JASPRIT SINGH
UNIVERSITY OF MICHIGAN
ANN ARBOR, MICHIGAN USA
INTRODUCTION: HOW DO
ELECTRONS AND PHOTONS
INTERACT?
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Optical Effects in Semiconductors
•  Lasers
•  Detectors
•  LEDs
•  Modulators
"
Communications, Display, Energy Conversion,
Detection, Spectroscopy, Healthcare …
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Optical Effects in Semiconductors
Basic processes: Photon absorption or emission
through interaction with electrons in the same band or
from one band to the other.
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Optical Effects in Semiconductors
Photons act as a perturbation on the electronic
system. The photon field has to be treated through
second quantization.
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Maxwell Equations
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Optical Effects
in
Semiconductors
Electron-photon
Hamiltonian
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Optical Effects
in
Semiconductors
Absorption
Emission Rates
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Optical Effects
in
Semiconductors
Absorption
Emission
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Optical Effects in Semiconductors:
Absorption
Rate and Coefficient
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Optical
Effects:
Polarization
control
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Optical Effects in Semiconductors
Photons
can be
destroyed
and
created.
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Optical Effects in Semiconductors
Electron and
photon
density of
states play a
role in the
optical
processes:
Density of
states
modification
can be
exploited.
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Optical Effects in Semiconductors
First order
electronic
transitions
are vertical
in the E-k
diagram
since
photon
momentum
is negligible
compared to
electron
momentum..
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Optical Effects in Semiconductors
Direct gap
Materials:
Absorption
coefficient
reaches
104cm-1
above
bandgap.
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Optical Effects in Semiconductors
Absorption
coefficient
has
staircase
form in
quantum
wells.
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Optical Effects in Semiconductors
Absorption
coefficient
has
staircase
form in
quantum
wells.
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Optical Effects in Semiconductors
Indirect gap
materials
have
second
order
transitions –
weak but
still
important for
absorption
applications
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Optical Effects in Semiconductors
Indirect gap
materials:
Slow rise in
absorption
coefficient
starting at
bandgap
photon
energy.
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Optical Effects in Semiconductors
Quantum wells;
Quantum wires;
Quantum dots:
Intersubband
transitions can
occur with strong
strength.
These have
applications in long
wavelength
detection
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Quantum wells;
Quantum wires;
Quantum dots:
Intersubband
transitions can
occur with strong
strength.
These have
applications in long
wavelength
detection
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Optical Effects in Semiconductors
Radiative lifetime
in semiconductors
controls light
emission. Lifetimes
depend on electron
hole injection
density and can be
about a
nanosecond for
high injection in
direct gap
materials.
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Radiative lifetime
in semiconductors
controls light
emission.
Lifetimes depend
on electron hole
injection density
and can be
about a
nanosecond for
high injection in
direct gap
materials.
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Optical Effects in Semiconductors
Electron-hole
injection can
alter optical
absorption and
allow gain.
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Optical Effects in Semiconductors
Electron-hole recombination can occur through nonradiative processes.
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Optical Effects in Semiconductors
Non-radiative
processes:
Auger
reombination.
Photon energy
is converted to
phonon energy.
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Optical Effects in Semiconductors
Spontaneous
and stimulated
emission.
Spontaneous
emission:
LEDs
Stimulated
emission:
Lasers.
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Optical Effects in Semiconductors
LEDs: p-n diodes under forward bias
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Optical Effects in Semiconductors
Laser Diodes:
p-n diodes
under forward
bias + optical
cavity with
mirrors
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Optical Gain
in
Semiconductors
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Optical Effects in Semiconductors
Gain in
semiconductors:
Under high
injection gain
can occur and
light signals can
grow.
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Optical Effects in Semiconductors
Light output in
the lasing mode
versus injection
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Optical Effects in Semiconductors
Spectral output
in a laser: the
lasing mode
starts to
dominate at
higher injection
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