The 100th anniversary of the four-point probe technique: the role of probe geometries in isotropic and anisotropic systems

The electrical conductivity of solid-state matter is a fundamental physical property and can be precisely derived from the resistance measured via the four-point probe technique excluding contributions from parasitic contact resistances. Over time, this method has become an interdisciplinary characterization tool in materials science, semiconductor industries, geology, physics, etc, and is employed for both fundamental and application-driven research. However, the correct derivation of the conductivity is a demanding task which faces several difficulties, e.g. the homogeneity of the sample or the isotropy of the phases. In addition, these sample-specific characteristics are intimately related to technical constraints such as the probe geometry and size of the sample. In particular, the latter is of importance for nanostructures which can now be probed technically on very small length scales. On the occasion of the 100th anniversary of the four-point probe technique, introduced by Frank Wenner, in this review we revisit and discuss various correction factors which are mandatory for an accurate derivation of the resistivity from the measured resistance. Among others, sample thickness, dimensionality, anisotropy, and the relative size and geometry of the sample with respect to the contact assembly are considered. We are also able to derive the correction factors for 2D anisotropic systems on circular finite areas with variable probe spacings. All these aspects are illustrated by state-of-the-art experiments carried out using a four-tip STM/SEM system. We are aware that this review article can only cover some of the most important topics. Regarding further aspects, e.g. technical realizations, the influence of inhomogeneities or different transport regimes, etc, we refer to other review articles in this field.DFG/FOR1700DFG/Te 386/9-

Space charge layer effects in silicon studied by in situ surface transport

Electronic properties of low dimensional structures on surfaces can be comprehensively explored by surface transport experiments. However, the surface sensitivity of this technique to atomic structures comes along with the control of bulk related electron paths and internal interfaces. Here we analyzed the role of Schottky-barriers and space charge layers for Si-surfaces. By means of a metal submonolayer coverage deposited on vicinal Si(1 1 1), we reliably accessed subsurface transport channels via angle- and temperature-dependent in situ transport measurements. In particular, high temperature treatments performed under ultra high vacuum conditions led to the formation of surface-near bulk defects, e.g. SiC-interstitials. Obviously, these defects act as p-type dopants and easily overcompensate lightly n-doped Si substrates

Synthesis of vertically-aligned GaAs nanowires on GaAs/(111)Si heterosubstrates by metalorganic vapour phase epitaxy

We report on the Au-catalysed synthesis of GaAs nanowires on hetero-structured GaAs/(111)Si substrates by metalorganic vapour phase epitaxy. It is demonstrated that the deposition of a 40-50 nm thin GaAs epilayer onto Si guarantees a high percentage of straight and vertically-aligned GaAs nanowires. GaAs epilayers were grown at 400 °C and subsequently annealed at 700 °C. Growth experiments performed on 4°-miscut and exactly-oriented (111)Si substrates show that a higher yield (close to 90%) of vertical nanowires is obtained using miscut substrates, an effect ascribed to the smoother surface morphology of GaAs epilayers on these substrates. Comparison between the cross-sectional shape of nanowires grown on GaAs/(111)Si heterosubstrates and those on (111)A-GaAs and (111)B-GaAs substrates demonstrates that both GaAs epilayers and over-grown nanowires are (111)B-oriented

Interwire coupling for In(4x1) /Si(111) probed by surface transport

The In/Si(111) system reveals an anisotropy in the electrical conductivity and is a prototype system for atomic wires on surfaces. We use this system to study and tune the interwire interaction by adsorption of oxygen. Through rotational square four-tip transport measurements, both the parallel (σ||) and perpendicular (σ⊥) components are measured separately. The analysis of the I(V) curves reveals that σ⊥ is also affected by adsorption of oxygen, showing clearly an effective interwire coupling, in agreement with density-functional-theory-based calculations of the transmittance. In addition to these surface-state mediated transport channels, we confirm the existence of conducting parasitic space-charge layer channels and address the importance of substrate steps by performing the transport measurements of In phases grown on Si(111) mesa structures.DFG/FOR/170

Atomic size effects studied by transport in single silicide nanowires

Ultrathin metallic silicide nanowires with extremely high aspect ratios can be easily grown, e.g., by deposition of rare earth elements on semiconducting surfaces. These wires play a pivotal role in fundamental research and open intriguing perspectives for CMOS applications. However, the electronic properties of these one-dimensional systems are extremely sensitive to atomic-sized defects, which easily alter the transport characteristics. In this study, we characterized comprehensively TbSi2 wires grown on Si(100) and correlated details of the atomic structure with their electrical resistivities. Scanning tunneling microscopy (STM) as well as all transport experiments were performed in situ using a four-tip STM system. The measurements are complemented by local spectroscopy and density functional theory revealing that the silicide wires are electronically decoupled from the Si template. On the basis of a quasiclassical transport model, the size effect found for the resistivity is quantitatively explained in terms of bulk and surface transport channels considering details of atomic-scale roughness. Regarding future applications the full wealth of these robust nanostructures will emerge only if wires with truly atomically sharp interfaces can be reliably grown. © 2016 American Physical Society.DFG/FOR/170

Tuning the conductivity along atomic chains by selective chemisorption

Adsorption of Au on vicinal Si(111) surfaces results in growth of long-range ordered metallic quantum wires. In this paper, we utilized site-specific and selective adsorption of oxygen to modify chemically the transport via different channels in the systems Si(553)-Au and Si(557)-Au. They were analyzed by electron diffraction and four-tip STM-based transport experiments. Modeling of the adsorption process by density functional theory shows that the adatoms and rest atoms on Si(557)-Au provide energetically favored adsorption sites, which predominantly alter the transport along the wire direction. Since this structural motif is missing on Si(553)-Au, the transport channels remain almost unaffected by oxidation. © 2017 American Physical Society.DFG/FOR/170

Shape, size evolution and nucleation mechanisms of GaAs nanoislands grown on (111)Si by low temperature metalorganic vapor phase epitaxy

The shape, size evolution, and nucleation mechanisms of GaAs nanoislands grown at 400 degrees C on As-stabilized (111)Si by metal-organic vapor phase epitaxy are reported for the first time. GaAs crystallizes in the zincblende phase in the very early nucleation stages until a continuous epilayer is formed. GaAs nanoislands grow (111)-oriented on Si as truncated hexagonal pyramids, bound by six equivalent {120} side facets and a (111) facet at the top. Their diameter and height appear to increase linearly with the deposition time, yielding a constant aspect ratio of similar to 1/4. The nanoisland density (before coalescence) stays constant with time at similar to 2 x 10^(10) cm(-2), suggesting that the nucleation occurs at specific Si surface sites (defects) during the very early growth stages, rather than being due to the continuous formation of new nuclei. To understand the molecular-level mechanisms driving the low-temperature MOVPE growth of GaAs on Si, we applied a deposition-diffusion-aggregation (DDA) nucleation model, which predicts a linear evolution of the overall GaAs growth rate with surface coverage, in good agreement with experimental observations, under the assumption that direct impingement of trimethylgallium (Me3Ga) molecules onto the nanoisland surface dominates the material nucleation and growth rate; the contribution of Me3Ga adsorbed onto the As-stabilized (111)Si is negligible, pointing out the reduced reactivity of the Si surface (As passivation). Our DDA model allows estimation of the effective reactive sticking coefficient of Me3Ga onto GaAs, which is equal to 2.82 X 10^(-5) : the small value is compatible with the Me3Ga large steric hindrance and the competitive role of methyl radicals in surface adsorption at low temperature

Shape, Size Evolution, and Nucleation Mechanisms of GaAs Nanoislands Grown on (111)Si by Low-Temperature Metal–Organic Vapor-Phase Epitaxy

The shape, size evolution, and nucleation mechanisms of GaAs nanoislands grown at 400 degrees C on As-stabilized (111)Si by metal-organic vapor phase epitaxy are reported for the first time. GaAs crystallizes in the zincblende phase in the very early nucleation stages until a continuous epilayer is formed. GaAs nanoislands grow (111)-oriented on Si as truncated hexagonal pyramids, bound by six equivalent {120} side facets and a (111) facet at the top. Their diameter and height appear to increase linearly with the deposition time, yielding a constant aspect ratio of similar to 1/4. The nanoisland density (before coalescence) stays constant with time at similar to 2 x 10^(10) cm(-2), suggesting that the nucleation occurs at specific Si surface sites (defects) during the very early growth stages, rather than being due to the continuous formation of new nuclei. To understand the molecular-level mechanisms driving the low-temperature MOVPE growth of GaAs on Si, we applied a deposition-diffusion-aggregation (DDA) nucleation model, which predicts a linear evolution of the overall GaAs growth rate with surface coverage, in good agreement with experimental observations, under the assumption that direct impingement of trimethylgallium (Me3Ga) molecules onto the nanoisland surface dominates the material nucleation and growth rate; the contribution of Me3Ga adsorbed onto the As-stabilized (111)Si is negligible, pointing out the reduced reactivity of the Si surface (As passivation). Our DDA model allows estimation of the effective reactive sticking coefficient of Me3Ga onto GaAs, which is equal to 2.82 X 10^(-5) : the small value is compatible with the Me3Ga large steric hindrance and the competitive role of methyl radicals in surface adsorption at low temperature

Surface-mediated electrical transport in single GaAs nanowires

III-V semiconductor compound based nanowires (NWs) are expected to impact the fields of nano-electronic, nano-photonic, and photovoltaic devices. Self-assembly of crystal-phase controlled and high optical quality III-V NWs has been demonstrated. However, important physical and technological issues, such as carrier transport properties and reproducible incorporation of high dopant concentrations in NW materials, remain to be addressed for enabling robust nano-devices fabrication. In this work, we show the use of a multi-probe scanning tunneling microscope for the rapid electrical characterization of free-standing GaAs NWs, without any need for post-growth sample processing and contact fabrication. In particular, 2-probe I-V measurements were performed along the axis of a single 60-nm diameter unpassivated GaAs NW, and its resistance profile determined, obtaining high (in the range of GOhm) resistance values. Due to its reduced radial dimension, the NW is expected to be completely depleted. Analysis of the NW resistance profile reveals instead, that carrier transport is mediated by the NW surface states. Finally, by using the substrate as a reference electrode and placing the other three STM-tips along the NWs, we demonstrate a 4-point probe geometry that can be used for the electrical characterization of highly doped NWs

Structural characterization of MOVPE-grown GaAs/AlGaAs core-shell nanowires through transmission electron microscopy

We investigated by means of transmission electron microscopy (TEM) GaAs-AlGaAs core-shell nanowires (NWs) grown by Au-catalyzed metalorganic vapor phase epitaxy under As-rich vapor conditions. The structural analysis reveals that the NWs exhibit zincblende phase only and a very low density of twin defects along the NW trunk; a higher amount of twins around the NW axial (growth) direction occur instead within a tapered region closeby the NW tip. We correlate this finding to the Alrich composition of the tapered region, as deduced by scanning-TEM (STEM) mass contrast analysis, this region being the effect of residual Au-assisted self-assembly of the material during shell overgrowth. In addition a few percent of NWs show branching during their growth, and we determine the crystal properties and defects of branched NWs. We propose that this phenomenon may be induced by Au nanoparticle instabilities during NW growth and further demonstrate that twin defects occur at the NW branching points