Zero Phonon and Phonon Assisted Radiative Transition Rates Based on Finite Potential well Approximation for Silicon Nanocrystallite Embedded in Silicon Oxide
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Date
2009-06
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Addis Ababa University
Abstract
The purpose of this thesis was to study phonon assisted and zero phonon radiative
lifetimes of electron-hole pair which are excited and recombine inside nc-Si, on the
basis of more realistic assumption of finite potential well and envelope wave approximations
for oxidized PS and nc-Si inside SiO2. Finite potential well approximation
results the spread of conduction and valence band edge wave functions in to SiO2.
Solving time independent Schr¨odinger equation in the two materials and applying
matching boundary condition at the interface for envelope wave function part; we
found bandgap energy closer to experimental results that increase at lower rate as
we shrink the size of nc-Si compared to infinitely deep potential well approximation.
Radiative rates for both zero phonon and phonon assisted transitions are calculated
with the newly developed wave functions and by separately calculating momentum
overlap factor and incorporating it into momentum matrix elements by hand. New
radiative lifetime estimation in the order of nanosecond for nc-Si size below 2 nm is
found. We also found μs order of life time for phonon assisted recombination rate
below 2 nm size of nc-Si. However, the value we got for phonon assisted radiative
transition rate does not show any significant difference from infinitely deep potential
well approximation results
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Keywords
Transition Rates Based on Finite Potential