Model for thickness dependence of mobility and concentration in highly conductive zinc oxide

The dependences of the 294 and 10 K mobility μ and volume carrier concentration n on thickness (d = 25 to 147 nm) are examined in aluminum-doped zinc oxide (AZO). Two AZO layers are grown at each thickness, one with and one without a 20-nm-thick ZnON buffer layer. Plots of the 10 K sheet concentration ns versus d for buffered (B) and unbuffered (UB) samples give straight lines of similar slope, n = 8.36 × 10²⁰ and 8.32 × 10²⁰ cm^-3, but different x-axis intercepts, δd = -4 and +13 nm, respectively. Plots of n_s versus d at 294 K produce substantially the same results. Plots of μ versus d can be well fitted with the equation μ(d) = μ(∞)/[1 + d*]/(d - δd)], where d* is the thickness for which μ(∞) 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(∞) we can use degenerate electron scattering theory to calculate bulk donor and acceptor concentrations of 1.23 × 10²¹ cm^-3 and 1.95 × 10²⁰ cm ^-3, respectively, and Drude theory to predict a plasmonic resonance at 1.34 μm. The latter is confirmed by reflectance measurements.