Electrostatic Mechanism of Emission Enhancement in Hybrid Metal-semiconductor Light-emitting Heterostructures Page: 42
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presented in Eq. 4.3.5 gives a single energy level for the electron and hole at 402.5 and
176.3 meV above the InGaN bandgap respectively By comparison, the first energy
levels for a square well (Fpz = 0) would be 141.6 and 30.1 meV respectively. While it
would seem that the energies have in fact increased in the presence of the electric field,
this is not the case. The bandgap before the application of the internal electric field is Eg
+ Ee + Eh = 2.524 eV + 141.6 meV + 30.1 meV = 2.696 eV. The bandgap in the
presence of the piezoelectric field, however, is Eg + Ee + Eh - Epz=2.524 eV + 402.5 meV
+ 176.3 meV - 656.9 meV = 2.446 eV. Therefore the presence of the internal
piezoelectric field results in a red-shift in the emission energy of roughly 250 meV.
Using these calculated energies we can then calculate the various interface
constants A-F, and then normalize the wavefunctions such that f4*(z)p(z)dz = 1. Doing
so yields the wavefunctions depicted in Figure 4.1b. I wish to point out here that the
electron and hole wavefunctions have been separated to opposite sides of the QW by
the internal electric field. This separation due to the QCSE is the origin of long decay
lifetime found in InGaN/GaN QWs, as the recombination rate is proportional to the
product of the electron and hole wavefunctions 4Je(Ze) *Wlh(Zh), which is obviously
significantly lower in the presence of the QCSE than for a square well.
Now that we have 4Je(Ze) and 1Wh(zh), we may now calculate the full exciton
wavefunction W(r,ze,zh). This is done using the method outlined in Ref . We begin by
assuming that the exciton wavefunction is separable into the electron and hole
wavefunctions in the z direction, and a hydrogenic wavefunction in the plane
perpendicular to z:
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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/m1/52/: accessed December 13, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .