Electrostatic Mechanism of Emission Enhancement in Hybrid Metal-semiconductor Light-emitting Heterostructures Page: 65
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Here e represents the elementary charge, Pn represents the mobility of the
carriers, D the diffusion coefficient of the carriers, and E an electric field present within
When inserted into Eq. 5.4.2 the first term of the carrier transport equations
represents the drift of carriers due to the presence of an external electric field, and the
second represents the diffusion of carriers from regions of high concentration towards
regions of lower concentration. Substituting in Eq. 5.4.2 into Eq. 5.4.1 and replacing R
with the total recombination rate from Eq. 5.3.2 gives us:
an e Dn
= Dn V2n+ TV-(nE)-An-Bnp+Gn
Op e D
- D V2p+I V- (pE)-Ap-Bnp+G,
Note that we have also rewritten the mobility pn in terms of the diffusion
coefficient using the Einstein relation Dn = JnkBT / e. In addition, we have used the
radiative recombination rate in its proper form Bnp, as the recombination rate is
proportional to the product of the carrier concentrations .
This set of coupled second-order non-linear partial differential equation (PDE)
describes the motion of carriers within the quantum well in the presence of an electric
field E, which in our system represents the electric field of the induced image charge,
and neglecting for the moment the geometry of the NP, essentially goes as -e/4r2,
where r is the distance of the carrier from the NP. In order to simplify the problem, we
assume that n p, which yields the following time-dependent PDE:
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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/m1/75/: accessed April 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .