2019-11-04 15:34:25 +00:00
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#LyX 2.3 created this file. For more info see http://www.lyx.org/
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2019-11-14 10:53:43 +00:00
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2019-11-11 13:39:57 +00:00
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\end_header
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\begin_body
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\begin_layout Title
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EEE3037 Nanotechnology Coursework
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\end_layout
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\begin_layout Author
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6420013
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\end_layout
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2019-11-11 20:00:41 +00:00
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\begin_layout Part
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2019-11-04 15:34:25 +00:00
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Quantum Engineering Design
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\end_layout
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2019-11-11 20:00:41 +00:00
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\begin_layout Section
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Structure Design
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\end_layout
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2019-11-11 13:39:57 +00:00
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\begin_layout Standard
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In order to design a quantum well which emits light of wavelength 1.55μm,
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a well material must be chosen such that an interband electron transition
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emits photons of this wavelength.
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\end_layout
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\begin_layout Standard
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This band gap energy can be found from the equation
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\end_layout
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\begin_layout Standard
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\begin_inset Formula
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\[
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E=hf
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\]
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\end_inset
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\end_layout
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\begin_layout Standard
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When considering photons,
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\begin_inset Formula $f$
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\end_inset
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can be substituted with
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\end_layout
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\begin_layout Standard
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\begin_inset Formula
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\[
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f=\frac{c}{\lambda}
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\]
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\end_inset
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\end_layout
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\begin_layout Standard
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2019-11-12 11:43:05 +00:00
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Therefore in order to find the
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\begin_inset Formula $E$
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\end_inset
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in terms of wavelength
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\end_layout
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\begin_layout Standard
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\begin_inset Formula
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\[
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E=\frac{hc}{\lambda}
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\]
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\end_inset
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\end_layout
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\begin_layout Standard
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Returning to the specifications, this allows 1.55μm to be expressed as 1.28x10
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\begin_inset script superscript
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\begin_layout Plain Layout
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-19
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\end_layout
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\end_inset
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2019-11-12 16:23:10 +00:00
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J or approximately 0.800 eV.
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\end_layout
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\begin_layout Standard
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This energy value will be the same as the total interband transition for
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the well from the first confined hole energy level to the first confined
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electron enery level,
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\end_layout
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\begin_layout Standard
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\begin_inset Formula
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\begin{equation}
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E_{g,transition}=E_{1h}+E_{g}+E_{1e}\thickapprox0.800\unit{eV}\label{eq:Energy-Gap-Sum}
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\end{equation}
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\end_inset
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\end_layout
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\begin_layout Standard
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see figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:Well-Band-structure"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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.
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\end_layout
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\begin_layout Standard
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\begin_inset Float figure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\align center
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\begin_inset Graphics
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filename WellBandStructure.png
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lyxscale 40
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width 50col%
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\end_inset
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\begin_inset Caption Standard
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\begin_layout Plain Layout
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Band structure of an AlGaAs/GaAs/AlGaAs quantum well including discrete
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confined energy levels
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\begin_inset CommandInset citation
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LatexCommand cite
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key "ieee_s6824198"
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literal "false"
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\end_inset
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\begin_inset CommandInset label
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LatexCommand label
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name "fig:Well-Band-structure"
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Formula $E_{g}$
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\end_inset
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2019-11-12 11:43:05 +00:00
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should be the dominant term in this equation and as such when investigating
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suitable materials the bulk band gap should be close to but lower than
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0.8eV.
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\end_layout
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\begin_layout Standard
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Ternary alloys were investigated in order to allow precise control over
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the lattice constants and band gap by varying the composition ratio.
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\end_layout
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\begin_layout Standard
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Indium gallium arsenide (In
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\begin_inset script subscript
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\begin_layout Plain Layout
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\begin_inset Formula $x$
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\end_inset
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\end_layout
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\end_inset
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Ga
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\begin_inset script subscript
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\begin_layout Plain Layout
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\begin_inset Formula $(1-x)$
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\end_inset
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\end_layout
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\end_inset
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2019-11-11 23:13:08 +00:00
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As) as a well material with indium phosphide (InP) as a barrier material
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would provide a suitable combination assuming that a composition ratio
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\begin_inset Formula $x$
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\end_inset
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could be found that satisfied the two conditions of having the required
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bulk band gap and being lattice matched.
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A common ratio in industry is In
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\begin_inset script subscript
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\begin_layout Plain Layout
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0.53
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\end_layout
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\end_inset
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Ga
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\begin_inset script subscript
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\begin_layout Plain Layout
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0.47
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\end_layout
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\end_inset
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As and as such this was tested first.
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\end_layout
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2019-11-11 20:00:41 +00:00
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\begin_layout Subsection
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Lattice Match
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\end_layout
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\begin_layout Standard
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Lattice matching is the process of ensuring that two crystalline structures
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are of similar dimensions in order to decrease strain at the interface
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between the two materials.
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This is particularly important for quantum wells formed through epitaxial
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growth as strain introduced between such thin layers can cause defects
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which ultimately negatively affect it's electronic properties.
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\end_layout
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\begin_layout Standard
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The lattice constants between the barrier and well materials should be as
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close as is deemed acceptable for the application.
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The lattice constants for the prospective materials are shown in table
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "tab:Lattice-constants"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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.
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\end_layout
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\begin_layout Standard
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\begin_inset Float table
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\align center
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\begin_inset Tabular
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<lyxtabular version="3" rows="4" columns="2">
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<features tabularvalignment="middle">
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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Material
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
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2019-11-11 15:33:04 +00:00
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Lattice Constant, α (Å)
|
2019-11-11 13:39:57 +00:00
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\end_layout
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\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
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InAs
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\end_layout
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\end_inset
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</cell>
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
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6.0583
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\end_layout
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\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
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GaAs
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\end_layout
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\end_inset
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</cell>
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
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2019-11-11 15:33:04 +00:00
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5.6532
|
2019-11-11 13:39:57 +00:00
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\end_layout
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\end_inset
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</cell>
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<row>
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
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InP
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\end_inset
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</cell>
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
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2019-11-11 15:33:04 +00:00
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5.8687
|
2019-11-11 13:39:57 +00:00
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\end_layout
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\end_inset
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</cell>
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</row>
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</lyxtabular>
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\begin_inset Caption Standard
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\begin_layout Plain Layout
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Lattice constants for prospective well and barrier materials
|
2019-11-11 15:33:04 +00:00
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\begin_inset CommandInset citation
|
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LatexCommand cite
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key "new_semiconductor_materials_archive"
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literal "false"
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\end_inset
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2019-11-11 13:39:57 +00:00
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\begin_inset CommandInset label
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LatexCommand label
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name "tab:Lattice-constants"
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
|
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|
In order to compute a compound lattice constant for InGaAs, Vegard's law
|
|
|
|
|
can be applied.
|
|
|
|
|
Vegard's law provides an approximation for the lattice constant of a solid
|
2019-11-12 11:43:05 +00:00
|
|
|
|
solution by finding the weighted average of the individual lattice constants
|
2019-11-11 15:33:04 +00:00
|
|
|
|
by composition ratio and is given by:
|
|
|
|
|
\end_layout
|
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|
\begin_layout Standard
|
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|
\begin_inset Formula
|
|
|
|
|
\[
|
2019-11-11 20:00:41 +00:00
|
|
|
|
\alpha_{A_{(1-x)}B_{x}}=\left(1-x\right)\alpha_{A}+x\alpha_{B}
|
2019-11-11 15:33:04 +00:00
|
|
|
|
\]
|
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\end_inset
|
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\end_layout
|
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|
\begin_layout Standard
|
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|
|
Applying this to the prospective well material gives the following,
|
|
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|
|
\end_layout
|
|
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|
|
\begin_layout Standard
|
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|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
\alpha_{In_{0.53}Ga_{0.47}As}=0.53\cdotp6.0583+0.47\cdotp5.6532=5.8679
|
|
|
|
|
\]
|
|
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|
|
\end_inset
|
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\end_layout
|
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\begin_layout Standard
|
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|
|
|
This shows that to 4 significant figures the composition of InGaAs is lattice
|
|
|
|
|
matched to InP to within 0.001Å which is sufficient for this application.
|
2019-11-11 13:39:57 +00:00
|
|
|
|
\end_layout
|
|
|
|
|
|
2019-11-11 20:00:41 +00:00
|
|
|
|
\begin_layout Subsection
|
2019-11-11 13:39:57 +00:00
|
|
|
|
Band Gap
|
|
|
|
|
\end_layout
|
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|
|
2019-11-11 20:00:41 +00:00
|
|
|
|
\begin_layout Standard
|
|
|
|
|
Vegard's law can also be used to approximate the band gap of a ternary alloy,
|
|
|
|
|
such as InGaAs.
|
|
|
|
|
The band gaps at 300K for each alloy can be seen in table
|
|
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|
|
\begin_inset CommandInset ref
|
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|
LatexCommand ref
|
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|
|
reference "tab:Band-gaps"
|
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|
|
plural "false"
|
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|
caps "false"
|
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|
noprefix "false"
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|
\end_inset
|
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.
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\end_layout
|
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\begin_layout Standard
|
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|
\begin_inset Float table
|
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|
wide false
|
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|
|
sideways false
|
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|
|
status open
|
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|
\begin_layout Plain Layout
|
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|
\align center
|
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|
\begin_inset Tabular
|
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|
|
<lyxtabular version="3" rows="4" columns="2">
|
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|
<features tabularvalignment="middle">
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<column alignment="center" valignment="top">
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<column alignment="center" valignment="top">
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<row>
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
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Material
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\end_inset
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</cell>
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
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Band Gap at 300K, E
|
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\begin_inset script subscript
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\begin_layout Plain Layout
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g
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\end_inset
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(eV)
|
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\end_layout
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\end_inset
|
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</cell>
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</row>
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<row>
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
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\begin_inset Text
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\begin_layout Plain Layout
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InAs
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\end_layout
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\end_inset
|
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|
</cell>
|
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|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
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\begin_inset Text
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\begin_layout Plain Layout
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0.35
|
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\end_layout
|
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\end_inset
|
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</cell>
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</row>
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<row>
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
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|
\begin_inset Text
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\begin_layout Plain Layout
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GaAs
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\end_layout
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\end_inset
|
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</cell>
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
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\begin_inset Text
|
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\begin_layout Plain Layout
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1.42
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\end_layout
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\end_inset
|
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</cell>
|
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</row>
|
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<row>
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|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
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\begin_inset Text
|
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\begin_layout Plain Layout
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InP
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\end_layout
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\end_inset
|
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</cell>
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
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|
\begin_inset Text
|
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\begin_layout Plain Layout
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1.34
|
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|
\end_layout
|
|
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|
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|
|
|
\end_inset
|
|
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|
</cell>
|
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|
|
</row>
|
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|
|
</lyxtabular>
|
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|
\end_inset
|
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|
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|
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|
\end_layout
|
|
|
|
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|
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|
|
\begin_layout Plain Layout
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
Band gaps for prospective well and barrier materials
|
|
|
|
|
\begin_inset CommandInset citation
|
|
|
|
|
LatexCommand cite
|
|
|
|
|
key "new_semiconductor_materials_archive"
|
|
|
|
|
literal "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\begin_inset CommandInset label
|
|
|
|
|
LatexCommand label
|
|
|
|
|
name "tab:Band-gaps"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
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|
\end_layout
|
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\end_inset
|
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\end_layout
|
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\end_inset
|
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|
\end_layout
|
|
|
|
|
|
|
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|
|
\begin_layout Standard
|
|
|
|
|
In this case the band gap approximates to,
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
E_{g,In_{0.53}Ga_{0.47}As}\thickapprox0.53\cdotp0.35+0.47\cdotp1.42\thickapprox0.85\unit{eV}
|
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
However the band gap has been experimentally found to be 0.75eV
|
|
|
|
|
\begin_inset CommandInset citation
|
|
|
|
|
LatexCommand cite
|
|
|
|
|
key "aip_complete10.1063/1.322570"
|
|
|
|
|
literal "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
.
|
|
|
|
|
This implies that the linear relationship provided by Vegard's law is not
|
|
|
|
|
accurate enough and in this case a modified version including a bowing
|
|
|
|
|
parameter
|
|
|
|
|
\begin_inset Formula $b$
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
should be used,
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
E_{g,total}=xE_{g,a}+\left(1-x\right)E_{g,b}-bx\left(1-x\right)
|
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
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|
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|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
For this application, however, the experimentally determined value will
|
|
|
|
|
be used.
|
|
|
|
|
This value is ideal for this application as it is comparable to and slightly
|
|
|
|
|
lower than the required 0.8eV energy value.
|
2019-11-04 15:34:25 +00:00
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Subsection
|
2019-11-11 20:00:41 +00:00
|
|
|
|
Width Calculation
|
2019-11-04 15:34:25 +00:00
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
2019-11-11 20:00:41 +00:00
|
|
|
|
Having found two materials that are lattice matched with a suitable band
|
|
|
|
|
gap value, the final calculation is that of the quantum well width.
|
2019-11-12 11:43:05 +00:00
|
|
|
|
In order to calculate this value, the equation for confined energy levels
|
|
|
|
|
within an infinite quantum well will be used,
|
2019-11-11 20:00:41 +00:00
|
|
|
|
\end_layout
|
|
|
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|
|
|
|
|
|
\begin_layout Standard
|
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|
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|
|
|
|
|
|
\emph on
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\begin{equation}
|
2019-11-11 23:13:08 +00:00
|
|
|
|
E_{n}=\frac{n^{2}\pi^{2}\mathcal{\text{\emph{ħ}}}^{2}}{2mL^{2}}\label{eq:Energy-levels}
|
2019-11-11 20:00:41 +00:00
|
|
|
|
\end{equation}
|
|
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|
|
|
2019-11-04 15:34:25 +00:00
|
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|
|
\end_inset
|
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|
|
\end_layout
|
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|
|
2019-11-11 20:00:41 +00:00
|
|
|
|
\begin_layout Standard
|
|
|
|
|
Referring back to equation
|
|
|
|
|
\begin_inset CommandInset ref
|
|
|
|
|
LatexCommand ref
|
|
|
|
|
reference "eq:Energy-Gap-Sum"
|
|
|
|
|
plural "false"
|
|
|
|
|
caps "false"
|
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|
|
|
noprefix "false"
|
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|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
, the terms for the first electron and hole energy levels can each be replaced
|
|
|
|
|
with equation
|
|
|
|
|
\begin_inset CommandInset ref
|
|
|
|
|
LatexCommand ref
|
|
|
|
|
reference "eq:Energy-levels"
|
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|
|
|
plural "false"
|
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|
|
caps "false"
|
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|
|
noprefix "false"
|
|
|
|
|
|
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|
|
\end_inset
|
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|
|
as seen below,
|
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|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
2019-11-12 11:43:05 +00:00
|
|
|
|
E_{g,transition}=0.8\unit{eV}=E_{1h}+E_{g,InGaAs}+E_{1e}=\frac{1^{2}\pi^{2}\text{\emph{ħ}}^{2}}{2m_{h}^{*}L^{2}}+E_{g,InGaAs}+\frac{1^{2}\pi^{2}\text{\emph{ħ}}^{2}}{2m_{e}^{*}L^{2}}
|
2019-11-11 20:00:41 +00:00
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
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|
|
\end_layout
|
|
|
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|
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|
|
|
\begin_layout Standard
|
|
|
|
|
With the experimentally determined value for
|
2019-11-12 11:43:05 +00:00
|
|
|
|
\begin_inset Formula $E_{g,,InGaAs}$
|
2019-11-11 20:00:41 +00:00
|
|
|
|
\end_inset
|
|
|
|
|
|
2019-11-12 11:43:05 +00:00
|
|
|
|
this equation becomes
|
2019-11-11 20:00:41 +00:00
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
2019-11-12 11:43:05 +00:00
|
|
|
|
0.8\unit{eV}=\frac{\pi^{2}\text{\emph{ħ}}^{2}}{2m_{h}^{*}L^{2}}+0.75\unit{eV}+\frac{\pi^{2}\text{\emph{ħ}}^{2}}{2m_{e}^{*}L^{2}}
|
2019-11-11 20:00:41 +00:00
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
0.05\unit{eV}=\frac{\pi^{2}\text{\emph{ħ}}^{2}}{2L^{2}}\left(\frac{1}{m_{h}^{*}}+\frac{1}{m_{e}^{*}}\right)
|
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
L=\sqrt{\frac{\pi^{2}\text{\emph{ħ}}^{2}}{2\cdotp(0.05\unit{eV})}\cdotp\left(\frac{1}{m_{h}^{*}}+\frac{1}{m_{e}^{*}}\right)}
|
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
As a frequently studied composition due to it's favourable structural parameters
|
|
|
|
|
with InP, The charge carrier effective masses of In
|
|
|
|
|
\begin_inset script subscript
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
0.53
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
Ga
|
|
|
|
|
\begin_inset script subscript
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
0.47
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
As have been found experimentally to be as shown in table
|
|
|
|
|
\begin_inset CommandInset ref
|
|
|
|
|
LatexCommand ref
|
|
|
|
|
reference "tab:Effective-masses"
|
|
|
|
|
plural "false"
|
|
|
|
|
caps "false"
|
|
|
|
|
noprefix "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
.
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Float table
|
|
|
|
|
wide false
|
|
|
|
|
sideways false
|
|
|
|
|
status open
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
\align center
|
|
|
|
|
\begin_inset Tabular
|
|
|
|
|
<lyxtabular version="3" rows="4" columns="2">
|
|
|
|
|
<features tabularvalignment="middle">
|
|
|
|
|
<column alignment="center" valignment="top">
|
|
|
|
|
<column alignment="center" valignment="top">
|
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|
|
|
<row>
|
|
|
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
|
|
|
\begin_inset Text
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
Charge Carrier
|
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|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
</cell>
|
|
|
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
|
|
|
\begin_inset Text
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
Effective mass ratio in In
|
|
|
|
|
\begin_inset script subscript
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
0.53
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
Ga
|
|
|
|
|
\begin_inset script subscript
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
0.47
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
As (
|
|
|
|
|
\begin_inset Formula $\frac{m^{*}}{m^{0}}$
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
)
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
</cell>
|
|
|
|
|
</row>
|
|
|
|
|
<row>
|
|
|
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
|
|
|
\begin_inset Text
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
Electron
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
</cell>
|
|
|
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
|
|
|
\begin_inset Text
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
0.041
|
|
|
|
|
\begin_inset CommandInset citation
|
|
|
|
|
LatexCommand cite
|
|
|
|
|
key "aip_complete10.1063/1.90860"
|
|
|
|
|
literal "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
</cell>
|
|
|
|
|
</row>
|
|
|
|
|
<row>
|
|
|
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
|
|
|
\begin_inset Text
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
Light Hole
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
</cell>
|
|
|
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
|
|
|
\begin_inset Text
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
0.051
|
|
|
|
|
\begin_inset CommandInset citation
|
|
|
|
|
LatexCommand cite
|
|
|
|
|
key "aip_complete10.1063/1.92393"
|
|
|
|
|
literal "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
</cell>
|
|
|
|
|
</row>
|
|
|
|
|
<row>
|
|
|
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
|
|
|
\begin_inset Text
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
Heavy Hole
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
</cell>
|
|
|
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
|
|
|
\begin_inset Text
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
0.2
|
|
|
|
|
\begin_inset CommandInset citation
|
|
|
|
|
LatexCommand cite
|
|
|
|
|
key "aip_complete10.1063/1.101816"
|
|
|
|
|
literal "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
</cell>
|
|
|
|
|
</row>
|
|
|
|
|
</lyxtabular>
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
Effective masses of charge carriers in
|
|
|
|
|
\begin_inset CommandInset label
|
|
|
|
|
LatexCommand label
|
|
|
|
|
name "tab:Effective-masses"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
As the electrical and optical properties of the valence band are governed
|
2019-11-14 10:53:43 +00:00
|
|
|
|
by the heavy hole interactions, this effective mass ratio will be used.
|
2019-11-11 20:00:41 +00:00
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
Substituting these ratios into the above provides,
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
L=\sqrt{\frac{\pi^{2}\text{\emph{ħ}}^{2}}{2\cdotp(0.05\unit{eV})\cdotp m_{e}}\cdotp\left(\frac{1}{0.2}+\frac{1}{0.041}\right)}
|
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
which reduces to a well length of 14.87nm.
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Subsection
|
2019-11-12 11:43:05 +00:00
|
|
|
|
Confined Energy Level Calculations
|
2019-11-11 20:00:41 +00:00
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
With all the parameters of the well ascertained the first and second confined
|
|
|
|
|
electron and hole energy levels can be found by utilising equation
|
|
|
|
|
\begin_inset CommandInset ref
|
|
|
|
|
LatexCommand ref
|
|
|
|
|
reference "eq:Energy-levels"
|
|
|
|
|
plural "false"
|
|
|
|
|
caps "false"
|
|
|
|
|
noprefix "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
.
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
For confined electron states:
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
|
|
|
|
|
\emph on
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
E_{1e}=\frac{1^{2}\pi^{2}\text{\emph{ħ}}^{2}}{2\cdotp m_{e}^{*}\cdotp\left(14.87\unit{nm}\right)^{2}}
|
|
|
|
|
\]
|
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|
\end_inset
|
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|
\end_layout
|
|
|
|
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|
|
\begin_layout Standard
|
|
|
|
|
|
|
|
|
|
\emph on
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
E_{1e}=6.65\times10^{-21}\unit{J}=0.041\unit{eV}
|
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
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|
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|
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|
|
\end_layout
|
|
|
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|
|
|
|
|
\begin_layout Standard
|
2019-11-12 11:43:05 +00:00
|
|
|
|
This equation shows that confiend energy level values are proportional to
|
|
|
|
|
the square of
|
2019-11-11 20:00:41 +00:00
|
|
|
|
\begin_inset Formula $n$
|
|
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|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
, the principal quantum number or energy level.
|
|
|
|
|
As such:
|
|
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|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
E_{2e}=2^{2}\cdotp E_{1e}
|
|
|
|
|
\]
|
|
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|
|
|
|
|
|
|
\end_inset
|
|
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|
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|
|
\end_layout
|
|
|
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|
|
|
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|
|
\begin_layout Standard
|
|
|
|
|
|
|
|
|
|
\emph on
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
E_{2e}=2.66\times10^{-20}\unit{J}=0.17\unit{eV}
|
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
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|
|
|
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|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
For confined hole states:
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
|
|
|
|
|
\emph on
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
E_{1h}=\frac{1^{2}\pi^{2}\text{\emph{ħ}}^{2}}{2\cdotp m_{h}^{*}\cdotp\left(14.87\unit{nm}\right)^{2}}
|
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
|
|
|
|
|
\emph on
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
E_{1h}=1.36\times10^{-21}\unit{J}=0.0085\unit{eV}
|
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
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|
|
|
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|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
E_{2h}=2^{2}\cdotp E_{1h}
|
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
|
|
|
|
|
\emph on
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
E_{2h}=5.45\times10^{-21}\unit{J}=0.034\unit{eV}
|
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
2019-11-12 11:43:05 +00:00
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
With the dimensions and first confined energy levels calculated, the final
|
|
|
|
|
design for the quantum well can be seen in figure
|
|
|
|
|
\begin_inset CommandInset ref
|
|
|
|
|
LatexCommand ref
|
|
|
|
|
reference "fig:quantum-well-design"
|
|
|
|
|
plural "false"
|
|
|
|
|
caps "false"
|
|
|
|
|
noprefix "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
.
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Float figure
|
|
|
|
|
wide false
|
|
|
|
|
sideways false
|
|
|
|
|
status open
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
\align center
|
|
|
|
|
\begin_inset Graphics
|
|
|
|
|
filename well-design.png
|
|
|
|
|
lyxscale 30
|
|
|
|
|
width 85col%
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
InP/InGaAs/InP quantum well design
|
|
|
|
|
\begin_inset CommandInset label
|
|
|
|
|
LatexCommand label
|
|
|
|
|
name "fig:quantum-well-design"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
2019-11-11 20:00:41 +00:00
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Section
|
|
|
|
|
Probability Plot
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
The probability of finding an electron in a quantum well is given by
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\begin{equation}
|
|
|
|
|
P=\int_{0}^{L}\psi^{*}\psi dx\label{eq:wave-function-probability}
|
|
|
|
|
\end{equation}
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
with
|
|
|
|
|
\begin_inset Formula $\psi$
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
in the case of an infinite quantum well being given by,
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
\psi\left(x\right)=A\sin\left(kx\right)=A\sin\left(\frac{n\pi}{L}x\right)
|
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
2019-11-12 11:43:05 +00:00
|
|
|
|
Here
|
2019-11-11 20:00:41 +00:00
|
|
|
|
\begin_inset Formula $A$
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
acts as a normalisation constant to satisfy the conditions
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
\int_{{\textstyle all\:space}}\psi^{*}\psi dV=1
|
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
in this case providing the wave function
|
|
|
|
|
\begin_inset Formula $\psi$
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
as
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\begin{equation}
|
|
|
|
|
\psi\left(x\right)=\sqrt{\frac{2}{L}}\sin\left(\frac{n\pi}{L}x\right)\label{eq:wave-function}
|
|
|
|
|
\end{equation}
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
Importantly, the above conditions are for an infinite quantum well where
|
|
|
|
|
an assumption is made that the well has a barrier region of infinite potential
|
|
|
|
|
such that the wavefunction is confined to the well.
|
|
|
|
|
A real quantum well is unable to satisfy this leading to the wavefunction
|
|
|
|
|
|
|
|
|
|
\begin_inset Quotes eld
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
spilling
|
|
|
|
|
\begin_inset Quotes erd
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
into the barrier region.
|
|
|
|
|
For the purposes of plotting the probability density, however, it is a
|
|
|
|
|
reasonable assumption to make.
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
Considering equation
|
|
|
|
|
\begin_inset CommandInset ref
|
|
|
|
|
LatexCommand ref
|
|
|
|
|
reference "eq:wave-function-probability"
|
|
|
|
|
plural "false"
|
|
|
|
|
caps "false"
|
|
|
|
|
noprefix "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
, if the probability can be found by integrating
|
|
|
|
|
\begin_inset Formula $\psi^{*}\psi$
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
, or in this situation
|
|
|
|
|
\begin_inset Formula $\psi^{2}$
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
then the probability can be shown by plotting
|
|
|
|
|
\begin_inset Formula $\psi^{2}$
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
, see figure
|
|
|
|
|
\begin_inset CommandInset ref
|
|
|
|
|
LatexCommand ref
|
|
|
|
|
reference "fig:Probability-plot"
|
|
|
|
|
plural "false"
|
|
|
|
|
caps "false"
|
|
|
|
|
noprefix "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
.
|
|
|
|
|
Here the well stretches from 0 to the blue line along the
|
|
|
|
|
\begin_inset Formula $x$
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
axis and
|
|
|
|
|
\begin_inset Formula $n$
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
has been set to 1 for the ground state.
|
2019-11-12 11:43:05 +00:00
|
|
|
|
This function for the first excited state can be seen in figure
|
|
|
|
|
\begin_inset CommandInset ref
|
|
|
|
|
LatexCommand ref
|
|
|
|
|
reference "fig:Probability-plot-n-2"
|
|
|
|
|
plural "false"
|
|
|
|
|
caps "false"
|
|
|
|
|
noprefix "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
.
|
2019-11-11 20:00:41 +00:00
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Float figure
|
|
|
|
|
wide false
|
|
|
|
|
sideways false
|
|
|
|
|
status open
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
\align center
|
|
|
|
|
\begin_inset Graphics
|
|
|
|
|
filename probability-plot.png
|
|
|
|
|
lyxscale 30
|
2019-11-15 18:17:08 +00:00
|
|
|
|
width 60col%
|
2019-11-11 20:00:41 +00:00
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
Probability plot for electron in ground state
|
|
|
|
|
\begin_inset CommandInset label
|
|
|
|
|
LatexCommand label
|
|
|
|
|
name "fig:Probability-plot"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
2019-11-11 23:13:08 +00:00
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Float figure
|
|
|
|
|
wide false
|
|
|
|
|
sideways false
|
|
|
|
|
status open
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
\align center
|
|
|
|
|
\begin_inset Graphics
|
|
|
|
|
filename probability-plot-with-n-2.png
|
|
|
|
|
lyxscale 30
|
2019-11-15 18:17:08 +00:00
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width 60col%
|
2019-11-11 23:13:08 +00:00
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\end_inset
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\end_layout
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\begin_layout Plain Layout
|
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\begin_inset Caption Standard
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\begin_layout Plain Layout
|
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Probability plot for electron in 1
|
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\begin_inset script superscript
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\begin_layout Plain Layout
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st
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\end_layout
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\end_inset
|
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excited state
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\begin_inset CommandInset label
|
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LatexCommand label
|
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|
name "fig:Probability-plot-n-2"
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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2019-11-11 20:00:41 +00:00
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\end_layout
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\begin_layout Section
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Probability Intervals
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\end_layout
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\begin_layout Standard
|
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Combining equations
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\begin_inset CommandInset ref
|
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|
LatexCommand ref
|
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|
|
reference "eq:wave-function-probability"
|
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plural "false"
|
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caps "false"
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noprefix "false"
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\end_inset
|
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and
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\begin_inset CommandInset ref
|
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LatexCommand ref
|
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|
reference "eq:wave-function"
|
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|
plural "false"
|
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|
caps "false"
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noprefix "false"
|
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\end_inset
|
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|
2019-11-12 11:43:05 +00:00
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gives the final probability function for a distance across the well from
|
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\begin_inset Formula $x=0$
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\end_inset
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to
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\begin_inset Formula $x=x_{0}$
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\end_inset
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:
|
2019-11-11 20:00:41 +00:00
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\end_layout
|
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\begin_layout Standard
|
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\begin_inset Formula
|
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|
\[
|
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|
P\left(0\leq x\leq x_{0}\right)=\frac{1}{L}\left(x_{0}-\frac{L}{2n\pi}\sin\left(\frac{2n\pi x_{0}}{L}\right)\right)
|
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\]
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\end_inset
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\end_layout
|
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\begin_layout Standard
|
2019-11-12 11:43:05 +00:00
|
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For an arbitrary interval across the well, this becomes:
|
2019-11-11 23:13:08 +00:00
|
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\end_layout
|
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\begin_layout Standard
|
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\begin_inset Formula
|
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|
\[
|
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|
P\left(a\leq x\leq b\right)=\frac{1}{L}\left(\left(b-a\right)-\frac{L}{2n\pi}\left(\sin\left(\frac{2n\pi b}{L}\right)-\sin\left(\frac{2n\pi a}{L}\right)\right)\right)
|
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\]
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\end_inset
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\end_layout
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|
2019-11-12 11:43:05 +00:00
|
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|
\begin_layout Standard
|
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|
This equation can be utilised in order to find the probability of finding
|
|
|
|
|
the electron between
|
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|
\begin_inset Formula $2\unit{nm}$
|
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|
\end_inset
|
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and
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|
\begin_inset Formula $4\unit{nm}$
|
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|
\end_inset
|
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and between
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\begin_inset Formula $6\unit{nm}$
|
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|
\end_inset
|
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and
|
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|
\begin_inset Formula $8\unit{nm}$
|
|
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|
|
\end_inset
|
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|
, the intervals for which can be seen plotted in figure
|
|
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|
\begin_inset CommandInset ref
|
|
|
|
|
LatexCommand ref
|
|
|
|
|
reference "fig:Probability-plot-with-bounds"
|
|
|
|
|
plural "false"
|
|
|
|
|
caps "false"
|
|
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|
|
noprefix "false"
|
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|
|
\end_inset
|
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.
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|
|
\end_layout
|
|
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|
|
2019-11-11 23:13:08 +00:00
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Float figure
|
|
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|
|
wide false
|
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|
|
sideways false
|
|
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|
|
status open
|
|
|
|
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|
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|
|
\begin_layout Plain Layout
|
|
|
|
|
\align center
|
|
|
|
|
\begin_inset Graphics
|
|
|
|
|
filename probability-plot-with-bounds.png
|
|
|
|
|
lyxscale 30
|
2019-11-15 18:17:08 +00:00
|
|
|
|
width 60col%
|
2019-11-11 23:13:08 +00:00
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
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|
|
\end_layout
|
|
|
|
|
|
2019-11-12 16:23:10 +00:00
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
\align center
|
|
|
|
|
Green: 2nm - 4nm
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
\align center
|
|
|
|
|
Purple: 6nm - 8nm
|
|
|
|
|
\end_layout
|
|
|
|
|
|
2019-11-11 23:13:08 +00:00
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
Probability plot for electron in ground state with distance intervals
|
|
|
|
|
\begin_inset CommandInset label
|
|
|
|
|
LatexCommand label
|
|
|
|
|
name "fig:Probability-plot-with-bounds"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
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|
|
\end_layout
|
|
|
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|
|
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|
|
\end_inset
|
|
|
|
|
|
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|
|
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|
|
\end_layout
|
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|
\end_inset
|
|
|
|
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|
|
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|
|
\end_layout
|
|
|
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|
|
|
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|
|
\begin_layout Subsection
|
|
|
|
|
\begin_inset Formula $2\unit{nm}$
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
to
|
|
|
|
|
\begin_inset Formula $4\unit{nm}$
|
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|
|
\end_inset
|
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|
|
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|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
P\left(2\unit{nm}\leq x\leq4\unit{nm}\right)=\frac{1}{L}\left(2\unit{nm}-\frac{L}{2n\pi}\left(\sin\left(\frac{2n\pi\cdotp\left(4\unit{nm}\right)}{L}\right)-\sin\left(\frac{2n\pi\cdotp\left(2\unit{nm}\right)}{L}\right)\right)\right)
|
|
|
|
|
\]
|
|
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|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
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|
|
\end_layout
|
|
|
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|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
P\left(2\unit{nm}\leq x\leq4\unit{nm}\right)=\frac{1}{14.87\unit{nm}}\left(2\unit{nm}-\frac{14.87\unit{nm}}{2\pi}\left(\sin\left(\frac{2\pi\cdotp\left(4\unit{nm}\right)}{14.87\unit{nm}}\right)-\sin\left(\frac{2\pi\cdotp\left(2\unit{nm}\right)}{14.87\unit{nm}}\right)\right)\right)
|
|
|
|
|
\]
|
|
|
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|
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|
|
\end_inset
|
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|
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|
\end_layout
|
|
|
|
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|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
2019-11-12 11:43:05 +00:00
|
|
|
|
P\left(2\unit{nm}\leq x\leq4\unit{nm}\right)\thickapprox0.0955
|
2019-11-11 23:13:08 +00:00
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
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|
|
|
|
|
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|
|
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|
|
\end_layout
|
|
|
|
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|
|
|
|
|
\begin_layout Subsection
|
|
|
|
|
\begin_inset Formula $6\unit{nm}$
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
to
|
|
|
|
|
\begin_inset Formula $8\unit{nm}$
|
|
|
|
|
\end_inset
|
|
|
|
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|
|
|
|
|
|
|
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|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
P\left(6\unit{nm}\leq x\leq8\unit{nm}\right)=\frac{1}{L}\left(2\unit{nm}-\frac{L}{2n\pi}\left(\sin\left(\frac{2n\pi\cdotp\left(8\unit{nm}\right)}{L}\right)-\sin\left(\frac{2n\pi\cdotp\left(6\unit{nm}\right)}{L}\right)\right)\right)
|
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
|
|
|
|
P\left(6\unit{nm}\leq x\leq8\unit{nm}\right)=\frac{1}{14.87\unit{nm}}\left(2\unit{nm}-\frac{14.87\unit{nm}}{2\pi}\left(\sin\left(\frac{2\pi\cdotp\left(8\unit{nm}\right)}{14.87\unit{nm}}\right)-\sin\left(\frac{2\pi\cdotp\left(6\unit{nm}\right)}{14.87\unit{nm}}\right)\right)\right)
|
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Formula
|
|
|
|
|
\[
|
2019-11-12 11:43:05 +00:00
|
|
|
|
P\left(6\unit{nm}\leq x\leq8\unit{nm}\right)\thickapprox0.263
|
2019-11-11 23:13:08 +00:00
|
|
|
|
\]
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
2019-11-12 16:23:10 +00:00
|
|
|
|
\begin_layout Subsection
|
|
|
|
|
Conclusions
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
Considering these two probabilities it is clear that it is more likely for
|
|
|
|
|
the electron to be found between 6nm and 8nm than between 2nm and 4nm across
|
|
|
|
|
the well.
|
2019-11-14 10:53:43 +00:00
|
|
|
|
This is as expected considering 6nm to 8nm places the interval towards
|
2019-11-15 18:17:08 +00:00
|
|
|
|
the center of the 14.87nm well.
|
2019-11-12 16:23:10 +00:00
|
|
|
|
As the probability density function is a
|
|
|
|
|
\begin_inset Formula $\sin^{2}$
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
function, the maxium area will be towards the center.
|
|
|
|
|
Referring to figure
|
|
|
|
|
\begin_inset CommandInset ref
|
|
|
|
|
LatexCommand ref
|
|
|
|
|
reference "fig:Probability-plot-with-bounds"
|
|
|
|
|
plural "false"
|
|
|
|
|
caps "false"
|
|
|
|
|
noprefix "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
this can be seen graphically as the region created by the purple lines
|
|
|
|
|
has a far greater area under the probability density function than the
|
2019-11-14 10:53:43 +00:00
|
|
|
|
region formed by the green lines.
|
2019-11-12 16:23:10 +00:00
|
|
|
|
\end_layout
|
|
|
|
|
|
2019-11-11 20:00:41 +00:00
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Newpage pagebreak
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Part
|
2019-11-18 19:10:06 +00:00
|
|
|
|
Application of Nanomaterials - Abraxane
|
2019-11-04 15:34:25 +00:00
|
|
|
|
\end_layout
|
|
|
|
|
|
2019-11-12 16:23:10 +00:00
|
|
|
|
\begin_layout Standard
|
2019-11-18 19:10:06 +00:00
|
|
|
|
The use of albumin protein nanoparticles has provided a new delivery aid
|
2019-11-14 10:53:43 +00:00
|
|
|
|
for the highly effective chemotherapy drug, paclitaxel, in turn reducing
|
2019-11-15 18:17:08 +00:00
|
|
|
|
side effects and toxicity caused by previous delivery schemes and increasing
|
|
|
|
|
circulation half life around the body.
|
2019-11-14 10:53:43 +00:00
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Section
|
|
|
|
|
Paclitaxel
|
|
|
|
|
\end_layout
|
|
|
|
|
|
2019-11-15 18:17:08 +00:00
|
|
|
|
\begin_layout Standard
|
|
|
|
|
Paclitaxel is a chemotherapy drug in the taxane family which function as
|
|
|
|
|
mitotic inhibitors.
|
2019-11-18 19:10:06 +00:00
|
|
|
|
This involves the suppression of mitosis or cell division by preventing
|
|
|
|
|
the breakdown of the microtubules helping provide structure to cells.
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
This is effective in treating cancer as constant, unmitigated cell mitosis
|
|
|
|
|
is how cancer spreads throughout the body, blocking this process causes
|
|
|
|
|
it to die without reproducing.
|
2019-11-15 18:17:08 +00:00
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
2019-11-18 19:10:06 +00:00
|
|
|
|
While taxanes are an effective cancer treatment, their use is made less
|
|
|
|
|
efficacious due to their particularly insolubility in water requiring additiona
|
|
|
|
|
l chemcials to act as a delivery vehicle in order to allow a solution to
|
|
|
|
|
be created for intraveneous application.
|
2019-11-15 18:17:08 +00:00
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|
\end_layout
|
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\begin_layout Standard
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\begin_inset Float figure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\align center
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|
\begin_inset Graphics
|
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|
filename Taxol.svg
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|
lyxscale 30
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width 30col%
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\begin_inset Caption Standard
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\begin_layout Plain Layout
|
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|
Chemical structure for paclitaxel
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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|
2019-11-14 10:53:43 +00:00
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\begin_layout Section
|
2019-11-15 18:17:08 +00:00
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|
Previous Delivery Methods
|
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\end_layout
|
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\begin_layout Standard
|
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|
As a result of the poor water solubility of taxanes and paclitaxel, a method
|
|
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|
|
for delivering a solution was required.
|
|
|
|
|
Polyethoxylated castor oil (commercially known as Kolliphor EL, formerly
|
|
|
|
|
Cremophor EL [CrEL]) combined with dehydrated ethanol provides a suitable
|
2019-11-18 19:10:06 +00:00
|
|
|
|
formulation vehicle for many poorly water soluble and lipophilic drugs
|
|
|
|
|
and has been the standard for many forms of commercially available paclitaxel
|
|
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|
|
such as Taxol.
|
2019-11-15 18:17:08 +00:00
|
|
|
|
\end_layout
|
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|
\begin_layout Standard
|
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|
|
While this solution has proved to be an effective delivery mechanism there
|
|
|
|
|
are significant side effects.
|
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|
|
|
CrEL has been shown to cause severe hypersensitivity reactions and peripheral
|
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|
|
neuropathy which are exacerbated by the high volumes of delivery agent
|
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|
|
which must be coadministered with the active ingredient
|
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|
|
\begin_inset CommandInset citation
|
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|
LatexCommand cite
|
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|
|
key "elsevier_sdoi_10_1016_S0959_8049_01_00171_X"
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|
literal "false"
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|
\end_inset
|
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.
|
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|
The use of CrEL also affects the behaviour of paclitaxel when administered,
|
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|
|
manifesting as undesirable non-linear absorption, distribution, metabolism
|
|
|
|
|
and excretion behaviour
|
|
|
|
|
\begin_inset CommandInset citation
|
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|
|
|
LatexCommand cite
|
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|
|
key "proquest78006535"
|
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|
|
literal "false"
|
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|
|
|
|
|
|
|
|
\end_inset
|
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|
|
|
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|
|
, typically referred to as a drug's pharmacokinetic characteristics.
|
2019-11-14 10:53:43 +00:00
|
|
|
|
\end_layout
|
|
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|
|
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|
|
\begin_layout Section
|
2019-11-15 18:17:08 +00:00
|
|
|
|
Human Serum Albumin
|
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|
|
\end_layout
|
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|
|
\begin_layout Standard
|
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|
|
Human serum albumin (HSA), sometimes referred to as blood albumin is the
|
|
|
|
|
most frequently found protein in the human body
|
|
|
|
|
\begin_inset CommandInset citation
|
|
|
|
|
LatexCommand cite
|
|
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|
|
key "proquest1881262578"
|
|
|
|
|
literal "false"
|
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|
|
|
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|
|
\end_inset
|
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|
|
|
2019-11-18 19:10:06 +00:00
|
|
|
|
and is part of the albumin protein family.
|
2019-11-15 18:17:08 +00:00
|
|
|
|
HSA is produced by the liver and performs important functions such as maintaini
|
|
|
|
|
ng oncotic pressure in the blood vessels, ensuring the right levels of fluids
|
|
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|
|
are found between blood vessels and body tissues, and transporting hormones
|
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|
|
|
and fatty acids around the body.
|
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|
|
|
\end_layout
|
|
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|
|
\begin_layout Standard
|
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|
|
\begin_inset Float figure
|
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|
|
wide false
|
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|
|
sideways false
|
|
|
|
|
status open
|
|
|
|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
\align center
|
|
|
|
|
\begin_inset Graphics
|
|
|
|
|
filename hsa.jpg
|
|
|
|
|
lyxscale 30
|
|
|
|
|
width 40col%
|
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|
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|
|
\end_inset
|
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|
\end_layout
|
|
|
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|
\begin_layout Plain Layout
|
|
|
|
|
\begin_inset Caption Standard
|
|
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|
|
|
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
Crystal structure of human serum albumin with binding sites annotated
|
|
|
|
|
\begin_inset CommandInset citation
|
|
|
|
|
LatexCommand cite
|
|
|
|
|
key "BARBOSA2014345"
|
|
|
|
|
literal "false"
|
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|
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|
|
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|
|
\end_inset
|
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|
\end_layout
|
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\end_inset
|
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|
\end_layout
|
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\end_inset
|
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|
\end_layout
|
|
|
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|
|
|
|
\begin_layout Standard
|
|
|
|
|
Importantly for the application of drug delivery HSA along with the rest
|
|
|
|
|
of the albumin proteins are water soluble and HSA effectively binds with
|
|
|
|
|
both hydrophobic and hydrophilic chemicals
|
|
|
|
|
\begin_inset CommandInset citation
|
|
|
|
|
LatexCommand cite
|
|
|
|
|
key "proquest1881262578"
|
|
|
|
|
literal "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
.
|
2019-11-18 19:10:06 +00:00
|
|
|
|
Critically HSA has been shown to be nontoxic, non-immunogenic (provoking
|
2019-11-15 18:17:08 +00:00
|
|
|
|
little response from the immune system), biocompatible and biodegradable
|
|
|
|
|
\begin_inset CommandInset citation
|
|
|
|
|
LatexCommand cite
|
|
|
|
|
key "wos000301045400002"
|
|
|
|
|
literal "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
2019-11-18 19:10:06 +00:00
|
|
|
|
providing many theoretical advantages over Cremophor EL delivery as a result
|
|
|
|
|
of using a native biological subtance.
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
The nanoparticles are biodegradable as nano particles of the sizes 10-100nm
|
|
|
|
|
can be shown to enter the capillaries and be expelled as part of normal
|
|
|
|
|
cell clearance.
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
While HSA is frequently used due to it's native presence in the body reducing
|
|
|
|
|
the chances of an immunologic response, suitable albumin can also be found
|
|
|
|
|
in egg whites (ovalbumin [OVA]) and bovine serum (bovine serum albumin
|
|
|
|
|
[BSA]) where abundance and low cost are advantages.
|
|
|
|
|
Many of the advantages provided by using albumin can be attributed to using
|
|
|
|
|
a biological protein.
|
2019-11-14 10:53:43 +00:00
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Section
|
|
|
|
|
NAB-Paclitaxel
|
2019-11-12 16:23:10 +00:00
|
|
|
|
\end_layout
|
|
|
|
|
|
2019-11-15 18:17:08 +00:00
|
|
|
|
\begin_layout Standard
|
2019-11-18 19:10:06 +00:00
|
|
|
|
While there are many ways to produce albumin nanoparticles including desolvation
|
|
|
|
|
, emulsification and thermal gelation, an albumin specific technology was
|
|
|
|
|
developed in order to capture lipophilic (tending to dissolve in lipids
|
|
|
|
|
or fats) drugs in albumin nanoparticles known as NAB-technology where NAB
|
|
|
|
|
refers to nanoparticle albumin-bound.
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
The formulation process involves the drug in question being mixed in an
|
|
|
|
|
aqueous solution with HSA before being passed through a high pressure jet.
|
|
|
|
|
This forms nanoparticles of sizes between 100nm and 200nm
|
|
|
|
|
\begin_inset CommandInset citation
|
|
|
|
|
LatexCommand cite
|
|
|
|
|
key "wos000301045400002"
|
|
|
|
|
literal "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
.
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
The solubility in water of the final product is increased as operating at
|
|
|
|
|
the nano-scale increases the surface area of the particles and increases
|
|
|
|
|
the dissolution of the formulation.
|
|
|
|
|
This protein based delivery solution also has the benefit of allowing higher
|
|
|
|
|
doses of paclitaxel than is deemed safe when delivered in combination with
|
|
|
|
|
Cremophor.
|
|
|
|
|
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Section
|
|
|
|
|
Abraxane
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
Abraxane is a NAB-paclitaxel drug sold by Celgene, a biotechnology company
|
|
|
|
|
developing drugs for cancer and inflammoatory diseases.
|
|
|
|
|
Abraxane is made up of nanoparticles roughly 130nm in size and represents
|
|
|
|
|
the first FDA approved use of a nanotechnology chemotherapy for metastatic
|
|
|
|
|
breast cancer
|
|
|
|
|
\begin_inset CommandInset citation
|
|
|
|
|
LatexCommand cite
|
|
|
|
|
key "wos000301045400002"
|
|
|
|
|
literal "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
.
|
|
|
|
|
The European Medicines Agency lists three applications for Abraxane
|
|
|
|
|
\begin_inset CommandInset citation
|
|
|
|
|
LatexCommand cite
|
|
|
|
|
key "epar_summary_for_the_public-abraxane_2015"
|
|
|
|
|
literal "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
:
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Itemize
|
|
|
|
|
Metastatic breast cancer
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_deeper
|
|
|
|
|
\begin_layout Itemize
|
|
|
|
|
Following failure of an initial treatment
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Itemize
|
|
|
|
|
When a standard treatment including an 'anthracycline' drug is not suitable
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_deeper
|
|
|
|
|
\begin_layout Itemize
|
|
|
|
|
Metastatic adenocarcinoma of the pancreas
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_deeper
|
|
|
|
|
\begin_layout Itemize
|
|
|
|
|
In combination with the drug gemcitabine
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_deeper
|
|
|
|
|
\begin_layout Itemize
|
|
|
|
|
Non-small cell lung cancer
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_deeper
|
|
|
|
|
\begin_layout Itemize
|
|
|
|
|
In combination with the drug carboplatin
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Itemize
|
|
|
|
|
When surgery or radiotherapy is not suitable
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\end_deeper
|
|
|
|
|
\begin_layout Section
|
|
|
|
|
Efficacy
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
The efficacy of abraxane can be measured by comparing the treatment results
|
|
|
|
|
of this nanoparticle based approach with the alternative solvent based
|
|
|
|
|
method.
|
|
|
|
|
The European Medicines Agency list the results from clinical studies for
|
|
|
|
|
each of the cancers listed above
|
|
|
|
|
\begin_inset CommandInset citation
|
|
|
|
|
LatexCommand cite
|
|
|
|
|
key "epar_summary_for_the_public-abraxane_2015"
|
|
|
|
|
literal "false"
|
|
|
|
|
|
|
|
|
|
\end_inset
|
|
|
|
|
|
|
|
|
|
, with the effectiveness measure defined as whether tumours disappeared
|
|
|
|
|
or were reduced by at least 30%.
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
Abraxane was found to be 31% effective compared to 16% for the alternative
|
|
|
|
|
paclitaxel based treatment for metastatic breast cancer.
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
However, when considering only patients who had not previously received
|
|
|
|
|
treatment following a metastatic diagnosis, the effectiveness was the same
|
|
|
|
|
for both.
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
For non-small cell lung cancer it was found to be 33% effective as opposed
|
|
|
|
|
to 25% for the alternative.
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
With regards to the pancreatic study a combination of Abraxane and gemcitabine
|
|
|
|
|
increased overall survival to 8.7 months from 6.7 months with a treatment
|
|
|
|
|
of just gemcitabine.
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
This indicates that the drug performance is as good or better than alternatives
|
|
|
|
|
for all three, an encouraging result for a delivery method that also reduces
|
|
|
|
|
side effects and increases efficiency of delivery.
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Section
|
|
|
|
|
Discussion
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
Considering these results the use of protein nanoparticles looks to represent
|
|
|
|
|
an effective alternative to solvent based methods in delivering lipophobic
|
|
|
|
|
drugs.
|
|
|
|
|
In doing so the side effects of the solvent based methods can be avoided.
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Standard
|
|
|
|
|
The landscape is further broadening with research being completed into applying
|
|
|
|
|
NAB-technology to other taxanes such as docetaxel and macrolides such as
|
|
|
|
|
rapamycin.
|
|
|
|
|
\end_layout
|
|
|
|
|
|
|
|
|
|
\begin_layout Paragraph*
|
|
|
|
|
Part II Word Count:
|
2019-11-15 18:17:08 +00:00
|
|
|
|
\end_layout
|
|
|
|
|
|
2019-11-04 15:34:25 +00:00
|
|
|
|
\begin_layout Standard
|
|
|
|
|
\begin_inset Newpage pagebreak
|
|
|
|
|
\end_inset
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2019-11-11 13:39:57 +00:00
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\end_layout
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\begin_layout Standard
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\begin_inset CommandInset bibtex
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LatexCommand bibtex
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btprint "btPrintCited"
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bibfiles "references"
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options "bibtotoc"
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\end_inset
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2019-11-04 15:34:25 +00:00
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\end_layout
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\end_body
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\end_document
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