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,
ultrathin sample requirements, or extensive fabrication. Here, we
overcome these limitations by extracting nanoscale temperature maps
from measurements of bandgap cathodoluminescence in GaN nanowires
of <300 nm diameter with spatial resolution limited by the electron
cascade. We use this thermometry method in three ways to determine
the thermal conductivities of the nanowires in the range of 19–68
W/m·K, well below that of bulk GaN. 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 in uniformly doped wires. We show feasible methods
for rapid,
in situ
, high-resolution thermal property
measurements of integrated circuits and semiconductor nanodevices
and enable electron-beam-based nanoscale phonon transport studies.