S b / S i ( 111 ) Adsorption: Hidden Phase Transitions Behind Langmuir-Like Isotherms
Résumé
The experimental study of the thermodynamic and kinetic properties of the Sb=Si111 interface reveals a surprising behavior: a 2D phase condensates when the Sb coverage increases, indicating strong attractive Sb-Sb interactions, whereas the isotherms present a quasi-Langmuir shape, suggesting that these interactions should be negligible. Ab initio calculations raise this contradiction: while the adsorption site evolves from ternary towards the on-top position with increasing coverage, the character of the Sb-Sb effective interactions changes from repulsive towards attractive, resulting in an almost constant average adsorption energy. A simple (Langmuir) thermodynamic behavior can then be the consequence of a surface phase transition. Although antimony adsorption on silicon has been extensively studied [1-16], only a few studies have been devoted to its thermodynamic and kinetic properties. These properties are studied here at the Sb=Si111 interface. Curiously, kinetic results put in evidence an attractive interaction between Sb adatoms leading to the formation, at equilibrium, of a 2D condensed phase whereas the adsorption or desorption isotherms are Langmuir-like, which a priori excludes any attractive lateral interaction between the adatoms. We will show here that a careful ab initio study of the energetics of the adsorption blows up this contradiction. Experimentally, the kinetic and thermodynamic properties of adsorption or desorption of Sb onto Si(111) surface are analyzed by means of mass spectroscopy [2]. Thus our previous kinetic study [3] revealed two different mechanisms as a function of coverage, involving either single Sb adatoms (< 0:5) or their condensation as a bidimensional gas (> 0:7). This means that the lateral Sb-Sb interactions are strong enough to induce such a condensation beyond a given critical adatom density [3]. In this Letter, the kinetic study is completed by plotting the isotherms P for various substrate temperatures [see Fig. 1(a)]. These isotherms present a sigmoı¨dsigmoı¨d trend specific of a Langmuir behavior. Let us recall that, in the Langmuir picture of adsorption, (i) the adsorption energy is the same for every adsorbed molecule independently of the other molecules, and (ii) every molecule that sticks on an already adsorbed molecule immediately returns to the gas phase. The Langmuir isotherm is thus based on the concept of noninteracting molecules adsorbed on definite sites on the surface so that the coverage varies from zero to one mono-layer without any accident. Therefore, at first sight, the quasi-Langmuir isotherms of Fig. 1(a) are the signature of weak or vanishing lateral interactions between Sb ada-toms. In order to be more quantitative, the experimental isotherms can be fitted by the more general mean-field expression: 1 ÿ P P 0 exp ÿ E ads kT ; (1) where E ads is given by : E ads E ads 0 ZV SbSb : (2) P 0 is a constant (P 0 10 9 Pa at the experimental temperature), E ads 0 is the adsorption energy of a single adatom, and V SbSb the effective interactions between Sb adatoms (either direct or mediated by the Si substrate) should be zero for perfect Langmuir isotherms. Z is the number of Sb-Sb neighbors (here Z 6). It is then easy to reverse the equation (1) to get the experimental variation of E ads . Its average value, derived from the isotherms of Fig. 1(a), is plotted in Fig. 1(b). At first order, this curve can indeed be fitted linearly according to Eq. (2) with: E ads 0 ÿ2:95= ÿ 0:03 eV and V SbSb ÿ0:02= ÿ 0:006 eV (referred to as fit 1). This value of V SbSb seems to confirm the previous qualitative conclusion: the lateral interaction between antimony adatoms are small. Nevertheless, even though this result perfectly agrees with some old results on thermodesorption experiments [4-7], it completely contradicts kinetic experiments which can only be interpreted by means of the existence of significant lateral interaction between Sb adatoms [3]. Moreover, the quasi-Langmuir isotherms drawn using this linear fit of E ads do not fit exactly the experimental ones [see Fig. 1(a)]. The weak deviations can be linked to variations of E ads with respect to the linear fit. Indeed, in spite of the experimental error bars, one can see [Fig. 1(b)] that the experimental data should be better described by two linear regimes (referred to as fit 2): PRL 94, 076101 (2005) P H Y S I C A L