Electrostatic Mechanism of Emission Enhancement in Hybrid Metal-semiconductor Light-emitting Heterostructures Page: 84
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Let us begin by defining the position vectors for the electron (re), the hole (rh) and
their images (rei, rhi). The diagram in Figure A.1 shows the relationships of the
various vectors we'll use in this derivation. We define the position of the electron and
hole in terms of the center of mass of the electron-hole pair as such:
re = rcm + r
rh --= rcm - r+ (A1)
Here rcm is the vector describing the position of the center of mass and r. and r the
relative positions of the electron and hole.
Next we note that the relationship between the position vectors of the electron
and hole and their images are related by a mirror transformation across the x-axis. This
transformation leaves the x-component of the vector untouched and inverts the z-
component. We will write the transformation
el" as such:
;' , r' - r ."(X - z)S (A.2)
At this point we will also define the
- . .. - identity transformation for future use:
rcm r' = r."(2+1)-r (A.3)
Using the mirror transformation given
by Eq. (A2.2) we can now define the vectors
which describe the positions of the electron
Figure A.1 Schematic Diagram of the
exciton used for this derivation. and hole images as such:
Here’s what’s next.
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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/m1/94/: accessed March 1, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .