Electrostatic Mechanism of Emission Enhancement in Hybrid Metal-semiconductor Light-emitting Heterostructures Page: 86
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e 1 1 1
( E re,hl Ire,eiI Ire,hil
e( 1 1 1
E R+I + 12re. I ? + (2 rm + R_) l
e 1 1 1
E R+ 2re-2 2
(R+ ,j)2 + ((2rcm+R_) z)
The x (z) component of R+,_ is given by R+,_Cos(O) (R+,_Sin(O)). Furthermore,
we assume that the center of mass of the electron-hole pair is rcm = d ,. Making these
substitutions into Eq. (A2.6) yields:
e 1 1 1
e R(++2re' -J(R+ .)2 + ((2rcm + R_)) z)
S 1 1 (A.7)
= + -
E R+ 2(d + r_Sin(6)) JR2Cos2() + (2 d + R_Sin(6))2
This time the potential experienced by the hole Ph may be obtained by letting r
- -r+ and e -- -e.
The electric field, in turn, is simply the minus the gradient of the potential.
Since we are interested specifically in the attraction towards the surface, we will only
consider the z-component of the electric field here. For the electron we have:
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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/m1/96/: accessed October 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .