Electrostatic Mechanism of Emission Enhancement in Hybrid Metal-semiconductor Light-emitting Heterostructures Page: 38
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Dm(q1) = -ffd2r dzedzhT(r,ze, zh)22 (4(q1)\.3.2)
x (ei'.-r(mh/M) Fm(qz1,Z) - e-iq r(me/M) 1m(q1,ze))
There are three main components in Eq. 4.3.2 which need to be determined in order to
calculate Dm (qi), and hence S: The exciton wavefunction W(r,ze,Zh), the phonon
dispersion relation wm(q), and the electron-phonon coupling strength Fm(q-L,Ze,h)-
4.3.1 The Exciton Wavefunction
Let us begin by calculating the wavefunction of an e-h pair within an
In0.20Ga0.80N/GaN QW. Solving for the wavefunction involves three steps, firstly
calculating the electron and hole wavefunctions independently, then assuming a
hydrogenic envelope wavefunction and minimizing the energy of the exciton to find the
exciton Bohr radius.
As previously discussed in 2.4, wurtzite InGaN/GaN QWs exhibit an internal
electric field which arises due to the piezoelectric nature of InGaN. This electric field is
oriented along the c-axis of the structure which results in a non-square well potential.
This "bending" of the potential in the QW due to the internal electric field is known as the
quantum-confined Stark effect  and results in a spatial separation of the electron
and hole wavefunctions as well as a decrease in the effective bandgap of the QW. In
order to find the energies and wavefunctions of the electron and hole within the QW we
must solve Schrodinger's equation:
Here’s what’s next.
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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/m1/48/: accessed April 25, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .