An offset of a straight step, called a kink, is occasionally formed on semiconductor surfaces. The motion of the kink on the Si(1 1 1) 7 x 7 surface in the [(1) over bar (1) over bar 2] step was studied in detail by high-temperature scanning tunneling microscopy (STM), and thermal fluctuations of the kink displacement along the step edges was observed. The kink displacement did not diverge with time, suggesting that a restoring force acts on the kink. The displacement, however, could be clearly represented by the gaussian distribution and it was therefore considered to be a Brownian particle. The temperature dependence of the mean square displacement of the kink position showed that the displacement is a thermal activation process with an apparent activation energy of 1.54 +/- 0.1 eV. From the equation of motion on the kink displacement including an incoming and outgoing flux as a fluctuation source, the phenomenological Langevin equation was derived. The activation energy of the kink displacement is related to the diffusion coefficient of the two-dimensional adatom gas and the latent heat of the atoms from the kink site to the surface adatom. (C) 2003 Elsevier Science B.V. All rights reserved.