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

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.