Transcript Spontaneous emission

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10.1 Measurement of the Optical Properties
The measurement of optical properties of solids is not easy in practice.
Metal is opaque with light – so the measurements have to be taken in Reflection
Light penetrates about 10 nm into a metal – surface sensitive, sample preparation is
important.
The most relevant optical properties, namely, n, k, e1, e2, and the energies for
interband transitions can not be easily deduced by simply measuring the reflectivity.
Thus, a wide range of techniques, such as
(a) Kramers-Kronig Analysis (Dispersion Relationship)
(b) Spectroscopic Ellipsometry
(c) Differential Reflectometry
have been developed, which we will skip.
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10.2 Optical Spectra of Pure Metals
10.2.1 Reflection Spectra
Light interacts with a certain number of free electrons and a certain number of
classical harmonic oscillators, or equivalently, by intraband and interband transitions.
Reflectivity spectrum for Ag
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For Silver
bound electron
Free electron
Free electron behavior
or intraband transition
-below 3.8 eV
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e1  n 2  k 2
e 2  2nk
Classical oscillator or interband transition
For Copper
From EF near the L-symmetry
Copper possesses an absorption band in the visible spectrum
2.2 eV threshold energy for interband transition (d-band-EF)
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For Aluminum
essentially showing free electron-like behavior
Interband transitions occur near 1.5 eV between the
W2’ and W1 symmetry
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10.2.2 Plasma Oscillations
Plasma : excited by light of proper photon energy to collectively perform fluidlike
oscillations
e2 N f
At plasma frequency, the dielectric constant = 0,
eˆ  1 
Both e1 and e2 must be zero.
4 e 0 m
2
2
(11.6)
Energy loss function (large for e1 >0, e2<1) , at the plasma frequency
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Al: 15.2 eV
Ag: can not solely attributed to free electrons
Originates by cooperation of d- as well as the
conduction electrons
e1f  0 at 9.2 eV
10.3 Optical Spectra of Alloys (skip)
10.4 Ordering (skip)
10.5 Corrosion (skip)
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10.6 Semiconductors
Intrinsic Semiconductor
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Differential reflectogram of Si
Momentum (wave vector k) is
furnished by a phonon
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Photon energies slightly below the gap energy
Exciton : a photon may excite an electron so that it remains in the
vicinity of its nucleus, thus forming an electron-hole pair
Exciton Level
Extrinsic Semiconductor
At high temperatures , optical transitions from and to these states can
take place, which also cause weak absorption peaks below the gap energy
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10.7 Insulators (Dielectric Materials and Glass
Fibers)
No intraband transitions, and large gap energy
From far IR to UV region
However, in the IR region a new absorption mechanism may take place:
Light induced vibrations of the lattice atoms
Excitation of phonons by photons
Caused by interactions of the phonons with lattice
imperfection or other things
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Resonance frequency for diatomic crystals
Reststrahlen absorption
Eg) Spectral reflectivity of NaCl
Eg) Spectral reflectivity of
borosilicate/phosphosilicate
glass
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caused by the oscillations of OH- ions
10.8 Emission of Light
10.8.1 Spontaneous Emission
The emission of light due to reversion of electrons from a higher energy state is called
luminescence.
Fluorescence: if the electron transition occurs within nanoseconds or faster
Phosphorescence: the emission takes place after microseconds or milliseconds
Afterglow: even slower emission
-Photoluminescence: photons impinge on a material which in turn re-emits light of
lower energy
-Electroluminescence: emit light as a consequence of an applied voltage or electric
field
-Cathodoluminescence: light emission due to the showering by electrons of higher
energy
-Thermoluminescence: spontaneous light emission from candles or incandescent
light bulbs
-bioluminescentce: only in living materials
Spontaneous emission:
1. Emitted through a wide-angle region in space
2. The light is phase incoherent
3. Often polychromatic (more than one wavelength)
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10.8.2 Simulated Emission (Lasers)
Population inversion
Stimulating a second electron
Photon is emitted
In phase
Light amplification by simulated emission of radiation with
monochromatic, in-phase wave
cavity
Collimation
Laser light is
(1) highly monochromatic
(2) Strong collimated
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Fully
silver
Optical pumping: absorption of light stemming from a polychromatic light source
Pumping efficiency
is large if the band width of the upper electron state is broad
Heisenberg’s uncertainty
principle
The time span which an electron
remains at the higher energy
level
Population inversion
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Three-level laser
Broad pump band E3 enables
a good pumping efficiency
Intermediate lever
: the electrons remain much longer
population inversion increases
Four-level laser
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Nonradiative,
phonon assisted
process
10.8.3 Helium-Neon Laser
0.1 Torr Ne and 1 Torr He
10.8.4 Carbon Dioxide Laser
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Produce three characteristic
wavelengths
10.8.5 Semiconductor Laser
ㅡ
The cavity for this laser consists of heavily doped n- and p-type semiconductor materials.
There occurs population inversion of electrons in the depletion layer.
A reflective coating is not necessary since the reflectivity of the semiconductor is already 35%.
Pumping occurs by direct injection of electrons and holes into the depletion region.
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10.8.6 Direct-Versus Indirect- Band Gap Semiconductor
Lasers
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10.8.7 Wavelength of Emitted Light
The emission wavelength depends on the temperature of
operation, because the band gap decreases with increasing
temperature
Optical absorption in glass is quite wavelength dependent, having minima in
absorption at 1.3 mm to 1.55 mm.
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10.8.8 Threshold current Density
Each diode laser has a certain power output characteristic which depends on the
input current density – Fig. 13.41. (spontaneous emission versus laising)
Light output
Spontaneous emission: incoherent and is not strongly
monochromatic
Laising
Spon. emis.
Laising: when the current density increases above a
certain threshold, stimulated emission dominates
Threshold
Input current density
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10.8.9 Homojunction Versus Heterojunction Lasers
Homojunction lasers: photon distribution extends considerably beyond the electrically
active region.
For instance, the total light emitting layer for GaAs is about 10 mm whereas the depletion
layer, namely the active region, might be as narrow as 1 mm.
Heterojunction lasers: use high refractive index of the active region and form optical
waveguide structure which contain the photon within the active layer
,
Snell’s law
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10.8.10 Laser Amplifier
Traveling-wave laser:
A weak optical signal enters a laser through one of its windows and there stimulates
the emission of photons.
-the amplified signal leaves the other window after having passed the cavity only once.
Erbium-doped fiber amplifier:
10.8.11 Laser Modulation
For telecommunication purposes it is necessary to impress an AC signal on the output
of a laser to modulate directly the emerging light by the speech. This can be
accomplished by amplitude modulation by biasing the laser initially above the
threshold and then superimposing on this DC. (Figure 13. 44)
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10.8.12 Quantum Well Lasers
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10.8.13 Light-Emitting Diodes (LED)
A given color is represented by two
parameters or percentages while
the percentage of third color is the
difference between x+y and 100%.
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10.8.14 Liquid Crystal Displays (LCDs)
TFT-LCD
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10.8.15 Emissive Flat-Panel Displays
Electroluminescent devices (EL) utilize a thin phosphor film, such as manganesedoped zinc sulfide, which is sandwiched between two insulating films. The light
emission is generally induced by an alternating electrical potential applied between
the two conducting electrodes. This generates an electric field amounting to about
106 V/m across the phosphor layer, which causes an injection of electrons into the
phosphor. Once the threshold voltage has been exceeded, the electrons become
ballistic and excite the electrons of the activator atom in the phosphor(Mn) into a
higher energy state. Upon reverting back into the ground state, photons of the
respective wavelength are generated
Plasma display panels (PDP) operate quite similar to fluorescence light bulbs. A
relatively high AC voltage is applied across a discharge gas to create a plasma.
Recombination of electron-ion pairs in the plasma causes photons of high energy.
They are absorbed by the phosphors which in turn emit visible light.
Field-emission displays (FED) are still in the experimental stage. The aim is to build
them flat with wide viewing angles and fast response times. They consist of a large
number of tip-shaped field-emitters that can be matrix-addressed and which emit,
when hermetically encapsulated into a vacuum, substantial amounts of electrons under
the influence of high electric fields. These electrons impinge on phosphors of various
kinds to cause cathodoluminescence in different colors
OLED (Organic Light Emitting Diode)
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10.10 Optical Storage Devices
The height of the bump is one quarter of a wavelength of the probe beam.
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1
1
2  (  )   (destructive interference)
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10.10 Optical Storage Devices
The spiral path on the useful area of a 120 mm diameter CD – 5.7 km long and
contains 22,188 tracks spaced 1.6 mm apart, spot diameter is about 1.2 mm.
Information density on a Cd is 800 kbits/mm2 and hold 7 x109 bits.
CD-R (recordable compact disk): utilize photosensitive dye
CD-RW (rewritable compact disk): utilized chalcogenide material called GeSbTe, phase
change material
DVD-ROM(digital video disk-read only): DVDs utilize a laser diode whose wavelength is 650
nm, shorter than CD (spacing between bump is 0.74 mm.
DVD-RW (digital video disk-rewritable):
BD or BRD(blue-ray disk): utilize 405 nm wave from the GaN laser, can store 25 GB on a
single layer.
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10.12 X-Ray Emission
Voltage dependence of
several white X-ray spectra
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The wavelength of characteristic X-rays depends
on the material on which the accelerated
electrons impinge