Within the "forbidden" range of electron energies between the valence and conduction bands of titanium dioxide, crystal lattice irregularities lead to the formation of electron trapping sites. These sites are known as shallow trap states, where "shallow" refers to the close energy proximity of those features to the bottom of the semiconductor conduction band. For wide bandgap semiconductors like titanium dioxide, shallow electron traps are the principle route for thermal excitation of electrons into the conduction band. The studies described here employ a novel infrared spectroscopic approach to determine the energy of shallow electron traps in titanium dioxide nanoparticles. Mobile electrons within the conduction band of semiconductors are known to absorb infrared radiation. As those electrons absorb the infrared photons, transitions within the continuum of the conduction band produce a broad spectral signal across the entire mid-infrared range. A Mathematical expression based upon Fermi–Dirac statistics was derived to correlate the temperature of the particles to the population of charge carriers, as measured through the infrared absorbance. The primary variable of interest in the Fermi – Dirac expression is the energy difference between the shallow trap states and the conduction band. Fitting data sets consisting of titanium dioxide nanoparticle temperatures and their associated infrared spectra, over a defined frequency range, to the Fermi–Dirac expression is used to determine the shallow electron trap state energy. / Master of Science