Exploiting flux shadowing for strain and bending engineering in core-shell nanowires.

Here we report on the non-uniform shell growth of InxGa1-xAs on the GaAs nanowire (NW) core by molecular beam epitaxy (MBE). The growth was realized on pre-patterned silicon substrates with the pitch size (p) ranging from 0.1 µm to 10 µm. Considering the preferable bending direction with respect to the MBE cells as well as the layout of the substrate pattern, we were able to modify the strain distribution along the NW growth axis and the subsequent bending profile. For NW arrays with a high number density, the obtained bending profile of the NWs is composed of straight (barely-strained) and bent (strained) segments with different lengths which depend on the pitch size. A precise control of the bent and straight NW segment length provides a method to design NW based devices with length selective strain distribution.

In situx-ray analysis of misfit strain and curvature of bent polytypic GaAs-InxGa1-xAs core-shell nanowires.

Misfit strain in core-shell nanowires can be elastically released by nanowire bending in case of asymmetric shell growth around the nanowire core. In this work, we investigate the bending of GaAs nanowires during the asymmetric overgrowth by an InxGa1-xAs shell caused by avoiding substrate rotation. We observe that the nanowire bending direction depends on the nature of the substrate's oxide layer, demonstrated by Si substrates covered by native and thermal oxide layers. Further, we follow the bending evolution by time-resolvedin situx-ray diffraction measurements during the deposition of the asymmetric shell. The XRD measurements give insight into the temporal development of the strain as well as the bending evolution in the core-shell nanowire.

Correlating in situ RHEED and XRD to study growth dynamics of polytypism in nanowires.

Design of novel nanowire (NW) based semiconductor devices requires deep understanding and technological control of NW growth. Therefore, quantitative feedback over the structure evolution of the NW ensemble during growth is highly desirable. We analyse and compare the methodical potential of reflection high-energy electron diffraction (RHEED) and X-ray diffraction reciprocal space imaging (XRD) for in situ growth characterization during molecular-beam epitaxy (MBE). Simultaneously recorded in situ RHEED and in situ XRD intensities show strongly differing temporal behaviour and provide evidence of the highly complementary information value of both diffraction techniques. Exploiting the complementarity by a correlative data analysis presently offers the most comprehensive experimental access to the growth dynamics of statistical NW ensembles under standard MBE growth conditions. In particular, the combination of RHEED and XRD allows for translating quantitatively the time-resolved information into a height-resolved information on the crystalline structure without a priori assumptions on the growth model. Furthermore, we demonstrate, how careful analysis of in situ RHEED if supported by ex situ XRD and scanning electron microscopy (SEM), all usually available at conventional MBE laboratories, can also provide highly quantitative feedback on polytypism during growth allowing validation of current vapour-liquid-solid (VLS) growth models.

Quantitative analysis of time-resolved RHEED during growth of vertical nanowires.

We present an approach for quantitative evaluation of time-resolved reflection high-energy electron diffraction (RHEED) intensity patterns measured during the growth of vertical, free-standing nanowires (NWs). The approach considers shadowing due to attenuation by absorption and extinction within the individual nanowires and estimates the time dependence of its influence on the RHEED signal of the nanowire ensemble as a function of instrumental RHEED parameters and the growth dynamics averaged over the nanowire ensemble. The developed RHEED simulation model takes into account the nanowire structure evolution related to essential growth aspects, such as axial growth, radial growth with tapering and facet growth, as well as so-called parasitic intergrowth on the substrate. It also considers the influence of the NW density, which turns out to be a sensitive parameter for the time-dependent interpretation of the intensity patterns. Finally, the application potential is demonstrated by evaluating experimental data obtained during molecular beam epitaxy (MBE) of self-catalysed GaAs nanowires. We demonstrate, how electron shadowing enables a time-resolved analysis of the crystal structure evolution at the top part of the growing NWs. The approach offers direct access to study growth dynamics of polytypism in nanowire ensembles at the growth front region under standard growth conditions.

Impact of the Shadowing Effect on the Crystal Structure of Patterned Self-Catalyzed GaAs Nanowires.

The growth of regular arrays of uniform III-V semiconductor nanowires is a crucial step on the route toward their application-relevant large-scale integration onto the Si platform. To this end, not only does optimal vertical yield, length, and diameter uniformity have to be engineered, but also, control over the nanowire crystal structure has to be achieved. Depending on the particular application, nanowire arrays with varying area density are required for optimal device efficiency. However, the nanowire area density substantially influences the nanowire growth and presents an additional challenge for nanowire device engineering. We report on the simultaneous in situ X-ray investigation of regular GaAs nanowire arrays with different area density during self-catalyzed vapor-liquid-solid growth on Si by molecular-beam epitaxy. Our results give novel insight into selective-area growth and demonstrate that shadowing of the Ga flux, occurring in dense nanowire arrays, has a crucial impact on the evolution of nanowire crystal structure. We observe that the onset of Ga flux shadowing, dependent on array pitch and nanowire length, is accompanied by an increase of the wurtzite formation rate. Our results moreover reveal the paramount role of the secondary reflected Ga flux for VLS NW growth (specifically, that flux that is reflected directly into the liquid Ga droplet).

Radial Growth of Self-Catalyzed GaAs Nanowires and the Evolution of the Liquid Ga-Droplet Studied by Time-Resolved in Situ X-ray Diffraction.

We report on a growth study of self-catalyzed GaAs nanowires based on time-resolved in situ X-ray structure characterization during molecular-beam-epitaxy in combination with ex situ scanning-electron-microscopy. We reveal the evolution of nanowire radius and polytypism and distinguish radial growth processes responsible for tapering and side-wall growth. We interpret our results using a model for diameter self-stabilization processes during growth of self-catalyzed GaAs nanowires including the shape of the liquid Ga-droplet and its evolution during growth.

Perspectives and limitations of symmetric X-ray Bragg reflections for inspecting polytypism in nanowires.

X-ray diffraction, possibly time-resolved during growth or annealing, is an important technique for the investigation of polytypism in free-standing nanowires. A major advantage of the X-ray diffraction approach for adequately chosen beam conditions is its high statistical significance in comparison with transmission electron microscopy. In this manuscript the interpretation of such X-ray intensity distribution is discussed, and is shown to be non-trivial and non-unique given measurements of the [111]c or [333]c reflection of polytypic nanowires grown in the (111)c direction. In particular, the diffracted intensity distributions for several statistical distributions of the polytypes inside the nanowires are simulated and compared. As an example, polytypic GaAs nanowires are employed, grown on a Si-(111) substrate with an interplanar spacing of the Ga (or As) planes in the wurtzite arrangement that is 0.7% larger than in the zinc blende arrangement along the (111)c direction. Most importantly, ambiguities of high experimental relevance in the case of strongly fluctuating length of the defect-free polytype segments in the nanowires are demonstrated. As a consequence of these ambiguities, a large set of deviations from the widely used Markov model for the stacking sequences of the nanowires cannot be detected in the X-ray diffraction data. Thus, the results here are of high relevance for the proper interpretation of such data.

Evolution of polytypism in GaAs nanowires during growth revealed by time-resolved in situ x-ray diffraction.

In III-V nanowires the energetic barriers for nucleation in the zinc blende or wurtzite arrangement are typically of a similar order of magnitude. As a result, both arrangements can occur in a single wire. Here, we investigate the evolution of this polytypism in self-catalyzed GaAs nanowires on Si(111) grown by molecular beam epitaxy with time-resolved in situ x-ray diffraction. We interpret our data in the framework of a height dependent Markov model for the stacking in the nanowires. In this way, we extract the mean sizes of faultless wurtzite and zinc blende segments-a key parameter of polytypic nanowires-and their temporal evolution during growth. Thereby, we infer quantitative information on the differences of the nucleation barriers including their evolution without requiring a model of the nucleus.

Polytypism in GaAs nanowires: determination of the interplanar spacing of wurtzite GaAs by X-ray diffraction.

In GaAs nanowires grown along the cubic [111]c direction, zinc blende and wurtzite arrangements have been observed in their stacking sequence, since the energetic barriers for nucleation are typically of similar order of magnitude. It is known that the interplanar spacing of the (111)c Ga (or As) planes in the zinc blende polytype varies slightly from the wurtzite polytype. However, different values have been reported in the literature. Here, the ratio of the interplanar spacing of these polytypes is extracted based on X-ray diffraction measurements for thin GaAs nanowires with a mean diameter of 18-25 nm. The measurements are performed with a nano-focused beam which facilitates the separation of the scattering of nanowires and of parasitic growth. The interplanar spacing of the (111)c Ga (or As) planes in the wurtzite arrangement in GaAs nanowires is observed to be 0.66% ± 0.02% larger than in the zinc blende arrangement.

Retrieving the displacement of strained nanoobjects: the impact of bounds for the scattering magnitude in direct space.

Coherent X-ray diffraction imaging (CXDI) of the displacement field and strain distribution of nanostructures in kinematic far-field conditions requires solving a set of non-linear and non-local equations. One approach to solving these equations, which utilizes only the object's geometry and the intensity distribution in the vicinity of a Bragg peak as a priori knowledge, is the HIO+ER-algorithm. Despite its success for a number of applications, reconstruction in the case of highly strained nanostructures is likely to fail. To overcome the algorithm's current limitations, we propose the HIO(O(R))(M)+ER(M)-algorithm which allows taking advantage of additional a priori knowledge of the local scattering magnitude and remedies HIO+ER's stagnation by incorporation of randomized overrelaxation at the same time. This approach achieves significant improvements in CXDI data analysis at high strains and greatly reduces sensitivity to the reconstruction's initial guess. These benefits are demonstrated in a systematic numerical study for a periodic array of strained silicon nanowires. Finally, appropriate treatment of reciprocal space points below noise level is investigated.