Electrostatic Mechanism of Emission Enhancement in Hybrid Metal-semiconductor Light-emitting Heterostructures Page: 43
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t(r, ze, z) = 1 4e(Ze)h(Zh)Q(r) (3
We choose 9(r) = 2/a0e-r/ao as a trial wavefunction, and then minimize the
energy of the exciton using the exciton Bohr radius ao as the variational parameter:
Eex = min ( IHIP)
=min [f9* (He + Hao- F (Ze - zh) (4.3.10)
- T I dr dze dzh
E1r2 -+ (Ze -Zft)2
While this minimization problem seems quite complex, it turns out that the only
portion of the integral which varies with ao is the excitonic portion of the Hamiltonian, -
e2/E 112. The other parts of the Hamiltonian depend only upon the z components of the
7 InGaN D
. T:::::+ dqw
Figure 4.2 Schematic diagram of the structure
used for the dispersion calculations. The numbers
on the left represent the indices used for the matrix
of each region of the heterostructure.
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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/m1/53/: accessed January 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .