  The electron dephasing processes in two-dimensional homogeneous and
inhomogeneous indium tin oxide thin films have been investigated in a wide
temperature range 0.3--90 K. We found that the small-energy-transfer
electron-electron ($e$-$e$) scattering process dominated the dephasing from a
few K to several tens K. At higher temperatures, a crossover to the
large-energy-transfer $e$-$e$ scattering process was observed. Below about 1--2
K, the dephasing time $\tau_\varphi$ revealed a very weak temperature
dependence, which intriguingly scaled approximately with the inverse of the
electron diffusion constant $D$, i.e., $\tau_\varphi (T \approx 0.3 \, {\rm K})
\propto 1/D$. Theoretical implications of our results are discussed. The reason
why the electron-phonon relaxation rate is negligibly weak in this
low-carrier-concentration material is presented.
