Transcript Plank Formula

Plank Formula
• The 1900 quantum hypothesis by Max Planck
that any energy is radiated and absorbed in
quantities divisible by discrete ‘energy elements’,
E,
• such that each of these energy elements is
proportional to the frequency ν with which they
each individually radiate energy, as defined by
the following formula:
• where h is Planck's Action Constant.
1-Dimensional Quantum Well
• For the 1-dimensional case in the x
direction, the time-independent
Schrödinger equation can be written as:
Solution
Internal & External Quantum
Efficiency
• ηint = # of photons emitted from active region per second
# of electrons injected in to LED per second
= Pint / (hν)
I/e
• ηextr = # of photons emitted into free space per second
# of photons emitted from active region per second
= P / (hν)
Pint / (hν)
Theoretical Emission Spectrum
Illustration
The linewidth of an LED emitting in the visible
range is relatively narrow compared with the
entire visible range (perceived as
monochromatic by the eye)
Optical fibers are dispersive, limiting the bit rate
X distance product achievable with LED’s
Modulation speeds achieved with LED’s are
1Gbit/s, as the spontaneous lifetime of carriers
in LED’s is 1-100 ns
Definition of Escape Cone
Calculation
• Total internal reflection at the
semiconductor air interface reduces the
external quantum efficiency.
• The angle of total internal reflection
defines the light escape cone.
sinθc = nair/ns
• Area of the escape cone = 2πr2(1-cosθc)
• Pescape / Psource = (1-cosθc)/2 = θc2/4 =
(nair2/ns2)/4
Profile of Emission of LED
Calculation
• Light intensity in air (Lambertian
emission pattern) is given by
Iair = (Psource/4πr2) X (nair2/ns2) cosΦ
• Index contrast between the light
emitting material and the surrounding
region leads to non-isotropic emission
pattern
LED Chip with Encapsulant
Illustration
• Light extraction efficiency can be increased
by using dome shaped encapsulants with a
large refractive index.
• Efficiency of a typical LED increases by a
factor of 2-3 upon encapsulation with an
epoxy of n = 1.5.
• The dome shape of the epoxy implies that
light is incident at an angle of 90o at the
epoxy-air interface. Hence no total internal
reflection.
Temperature Dependence of Emission
• Emission intensity decreases with
increasing temperature.
• Causes include non-radiative
recombination via deep levels, surface
recombination, and carrier loss over
heterostucture barriers.
Illustration
• Radiative recombination probability needs to
be increased and non-radiative recombination
probability needs to be decreased.
• High carrier concentration in the active
region, achieved through double
heterostructure (DH) design, improves
radiative recombination.
R=Bnp
• DH design is used in all high efficiency
designs today.
High Internal Efficiency Designs
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Doping of the active regions and that of the cladding regions
strongly affects internal efficiency.
Active region should not be heavily doped, as it causes carrier spillover in to the confinement regions decreasing the radiative
efficiency
Doping levels of 1016-low 1017 are used, or none at all.
P-type doping of the active region is normally done due to the
larger electron diffusion length.
Carrier lifetime depends on the concentration of majority carriers.
In low excitation regime , the radiative carrier lifetime decreases
with increasing free carrier concentration.
Hence efficiency increases with doping.
At high concentration, dopants induce defects acting as
recombination centers.
P-N Junction Displacement
• Displacement of the P-N junction causes
significant change in the internal
quantum efficiency in DH LED
structures.
• Dopants can redistribute due to
diffusion, segregation or drift.
Doping of Confinement Regions
• Resistivity of the confinement regions should
be low so that heating is minimal.
• High p-type conc. in the cladding region keeps
electrons in the active region and prevents
them from diffusing in to the confinement
region.
• Electron leakage out of the active region is
more severe than hole leakage.
Non-radiative Recombination
Illustration
• The concentration of defects which cause deep levels
in the active region should be minimum.
• Also surface recombination should be minimized, by
keeping all surfaces several diffusion lengths away
from the active region.
• Mesa etched LEDs and lasers where the mesa etch
exposes the active region to air, have low internal
efficiency due to recombination at the surface.
• Surface recombination also reduces lifetime of LEDs.
Lattice matching
Lattice Matching
Lattice Matching
High Extraction Efficiency Structures
Illustration
• Shaping of the LED die is critical to
improve their efficiency.
• LEDs of various shapes; hemispherical
dome, inverted cone, truncated cones etc
have been demonstrated to have better
extraction efficiency over conventional
designs.
• However cost increases with complexity.
High Extraction Efficiency Structures
Illustration
• The TIP LED employs advanced LED die
shaping to minimize internal loss mechanisms.
• The shape is chosen to minimize trapping of
light.
• TIP LED is a high power LED, and the luminous
efficiency exceeds 100 lm/W.
• TIP devices are sawn using beveled dicing
blade to obtain chip sidewall angles of 35o to
vertical.
Emission Spectrum of RGB LED
White Light LED
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White light can be generated in several different ways.
One way is to mix to complementary colors at a certain power ratio.
Another way is by the emission of three colors at certain wavelengths
and power ratio.
Most white light emitters use an LED emitting at short wavelength and
a wavelength converter.
The converter material absorbs some or all the light emitted by the
LED and re-emits at a longer wavelength.
Two parameters that are important in the generation of white light are
luminous efficiency and color rendering index.
It is shown that white light sources employing two monochromatic
complementary colors result in highest possible luminous efficiency.
WLED (Continued)
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Wavelength converter materials include phosphors, semiconductors and
dyes.
The parameters of interest are absorption wavelength, emission
wavelength and quantum efficiency.
The overall energy efficiency is given by
η = ηext(λ1/ λ2)
Even if the external quantum efficiency is 1, there is always an energy
loss associated with conversion.
Common wavelength converters are phosphors, which consist of an
inorganic host material doped with an optically active element.
A common host is Y3Al5O12.
The optically active dopant is a rare earth element, oxide or another
compound.
Common rare earth elements used are Ce, Nd, Er and Th.
Absorption & Emission of
Phosphor