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Optoelectronic Devices & Communication Networks
Amplifier
Add/Drop
WDM
Amplifier
WDM
WDM
Switch
Switch
1
2
3
1
n
2
3
n
Montreal
Toronto
Ottawa
Optoelectronic Devices for Communication Networks
» Optical Sources
» LED
» Laser
» Optical Diodes
» WDM
» Fiber Optics
» Optical Amplifiers
» Optical Attenuators
» Optical Isolators
» Optical Switches
» Add/Drop Devices
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.
The wave nature of Light
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
The wave nature of Light
y
z
k
Direction of propagation
r
O
E(r,t)r
A travelling plane EM wave along a direction k.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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).
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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)
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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 .
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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).
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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,
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
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 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.
© 1999 S.O. Kasap , Optoelectronics (Prentice Hall)
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,
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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)
Dispersion coefficient (ps km-1 nm-1)
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
Dispersion coefficient (ps km-1 nm-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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
1-xAs (Confining layer)
12 3
Cleaved reflecting surface
Substrate
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
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.
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.
Generation-Recombination Rates
• 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.
Generation-Recombination Rates
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).
Generation-Recombination Rates
• 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
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
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.
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
1-xAs (Confining layer)
12 3
Cleaved reflecting surface
Substrate
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
• 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.
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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).
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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)
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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;
Laser Diode Rate Equations
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.
Laser Diode Rate Equations
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.
Laser Diode Rate Equations
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
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Laser Characteristics
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 ; ;
Laser Characteristics
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
Laser Characteristics
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 .
Laser Characteristics
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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)
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
GaAs
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
1-xAs (Confining layer)
12 3
Cleaved reflecting surface
Substrate
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Oxide insulation
n-AlGaAs
p+-AlGaAs (Contacting layer)
n-GaAs (Substrate)
p-GaAs (Active layer)
n-AlGaAs (Confining layer)
p-AlGaAs (Confining layer)
Schematic illustration of the cross sectional structure of a buriedheterostructure laser diode.
Electrode
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Height, HWidth W
Length, L
The laser cavity definitions and the output laser beamcharacteristics.
Fabry-Perot cavity
Dielectric mirror
Diffraction
limited laser
beam
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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)
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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) = .
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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)
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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)
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)