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With the development of single-photon-sources of ultra-efficient light extraction, nanowire structures, with embedded quantum wells, present unprecedented opportunity to enhance the light extraction efficiency (LEE) of light emitting diodes (LEDs). In this paper, the finite-difference time-domain method is carried out in graphics processing units to explore mechanisms by which nanowire arrays can effectively improve LEE. The results show that the LEE strongly depends on the radius of the nanowire and the distance between the nanowires. On analyzing the emitted power distribution of the dipole in the semiconductor nanowire, the LEE of LEDs agrees with guided power portion of the total power with respect to the radius of the nanowire and the distance between the nanowires. The guided mode has an important role in enhancing the LEE of LEDs. The free-space mode, however, becomes the whispering gallery mode which is not important in LEE. The LEE obtains the maximum at the mode cutoff radius. The height is also discussed in this paper. With the optimized parameters, ~11 times increment in LEE is achieved.