2237 lines
42 KiB
Plaintext
2237 lines
42 KiB
Plaintext
#LyX 2.3 created this file. For more info see http://www.lyx.org/
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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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\begin_layout Part
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Quantum Engineering Design
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\end_layout
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\begin_layout Section
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Structure Design
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\end_layout
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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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||
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\end_layout
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||
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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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||
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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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Therefore in order to find the energy,
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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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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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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,bulk}+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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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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.
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filename WellBandStructure.png
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lyxscale 40
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width 50col%
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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
|
||
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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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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||
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||
\end_layout
|
||
|
||
\begin_layout Standard
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||
\begin_inset Formula $E_{g}$
|
||
\end_inset
|
||
|
||
should be the dominant term in this equation and as such when investigating
|
||
suitable materials the bulk band gap should be close to but lower than
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||
0.8eV.
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Ternary alloys were investigated in order to allow precise control over
|
||
the lattice constants and band gap by varying the composition ratio.
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Indium gallium arsenide (In
|
||
\begin_inset script subscript
|
||
|
||
\begin_layout Plain Layout
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||
\begin_inset Formula $x$
|
||
\end_inset
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||
|
||
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||
\end_layout
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||
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||
\end_inset
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||
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||
Ga
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||
\begin_inset script subscript
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||
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\begin_inset Formula $(1-x)$
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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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||
\end_inset
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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 $x$
|
||
\end_inset
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||
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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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||
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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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||
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||
\end_inset
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||
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As and as such this was tested first.
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||
\end_layout
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||
|
||
\begin_layout Subsection
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||
Lattice Match
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Lattice matching is the process of ensuring that two crystalline structures
|
||
are of similar dimensions in order to decrease strain at the interface
|
||
between the two materials.
|
||
This is particularly important for quantum wells formed through epitaxial
|
||
growth as strain introduced between such thin layers can cause defects
|
||
which ultimately negatively affect it's electronic properties.
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
The lattice constants between the barrier and well materials should be as
|
||
close as is deemed acceptable for the application.
|
||
The lattice constants for the prospective materials are shown in table
|
||
|
||
\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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\begin_layout Standard
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Material
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Lattice Constant, α (Å)
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InAs
|
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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" rightline="true" usebox="none">
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\begin_layout Plain Layout
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6.0583
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\end_layout
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GaAs
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5.6532
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\end_layout
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InP
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|
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\begin_layout Plain Layout
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5.8687
|
||
\end_layout
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</lyxtabular>
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|
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|
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|
||
|
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\begin_inset Caption Standard
|
||
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\begin_layout Plain Layout
|
||
Lattice constants for prospective well and barrier materials
|
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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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LatexCommand label
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name "tab:Lattice-constants"
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|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
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
|
||
solution by finding the weighted average of the individual lattice constants
|
||
by composition ratio and is given by:
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\[
|
||
\alpha_{A_{(1-x)}B_{x}}=\left(1-x\right)\alpha_{A}+x\alpha_{B}
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Applying this to the prospective well material gives the following,
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\[
|
||
\alpha_{In_{0.53}Ga_{0.47}As}=0.53\cdotp6.0583+0.47\cdotp5.6532=5.8679
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
This shows that this combination of InGaAs is lattice matched to InP to
|
||
within 0.001Å, a sufficient offset for this application.
|
||
\end_layout
|
||
|
||
\begin_layout Subsection
|
||
Band Gap
|
||
\end_layout
|
||
|
||
\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
|
||
\begin_inset CommandInset ref
|
||
LatexCommand ref
|
||
reference "tab:Band-gaps"
|
||
plural "false"
|
||
caps "false"
|
||
noprefix "false"
|
||
|
||
\end_inset
|
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|
||
.
|
||
\end_layout
|
||
|
||
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|
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Material
|
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\begin_inset Text
|
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|
||
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|
||
Band Gap at 300K, E
|
||
\begin_inset script subscript
|
||
|
||
\begin_layout Plain Layout
|
||
g
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
(eV)
|
||
\end_layout
|
||
|
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|
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|
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|
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InAs
|
||
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|
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|
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|
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|
||
0.35
|
||
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|
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|
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|
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<row>
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GaAs
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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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|
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\begin_layout Plain Layout
|
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1.42
|
||
\end_layout
|
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|
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\end_inset
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</cell>
|
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|
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<row>
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|
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|
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|
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InP
|
||
\end_layout
|
||
|
||
\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
|
||
1.34
|
||
\end_layout
|
||
|
||
\end_inset
|
||
</cell>
|
||
</row>
|
||
</lyxtabular>
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\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
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\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
|
||
|
||
|
||
\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.
|
||
\end_layout
|
||
|
||
\begin_layout Subsection
|
||
Width Calculation
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Having found two materials that are lattice matched with a suitable band
|
||
gap value, the final calculation is that of the quantum well width.
|
||
In order to calculate this value, the equation for confined energy levels
|
||
within an infinite quantum well will be used,
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
|
||
\emph on
|
||
\begin_inset Formula
|
||
\begin{equation}
|
||
E_{n}=\frac{n^{2}\pi^{2}\mathcal{\text{ħ}}^{2}}{2mL^{2}}\label{eq:Energy-levels}
|
||
\end{equation}
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Referring back to equation
|
||
\begin_inset CommandInset ref
|
||
LatexCommand ref
|
||
reference "eq:Energy-Gap-Sum"
|
||
plural "false"
|
||
caps "false"
|
||
noprefix "false"
|
||
|
||
\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"
|
||
plural "false"
|
||
caps "false"
|
||
noprefix "false"
|
||
|
||
\end_inset
|
||
|
||
as seen below,
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\[
|
||
E_{g,transition}=E_{1h}+E_{g,InGaAs}+E_{1e}=\frac{1^{2}\pi^{2}\text{\emph{ħ}}^{2}}{2m_{h}^{*}L^{2}}+E_{g,InGaAs}+\frac{1^{2}\pi^{2}\text{\emph{ħ}}^{2}}{2m_{e}^{*}L^{2}}=0.8\unit{eV}
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
With the experimentally determined value for
|
||
\begin_inset Formula $E_{g,,InGaAs}$
|
||
\end_inset
|
||
|
||
this equation becomes
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\[
|
||
0.8\unit{eV}=\frac{\pi^{2}\text{\emph{ħ}}^{2}}{2m_{h}^{*}L^{2}}+0.75\unit{eV}+\frac{\pi^{2}\text{\emph{ħ}}^{2}}{2m_{e}^{*}L^{2}}
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\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
|
||
|
||
|
||
\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">
|
||
<row>
|
||
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
||
\begin_inset Text
|
||
|
||
\begin_layout Plain Layout
|
||
Charge Carrier
|
||
\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
|
||
by the heavy hole interactions, this effective mass ratio will be used.
|
||
\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
|
||
Confined Energy Level Calculations
|
||
\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
|
||
\[
|
||
E_{1e}=\frac{1^{2}\pi^{2}\text{ħ}^{2}}{2\cdotp m_{e}^{*}\cdotp\left(14.87\unit{nm}\right)^{2}}
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
|
||
\emph on
|
||
\begin_inset Formula
|
||
\[
|
||
E_{1e}=6.65\times10^{-21}\unit{J}=0.041\unit{eV}
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
This equation shows that confiend energy level values are proportional to
|
||
the square of
|
||
\begin_inset Formula $n$
|
||
\end_inset
|
||
|
||
, the principal quantum number or energy level.
|
||
As such:
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\[
|
||
E_{2e}=2^{2}\cdotp E_{1e}
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
|
||
\emph on
|
||
\begin_inset Formula
|
||
\[
|
||
E_{2e}=2.66\times10^{-20}\unit{J}=0.17\unit{eV}
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
For confined hole states:
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
|
||
\emph on
|
||
\begin_inset Formula
|
||
\[
|
||
E_{1h}=\frac{1^{2}\pi^{2}\text{ħ}^{2}}{2\cdotp m_{h}^{*}\cdotp\left(14.87\unit{nm}\right)^{2}}
|
||
\]
|
||
|
||
\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
|
||
|
||
|
||
\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
|
||
|
||
|
||
\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, relative confined energy level heights
|
||
are not to scale
|
||
\begin_inset CommandInset label
|
||
LatexCommand label
|
||
name "fig:quantum-well-design"
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\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
|
||
Here
|
||
\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 within 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.
|
||
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
|
||
|
||
.
|
||
\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
|
||
width 60col%
|
||
|
||
\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
|
||
|
||
|
||
\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
|
||
width 60col%
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Plain Layout
|
||
\begin_inset Caption Standard
|
||
|
||
\begin_layout Plain Layout
|
||
Probability plot for electron in 1
|
||
\begin_inset script superscript
|
||
|
||
\begin_layout Plain Layout
|
||
st
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
excited state
|
||
\begin_inset CommandInset label
|
||
LatexCommand label
|
||
name "fig:Probability-plot-n-2"
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Section
|
||
Probability Intervals
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Combining equations
|
||
\begin_inset CommandInset ref
|
||
LatexCommand ref
|
||
reference "eq:wave-function-probability"
|
||
plural "false"
|
||
caps "false"
|
||
noprefix "false"
|
||
|
||
\end_inset
|
||
|
||
and
|
||
\begin_inset CommandInset ref
|
||
LatexCommand ref
|
||
reference "eq:wave-function"
|
||
plural "false"
|
||
caps "false"
|
||
noprefix "false"
|
||
|
||
\end_inset
|
||
|
||
gives the final probability function for a distance across the well from
|
||
|
||
\begin_inset Formula $x=0$
|
||
\end_inset
|
||
|
||
to
|
||
\begin_inset Formula $x=x_{0}$
|
||
\end_inset
|
||
|
||
:
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\[
|
||
P\left(0\leq x\leq x_{0}\right)=\frac{1}{L}\left(x_{0}-\frac{L}{2n\pi}\sin\left(\frac{2n\pi x_{0}}{L}\right)\right)
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
For an arbitrary interval across the well, this becomes:
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\[
|
||
P\left(a\leq x\leq b\right)=\frac{1}{L}\left(\left(b-a\right)-\frac{L}{2n\pi}\left(\sin\left(\frac{2n\pi b}{L}\right)-\sin\left(\frac{2n\pi a}{L}\right)\right)\right)
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
This equation can be utilised in order to find the probability of finding
|
||
the electron between
|
||
\begin_inset Formula $2\unit{nm}$
|
||
\end_inset
|
||
|
||
and
|
||
\begin_inset Formula $4\unit{nm}$
|
||
\end_inset
|
||
|
||
and between
|
||
\begin_inset Formula $6\unit{nm}$
|
||
\end_inset
|
||
|
||
and
|
||
\begin_inset Formula $8\unit{nm}$
|
||
\end_inset
|
||
|
||
, the intervals for which can be seen plotted in figure
|
||
\begin_inset CommandInset ref
|
||
LatexCommand ref
|
||
reference "fig:Probability-plot-with-bounds"
|
||
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 probability-plot-with-bounds.png
|
||
lyxscale 30
|
||
width 60col%
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Plain Layout
|
||
\align center
|
||
Green: 2nm - 4nm
|
||
\end_layout
|
||
|
||
\begin_layout Plain Layout
|
||
\align center
|
||
Purple: 6nm - 8nm
|
||
\end_layout
|
||
|
||
\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
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Subsection
|
||
\begin_inset Formula $2\unit{nm}$
|
||
\end_inset
|
||
|
||
to
|
||
\begin_inset Formula $4\unit{nm}$
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\[
|
||
P\left(2\unit{nm}\leq x\leq4\unit{nm}\right)=\frac{1}{L}\left(2\unit{nm}-\frac{L}{2n\pi}\left(\sin\left(\frac{2n\pi\cdotp\left(4\unit{nm}\right)}{L}\right)-\sin\left(\frac{2n\pi\cdotp\left(2\unit{nm}\right)}{L}\right)\right)\right)
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\[
|
||
P\left(2\unit{nm}\leq x\leq4\unit{nm}\right)=\frac{1}{14.87\unit{nm}}\left(2\unit{nm}-\frac{14.87\unit{nm}}{2\pi}\left(\sin\left(\frac{2\pi\cdotp\left(4\unit{nm}\right)}{14.87\unit{nm}}\right)-\sin\left(\frac{2\pi\cdotp\left(2\unit{nm}\right)}{14.87\unit{nm}}\right)\right)\right)
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\[
|
||
P\left(2\unit{nm}\leq x\leq4\unit{nm}\right)\thickapprox0.0955
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Subsection
|
||
\begin_inset Formula $6\unit{nm}$
|
||
\end_inset
|
||
|
||
to
|
||
\begin_inset Formula $8\unit{nm}$
|
||
\end_inset
|
||
|
||
|
||
\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
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Formula
|
||
\[
|
||
P\left(6\unit{nm}\leq x\leq8\unit{nm}\right)\thickapprox0.263
|
||
\]
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\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.
|
||
This would be expected considering 6nm to 8nm places the interval towards
|
||
the center of the 14.87nm long well.
|
||
As the probability density function is a
|
||
\begin_inset Formula $\sin^{2}$
|
||
\end_inset
|
||
|
||
function, the majority of the 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
|
||
region formed by the green lines.
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Newpage pagebreak
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Part
|
||
Application of Nanomaterials - Abraxane
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
The use of albumin protein nanoparticles has provided a new delivery aid
|
||
for the highly effective chemotherapy drug, paclitaxel, in turn reducing
|
||
side effects and toxicity caused by previous delivery schemes and increasing
|
||
circulation half life around the body.
|
||
\end_layout
|
||
|
||
\begin_layout Section
|
||
Paclitaxel
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
Paclitaxel is a chemotherapy drug in the taxane family which together function
|
||
as mitotic inhibitors.
|
||
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
|
||
the cells to die without reproducing.
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
While taxanes are an effective cancer treatment, their use is made less
|
||
efficacious due to their practical insolubility in water.
|
||
In order to allow intravenous treatment, additional chemicals must be used
|
||
as delivery 'vehicles' to improve solubility.
|
||
\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 Taxol.svg
|
||
lyxscale 30
|
||
width 30col%
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Plain Layout
|
||
\begin_inset Caption Standard
|
||
|
||
\begin_layout Plain Layout
|
||
Chemical structure for paclitaxel
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Section
|
||
Previous Delivery Methods
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
As a result of the poor water solubility of taxanes and paclitaxel, a method
|
||
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
|
||
formulation vehicle for many poorly water soluble and lipophilic (tending
|
||
to dissolve in lipids or fats) drugs and has been the standard for many
|
||
forms of commercially available paclitaxel such as Taxol.
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
While this solution has proved to be an effective delivery mechanism there
|
||
are significant side effects.
|
||
CrEL has been shown to cause severe hypersensitivity reactions and peripheral
|
||
neuropathy which are exacerbated by the high volumes of delivery agent
|
||
which must be coadministered with the active ingredient
|
||
\begin_inset CommandInset citation
|
||
LatexCommand cite
|
||
key "elsevier_sdoi_10_1016_S0959_8049_01_00171_X"
|
||
literal "false"
|
||
|
||
\end_inset
|
||
|
||
.
|
||
The use of CrEL also affects the behaviour of paclitaxel when administered,
|
||
manifesting as undesirable non-linear absorption, distribution, metabolism
|
||
and excretion behaviour
|
||
\begin_inset CommandInset citation
|
||
LatexCommand cite
|
||
key "proquest78006535"
|
||
literal "false"
|
||
|
||
\end_inset
|
||
|
||
, typically referred to as a drug's pharmacokinetic characteristics.
|
||
\end_layout
|
||
|
||
\begin_layout Section
|
||
Human Serum Albumin
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
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
|
||
key "proquest1881262578"
|
||
literal "false"
|
||
|
||
\end_inset
|
||
|
||
and is part of the albumin protein family.
|
||
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
|
||
are found between blood vessels and body tissues) and transporting hormones
|
||
and fatty acids around the body.
|
||
\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 hsa.jpg
|
||
lyxscale 30
|
||
width 40col%
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Plain Layout
|
||
\begin_inset Caption Standard
|
||
|
||
\begin_layout Plain Layout
|
||
Crystal structure of human serum albumin with binding sites annotated
|
||
\begin_inset CommandInset citation
|
||
LatexCommand cite
|
||
key "BARBOSA2014345"
|
||
literal "false"
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\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
|
||
|
||
.
|
||
Critically HSA has been shown to be nontoxic, non-immunogenic (provoking
|
||
little response from the immune system), biocompatible and biodegradable
|
||
\begin_inset CommandInset citation
|
||
LatexCommand cite
|
||
key "wos000301045400002"
|
||
literal "false"
|
||
|
||
\end_inset
|
||
|
||
providing many theoretical advantages over Cremophor EL delivery as a result
|
||
of using a native biological subtance.
|
||
\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.
|
||
\end_layout
|
||
|
||
\begin_layout Section
|
||
NAB-Paclitaxel
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
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 drugs in albumin nanoparticles
|
||
known as NAB-technology where NAB refers to nanoparticle albumin-bound.
|
||
\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 nab-pac.png
|
||
lyxscale 30
|
||
width 60col%
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Plain Layout
|
||
\begin_inset Caption Standard
|
||
|
||
\begin_layout Plain Layout
|
||
Diagram showing albumin nanoparticles in combination with paclitaxel
|
||
\begin_inset CommandInset citation
|
||
LatexCommand cite
|
||
key "veeda_edge"
|
||
literal "false"
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Plain Layout
|
||
|
||
\end_layout
|
||
|
||
\end_inset
|
||
|
||
|
||
\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 Standard
|
||
Drug delivery is one of the largest areas within the field of nanomedicine
|
||
with other sectors including direct cancer treatment, medical imaging and
|
||
blood purification.
|
||
\end_layout
|
||
|
||
\begin_layout Paragraph*
|
||
Part II Word Count: 989
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset Newpage pagebreak
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\begin_layout Standard
|
||
\begin_inset CommandInset bibtex
|
||
LatexCommand bibtex
|
||
btprint "btPrintCited"
|
||
bibfiles "references"
|
||
options "bibtotoc"
|
||
|
||
\end_inset
|
||
|
||
|
||
\end_layout
|
||
|
||
\end_body
|
||
\end_document
|