  Most studies of the mean-free path accumulation function (MFPAF) rely on
optical techniques to probe heat transfer at length scales on the order of the
phonon mean-free path. In this paper, we propose and implement a purely
electrical probe of the MFPAF that relies on photo-lithographically defined
heater-thermometer separation to set the length scale. An important advantage
of the proposed technique is its insensitivity to the thermal interfacial
impedance and its compatibility with a large array of temperature-controlled
chambers that lack optical ports. Detailed analysis of the experimental data
based on the enhanced Fourier law (EFL) demonstrates that heat-carrying phonons
in gallium arsenide have a much wider mean-free path spectrum than originally
thought.
