Atomically flat Ge buffer layers and alternating shutter growth of CaGe$_{\mathrm{2}}$ for large area germanane

Germanane (GeH), which is converted from CaGe$_{\mathrm{2}}$ by soaking in HCl acid, has recently attracted interest because of its novel properties, such as large band gap (1.56eV), spin orbit coupling and predictions of high mobility (18000 cm$^{\mathrm{2}}$/Vs). Previously CaGe$_{\mathrm{2}}$ was successfully grown on Ge(111) substrates by molecular beam epitaxy (MBE) growth. But there were cracks between \textmu m-sized islands, which is not desirable for scientific study and application, and limits the material quality. By growing atomically flat Ge buffer layers and using alternating shutter MBE growth, we are able to grow crack-free, large area films of CaGe$_{\mathrm{2}}$ films. Reflection high energy electron diffraction (RHEED) patterns of Ge buffer layer and CaGe$_{\mathrm{2}}$ indicates high quality two dimensional surfaces, which is further confirmed by atomic force microscopy (AFM), showing atomically flat and uniform Ge buffer layer and CaGe$_{\mathrm{2}}$. The appearance of Laue oscillation in X-ray diffraction (XRD) and Kiessig fringes in X-ray reflectivity (XRR) proves the uniformity of CaGe$_{\mathrm{2}}$ film and the smoothness of the interface. The high quality of CaGe$_{\mathrm{2}}$ film makes it promising to explore novel properties of GeH.