Growth kinetics and theoretical modeling of selective molecular beam epitaxy for growth of GaAs nanowires on nonplanar (001) and (111)B substrates

Abstract

The growth kinetics involved in the selective molecular beam epitaxy growth of GaAs quantum wires ͑QWRs͒ on mesa-patterned substrates is investigated in detail experimentally, and an attempt is made to model the growth theoretically, using a phenomenological continuum model. Experimentally, ͗Ϫ110͘-oriented QWRs were grown on ͑001͒ and ͑113͒A substrates, and ͗Ϫ1Ϫ12͘-oriented QWRs were grown on ͑111͒B substrates. From a detailed investigation of the growth profiles, it was found that the lateral wire width is determined by facet boundaries ͑FBs͒ within AlGaAs layers separating growth regions on top facets from those on side facets of mesa structures. Evolution of FBs during growth was complicated. For computer simulation, measured growth rates of various facets were fitted into a theoretical formula to determine the dependence of a lifetime of adatoms on the slope angle of the growing surface. The continuum model using the slope angle dependent lifetime reproduced the details of the experimentally observed growth profiles very well for growth on ͑001͒, ͑113͒A, and ͑111͒B substrates, including the complex evolution of facet boundaries

Growth Simulation and Actual MBE Growth of Triangular GaAs Nanowires on Patterned (111)B Substrates

“…(2) are the two important parameters that determine the growth features. ?n our previous work [20], we have shown that the following theoretical formula for τ (θ) obtained by Ohtsuka, et al [14,15] by solving a diffusion equation on a terrace with steps, gives satisfactory results in reproducing experiments. Therefore, this equation was used here again for simulation.…”

“…In both samples, the boundary separating the growth region between the top and the side facets can be clearly identified after repeated growth. We call this boundary the facet boundary (FB) as we did in our previous study [20]. Apparently, two FBs determine the lateral size of the bottom width of QWRs formed selectively on the mesa top.…”

“…For these, we know from our previous experience [20] that growth on (111)B substrates were characterized by the appearance of specific facets of (513) and (512) planes in addition to the initial (111)B plane. Based on the previous results, the relation of lifetime, τ 111B , τ 513 , and τ 5−12 , respectively on (111)B, (513) and (512) planes was set to be τ 111B : τ 512 : τ 5−13 = 1 : 0.9 : 2.5 with τ 111B = 1.5 sec.…”

“…As a means of quantitative theoretical description, a computer simulation method which our group recently developed [19,20] was applied in an attempt to reproduce the present experimental results. This computer simulation was based on a phenomenological continuum growth model in which the growth process is described by a diffusion equation with macroscopic parameters such as diffusion constant and lifetime of adsorbed adatoms on growing surfaces.…”

“…Thus, it is not clear whether a suitable model can quantitatively reproduce the experimentally observed evolution of cross-sectional features of nanometer-sized quantum structures so that it can be utilized for design and control of growth of nanostructures. From such a view point, we have recently carried out a series of works on detailed comparison between growth experiments and the continuum modeling for selective MBE growth of GaAs QWRs on (001) and (111)B patterned substrates [19,20]. As a result, we established the basis of realistic simulation procedure by which actual growth can be predicted, designed and controlled.…”