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Report/moores-law-owid.png
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@ -65,3 +65,48 @@
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year = {2011}
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}
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@article{graphene-review-2010,
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abstract = {Graphene has changed from being the exclusive domain of condensed-matter physicists to being explored by those in the electron-device community. In particular, graphene-based transistors have developed rapidly and are now considered an option for post-silicon electronics. However, many details about the potential performance of graphene transistors in real applications remain unclear. Here I review the properties of graphene that are relevant to electron devices, discuss the trade-offs among these properties and examine their effects on the performance of graphene transistors in both logic and radiofrequency applications. I conclude that the excellent mobility of graphene may not, as is often assumed, be its most compelling feature from a device perspective. Rather, it may be the possibility of making devices with channels that are extremely thin that will allow graphene field-effect transistors to be scaled to shorter channel lengths and higher speeds without encountering the adverse short-channel effects that restrict the performance of existing devices. Outstanding challenges for graphene transistors include opening a sizeable and well-defined bandgap in graphene, making large-area graphene transistors that operate in the current-saturation regime and fabricating graphene nanoribbons with well-defined widths and clean edges.},
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author = {Schwierz, Frank},
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doi = {10.1038/nnano.2010.89},
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issn = {1748-3395},
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journal = {Nature Nanotechnology},
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number = {7},
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pages = {487--496},
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risfield_0_da = {2010/07/01},
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title = {Graphene transistors},
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url = {https://www.nature.com/articles/nnano.2010.89},
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urldate = {2021-04-25},
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volume = {5},
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year = {2010}
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}
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@misc{warda-gfet-review,
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archiveprefix = {arXiv},
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author = {Warda, Mohamed},
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eprint = {2010.10382},
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primaryclass = {cond-mat.mes-hall},
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title = {Graphene Field Effect Transistors: A Review},
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url = {https://arxiv.org/abs/2010.10382},
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urldate = {2021-04-25},
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year = {2020}
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}
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@article{owidtechnologicalprogress,
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author = {Roser, Max and Ritchie, Hannah},
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journal = {Our World in Data},
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title = {Technological Progress},
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url = {https://ourworldindata.org/technological-progress},
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urldate = {2021-04-25},
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year = {2013}
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}
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@misc{transistors-21,
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author = {Courtland, Rachel},
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organization = {IEEE Spectrum},
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title = {Transistors Could Stop Shrinking in 2021},
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url = {https://spectrum.ieee.org/semiconductors/devices/transistors-could-stop-shrinking-in-2021},
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urldate = {2021-04-25},
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year = {2016}
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}
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@ -273,7 +273,9 @@ Introduction
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\end_layout
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\begin_layout Standard
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Graphene is a 2D allotrope of carbon with
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Graphene is a 2D allotrope of carbon with highly interesting mechanical
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and electrical properties that have made it a target of significant research
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in the last two decades since it's experimental discovery in 2004.
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\end_layout
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\begin_layout Standard
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@ -288,8 +290,8 @@ noprefix "false"
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\end_inset
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presents two applications of graphene that take advantage of it's behaviour
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at high frequencies.
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presents two applications of graphene that take advantage of it's electrical
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and mechanical behaviour at high frequencies.
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Section
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\begin_inset CommandInset ref
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LatexCommand ref
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@ -312,10 +314,259 @@ name "sec:Applications"
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\end_inset
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\end_layout
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\begin_layout Standard
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This section explores two uses of graphene for high frequency applications.
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First, the applicability of graphene for field effect transisitors will
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be considered as a channel material.
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Throughout, a particular focus will be paid to use in digital logic and
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thus as a possible replacement for the current Silicon CMOS/MOSFET paradigm.
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\end_layout
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\begin_layout Standard
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\begin_inset Flex TODO Note (inline)
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status open
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\begin_layout Plain Layout
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second application
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Subsection
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Graphene Transistors
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Digital Logic
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\end_layout
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\begin_layout Standard
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Silicon-based CMOS/MOSFET digital logic is the basis on which much of the
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modern electronics landscape has been built.
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From intergrated logic circuits to CPUs, it is hard to overstate how important
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this technology has proven to be.
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The need for more powerful devices has increased pressure for smaller and
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more efficient transistors, such that more can fit into a single device.
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This progress is typically described by Moore's Law and can be seen graphically
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in figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:cpu-transistor-number"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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.
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\end_layout
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\begin_layout Standard
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\begin_inset Float figure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\noindent
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\align center
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\begin_inset Graphics
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filename moores-law-owid.png
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lyxscale 20
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width 80col%
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\begin_inset Caption Standard
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\begin_layout Plain Layout
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The number of transistors in commercial CPUs between 1970 and 2020
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\begin_inset CommandInset citation
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LatexCommand cite
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key "owidtechnologicalprogress"
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literal "false"
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\end_inset
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\begin_inset CommandInset label
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LatexCommand label
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name "fig:cpu-transistor-number"
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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However, as transistors are made smaller, theoretical limits for many limiting
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factors are approached.
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In 2015, the ITRS predicted that by 2021 the current push for smaller transisto
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rs would no longer be economically viable, instead requiring innovative
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3D device structures
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\begin_inset CommandInset citation
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LatexCommand cite
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key "transistors-21"
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literal "false"
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\end_inset
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.
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Some of the most important limiting factors in the current Silicon landscape
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are short-channel effects, a group of undesirable electrical properties
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that can occur when the channel length of a MOSFET device is of the same
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order of magnitude as the depletion layer
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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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cite
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\end_layout
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\end_inset
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.
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\end_layout
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\begin_layout Standard
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\begin_inset Flex TODO Note (inline)
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status open
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\begin_layout Plain Layout
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Limitations of silicon
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Flex TODO Note (inline)
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status open
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\begin_layout Plain Layout
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Terahertz switching
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Flex TODO Note (inline)
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status open
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\begin_layout Plain Layout
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Electron mobility
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Flex TODO Note (inline)
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status open
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\begin_layout Plain Layout
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Thermal conductivity
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Flex TODO Note (inline)
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status open
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\begin_layout Plain Layout
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Sensitivity
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Flex TODO Note (inline)
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status open
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\begin_layout Plain Layout
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2D channel
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Flex TODO Note (inline)
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status open
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\begin_layout Plain Layout
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Short channel effects
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Flex TODO Note (inline)
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status open
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\begin_layout Plain Layout
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Hard to turn off, low on-off I multiplier (bandgap stuff)
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\end_layout
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\begin_layout Plain Layout
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Need to introduce a bandgap which decimates mobility
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Flex TODO Note (inline)
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status open
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\begin_layout Plain Layout
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Hard to fabricate, delamination and stuff
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Subsection
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@ -498,8 +749,17 @@ noprefix "false"
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\end_inset
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.
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Similarly to the original, the magnitude of the function can be seen to
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be between 48 and 63 mS for TTF and CoCp
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Similarly to the original, the magnitude (figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:david-magnitude"
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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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) of the function can be seen to be between 48 and 63 mS for TTF and CoCp
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\begin_inset script subscript
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\begin_layout Plain Layout
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@ -527,10 +787,20 @@ noprefix "false"
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the magnitude tends closer to the imaginary component than the real.
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Beyond 100 THz, the imaginary component dips below zero, with a trough
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of -0.5 mS around 250 THz.
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Looking to the phase information, before 10 GHz the phase can be seen to
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be 0, however as the imaginary component begins to peak, the phase increases
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to a max of 90 degrees, continuing until 100 THz where the negative imaginary
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peak causes the phase to sharply drop to -90 degrees.
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Looking to the phase information (figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:david-phase"
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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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), before 10 GHz the phase can be seen to be 0, however as the imaginary
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component begins to peak, the phase increases to a max of 90 degrees, continuin
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g until 100 THz where the negative imaginary peak causes the phase to sharply
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drop to -90 degrees.
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There is little difference between the two dopants, they are equal until
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100 THz where the TTF shows a -100 THz offset from the CoCp
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\begin_inset script subscript
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@ -740,6 +1010,14 @@ wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\noindent
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\align center
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\begin_inset Float figure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\noindent
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\align center
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@ -751,6 +1029,37 @@ status open
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\begin_inset Caption Standard
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\begin_layout Plain Layout
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\begin_inset CommandInset label
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LatexCommand label
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name "fig:david-magnitude"
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\begin_inset Float figure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\noindent
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\align center
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\begin_inset Graphics
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filename ../Resources/david-recreation-phase.png
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lyxscale 20
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@ -765,7 +1074,30 @@ status open
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\begin_inset Caption Standard
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\begin_layout Plain Layout
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Complex conductivity magnitude and phase for TTF and CoCp
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\begin_inset CommandInset label
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LatexCommand label
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name "fig:david-phase"
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\begin_inset Caption Standard
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\begin_layout Plain Layout
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Complex conductivity magnitude (a) and phase (b) for TTF and CoCp
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\begin_inset script subscript
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\begin_layout Plain Layout
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@ -850,6 +1182,14 @@ wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\noindent
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\align center
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\begin_inset Float figure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\noindent
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\align center
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@ -861,6 +1201,37 @@ status open
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\begin_inset Caption Standard
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\begin_layout Plain Layout
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\begin_inset CommandInset label
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LatexCommand label
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name "fig:david-intraband"
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\begin_inset Float figure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\noindent
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\align center
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\begin_inset Graphics
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filename ../Resources/david-recreation-inter-mag.png
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lyxscale 20
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@ -875,7 +1246,30 @@ status open
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\begin_inset Caption Standard
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\begin_layout Plain Layout
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Intraband and interband conductivity for TTF and CoCp
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\begin_inset CommandInset label
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LatexCommand label
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name "fig:david-interband"
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\begin_inset Caption Standard
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\begin_layout Plain Layout
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Intraband (a) and interband (b) conductivity for TTF and CoCp
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\begin_inset script subscript
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\begin_layout Plain Layout
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@ -1186,6 +1580,14 @@ wide false
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sideways false
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||||
status open
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||||
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||||
\begin_layout Plain Layout
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\noindent
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||||
\align center
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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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||||
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||||
\begin_layout Plain Layout
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\noindent
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\align center
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@ -1199,6 +1601,37 @@ status open
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||||
\end_layout
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||||
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||||
\begin_layout Plain Layout
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||||
\begin_inset Caption Standard
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||||
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\begin_layout Plain Layout
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||||
\begin_inset CommandInset label
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LatexCommand label
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name "fig:surf-carrier-conc-real"
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\end_inset
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||||
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\noindent
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||||
\align center
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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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||||
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||||
\begin_layout Plain Layout
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||||
\noindent
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||||
\align center
|
||||
@ -1210,6 +1643,29 @@ status open
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\begin_inset Caption Standard
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\begin_inset CommandInset label
|
||||
LatexCommand label
|
||||
name "fig:surf-carrier-conc-im"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Plain Layout
|
||||
@ -1259,7 +1715,7 @@ The conductivity can broadly be seen to follow the same spectral profile
|
||||
over the range of carrier concentrations as can be seen in figure
|
||||
\begin_inset CommandInset ref
|
||||
LatexCommand ref
|
||||
reference "fig:david-simulation-conductivity"
|
||||
reference "fig:david-magnitude"
|
||||
plural "false"
|
||||
caps "false"
|
||||
noprefix "false"
|
||||
@ -1857,7 +2313,7 @@ m
|
||||
figure
|
||||
\begin_inset CommandInset ref
|
||||
LatexCommand ref
|
||||
reference "fig:david-simulation-conductivity"
|
||||
reference "fig:david-magnitude"
|
||||
plural "false"
|
||||
caps "false"
|
||||
noprefix "false"
|
||||
@ -1930,6 +2386,14 @@ wide false
|
||||
sideways false
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\noindent
|
||||
\align center
|
||||
\begin_inset Float figure
|
||||
wide false
|
||||
sideways false
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\noindent
|
||||
\align center
|
||||
@ -1941,6 +2405,37 @@ status open
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\begin_inset Caption Standard
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\begin_inset CommandInset label
|
||||
LatexCommand label
|
||||
name "fig:carrier-conc-intra"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\begin_inset Float figure
|
||||
wide false
|
||||
sideways false
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\noindent
|
||||
\align center
|
||||
\begin_inset Graphics
|
||||
filename ../Resources/carrier-density/interband-lines-mag.png
|
||||
lyxscale 20
|
||||
@ -1955,8 +2450,31 @@ status open
|
||||
\begin_inset Caption Standard
|
||||
|
||||
\begin_layout Plain Layout
|
||||
Inter- and intraband conductivity for high and low carrier concentration
|
||||
graphene species
|
||||
\begin_inset CommandInset label
|
||||
LatexCommand label
|
||||
name "fig:carrier-conc-inter"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\begin_inset Caption Standard
|
||||
|
||||
\begin_layout Plain Layout
|
||||
Intraband (a) and interband (b) conductivity for high and low carrier concentrat
|
||||
ion graphene species
|
||||
\begin_inset CommandInset label
|
||||
LatexCommand label
|
||||
name "fig:inter-intra-carrier-conc"
|
||||
@ -2440,6 +2958,14 @@ wide false
|
||||
sideways false
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\noindent
|
||||
\align center
|
||||
\begin_inset Float figure
|
||||
wide false
|
||||
sideways false
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\noindent
|
||||
\align center
|
||||
@ -2451,6 +2977,37 @@ status open
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\begin_inset Caption Standard
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\begin_inset CommandInset label
|
||||
LatexCommand label
|
||||
name "fig:temp-intra"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\begin_inset Float figure
|
||||
wide false
|
||||
sideways false
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\noindent
|
||||
\align center
|
||||
\begin_inset Graphics
|
||||
filename ../Resources/temperature/interband-lines-mag.png
|
||||
lyxscale 20
|
||||
@ -2465,8 +3022,31 @@ status open
|
||||
\begin_inset Caption Standard
|
||||
|
||||
\begin_layout Plain Layout
|
||||
Inter- and intraband conductivity for low, room and high temperature graphene
|
||||
using TTF doping
|
||||
\begin_inset CommandInset label
|
||||
LatexCommand label
|
||||
name "fig:temp-inter"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\begin_inset Caption Standard
|
||||
|
||||
\begin_layout Plain Layout
|
||||
Intraband (a) and interband (b) conductivity for low, room and high temperature
|
||||
graphene using TTF doping
|
||||
\begin_inset CommandInset label
|
||||
LatexCommand label
|
||||
name "fig:inter-intra-temperature"
|
||||
@ -2620,6 +3200,14 @@ wide false
|
||||
sideways false
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\noindent
|
||||
\align center
|
||||
\begin_inset Float figure
|
||||
wide false
|
||||
sideways false
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\noindent
|
||||
\align center
|
||||
@ -2633,6 +3221,37 @@ status open
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\begin_inset Caption Standard
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\begin_inset CommandInset label
|
||||
LatexCommand label
|
||||
name "fig:surf-scatter-intra"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\noindent
|
||||
\align center
|
||||
\begin_inset Float figure
|
||||
wide false
|
||||
sideways false
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\noindent
|
||||
\align center
|
||||
@ -2644,6 +3263,29 @@ status open
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\begin_inset Caption Standard
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\begin_inset CommandInset label
|
||||
LatexCommand label
|
||||
name "fig:surf-scatter-inter"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Plain Layout
|
||||
@ -2710,6 +3352,14 @@ wide false
|
||||
sideways false
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\noindent
|
||||
\align center
|
||||
\begin_inset Float figure
|
||||
wide false
|
||||
sideways false
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\noindent
|
||||
\align center
|
||||
@ -2721,6 +3371,37 @@ status open
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\begin_inset Caption Standard
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\begin_inset CommandInset label
|
||||
LatexCommand label
|
||||
name "fig:scatter-intraband"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\begin_inset Float figure
|
||||
wide false
|
||||
sideways false
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\noindent
|
||||
\align center
|
||||
\begin_inset Graphics
|
||||
filename ../Resources/scatter-lifetime/interband-lines-mag.png
|
||||
lyxscale 20
|
||||
@ -2735,8 +3416,31 @@ status open
|
||||
\begin_inset Caption Standard
|
||||
|
||||
\begin_layout Plain Layout
|
||||
Inter- and intraband conductivity with 3 different scattering times for
|
||||
graphene using TTF doping
|
||||
\begin_inset CommandInset label
|
||||
LatexCommand label
|
||||
name "fig:scatter-inter"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\begin_inset Caption Standard
|
||||
|
||||
\begin_layout Plain Layout
|
||||
Intraband (a) and interband (b) conductivity with 3 different scattering
|
||||
times for graphene using TTF doping
|
||||
\begin_inset CommandInset label
|
||||
LatexCommand label
|
||||
name "fig:inter-intra-scatter-lifetime"
|
||||
@ -3155,6 +3859,32 @@ From the presented trends for how conductivity is affected by a varied carrier
|
||||
lifetime.
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
\begin_inset Flex TODO Note (inline)
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
Equation analysis
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
\begin_inset Flex TODO Note (inline)
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
Why?
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Section
|
||||
Conclusion
|
||||
\end_layout
|
||||
|
||||
Loading…
Reference in New Issue
Block a user