Crystal phase engineering of self-catalyzed GaAs nanowires using a RHEED diagram

It is well known that the crystalline structure of the III–V nanowires (NWs) is mainly controlled by the wetting contact angle of the catalyst droplet which can be tuned by the III and V flux. In this work we present a method to control the wurtzite (WZ) or zinc-blende (ZB) structure in self-catalyzed GaAs NWs grown by molecular beam epitaxy, using in situ reflection high energy electron diffraction (RHEED) diagram analysis. Since the diffraction patterns of the ZB and WZ structures differ according to the azimuth [11̄0], it is possible to follow the evolution of the intensity of specific ZB and WZ diffraction spots during NW growth as a function of the growth parameters such as the Ga flux. By analyzing the evolution of the WZ and ZB spot intensities during NW growth with specific changes of the Ga flux, it is then possible to control the crystal structure of the NWs. ZB GaAs NWs with a controlled WZ segment have thus been realized. Using a semi-empirical model for the NW growth and our in situ RHEED measurements, the critical wetting angle of the Ga catalyst droplet for the structural transition is deduced.

The probed depth of the electron beam could be estimated using the intensity ratios (IR) curves  The movie recorded during the growth and used to plot the intensity ratio (IR) curves shown in Figure 4 (a). The lm has been accelerated 50 times for convenient reasons.

Movie_x50_Fig4.avi
The movie recorded during the growth and used to plot the IR curves shown in Figure 5 (a). The lm has been accelerated 50 times for convenient reasons.

Model for NW growth
The results presented in Fig. 7 are obtained by the numerical implementation of a model for NW growth detailed in [1] but for completeness we recall here the main features of the model. 1 Electronic Supplementary Material (ESI) for Nanoscale Advances. This journal is © The Royal Society of Chemistry 2020 Assume given at time t : the NW length further denoted L(t); the NW radius under the droplet denoted r(t), the value for the critical concentration c ? , the values of Ga and As nominal uxes (i.e. number of atoms/(unit time)(unit surface normal to the ux direction)) and the radius and the As concentration of the droplet further denoted R(t) and c(t) and such that c(t) c ? (subcritical concentration): Obviously, the knowledge of the concentration in the droplet and its volume allow to compute the amount of Ga and As atoms in the droplet, further denoted Q Ga (t) and Q As (t).
The evolution of the NW is driven by the amount of Ga and As atoms feeding the droplet and the following two requirements: (a) solidication occurs only when the droplet concentration attains the critical value c ? and (b) the droplet wetting angle is such that min (t) max where the two limit angles min and max depend on the crystallographic properties of the NW.
The NW growth process is described as follows: in a small time-interval (t; t + t) we assume that the droplet incorporates an amount of Ga atoms, denoted Q Ga (t) coming from one of the following sources: (i) direct impingement, (ii) diusion along the the NW facets with diusion length facet and (iii) diusion on the substrate, caracterized by a diusion length substrate . Obviously, the last contribution is lost when the NW length overcome the diusion length on the NW facets. Meanwhile, we assume that the amount of As atoms feeding the droplet, further denoted Q As (t) is due to direct impingement only.
Two situations may occur: 1. The As potential concentration in the droplet at t + t, dened as is c ? : In this case no solidication occurs and we distinguish two sub-cases: (i) If the droplet can be pinned on the top of the NW with an wetting angle max then the droplet volume increases but the NW length remains constant (no axial growth). (ii) If the droplet volume is such that the wetting angle is greater than max the computation is stopped from droplet stability considerations.
2. The As potential concentration in the droplet is such that Q As (t) + Q As (t) Q As (t) + Q As (t) + Q Ga (t) + Q Ga (t) > c ? : In this case there exist unique equal quantities Q of Ga and As atoms such that Otherwise stated, only the excess of Ga and As atoms (due to supersaturation) will contribute to the solidication process. But the volume of solid material can contibute to both axial and radial growth, depending on the remaining volume of the droplet which now includes a total amount of Ga and As atoms given by Q As (t) + Q As (t) + Q Ga (t) + Q Ga (t) ¡ 2Q: If this volume can be pinned on the top of the NW with an angle (t + t) such that min (t + t) max then we have only axial growth. We update the NW length L(t + t) and the droplet radius R(t): If not, two sub-cases may occur: a) If (t + t) > max we have both axial growth and inverse tappering. The inverse tappering is such that the NW radius r(t + t) is the unique value that can support the xed droplet volume at wetting angle max : As a consequence, the axial growth will place the solid material in a truncated cone geometry with lower radius r(t); upper radius r(t + t) and height determined by the amount of equal solid quantities Q of Ga and As atoms. b) If (t + t) < min we have axial growth and direct tappering and the situation is similar to the previous one. There is an unique value of r(t + t) that can support the droplet at a wetting angle min : The solid material will be placed in a truncated cone geometry with lower radius r(t), upper radius r(t + t) < r(t) and height determined by the amount of equal solid quantities Q of Ga and As atoms.