In recent years, frequency diverse array (FDA) has attracted widespread attention owing to its unique range-angle dependent beampattern. However, existing FDA-based research and applications mainly focus on linear arrays, which are limited in many practical scenarios. In this work, we extend the linear FDA theory to planar FDA (PFDA), investigating its transmit beampattern and revealing the three-dimensional (3-D) spatial beam automatic scanning characteristic of its beam. The variation of the beam with respect to pulse duration are systematically studied, accompanied by derivation of the fundamental relationship between this beam scanning characteristic and two-dimensional (2-D) frequency increment configurations. Simulations confirm the wide-angle automatic scanning of PFDA beams in 3-D space, exhibiting potential advantages over conventional planar phased arrays (PA).