An alternative approach to realize 2D beam steering with ultra-wide range by silicon integrated optical phased array is proposed. A dot matrix scanning method, using the phase control and grating emitters with different periods, is conceived to design the optical phased array device without the requirement of tunable lasers. Simulations demonstrate an ultra-wide steering range up to 120°×100°, together with over 16×400 resolvable points by using a single-wavelength laser. Moreover, the designed optical phased array device demands only a part of active elements working simultaneously, which benefits to reduce the electrical power consumption. The proposed approach provides a promising solution for wide-angle, low-cost, and low-power consumption 2D beam steering devices, especially suitable for solid-state light detection and ranging systems.