Understanding the Origin of Surface Depletion in $\delta $-doped SrTiO$_{\mathrm{3}}$ Structures

Unlike most of the conventional semiconductors, the large dielectric constant of SrTiO$_{\mathrm{3}}$ results in a pronounced surface depletion width [1]. In thin films, the effect of surface depletion is even more dramatic: reduction of mobility and two-dimensional carrier density. To avoid this effect, capping and buffering a narrow channel of $n$-type doped SrTiO$_{\mathrm{3}}$, so called $\delta $-doping, is designed to make the channel free from surface scattering, resulting in highly mobile carriers [2-4] We have investigated systematic changes in electronic transport by tuning the thicknesses of the undoped surface buffering cap and the $\delta $-doped layer. This has allowed us to map the phase diagram consisting of a three-dimensional metal, two-dimensional metallic behavior, and an insulating phase. We also show the surface depletion width as a function of doping density in order to study the origin of surface depletion of SrTiO$_{\mathrm{3}}$ [1] A. Ohtomo and H. Y. Hwang, \textit{Appl. Phys. Lett.} \textbf{84}, 1716 (2004). [2] Y. Kozuka \textit{et al}., \textit{Appl. Phys. Lett.} \textbf{97}, 222115 (2010). [3] Y. Kozuka, M. Kim \textit{et al., Nature} \textbf{462}, 487 (2009). [4] M. Kim \textit{et al., Phys. Rev. Lett.} \textbf{107}, 106801 (2011).