Current induced bunches of steps on the Si(111) surface – a key to measuring the temperature dependence of the step interaction coefficient

Abstract

The central result of this work is the experimentally determined temperature dependence g( T) of the step interaction coefficient in the expression f( ρ)= f(0)+ κρ+ gρ 3 for the surface free energy (per unit projected area) of a vicinal surface of Si(111) with a density of steps ρ. We measured the width L b of a bunch, consisting of a fixed number of steps, as a function of the temperature of the Si crystal, heated by direct electric current. We carried out these measurements in three different regimes – during crystal–vapour equilibrium, during sublimation and during crystal growth. For the interpretation of the experimental results we used the hypothesis of electromigration of the Si adatoms and we derived and integrated numerically a set of equations for the step motion under crystal–vapour equilibrium. We evaluated the temperature dependence g( T) in the high temperature interval on the basis of the derived expression g(T) g(T 0) = L b 3(T) L b 3(T 0) I(T) I(T 0) and the measured values of L b and I( T) during crystal–vapour equilibrium [ I( T) is the electric current, flowing through the Si crystal to keep it at a temperature T). We found a strong temperature dependence g( T) in the interval 1300–1340°C [taking T 0=1300°C we obtained g(1340° C) g(1300° C) =2.4 ]; an Arrhenius plot of the experimental data for g( T) in this temperature interval results an activation energy E g=4.2±0.4 eV. The experiments on the temperature dependence of the bunch width L b under non-equilibrium conditions (growth of the Si crystal) manifest a sharp peak (at T=1230°C), which indicates a significant change of the structure of the Si(111) surface.