Modeling of Solution Growth of ZnO Hexagonal Nanorod Arrays in Batch Reactors

Abstract

Low temperature solution growth is an attractive method for the preparation of nanostructured semiconductor materials with a wide range of applications from optoelectronics to chemical sensing. Despite the widespread application of low temperature solution growth, basic phenomena taking place during the growth are still under debate. The growth is mostly carried out in batch reactors, which are largely scalable and convenient for applied research and industrial applications. The batch reactors are filled with reactants and sealed, and there is no further inflow of the reactants during the growth. As the growth proceeds, the reactants are depleted, and the growth velocities decrease. Conventionally, the growth process is analyzed in static conditions, where the gradual depletion of the reactants in time is neglected. We analyzed time evolution of the growth of ZnO nanorod arrays on conventional sol–gel seed layers and on GaN substrates patterned by focused ion beam lithography. The focused ion beam lithography allows for precise control of the distances between the nanorods in the arrays. We show that for short growth times the growth is reaction limited, while for longer times the growth regime depends on the distance between the nanorods and changes from reaction limited to diffusion limited as the distance between the nanorods decreases. Under diffusion limited growth conditions, the nanorod height depends on the position within the pattern. The nanorods at the edge of the hexagonal pattern with 19 nanorods in diameter are significantly taller than the nanorods in the center. These experimental observations are validated by the solution of the diffusion equation by a finite element method.

Implementing the Reactor Geometry in the Modeling of Chemical Bath Deposition of ZnO Nanowires

“…However, despite the progress mentioned, it also presents several limitations that need to be considered. Firstly, more precise implementation of the homogeneous growth of ZnO in the calculated NW axial growth rate is required and may be achieved for instance by directly modifying the diffusion equation, as described by Černohorský et al [ 34 ], although this approach considerably increases the difficulty of the analytical solution and typically requires more complex numerical methods. Secondly, the occurrence of spontaneous natural convection at the microscopic scale is currently not implemented despite its contribution to the diffusion of chemical species [ 42 , 43 ].…”

“…In this context, the theoretical modeling of the elongation process of ZnO NWs by CBD deserves particular attention [ 30 , 31 , 32 , 33 , 34 ]. However, the expression of their axial growth rate has mainly been limited to static conditions, in which the concentration profile of the reactants in the chemical bath is considered constant with time, and thus, its temporal dependance is neglected [ 30 , 31 , 32 ].…”

“…The expressions of the time-dependent axial growth rate of ZnO NWs, R c dyn , and of their elongation, L dyn , are formulated as follows: where C eq is the equilibrium concentration of Zn(II) ions (m −3 ). Using a similar approach, Černohorský et al employed finite element method calculations to solve the Fick’s diffusion equation in two dimensions and assessed the impact of the transverse diffusion of chemical reactants on the growth of small arrays of ZnO NWs [ 34 ]. However, these different studies have systematically considered the reactor as an infinite reservoir of chemical reactants, and the influence of the reactor size on the elongation process of ZnO NWs has basically not been investigated yet despite its critical importance.…”

Hydrothermally grown defect-free ZnO nanorods with high angular distribution for enhanced excitonic emission

“…In fact, most reports, which use a similar approach of hydrothermal growth, show ZnO rods with an average diameter well above 100 nm. [53][54][55] 1…”

In situ analysis of the nucleation of O- and Zn-polar ZnO nanowires using synchrotron-based X-ray diffraction

“…41 The elongation process of ZnO NWs is limited either by i) the surface reaction at the top polar c-face for small S values, or by ii) the diffusive transport of reactants (e.g., the limiting Zn(II) species) for larger S values. [41][42][43][44] In the vast majority of cases, a high number density of ZnO NWs on the polycrystalline ZnO seed layer results in large S values such that growth occurs in the diffusive transport-limited regime. 41 The diameter and length of ZnO NWs are thus inversely proportional to the number density.…”