diff --git a/Report/report.lyx b/Report/report.lyx index 29d3989..8ed32c9 100644 --- a/Report/report.lyx +++ b/Report/report.lyx @@ -314,6 +314,18 @@ name "sec:Applications" \end_layout +\begin_layout Subsection +Graphene Transistors +\end_layout + +\begin_layout Subsection +Terahertz Radiation +\end_layout + +\begin_layout Subsection +Summary +\end_layout + \begin_layout Section Sheet Conductivity Modelling \begin_inset CommandInset label @@ -781,6 +793,11 @@ noprefix "false" . Comparing the two, it can be seen that the interactions happen over largely separate frequency ranges. + In general, the intraband conductivity can be seen to exist up to the THz + portion of the spectrum while the interband has the majority of it's contributi +ons above the THz range. + The intraband can be seen to dominate the total contribution and is responsible + for the conductance up to the previously mentioned 20 GHz cutoff. The interband interactions begin after the 10 THz range, initially the imaginary component sharply drops and relaxes with a minima at 187 THz and 248 THz for TTF and CoCp @@ -1551,8 +1568,9 @@ m \end_inset threshold, the cutoff frequency begins to increase as can be seen from - higher peak smearing the lighter blue across a higher frequency band. - This moves the cutoff from around 120 GHz to about 180 GHz. + the higher 20 GHz peak smearing the lighter blue across a higher frequency + band. + This moves the cutoff from 120 GHz to around 180 GHz. The value that the real conductance takes above the cutoff frequency decreases past the 10 \begin_inset script superscript @@ -1624,7 +1642,7 @@ m \end_inset -carrier concentration threshold, from 58 + carrier concentration threshold, from 58 \family default \series default \shape default @@ -1935,37 +1953,103 @@ noprefix "false" presents the conductance for three graphene species of differing carrier concentrations decomposed into the intraband and interband components. - From comparing the relative magnitudes from the two, it is clear that the - majority contribution for conductance throughout the selected frequency - range is from the intraband transitions. - This is also apparent from the similarity in spectral profile between the - intraband conductivity and both the surfaces of figure -\begin_inset CommandInset ref -LatexCommand ref -reference "fig:surf-carrier-concentration" -plural "false" -caps "false" -noprefix "false" - + The blue series, +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\xout off +\uuline off +\uwave off +\noun off +\color none +a carrier density of +\begin_inset Formula $1.3\times10^{17}$ \end_inset - and the reproduced results of figure -\begin_inset CommandInset ref -LatexCommand ref -reference "fig:david-simulation-conductivity" -plural "false" -caps "false" -noprefix "false" - -\end_inset - -. - In general, the intraband conductivity can be seen to exist up to the THz - portion of the spectrum while the interband has the majority of it's contributi -ons above the THz range. - The interband conductance can be seen to be responsible for the previously - noted negative imaginary conductance behaviour seen in the surface of figure +\family default +\series default +\shape default +\size default +\emph default +\bar default +\strikeout default +\xout default +\uuline default +\uwave default +\noun default +\color inherit +m +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\xout off +\uuline off +\uwave off +\noun off +\color none + +\begin_inset script superscript + +\begin_layout Plain Layout + +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\xout off +\uuline off +\uwave off +\noun off +\color none +-2 +\end_layout + +\end_inset + + +\family default +\series default +\shape default +\size default +\emph default +\bar default +\strikeout default +\xout default +\uuline default +\uwave default +\noun default +\color inherit +, recreates TTF doping from figure +\begin_inset CommandInset ref +LatexCommand ref +reference "fig:david-simulation-inter-intra" +plural "false" +caps "false" +noprefix "false" + +\end_inset + + with two further theoretical species of lower dopant concentration. +\end_layout + +\begin_layout Standard +Looking to the intraband interactions, the real and imaginary components + can be seen to have the same profile as seen previously, the differences + lie in magnitude. + Higher net carrier concentrations can be seen to increase the magnitude, + looking back to figure \begin_inset CommandInset ref LatexCommand ref reference "fig:surf-carrier-concentration" @@ -1975,11 +2059,16 @@ noprefix "false" \end_inset -. - Low carrier concentration result in a higher initial imaginary component - that does not lower into negative values. - As concentration increases, the imaginary component decreases more forming - a sharp trough that also bottoms out at a higher frequency. +, this relationship is non-linear. +\end_layout + +\begin_layout Standard +The interband conductance can be seen to show more variation over the prescribed + carrier concentration range. + Low carrier concentrations result in a higher initial imaginary component + that does not descend into negative values. + As concentration increases, the imaginary component decreases more, forming + a sharp trough that also reaches its lowest value at a higher frequency. \end_layout \begin_layout Standard @@ -2003,7 +2092,7 @@ Alongside this imaginary decrease, the real component can be seen to increase \begin_inset Formula $\mu S$ \end_inset - value and decreases only slightly to the limit over a wider spectral range. + value and increases only slightly to the limit over a wider spectral range. The higher carrier concentration species begins much lower at 1 \begin_inset Formula $\mu S$ \end_inset @@ -2045,11 +2134,26 @@ noprefix "false" both real and imaginary. \end_layout +\begin_layout Standard +From the real component, the pre-cutoff peak can be seen to increase from + 224 mS to 253 mS when moving from near-room temperature to the breakdown + temperature of graphene. +\end_layout + +\begin_layout Standard +Looking to the imaginary component, the peak conductance increases by roughly + 15 mS. + More variation occurs at the higher frequency, interband conductivity. + The sharper colour gradient at lower temperatures become more gradual at + higher temperatures, this indicates that the intraband imaginary negative + peak takes place over a more gradual spectral range. +\end_layout + \begin_layout Standard \begin_inset Float figure wide false sideways false -status open +status collapsed \begin_layout Plain Layout \noindent @@ -2101,6 +2205,30 @@ name "fig:surf-temperature" \end_layout +\begin_layout Standard +Figure +\begin_inset CommandInset ref +LatexCommand ref +reference "fig:inter-intra-temperature" +plural "false" +caps "false" +noprefix "false" + +\end_inset + + presents the decomposed intraband and interband conductivity contributions, + the previously mentioned high frequency behaviour can be seen clearer. + As the temperature increases, the negative imaginary peak gets smaller + in value with a smoother gradient. + For the real component, althought the final value does not change, the + gradient with which it is aproached changes. + At low temperatures, the increase takes place over a tight spectral range + with a sharp step action. + As the temperature increases, the spectral band over which the transition + occurs broadens with a smoother gradient while maintaining the centre frequency + of 200 THz. +\end_layout + \begin_layout Standard \begin_inset Float figure wide false @@ -2157,11 +2285,68 @@ name "fig:inter-intra-temperature" Scattering Lifetime \end_layout +\begin_layout Standard +This section explores the effect of varying scatter lifetime, +\begin_inset Formula $\tau$ +\end_inset + +, on the conductance. + For the range of values to use, existing data was considered. + 1 ps is a typical figure in literature +\begin_inset CommandInset citation +LatexCommand cite +key "david-paper" +literal "false" + +\end_inset + +, with this in mind values between 100 ps and 0.01 ps were simulated. + Figure +\begin_inset CommandInset ref +LatexCommand ref +reference "fig:surf-scatter-lifetime" +plural "false" +caps "false" +noprefix "false" + +\end_inset + + explores the general trends throughout the prescribed range. + +\end_layout + +\begin_layout Standard +Looking to the real component, the scatter lifetime can be seen to affect + both the cutoff frequency and the magnitude of the pre-cutoff value. + As the lifetime increases, the cutoff frequency occurs at a lower value, + from +\begin_inset Flex TODO Note (Margin) +status open + +\begin_layout Plain Layout +values +\end_layout + +\end_inset + +. + The magnitude of the conductance also increases exponentially as the lifetime + is increased. +\end_layout + +\begin_layout Standard +Considering the imaginary component, a somewhat similar behaviour can be + seen. + The same exponential growth in magnitude can be seen in the 20 GHz peak. + With regards to the spectral behaviour, increasing scatter lifetime reduces + the frequency of the leading peak, broadening the range of the peak. +\end_layout + \begin_layout Standard \begin_inset Float figure wide false sideways false -status open +status collapsed \begin_layout Plain Layout \noindent @@ -2213,6 +2398,25 @@ name "fig:surf-scatter-lifetime" \end_layout +\begin_layout Standard +Figure +\begin_inset CommandInset ref +LatexCommand ref +reference "fig:inter-intra-scatter-lifetime" +plural "false" +caps "false" +noprefix "false" + +\end_inset + + presents the interband and intraband conductivity contributions for three + different scattering lifetimes. + The previously identified spectral changes and magnitude growth can be + seen in the intraband conductivity. + Looking to the interband contributions, the three series show no variation, + the scatter lifetime has no effect. +\end_layout + \begin_layout Standard \begin_inset Float figure wide false