writing results section
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@ -314,6 +314,18 @@ name "sec:Applications"
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\end_layout
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\begin_layout Subsection
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Graphene Transistors
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\end_layout
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\begin_layout Subsection
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Terahertz Radiation
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\end_layout
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\begin_layout Subsection
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Summary
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\end_layout
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\begin_layout Section
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Sheet Conductivity Modelling
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\begin_inset CommandInset label
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@ -781,6 +793,11 @@ noprefix "false"
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.
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Comparing the two, it can be seen that the interactions happen over largely
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separate frequency ranges.
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In general, the intraband conductivity can be seen to exist up to the THz
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portion of the spectrum while the interband has the majority of it's contributi
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ons above the THz range.
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The intraband can be seen to dominate the total contribution and is responsible
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for the conductance up to the previously mentioned 20 GHz cutoff.
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The interband interactions begin after the 10 THz range, initially the
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imaginary component sharply drops and relaxes with a minima at 187 THz
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and 248 THz for TTF and CoCp
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@ -1551,8 +1568,9 @@ m
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\end_inset
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threshold, the cutoff frequency begins to increase as can be seen from
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higher peak smearing the lighter blue across a higher frequency band.
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This moves the cutoff from around 120 GHz to about 180 GHz.
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the higher 20 GHz peak smearing the lighter blue across a higher frequency
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band.
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This moves the cutoff from 120 GHz to around 180 GHz.
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The value that the real conductance takes above the cutoff frequency decreases
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past the 10
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\begin_inset script superscript
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@ -1935,11 +1953,103 @@ noprefix "false"
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presents the conductance for three graphene species of differing carrier
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concentrations decomposed into the intraband and interband components.
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From comparing the relative magnitudes from the two, it is clear that the
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majority contribution for conductance throughout the selected frequency
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range is from the intraband transitions.
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This is also apparent from the similarity in spectral profile between the
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intraband conductivity and both the surfaces of figure
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The blue series,
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\family roman
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\series medium
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\shape up
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\size normal
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\emph off
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\bar no
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\strikeout off
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\xout off
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\uuline off
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\uwave off
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\noun off
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\color none
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a carrier density of
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\begin_inset Formula $1.3\times10^{17}$
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\end_inset
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\family default
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\series default
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\shape default
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\size default
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\emph default
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\bar default
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\strikeout default
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\xout default
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\uuline default
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\uwave default
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\noun default
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\color inherit
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m
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\family roman
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\series medium
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\shape up
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\size normal
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\emph off
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\bar no
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\strikeout off
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\xout off
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\uuline off
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\uwave off
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\noun off
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\color none
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\begin_inset script superscript
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\begin_layout Plain Layout
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\family roman
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\series medium
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\shape up
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\size normal
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\emph off
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\bar no
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\strikeout off
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\xout off
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\uuline off
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\uwave off
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\noun off
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\color none
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-2
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\end_layout
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\end_inset
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\family default
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\series default
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\shape default
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\size default
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\emph default
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\bar default
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\strikeout default
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\xout default
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\uuline default
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\uwave default
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\noun default
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\color inherit
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, recreates TTF doping from figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:david-simulation-inter-intra"
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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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with two further theoretical species of lower dopant concentration.
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\end_layout
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\begin_layout Standard
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Looking to the intraband interactions, the real and imaginary components
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can be seen to have the same profile as seen previously, the differences
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lie in magnitude.
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Higher net carrier concentrations can be seen to increase the magnitude,
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looking back to figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:surf-carrier-concentration"
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@ -1949,37 +2059,16 @@ noprefix "false"
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\end_inset
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and the reproduced results of figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:david-simulation-conductivity"
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plural "false"
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caps "false"
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noprefix "false"
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, this relationship is non-linear.
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\end_layout
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\end_inset
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.
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In general, the intraband conductivity can be seen to exist up to the THz
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portion of the spectrum while the interband has the majority of it's contributi
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ons above the THz range.
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The interband conductance can be seen to be responsible for the previously
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noted negative imaginary conductance behaviour seen in the surface of figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:surf-carrier-concentration"
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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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Low carrier concentration result in a higher initial imaginary component
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that does not lower into negative values.
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As concentration increases, the imaginary component decreases more forming
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a sharp trough that also bottoms out at a higher frequency.
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\begin_layout Standard
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The interband conductance can be seen to show more variation over the prescribed
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carrier concentration range.
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Low carrier concentrations result in a higher initial imaginary component
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that does not descend into negative values.
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As concentration increases, the imaginary component decreases more, forming
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a sharp trough that also reaches its lowest value at a higher frequency.
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\end_layout
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\begin_layout Standard
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@ -2003,7 +2092,7 @@ Alongside this imaginary decrease, the real component can be seen to increase
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\begin_inset Formula $\mu S$
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\end_inset
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value and decreases only slightly to the limit over a wider spectral range.
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value and increases only slightly to the limit over a wider spectral range.
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The higher carrier concentration species begins much lower at 1
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\begin_inset Formula $\mu S$
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\end_inset
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@ -2045,11 +2134,26 @@ noprefix "false"
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both real and imaginary.
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\end_layout
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\begin_layout Standard
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From the real component, the pre-cutoff peak can be seen to increase from
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224 mS to 253 mS when moving from near-room temperature to the breakdown
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temperature of graphene.
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\end_layout
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\begin_layout Standard
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Looking to the imaginary component, the peak conductance increases by roughly
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15 mS.
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More variation occurs at the higher frequency, interband conductivity.
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The sharper colour gradient at lower temperatures become more gradual at
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higher temperatures, this indicates that the intraband imaginary negative
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peak takes place over a more gradual spectral range.
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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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status collapsed
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\begin_layout Plain Layout
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\noindent
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@ -2101,6 +2205,30 @@ name "fig:surf-temperature"
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\end_layout
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\begin_layout Standard
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Figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:inter-intra-temperature"
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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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presents the decomposed intraband and interband conductivity contributions,
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the previously mentioned high frequency behaviour can be seen clearer.
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As the temperature increases, the negative imaginary peak gets smaller
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in value with a smoother gradient.
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For the real component, althought the final value does not change, the
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gradient with which it is aproached changes.
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At low temperatures, the increase takes place over a tight spectral range
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with a sharp step action.
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As the temperature increases, the spectral band over which the transition
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occurs broadens with a smoother gradient while maintaining the centre frequency
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of 200 THz.
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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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@ -2157,11 +2285,68 @@ name "fig:inter-intra-temperature"
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Scattering Lifetime
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\end_layout
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\begin_layout Standard
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This section explores the effect of varying scatter lifetime,
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\begin_inset Formula $\tau$
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\end_inset
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, on the conductance.
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For the range of values to use, existing data was considered.
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1 ps is a typical figure in literature
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\begin_inset CommandInset citation
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LatexCommand cite
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key "david-paper"
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literal "false"
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\end_inset
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, with this in mind values between 100 ps and 0.01 ps were simulated.
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Figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:surf-scatter-lifetime"
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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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explores the general trends throughout the prescribed range.
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\end_layout
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\begin_layout Standard
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Looking to the real component, the scatter lifetime can be seen to affect
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both the cutoff frequency and the magnitude of the pre-cutoff value.
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As the lifetime increases, the cutoff frequency occurs at a lower value,
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from
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\begin_inset Flex TODO Note (Margin)
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status open
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\begin_layout Plain Layout
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values
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\end_layout
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\end_inset
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.
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The magnitude of the conductance also increases exponentially as the lifetime
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is increased.
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\end_layout
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\begin_layout Standard
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Considering the imaginary component, a somewhat similar behaviour can be
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seen.
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The same exponential growth in magnitude can be seen in the 20 GHz peak.
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With regards to the spectral behaviour, increasing scatter lifetime reduces
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the frequency of the leading peak, broadening the range of the peak.
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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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status collapsed
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\begin_layout Plain Layout
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\noindent
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@ -2213,6 +2398,25 @@ name "fig:surf-scatter-lifetime"
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\end_layout
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\begin_layout Standard
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Figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:inter-intra-scatter-lifetime"
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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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presents the interband and intraband conductivity contributions for three
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different scattering lifetimes.
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The previously identified spectral changes and magnitude growth can be
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seen in the intraband conductivity.
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Looking to the interband contributions, the three series show no variation,
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the scatter lifetime has no effect.
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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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