Determining Energy Relaxation Length Scales in Two-Dimensional Electron Gases
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Authors
Billiald, Jordan
Advisors
Ritchie, David
Date
2021-03-15Awarding Institution
University of Cambridge
Qualification
Doctor of Philosophy (PhD)
Type
Thesis
Metadata
Show full item recordCitation
Billiald, J. (2021). Determining Energy Relaxation Length Scales in Two-Dimensional Electron Gases (Doctoral thesis). https://doi.org/10.17863/CAM.83783
Abstract
Modern semiconductor physics research is often carried out at low
temperatures where the carrier mobility is high and the thermal broad-
ening of quantised energy levels is minimised. 4.2 K, the temperature
of liquid helium, is thought of as relatively warm. Temperatures
of 300 mK and below are readily accessible with sorption-pumped
helium-3 and 3He/4He dilution refrigerators. At such low tempera-
tures, the phonons that normally facilitate thermal equilibrium be-
tween the charge carriers and the lattice are greatly suppressed. This
can lead to the electron system thermally decoupling from the lattice.
Conventional thermometers such as ceramic oxide or ruthenium ox-
ide resistance thermometers thermally couple to the lattice, meaning
that in this regime, they only effectively measure the lattice temper-
ature, TL. The effect is further pronounced in low dimensional car-
rier systems such as two-dimensional electron gases (2DEGs). This
is problematic because the electron temperature, Te, is often of far
greater importance than TL in such systems. Recent efforts have been
made to develop thermometry techniques that are directly sensitive
to Te. These techniques include using the thermopower of quantum
point contacts and the Coulomb blockade of quantum dots. However,
these techniques have issues with the ease and reliability of fabrication
of the thermocouples, and the complexity of their subsequent oper-
ation. This thesis presents a direct electron thermometry technique
called bar-gate thermometry (BGT) that utilises the diffusion ther-
mopower of the 2DEG as a thermocouple. BGT uses simple metal-
lic bar-gates, fabricated directly onto the semiconductor wafer, and
requires no particularly sophisticated electronic instruments. BGT
proves to be a reliable and relatively simple thermometry technique.
A device featuring a BGT is presented which allows a determination
of the thermal relaxation length, l, of the 2DEG. This comes hand
in hand with effective measurements of the inelastic scattering time,
τi, and the inelastic scattering exponent, αi, of the system, which are
not otherwise easily measured. Finally, an example of how BGTs can
be used to measure the thermal conductivity of mesoscopic 2DEGs
is given, which is just one possible use case of the technique. An
overview of all the necessary and relevant theory needed to under-
stand the techniques and results, as well as information on the design
and fabrication of the devices used in the experiments is also included.
Keywords
Bar-gate thermometry, Semiconductor physics, Thermovoltage, Thermopower
Sponsorship
The Leverhulme Trust
Identifiers
This record's DOI: https://doi.org/10.17863/CAM.83783
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