A Quantitative Evaluation of the Dimer Concentration during the (2x1)-(1x1) Phase Transition on Ge(001)

We propose a new quantitative model of the high-temperature (2 × 1)-(1 × 1) phase transition on Ge(0 0 1). We demonstrate that the transition is driven by an entropy facilitated breakup of dimers. A full quantitative description of the reversible variation of the dimer concentration requires incorporation of vibration entropy, not only of the topmost atoms, but also of those in two layers beneath. The main ingredients of our new model include the dimer formation energy and the difference in vibration entropy between the reconstructed (2 × 1) and the bulk-terminated (1 × 1)-phase. This entropy difference amounts to about 1.4 meV/K and the obtained dimer formation energy of 1.5 ± 0.2 eV is in good agreement with calculated values.