternary (compounds that containing three elements) and quaternary (consisting of four elements) semiconductors of the form AxB1-xCyD1-y; variation of x and y are required by the need to adjust the band-gap energy (or desired wavelength) and for better lattice matching. Quaternary crystals have more flexibility in that the band gap can be widely varied while simultaneously keeping the lattice completely matched to a binary crystal substrate. The important substrates that are available for the laser diode technology are GaAs, InP and GaP. A few semiconductors and their alloys can match with these substrates. GaAs was the first material to emit laser radiation, and its related to III-V compound alloys, are the most extensively studied developed.

Materials

III-V semiconductors • Ternary Semiconductors; Mixture of binary-binary

semiconductors; AxB1-xC; mole fraction, x, changes from 0 to 1 (x will be adjusted for specific required wavelength). GaxAl1-xAs ; In0.53Ga0.47As; In0.52Al0.48As - Vegard’s Law: The lattice constant of AxB1-xC varies linearly

from the lattice constant of the semiconductor AC to that of the semiconductor BC.

- The bandgap energy changes as a quadratic function of x. - The index of refraction changes as x changes.

• The above parameters cannot vary independently • Quaternary Semiconductors; AxB1-xCyD1-y

(x and y will be adjusted for specific wavelength and matching lattices). GaxIn1-xPyAs1-y ; (AlxGa1-x)yIn1-yP; AlxGa1-xAsySb1-y

2cxbxaEg

Materials

• II-VI Semiconductors

• CdZnSe/ZnSe; visible blue lasers. Hard to dope p-type impurities at

concentration larger than 21018cm-3 (due to

self-compensation effect). Densities on this

order are required for laser operation.

Materials

• IV-VI semiconductors

• PbSe; PbS; PbTe

• By changing the proportion of Pb atoms in these materials semiconductor changes from n- to p-type.

• Operate around 50 Ko

• PbTe/Pb1-xEuxSeyTe1-y operates at 174 Ko

Materials

Materials

• In the near infrared region, the most important and certainly the most extensively characterized semiconductors are GaAs, AlAs and their ternary derivatives AlxGa1-xAs.

• At longer wavelengths, the materials of importance are InP and ternary and quaternary semiconductors lattice matched to InP. The smaller band-gap materials are useful for application in the long wavelength range.

Energy Band Structure of Semiconductors

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62

Lattice constant, a (nm)

GaP

GaAs

InAs

InP

Direct bandgap

Indirect bandgap

In0.535Ga0.465AsX

Quaternary alloys

with direct bandgap

In1-xGaxAs

Quaternary alloys

with indirect bandgap

Eg (eV)

Bandgap energy Eg and lattice constant a for various III-V alloys ofGaP, GaAs, InP and InAs. A line represents a ternary alloy formed withcompounds from the end points of the line. Solid lines are for directbandgap alloys whereas dashed lines for indirect bandgap alloys.Regions between lines represent quaternary alloys. The line from X toInP represents quaternary alloys In1-xGaxAs1-yPy made fromIn0.535Ga0.465As and InP which are lattice matched to InP.


3.6 III-V compound semiconductors in optoelectronics Figure

3Q6 represents the bandgap Eg and the lattice parameter a in the

quarternary III-V alloy system. A line joining two points represents

the changes in Eg and a with composition in a ternary alloy composed

of the compounds at the ends of that line. For example, starting at

GaAs point, Eg = 1.42 eV and a = 0.565 nm, and Eg decreases and a

increases as GaAs is alloyed with InAs and we move along the line

joining GaAs to InAs. Eventually at InAs, Eg = 0.35 eV and a =

0.606 nm. Point X in Figure 3Q6 is composed of InAs and GaAs and

it is the ternary alloy InxGa1-xAs. It has Eg = 0.7 eV and a = 0.587

nm which is the same a as that for InP. InxGa1-xAs at X is therefore

lattice matched to InP and can hence be grown on an InP substrate

without creating defects at the interface.

Further, InxGa1-xAs at X can be alloyed with InP to obtain a quarternary alloy

InxGa1-xAsyP1-y whose properties lie on the line joining X and InP and

therefore all have the same lattice parameter as InP but different bandgap. Layers

of InxGa1-xAsyP1-y with composition between X and InP can be grown

epitaxially on an InP substrate by various techniques such as liquid phase epitaxy

(LPE) or molecular beam expitaxy (MBE) .

The shaded area between the solid lines represents the possible values

of Eg and a for the quarternary III-V alloy system in which the bandgap is direct

and hence suitable for direct recombination.

The compositions of the quarternary alloy lattice matched to InP follow

the line from X to InP.

a Given that the InxGa1-xAs at X is In0.535Ga0.465As show that quarternary

alloys In1-xGaxAsyP1-y are lattice matched to InP when y = 2.15x.

b The bandgap energy Eg, in eV for InxGa1-xAsyP1-y lattice matched to

InP is given by the empirical relation,

Eg (eV) = 1.35 - 0.72y + 0.12 y2

Find the composition of the quarternary alloy suitable for an emitter

operating at 1.55 mm.

Materials

Materials

y = 2.2 x

Basic Semiconductor Luminescent Diode Structures

LEDs (Light Emitting Diode)

• Under forward biased when excess minority carriers diffuse

into the neutral semiconductor regions where they recombine with majority carriers. If this recombination process is direct band-to-band process, photons are emitted. The output photon intensity will be proportional to the ideal diode diffusion current.

• In GaAs, electroluminescence originated primarily on the p-side of the junction because the efficiency for electron injection is higher than that for hole injection.

• The recombination is spontaneous and the spectral outputs have a relatively wide wavelength bandwidth of between 30 – 40 nm.

• = hc/Eg = 1.24/ Eg

Light output

Insulator (oxide)p

n+ Epit axial layer

A schematic illustration of typical planar surface emitting LED devices . (a) p-layergrown epitaxially on an n+ substrate. (b) Firs t n+ is epitaxially grown and then p regionis formed by dopant diffusion into the epitaxial layer.

Light output

pEpit axial layers

(a) (b)

n+

Substrate Substrate

n+

n+

Met al electrode


Basic Semiconductor Luminescent Diode Structures

2 eV

2 eVeVo

Holes in VB

Electrons in CB

1.4 eVNo bias

With

forward

bias

Ec

EvEc

Ev

EFEF

(a)

(b)

(c)

(d)

pn+ p

Ec

GaAs AlGaAsAlGaAs

ppn+

~ 0.2 m

AlGaAsAlGaAs

(a) A doubleheterostructure diode hastwo junctions which arebetween two differentbandgap semiconductors(GaAs and AlGaAs)

(b) A simplified energyband diagram withexaggerated features. EF

must be uniform.

(c) Forward biasedsimplified energy banddiagram.

(d) Forward biased LED.Schematic illustration ofphotons escapingreabsorption in theAlGaAs layer and beingemitted from the device.


GaAs

Ec

Ev

E1

E1

h = E1 – E

1

E

In single quantum well (SQW) lasers electrons areinjected by the forward current into the thin GaAslayer which serves as the active layer. Populationinversion between E1 and E1 is reached even with a

small forward current which results in stimulatedemissions.


0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6

Blu

e

Gre

en

Ora

ng

eY

ello

w

Red

1.7

Infrared

Vio

let

GaA

s

GaA

s 0.5

5P0.4

5

GaAs1-yPy

InP

In0.1

4Ga 0

.86A

s

In1-xGaxAs1-yPy

AlxGa1-xAs

x = 0.43

GaP

(N)

GaS

b

Indirect

bandgap

InG

aNS

iC(A

l)

In0.7G

a 0.3A

s 0.6

6P0.3

4

In0.5

7Ga 0

.43A

s 0.9

5P0.0

5

Free space wavelength coverage by different LED materials from the visible spectrum to theinfrared including wavelengths used in optical communications. Hatched region and dashedlines are indirect Eg materials.

In0.49AlxGa0.51-xP


E

Ec

Ev

Carrier concentration

per unit energy

Electrons in CB

Holes in VB

h

1

0

Eg

h

h

h

CB

VB

Relative intensity

1

0

h

Relative intensity

(a) (b) (c) (d)

Eg + kBT

(2.5-3)kBT

1/2kBT

Eg

1 2 3

2kBT

(a) Energy band diagram with possible recombination paths. (b) Energy distribution ofelectrons in the CB and holes in the VB. The highest electron concentration is (1/2)kBT above

Ec . (c) The relative light intensity as a function of photon energy based on (b). (d) Relativeintensity as a function of wavelength in the output spectrum based on (b) and (c).


LED Characteristics

V

2

1

(c)

0 20 40

I (mA)0

(a)

600 650 700

0

0.5

1.0

Relative

intensity

24 nm

655nm

(b)

0 20 40I (mA)0

Relative light intensity

(a) A typical output spectrum (relative intensity vs wavelength) from a red GaAsP LED.(b) Typical output light power vs. forward current. (c) Typical I-V characteristics of ared LED. The turn-on voltage is around 1.5V.


800 900

–40°C

25°C

85°C

0

1

740

Relative spectral output power

840 880

Wavelength (nm)

The output spectrum from AlGaAs LED. Valuesnormalized to peak emission at 25°C.


Light output

p

Electrodes

Light

Plastic dome

Electrodes

Domed

semiconductor

pn Junction

(a) (b) (c)

n+

n+

(a) Some light suffers total internal reflection and cannot escape. (b) Internal reflectionscan be reduced and hence more light can be collected by shaping the semiconductor into adome so that the angles of incidence at the semiconductor-air surface are smaller than thecritical angle. (b) An economic method of allowing more light to escape from the LED isto encapsulate it in a transparent plastic dome.

Substrate


Electrode

SiO2 (insulator)

Electrode

Fiber (multimode)

Epoxy resin

Etched well

Double heterostructure

Light is coupled from a surface emitting LEDinto a multimode fiber using an index matchingepoxy. The fiber is bonded to the LEDstructure.

(a)

Fiber

A microlens focuses diverging light from a surfaceemitting LED into a multimode optical fiber.

Microlens (Ti2O3:SiO2 glass)

(b)


Schematic illustration of the the structure of a double heterojunction stripe

contact edge emitting LED

InsulationStripe electrode

SubstrateElectrode

Active region (emission region)

p+-InP (Eg = 1.35 eV, Cladding layer)

n+-InP (Eg = 1.35 eV, Cladding/Substrate)

n-InGaAs (Eg = 0.83 eV, Active layer)

Current

paths

L

60-70 m

Light beam

p+-InGaAsP (Eg 1 eV, Confining layer)

n+-InGaAsP (Eg 1 eV, Confining layer) 12 3

200-300 m


Active layer Barrier layer

Ec

Ev

E

A multiple quantum well (MQW) structure.Electrons are injected by the forward currentinto active layers which are quantum wells.


Multimode fiberLens

(a)

ELED

Active layer

Light from an edge emitting LED is coupled into a fiber typically by using a lens or aGRIN rod lens.

GRIN-rod lens

(b)

Single mode fiberELED


LASERS

• The sensitivity of most photosensitive material is greatly increased at wave-length < 0.7 m; thus, a laser with a short wave-length is desired for such applications as printers and image processing. The sensitivity of the human eye range between the wavelengths of 0.4 and 0.8m and the highest sensitivity occur at 0.555m or green so it is important to develop laser in this spectral regime for visual applications.

• Lasers with wavelength between 0.8 – 1.6 m are used in

optical communication systems.

LASERS

• The semiconductor laser diode is a forward bias p-n junction. The structure appears to be similar to the LED as far as the electron and holes are concerned, but it is quite different from the point of view of the photons. Electrons and holes are injected into an active region by forward biasing the laser diode. At low injection, these electrons and holes recombine (radiative) via the spontaneous process to emit photons. However, the laser structure is so designed that at higher injections the emission process occurs by stimulated emission. As we will discuss, the stimulated emission process provides spectral purity to the photon output, provides coherent photons, and offers high-speed performance.

• The exact output spectrum from the laser diode depends both on the nature of the optical cavity and the optical gain versus wavelength characteristics.

• Lasing radiation is only obtained when optical gain in the medium can overcome the photon loss from the cavity, which requires the diode current I to exceed a threshold value Ith and gop>gth

• Laser-quality crystals are obtained only with lattice mismatches <0.01% relative to the substrate.

A

B

L

M1 M2 m = 1

m = 2

m = 8

Relative intensity

m

m m + 1m - 1

(a) (b) (c)

R ~ 0.4

R ~ 0.81 f

Schematic illus tration of the Fabry-Perot optical cavity and its properties. (a) Reflectedwaves interfere. (b) Only standing EM waves, modes, of certain wavelengths are allowed

in the cavity. (c) Intens ity vs. frequency for various modes. R is mirror reflectance and

lower R means higher loss from the cavity.


Lm

2

m=1,2,3….

KLRR

II cavity 22

0

sin41

fm mL

cm )

2(

L

cf

2 Lowest frequency; m=1

Fabry-Perot Optical Resonator

L

m

m - 1

Fabry-Perot etalon

Partially reflecting plates

Output lightInput light

Transmitted light

Transmitted light through a Fabry-Perot optical cavity.


2

0

max1 R

II

kLRR

RII incidentdtransmitte 22

2

sin41

1

R

RF

1

2/1Finesse measures the

loss in the cavity, F

increases as loss

decreases

It is maximum when kL=mπ

m

fF

=ratio of the mode separation to

spectral width

LASER Diode Modes of Threshold Conditions

Lasing Conditions:

Population Inversion

Fabry-Perot cavity

gain (of one or several modes) > optical loss

zhvhvg

eIzI

)(

)0()(

I – optical field intensity

g – gain coefficient in F.P. cavity

- effective absorption coefficient

Γ – optical field confinement factor. (the

fraction of optical power in the active layer)

In one round trip i.e. z = 2L gain

should be > loss for lasing;

During this round trip only R1 &

R2 fractions of optical radiation

are reflected from the two laser

ends 1 & 2.

2

21

21

nn

nnR

LASER Diode Modes of Threshold Conditions

From the laser conditions: ,)()2( oILI 12 Lje mL 22

)0()0()2(

_

2

21 IeRRILIgL

21

2 1_

RRe

gL

21

_ 1ln2

RRgL

endthRRL

g _

21

_ 1ln

2

1

Lasing threshold is the point at

which the optical gain is equal to the

total loss αt

endtthg _

thth Jgg

M– is constant and depends on the

specific device construction.

Thus the gain

zjeoEzE )()(

Laser Diode Rate Equations

Rate Equations govern the interaction of photons and electrons in

the active region.

ph

spRBndt

d

= stimulated emission + spontaneous emission - photon loss

Bnn

qd

J

dt

dn

sp

= injection - spontaneous recombination - stimulated emission

(shows variation of electron concentration n).

Variation of photon concentration:

The relationship between optical output and the diode drive current:

d - is the depth of carrier-confinement region

B - is a coefficient (Einstein’s) describing the strength of

the optical absorption and emission interactions,;

Rsp - is rate of spontaneous emission into the lasing mode;

τph

– is the photon lifetime;

τsp

– is the spontaneous recombination lifetime;

J – is the injection current density;


Solving the above Equations for a steady-state condition yields an

expression for the output power.

0dt

d0

dt

dnSteady-state => and

n must exceed a threshold value nth in order for Φ to increase.

In other words J needs to exceed Jth in steady-state condition, when the number

of photons Φ=0.

sp

thth n

qd

J

No stimulating emission

This expression defines the current required to sustain an excess

electron density in the laser when spontaneous emission is the only

decay mechanism.


0

0

qd

JnBn

RBn

sp

thsth

ph

sspsth

Now, under steady-state condition at the lasing threshold:

Фs is the steady-state photon density.

0qd

JnR

sp

th

ph

ssp

phph

sp

thphsps

qd

JnR

qd

Jn th

sp

th

phspth

ph

s RJJqd

# of photon resulting from stimulated emission

Adding these two equations: but

The power from the first term is generally concentrated in one or few modes;

The second term generates many modes, in order of 100 modes.


To find the optical power P0:

c

nLt time for photons to cross cavity length L.

s2

1- is the part travels to right or left (toward output

face)

R is part of the photons reflected and 1-R

part will escape the facet

t

Rhvvolume

Ps

12

1

0

th

phJJ

qn

RWhcP

2

)1(2

0

W is the width of active layer

Laser Characteristics

P0

J

Jth

nth

P0 lasing output power ≡ Фs

Threshold

population

inversion

n

Typical output optical power vs. diode current (I) characteristics and the correspondingoutput spectrum of a laser diode.

Laser

LaserOptical Power

Optical Power

I0

LEDOptical Power

Ith

Spontaneous

emission

Stimulated

emission

Optical Power



Resonant Frequency

mL 22 /2 n

mLn

2

22

c

nLv2

nLm

2

So:

n

Lm

2

This states that the cavity resonates (i.e. a standing wave pattern exists

within it) when an integer number m of λ/2 spans the region between the

mirrors. Depending on the laser structures, any number of freq. can satisfy

1&)0()2( 2 LjeILI

Thus some lasers are single - & some are multi-modes.

The relationship between gain & freq. can be assumed

to have Gaussian form:

2

20

2)0()(

egg

where λ0 is the wavelength at the center of spectrum;

σ is the spectrum width of gain & maximum g(0) is

proportional to the population inversion.

Remember that inside the

optical cavity for

zero phase difference :

12 Lje ; ;


Spacing between the modes:

mvc

Lnm

2 L

n

m

2

1

21 mv

c

Lnm

Lnm

Ln

m

Ln

m

Lnm

2

2

1

22 2

2

122

1 vc

Lnvv

c

Lnmm

Ln

cv

2

vc 2

cv

cv

LnLn

cc

22

2

2

m

Ln2or


Internal & External Quantum Efficiency

Quantum Efficiency (QE) = # of photons generated for each EHP

injected into the semiconductor junction a measure of the efficiency

of the electron-to-photon conversion process.

If photons are counted at the junction region, QE is called internal

QE (int

), which depends on the materials of the active junction and

the neighboring regions. For GaAs int

= 65% to 100%.

If photons are counted outside the semiconductor diode QE is

external QE(ext

).

Consider an optical cavity of length L , thickness W and width S. Defining a

threshold gain gth as the optical gain needed to balance the total power loss,

due to various losses in the cavity, and the power transmission through the

mirrors .


Internal & External Quantum Efficiency

The optical intensity due to the gain is equal to:

I = Io exp(2Lgth),

There will be lost due to the absorption and the reflections on both ends

by

R1R2 exp(-2Lα)

So: I = Io exp(2Lgth){ R1R2 exp(-2Lα)} = Io (at threshold). Therefore:

1)(2

21 thgL

eRR

where R1 and R2 are power reflection coefficients of the mirrors, is

attenuation constant.

Laser Characteristics Internal & External Quantum Efficiency

21

1ln

2

1

RRLgth

g is gain constant of the active

region and is roughly

proportional to current density (g

= J). is a constant.

21

1ln

2

1)/1(

RRLJ th

By measuring Jth, , L, R1 and R2 one

can calculate (dependent upon the

materials and the junction structure).

The ratio of the power radiated

through mirrors to the total power

generated by the semiconductor

junction is total

ra

P

P

RRL

RRL

21

21

1ln

2

1

1ln

2

1

Laser Characteristics Internal & External Quantum Efficiency

Therefore ext= int(Pra/Ptotal) which can be determined

experimentally from PI characteristic.

For a given Ia (in PI curve current at point a) the number of

electrons injected into the active area/sec = Ia /q and the number

of photons emitted /second = Pa /h

qI

hP

a

a

ext/

/

qI

hP

b

b

ext/

/

I

P

h

q

hII

PPq

ba

ba

ext

)(

)(

i.e. ext is proportional to slope of PI curve in the region of I >

Ith.

th

extII

P

h

q

If we choose Ib = Ith , Pb0 and

h Eg and h/q = Eg /q gives voltage

across the junction in volts.

Laser Characteristics Power Efficiency

At dc or low frequency the equivalent circuit to a LASER diode may be

viewed as an ideal diode in series with rs.

Therefore the power efficiency =

p =(optical power output)/ (dc electrical power input)

sg

prIqEI

P2)/(

extthIIq

hP

)(

sg

gthext

prIqEI

qEII2)/(

/)(

LElectrode

Current

GaAs

GaAsn+

p+

Cleaved surface mirror

Electrode

Active region(stimulated emission region)

A schematic illustration of a GaAs homojunction laserdiode. The cleaved surfaces act as reflecting mirrors.

L


Typical output optical power vs. diode current (I) characteristics and the correspondingoutput spectrum of a laser diode.

Laser

LaserOptical Power

Optical Power

I0

LEDOptical Power

Ith

Spontaneous

emission

Stimulated

emission

Optical Power


Refractiveindex

Photondensity

Active

region

n ~ 5%

2 eV

Holes in VB

Electrons in CB

AlGaAsAlGaAs

1.4 eV

Ec

Ev

Ec

Ev

(a)

(b)

pn p

Ec

(a) A doubleheterostructure diode hastwo junctions which arebetween two differentbandgap semiconductors(GaAs and AlGaAs).

2 eV

(b) Simplified energyband diagram under alarge forward bias.Lasing recombinationtakes place in the p-GaAs layer, theactive layer

(~0.1 m)

(c) Higher bandgapmaterials have alower refractiveindex

(d) AlGaAs layersprovide lateral opticalconfinement.

(c)

(d)


GaAs


Oxide insulator

Stripe electrode

SubstrateElectrode


(Emission region)


n-GaAs (Substrate)


Current

paths

L

W


laser

beam

p-AlxGa


n-AlxGa


12 3


Substrate


Oxide insulation

n-AlGaAs

p+-AlGaAs (Contacting layer)

n-GaAs (Substrate)


n-AlGaAs (Confining layer)

p-AlGaAs (Confining layer)

Schematic illustration of the cross sectional structure of a buriedheterostructure laser diode.

Electrode


Height, HWidth W

Length, L

The laser cavity definitions and the output laser beamcharacteristics.

Fabry-Perot cavity

Dielectric mirror

Diffraction

limited laser

beam


778 780 782

Po = 1 mW

Po = 5 mW

Relative optical power

(nm)

Po = 3 mW

Output spectra of lasing emission from an index guided LD.At sufficiently high diode currents corresponding to highoptical power, the operation becomes single mode. (Note:Relative power scale applies to each spectrum individually andnot between spectra)


Typical optical power output vs. forward currentfor a LED and a laser diode.

Current0

Light powerLaser diode

LED

100 mA50 mA

5 mW

10 mW


Corrugated

dielectric structure

Distributed Bragg

reflector

(a) (b)

A

B

q(B/2n) =

Active layer

(a) Distributed Bragg reflection (DBR) laser principle. (b) Partially reflected wavesat the corrugations can only constitute a reflected wave when the wavelengthsatisfies the Bragg condition. Reflected waves A and B interfere constructive when

q(B/2n) = .


Active layer

Corrugated grating

Guiding layer

(a)

(a) Distributed feedback (DFB) laser structure. (b) Ideal lasing emission output. (c)Typical output spectrum from a DFB laser.

Optical power

(nm)

0.1 nm

Ideal lasing emission

B(b) (c)


Fiber Bragg grating

Bowei Zhang, Presentation for the

Degree of Master of Applied Science

Department of Electrical

and Computer Engineering

Fiber Bragg grating fabrication Phase Mask: Direct Imprinting

Bowei Zhang, Presentation for the

Degree of Master of Applied Science

Department of Electrical

and Computer Engineering

0th order

(Suppressed)

Diffraction

m = -1 Diffraction

m = +1

Phase Mask ΛPM

Ge doped

Fiber

248 nm Laser

Active

layer

L D

(a)

Cleaved-coupled-cavity (C3) laser

Cavity Modes

In L

In D

In both

L and D

(b)


A quantum well (QW) device. (a) Schematic illustrat ion of a quantum well (QW) structure in which athin layer of GaAs is sandwiched between two wider bandgap semiconductors (AlGaAs). (b) Theconduction electrons in the GaAs layer are confined (by ² Ec) in the x-direction to a small length d so

that their energy is quantized. (c) The density of stat es of a two-dimensional QW. The density of statesis constant at each quantized energy level.

AlGaAs AlGaAs

GaAs

y

z

x

d

Ec

Ev

d

E1

E2

E3

g(E)Density of states

E

BulkQW

n = 1

Eg2Eg1

E n = 2² Ec

BulkQW

² Ev

(a) (b) (c)

Dy

Dz


Ec

Ev

E1

E1

h = E1 – E

1

E

In single quantum well (SQW) lasers electrons areinjected by the forward current into the thin GaAslayer which serves as the active layer. Populationinversion between E1 and E1 is reached even with a

small forward current which results in stimulatedemissions.


Active layer Barrier layer

Ec

Ev

E

A multiple quantum well (MQW) structure.Electrons are injected by the forward currentinto active layers which are quantum wells.


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