Electrostatic Mechanism of Emission Enhancement in Hybrid Metal-semiconductor Light-emitting Heterostructures Page: 47
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) = M9,M ...Mo (o V
Of which the component v12,2 B0 = 0 provides us with the dispersion relation.
Since B0 = 0 would result in a trivial solution the modes must be described by 1vM2,2=0.
As this equation for the dispersion relation has no analytical solutions, so the solutions
were found using numerical methods. Figure 4.3 shows the calculated solutions using
the parameters presented in Table 4.2.
Table 4.2 Material parameters used to calculate the phonon dispersion relation. InN and
GaN values from Ref. , InGaN values calculated using Vegard's Law.
4.3.3 Aj,B - The Interface Constants
The step in calculating S is obtaining the interface constants used in the transfer
matrices in Eqs. 4.3.14 and 4.3.15. Per Ref. , the constants in Eq. 4.3.14 may all be
rewritten in terms of one constant, Bo as such:
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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/m1/57/: accessed November 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .