Understanding Zn Doping of Vapor-Liquid-Solid Grown GaAs Nanowires

III-V semiconductor nanowires are promising building blocks in nanoscale energy conversion. Most prominently in photovoltaics and solid state lighting. In order to fabricate such pn-junction based devices we need to be able to p- and n-dope the nanowires but also understand the doping mechanisms. Here, thermodynamic knowledge of the nanowire-catalyst particle materials system is key.<br/>We have previously demonstrated that we can grow p-type doped GaAs nanowires using aerotaxy [1]. This is a method where the nanowires are formed in the gas phase without substrate [2]. It is a continuous process, where a large number of nanowires per time unit can be produced. Thus, it is very promising for upscaling and for industrial production of nanowires. Moreover, the aerotaxy process also admits doping, which is necessary for electronic device fabrication. In this regard we have experimentally controlled the hole concentration by varying the Zn/Ga ratio during aerotaxy growth.<br/>In this investigation we demonstrate that we can calculate the hole concentration in Zn-doped, gold alloy catalyzed GaAs nanowires grown by the VLS (vapor-liquid-solid) mechanism. We base the calculation on the defect formation energy proposed by Zhang and Northrup [3]. Using density functional theory (DFT), we calculate the energy of the defect, a Zn atom on a Ga site, using a supercell approach. The chemical potentials of Zn and Ga in the liquid catalyst particle are calculated from a thermodynamically assessed CALPHAD (CALculation of PHAse Diagrams) database including Au, Zn, Ga, and As. Using these quantities together with the chemical potential of the carriers, we calculate the hole concentration self-consistently.<br/>Our calculations compare well with the experimental hole concentrations in the Zn-doped GaAs nanowires grown by aerotaxy. Specifically, it is interesting to note that the calculations confirm our experimental observation that it is difficult to achieve low and intermediate doping levels. Except for very low Zn concentrations in the catalyst particle and low growth temperatures, the hole concentration in the nanowire tends to be high (around 10¹⁹ cm^-3 and higher).<br/>To conclude, we demonstrate accurate calculations of the doping concentration of VLS grown nanowires using a combination of DFT and CALPHAD. Such calculations are of great advantage when controlling and predicting the doping concentrations for a wide variety of experimental conditions.<br/>References:<br/>[1] F. Yang, <i>et al.</i>, J. Cryst. Growth <b>414</b>, 181–186 (2015)<br/>[2] M. Heurlin, <i>et al.</i>, Nature, <b>492</b>, 90–94 (2012)<br/>[3] S. B. Zhang and J. E. Northrup, Phys. Rev. Lett. <b>67</b>, 2339-2342 (1991)