Theoretical and numerical studies of the two-dimensional (2D) global stability and mode structures of high-n beta-induced Alfvén eigenmodes excited by magnetically trapped energetic electrons in tokamaks are carried out by employing the WKB-ballooning mode representation along with the generalized fishbone-like dispersion relation. Depending on parameter regimes, it is found that (i) the mode growth rate has a maximum with increasing energetic electron density at the ground radial eigenstate; (ii) the ground and excited radial eigenstates can be unstable simultaneously, and the most unstable mode is related not only to the pressure gradient of energetic electrons, but also to the width of the mode itself; (iii) the corresponding 2D mode structures are twisted due to the anti-Hermitian contribution from wave-energetic electron interaction and show opposite deformation directions compared with that in the presence of energetic ions; and (iv) the mode structures, especially, the mode width and its radial asymmetry, can be affected by radial eigen-mode number, energetic electron density, and magnetic shear. Finally, the radial symmetry breaking of the localized e-BAE mode structure with respect to parallel wave-number has a potential impact on toroidal momentum transport.