  Thermal properties have an outsized impact on efficiency and sensitivity of
devices with nanoscale structures, such as in integrated electronic circuits. A
number of thermal conductivity measurements for semiconductor nanostructures
exist, but are hindered by the diffraction limit of light, the need for
transducer layers, the slow-scan rate of probes, ultra-thin sample
requirements, or extensive fabrication. Here, we overcome these limitations by
extracting temperature from measurements of bandgap cathodoluminescence in GaN
nanowires with spatial resolution limited by the electron cascade, and use this
to determine thermal conductivities in the range of 19-68 W/m*K in three new
ways. The electron beam acts simultaneously as a temperature probe and as a
controlled delta-function-like heat source to measure thermal conductivities
using steady-state methods, and we introduce a frequency-domain method using
pulsed electron beam excitation. The different thermal conductivity
measurements we explore agree within error where comparable. Our results
provide novel methods of measuring thermal properties that allow for rapid,
in-situ, high-resolution measurements of integrated circuits and semiconductor
nanodevices, and open the door for electron-beam based nanoscale phonon
transport studies.
