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The electrical resistivity of Fermi liquids (FLs) displays a quadratictemperature ($T$) dependence because of electron-electron (e-e) scattering. Forsuch collisions to decay the charge current, there are two known mechanisms:inter-band scattering (identified by Baber) and Umklapp events. However, dilutemetallic strontium titanate (STO) was found to display $T^2$ resistivity inabsence of either of these two mechanisms. The presence of soft phonons andtheir possible role as scattering centers raised the suspicion that $T$-squareresistivity in STO is not due to e-e scattering. Here, we present the case ofBi$_2$O$_2$Se, a layered semiconductor with hard phonons, which becomes adilute metal with a small single-component Fermi surface upon doping. Itdisplays $T$-square resistivity well below the degeneracy temperature whereneither Umklapp nor interband scattering is conceivable. We observe a universalscaling between the prefactor of $T^2$ resistivity and the Fermi energy, whichis an extension of the Kadowaki-Woods plot to dilute metals. Our results implythe absence of a satisfactory theoretical basis for the ubiquity of e-e driven$T$-square resistivity in Fermi liquids.

T-square resistivity without Umklapp scattering in dilute metallic Bi$_2$O$_2$Se