Phase stability of monolayer Si _1−x Ge _x alloys with a Dirac cone

The phase stability and electronic properties of two-dimensional Si1-xGex alloys are investigated via the first-principles method in combination with the cluster expansion and Monte Carlo simulations. The calculated composition-temperature phase diagram indicates that at low temperatures (below 200 K) monolayer Si1-xGex alloys energetically favor phase separation, whereas when the temperature is increased above 550 K, Si1-xGex alloys can be stabilized and thereby form solid solutions across the whole composition range. Special quasi-random structures were constructed to model the monolayer Si1-xGex. The Si1-xGex alloys are found to possess a robust Dirac cone against composition variation. These results provide a guideline for the experimental realization of Si1-xGex alloys and monolayer Si1-xGex alloys are believed to hold great potential for realization of applications in nanoelectronics and nano-optoelectronics.