Electrostatic Mechanism of Emission Enhancement in Hybrid Metal-semiconductor Light-emitting Heterostructures Page: 85
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rei = re" (22- ) = (rcm + r_). (22- )
rhi = rh " (ii - 2) = (rcm - r+) . ( - 2) (A.4)
From these four vectors (re, rh, rei, rhi) we can then define the vectors describing
the distances between all the pairs of charges except the image charges, which cannot
exert a force upon each other. In calculating the vectors between the real charges and
their images, we will make use of the identity transformation to simplify notation.
re,h = re - rh = (rcm + r_) - (rcm - r+)
= r_ + r R+
re,ei = re - rei
= re" (aa + 2) - re " ( - )
= re (2i + ~ - ii + 2)
= 2 re. ~
re,hi = re - rhi (A.5)
- re ( XX + zz) -rh " (X- zz)
= (re - rh) -i"? + (re + rh) zz
= R+ -i + (2 rcm+r_ - r+) "
= R+. - + (2rcm+R_) ZZ
The remaining two vectors (rh,hi, rh,ei) can be obtained from those for the electron
by letting e - h and 22? - -i?. For convenience we have defined R+ and R_ to
represent the quantities (r_ + r+) and (r_- r+) respectively.
The electric potential experienced by the electron is given by the the equation:
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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/m1/95/: accessed October 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .