The applicability of models based on fractal geometry to characterize the surface of the EL devices was investigated. Insulating layer and phosphor layer of EL devices were deposited on ITO glass using e-beam method. The images of phosphor layer by scanning electron microscope(SEM) were transformed to binary coded data. The relations between fractal geometry and electrical characteristics of EL devices were investigated. When the fractal dimension of $Cas:EuF_3$ EL device was 1.82 and its grain boundary area was 19%, the brightness of $Cas:EuF_3$ EL device was 261 cd/$ extrm{m}^2$.