Impact of the liquid phase shape on the structure of III-V nanowires
Résumé
The III-V nanowire structure (zinc blende or wurtzite) grown by the vapor-liquid-solid process is shown to be highly dependent on the parameters which shape the droplet at the top of the nanowire. Under conditions that the droplet volume does not exceed a certain value, it is demonstrated that when the nucleation of the solid starts at the solid-liquid-vapor triple line, a relatively large droplet volume and low wetting angle favor the formation of the wurtzite structure. We show that the effective V/III flux ratio is the primary parameter controlling the structure. Most of the III-V semiconductor nanowires (NW) are grown by the vapor-liquid-solid (VLS) process [1], in which a supersaturated liquid droplet initiates NW growth in the (111) direction of the stable zinc blende (ZB) structure or in the equivalent (0001) direction of the metastable wurtzite (WZ) structure. It is now well accepted that the liquid-solid transformation is 2D nucleation limited and that the nucleation events take place preferentially at the vapor-liquid-solid triple phase line (TL) [2,3]. However, for sufficiently small liquid surface energies [4] and sufficiently large contact angles between the top-facet and liquid surface, the probability of nucleating away from the TL may be energetically possible. Assuming a cylindrical shaped NW with a spherical shaped droplet, Glas et al. [2] used classical nucleation theory to show that Au-catalyzed NWs should adopt the metastable hexagonal wurtzite (WZ) structure under conditions of a large difference of chemical potentials between the liquid and the solid, Á, which acts as a driving force for solidification from the supersaturated liquid phase. Taking into account that the NW top facet has a hexagonal shape, we show that the droplet shape will change as a function of its relative size, implying a huge change in the nucleation statistics. We show that the important parameters determining the growth structure are those that determine the shape of the droplet. In agreement with many experiments [5–10], we show that this is determined primarily by the effective V/III current ratio, defined to be the ratio of currents of group V and III elements sorbed in the droplet. The VLS growth can generally be divided into two regimes. Regime I: the droplet is solely in contact with the (111) top surface. Regime II: a part of the TL has expanded onto the side-facet. In this study we focus on regime I which is the most common growth regime. The nucleation barrier is given by the maximum value of the free energy increase upon nucleation, ÁG Ã ZBðWZÞ ð!Þ ¼ cð!Þ À 2 ZBðWZÞ ð!Þ Á ZBðWZÞ , where cð!Þ and À ZBðWZÞ ð!Þ are the nucleus shape factor and the effective specific surface energy of the nucleus, respectively, and ! is the angle between the middle of the side facet and the nucleation site, as measured from the center of the top facet, see Fig. 1. At a given !, the nucleation probability for the ZB (WZ) phase is dominated by the factor exp Àcð!Þ À 2 ZBðWZÞ ð!Þ Á ZBðWZÞ kT : (1) Thus, the driving force Á ZBðWZÞ is in principle the dominating parameter which determines the preferred growth structure at ! for a given droplet shape. Because the free energy of the volume WZ structure is higher than that of the ZB volume [11] we have Á ZB > Á WZ for the same liquid supersaturation. A calculation of the normalized probabilities of nucleating ZB and WZ at a given !, is shown in Fig. 2(a) for Au-assisted GaAs NW growth. Because of the exponential factor in Eq. (1), the total probability of nucleation is practically zero below a critical driving force Á c and increases sharply above, see Fig. 2(b), which means that the driving force will oscillate around Á c due to lowering of the liquid concentrations c III and primarily c V , upon forming each ML. As the equilibrium shape of a NW top facet and a droplet on a 2D surface has a hexagonal shape and is a truncated sphere, respectively, the nucleation conditions are different along the TL. Thus, the total probabilities of WZ or ZB nuclea-tion at the TL can be approximated by integrating over ! P ZBðWZÞ / Z 30 0 exp Àcð!Þ À 2 ZBðWZÞ ð!Þ Á ZBðWZÞ kT d!; (2) where only the interval 0 ! 30 is considered because of the sixfold symmetry of the NW top facet. In order to understand why growth conditions have a huge effect on the structure, we have to examine how cð!ÞÀ 2 ZBðWZÞ ð!Þ depends on changes in the shape of the drop. The nucleus effective step energy can be written as PRL