Ga-doped ZnO films of thicknesses 3 – 500 nm were grown on either Si or ZnO at 200 °C by pulsedlaser deposition in 10 mTorr of Ar. Sheet carrier concentration ns and mobility μ were measured at room temperature by the Hall effect and were fitted, respectively, to the equations ns(d) = n(∞)(d - δd) and μ(d) = μ(∞)/[1 + d*/(d - δd)], where n is the volume carrier concentration at d = ∞ (the bulk value), δd is the thickness of the dead layer, μ(∞) is the mobility at d = ∞, and d* is a figure of merit for the electrical properties of the interface. Roughly, d* may be thought of as the minimum layer thickness that will produce good conductance. For GZO/Si, the fitted d* = 23 nm, and for GZO/ZnO, 3 nm. As evidence of the usefulness of d*, a 3-nm layer of GZO/Si showed no measurable conductance (since d << d*), whereas a 5-nm layer of GZO had excellent conductance (since d ≈ d*). In fact, the latter had a resistivity of about 4 × 10-4 Ω-cm at room temperature, possibly the lowest value ever reported in ZnO at this thickness.