Electrostatic Mechanism of Emission Enhancement in Hybrid Metal-semiconductor Light-emitting Heterostructures Page: 90
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For light exiting from a high index-of-refraction material to a lower index material,
there will be an angle Oc at which light ceases to exit the material. All angles of emission
greater than Oc will result in the total internal reflection of the emitted light back into the
sample. Fig B.1 shows the critical angle and emission/internal reflection depending on
whether 0 > 0c or < Oc. In measuring the angle-dependent intensity of a sample, we must
account for the fact that some portion of the light is internally reflected by the dielectric-
air interface. Furthermore, we must keep in mind that, in our experiment, the angle of
measurement is 0' and not 0. Therefore in the following equations we will use Snell's
law to put 0 in terms 0'.
0 = Sin-' nAir Sin(O')
GaN I - '
Figure B.1 Schematic diagram of the path
of a light ray from a source outwards at thre(
angles: e, e8 and >ec. Only light emitted at
< ec will be measured can exit the sample
and be measured. The angle-dependen
intensity measurement will see the light a:
having been emitted at angle e' instead of 8.
In order to calculate the reflection
coefficient at the boundary we will make
use of Frensel equations, which allow us
to calculate the reflection R as a function
of the incident and transmitted angles,
along with the indices of refraction of the
two materials involved. For s-polarized
e light at the interface (E perpendicular to
e the plane-of-incidence) the reflection
s coefficient is:
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Llopis, Antonio. Electrostatic Mechanism of Emission Enhancement in Hybrid Metal-semiconductor Light-emitting Heterostructures, dissertation, May 2012; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc115113/m1/100/: accessed January 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .