Using scanning tunneling microscopy (STM) observations, it has been found that bismuth and aluminum form the only 2 × 2 ordered structure over the entire Si(111) surface, covering it either with small-sized domains, large-sized domains or ordered 9 × 9 domains depending on the way of formation. This structure can be formed in wide range of temperature, from room temperature to 500 °C, and on various initial surfaces. Angle-resolved photoelectron spectroscopy (ARPES) has demonstrated that the 2 × 2-(Bi, Al) is semiconducting. The structural model of the 2 × 2 has been determined using ab-initio random structure searching method and confirmed by comparison of simulated and experimental STM images as well as experimental ARPES spectrum and calculated energy-band dispersion.