  While several 2D thermometry techniques exist, there is a lack of 3D
thermometry techniques that work for wide range of materials and offer good
resolution in time, space and temperature. X-ray diffraction (XRD) and nuclear
magnetic resonance (NMR) imaging can provide 3D temperature information.
However, XRD is typically limited to crystalline materials while NMR is largely
limited to liquids where the resonance lines are narrow. We investigate
electron paramagnetic resonance (EPR) of n-type silicon and germanium for 3D
thermometry. While in germanium the EPR linewidths are too broad, EPR
linewidths in silicon are reasonably narrow and exhibit a strong temperature
dependence. The temperature dependence of the spin-lattice relaxation rate
(1/T1) of conduction electrons in n-type Si for low dopant concentrations
follows a T^3 law due to phonon broadening. For heavily doped Si, which is
desirable for good signal to noise ratio (SNR) for application in thermometry,
impurity scattering is expected to decrease the temperature dependence of 1/T1.
Our results show, in heavily doped n-type Si, spin-lattice relaxation induced
by impurity scattering does not drastically decrease the temperature dependence
of EPR linewidths. In P-doped Si with donor concentration of 7 x 10^18 /cm^3,
the EPR linewidth has a T^(5/2) temperature dependence; the temperature
dependence decreases to T^(3/2) when the donor concentration is 7 x 10^19
/cm^3. While the temperature dependence of linewidth decreases for heavier
doping, EPR linewidth is still a sensitive thermometer. We define a figure of
merit for SNR for thermometry from EPR linewidths of n-type Si and observe that
increasing the doping results in a better SNR. Using effective medium theory,
we show that EPR linewidth can be a sensitive thermometer for application in 3D
thermometry with systems embedding microparticles of heavily doped n-type Si.
