Model for thickness dependence of mobility and concentration in highly conductive ZnO

The dependences of the 294-K and 10-K mobility μ and volume carrier concentration n on thickness (d = 25 -147 nm) were examined in Al-doped ZnO (AZO) layers grown in Ar ambient at 200 °C on quartz-glass substrates. Two AZO layers were grown at each thickness, one with and one without a 20-nm-thick ZnON buffer layer grown at 300 °C in Ar/N2 ambient. Plots of the 10-K sheet concentration ns vs d for buffered (B) and unbuffered (UB) samples give straight lines of similar slope, n = 8.36 x 10²⁰ and 8.32 x 10²⁰ cm^-3, but different x-axis intercepts, δd = -4 and +13 nm, respectively. Thus, the electrical thicknesses are d -δd = d + 4 and d -13 nm, respectively. Plots of ns vs d at 294 K produced substantially the same results. Plots of μ vs d can be well fitted with the equation μ(d) = μ(infinity symbol)/[1 + d*/(d-δd)], where d* is the thickness for which μ(infinity symbol) is reduced by a factor 2. For the B and UB samples, d* = 7 and 23 nm, respectively, showing the efficacy of the ZnON buffer. Finally, from n and μ(infinity symbol) we can use degenerate electron scattering theory to calculate bulk donor and acceptor concentrations of 1.23 x 10²¹ cm^-3 and 1.95 x 10²⁰ cm ^-3, respectively, and Drude theory to predict a plasmonic resonance at1.34 μm. The latter is confirmed by reflectance measurements.