Electrostatic Mechanism of Emission Enhancement in Hybrid Metal-semiconductor Light-emitting Heterostructures Page: 51
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as a function of position within the heterostructure.
4.4 S and Strain
The Huang-Rhys parameter S then can be calculated by substituting the results
of the calculations of wm(q) and Fm(q-L,ze,h) along with the exciton wavefunction Psi into
Eq. 4.3.2 and then into Eq. 4.3.1. While this gives us a value of S for the system, I have
not explained yet how to derive S as a function of the biaxial strain Exx for the system. In
these equations the phonon frequency enters via the phonon dispersion relation wm(q)
in both Fm(q-L,ze,h) and S itself. The phonon frequencies in the system are a function of
the strain and change at a rate proportional to the phonon deformation potentials
(PDPs) aA, bA for a given phonon mode. The change in the phonon frequency of mode A
is given as AWA= 2 aA Exx + bA Ezz, assuming that Eyy = Exx . If the QW has been grown
pseudomorphic to the GaN then we can assume biaxial strain and can thereby relate
the two remaining strain components in the active region as such Ezz = 2 Exx C311C33 .
Together these allow us to define AA(Exx) = 2(aA + bA C31/C33) Exx , i.e. the change in
phonon frequency as a function of the biaxial strain in the system. In our system, the
relevant phonon modes for the I-LO phonon interactions are the A1[LO] and E1[LO]
modes. For our calculations I have derived the A1[LO] and E1[LO] PDPs using a
"Vegard's Law"-like formula from published values of the PDPs for GaN and InN. Since
the E1 [LO] and A1[LO] mode PDPs for InN are poorly covered in the literature, I have
instead used the PDPs for the E2 mode and the method described by Briot, et al. 
for relating AWE[L],, to AWEH. Table 4.3 lists the values of the PDPs for the modes used
in our calculations of S(Exx).
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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/m1/61/: accessed December 11, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .