We found that electron beam (EB) irradiation induces structural modification Si(001)-c(4×2) surfaces below ∼40 K. At 24 K, we observed a clear c(4×2) low energy electron diffraction (LEED) pattern immediately after opening the observation, while quarter-order diffraction spots became dim and streaky during the subsequent observation. The results indicate that the c(4×2) arrangement of asymmetric dimers is the most stable structure in the Si(001) surface even below 40 K. The proposed phase transition at 40 K [Matsumoto et al.: Phys. Rev. Lett. 90, 106103 (2003)] is improbable. We quantitatively investigated the current density, beam energy, and substrate temperature dependences of the EB induced decrease in intensity of the quarter-order spots to reveal the origin of the EB effect. Results obtained indicate that electronic excitation and the drop in the carrier concentration at low temperatures cause the EB effect.