Page 123 - Photonics Essentials an introduction with experiments

Light-Emitting Diodes

Light-Emitting Diodes 117

face of an LED structure is planar, and b) the light from recombina-
tion is emitted uniformly over 4 steradians. It is clear that we could
improve the external efficiency of LEDs if we could find a way to re-
place these assumptions. In this section, we explore ways to a) defeat
the restrictions seemingly imposed by Fresnel’s equations and b)
change the angular distribution of light.
Fresnel’s equation is straightforward to apply to a simple, flat in-
terface between two materials. Under these circumstances, it is quite
accurate. Analysis of reflection and transmission for rough interfaces
is a more difficult case, particularly when the roughness has dimen-
sions similar to the wavelength of light. Then Fresnel’s equations can
no longer be used, because it becomes impossible to define the angle
between the light ray and the interface. So, examination of this case
has been largely ignored. As we will see shortly, this was a mistake.
New thinking has shown that exploitation of this situation is the back
door that allows you to beat the limits of Fresnel’s equations.
The escape angle of the LED can be enlarged by capping the diode
with a transparent material such as an acrylic plastic, the refractive
index of which will be greater than 1, typically 1.5. This improves the
fraction of light that can escape by nearly a factor of two. The inter-
face between the plastic and the air can be shaped into a hemisphere.
This geometry allows almost all the light to exit normal to the surface
with only 5% losses. The hemispherical cap acts like a lens and more
of the light is focussed in the forward direction, as shown in Fig 6.9.
The example of Fig. 6.9 shows that it is possible to recover and use
some of the emitted light that is not propagating in the forward direc-

Figure 6.9. The amount of light emitted in the forward direction can be increased dur-
ing the packaging operation by deposition of a hemispherical lens on the LED surface.
This tends to project more of the emitted light in the forward direction.

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