Limits of Conductivity in ZnO Thin Films: Experiment and Theory

Transparent conductive oxides (TCOs) have major (multi-{\$}B) roles in applications such as flat-panel displays, solar cells, and architectural glass. The present workhorse TCO is indium-tin-oxide (ITO), but the recent huge demand for ITO has made In very expensive; moreover, it is toxic. The most commonly suggested replacement for ITO is ZnO, doped with Al, Ga, or In, and indeed the ISI lists 628 papers on Group-III-doped ZnO in 2009. However, to our knowledge, none of these papers has included calculations of donor N$_{D}$ and acceptor N$_{A}$ concentrations, the fundamental components of conductivity in semiconductors. We have developed a simple model for the calculation of N$_{D}$ and N$_{A}$ from temperature-dependent measurements of carrier concentration n, mobility $\mu $, and film thickness d. With the inclusion of phonon scattering in the model, excellent fits of n and $\mu $ are obtained from 15 -- 300 K. Experimentally, we have shown that highly conductive ZnO films can be grown by pulsed laser deposition in a pure Ar ambient, rather than the usual O$_{2}$. In a 278-$\mu $m-thick film, we have achieved a room-temperature resistivity $\rho $ = 1.96 x 10$^{-4}$ $\Omega $-cm, carrier concentration n = 1.14 x 10$^{21}$ cm$^{-3}$, and mobility $\mu $ = 28.0 cm$^{2}$/V-s. From our model, we calculate N$_{D}$ = 1.60 x 10$^{21}$ and N$_{A}$ = 4.95 x 10$^{20}$ cm$^{-3}$; however, the model also predicts that a significant reduction of N$_{A}$ would give $\mu $ = 42.5 cm$^{2}$/V-s and $\rho $ = 7.01 x 10$^{-5} \quad \Omega $-cm, a world record. Such a reduction in N$_{A}$ may be possible by in-diffusion of Zn after growth, since there is evidence that one of the major acceptor species in these films is the Zn-vacancy/Ga$_{Zn}$ complex. We can also decrease the resistivity by annealing in forming gas, and have recently attained $\rho $ = 1.46 x 10$^{-4} \quad \Omega $-cm, n = 1.01 x 10$^{21}$ cm$^{-3}$, and $\mu $ = 42.2 cm$^{2}$/V-s, giving N$_{D}$ = 1.13 x 10$^{21}$ and N$_{A}$ = 1.09 x 10$^{20}$ cm$^{-3}$. In very thin films, quantum effects must be considered.