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Plank Formula. The 1900 quantum hypothesis by Max Planck that any energy is radiated and absorbed in quantities divisible by discrete ‘energy elements’, E,

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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 frequencyν with which they each individually radiate energy, as defined by the following formula:
  • where h is Planck's Action Constant.
1 dimensional quantum well
1-Dimensional Quantum Well
  • For the 1-dimensional case in the x direction, the time-independent Schrödinger equation can be written as:
internal external quantum efficiency
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)


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

  • 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
  • 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
  • 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
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.
  • 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.


  • DH design is used in all high efficiency designs today.
high internal efficiency designs
High Internal Efficiency Designs
  • 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 spill-over 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
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
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.
  • 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.
  • 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.
  • 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.
white light led
White Light LED
  • 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
WLED (Continued)
  • 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.