Mapping Active Dopants in Single Silicon Nanowires Using Off-Axis

Sep 25, 2009 - We demonstrate that state-of-the-art off-axis electron holography can be used to map active dopants in silicon nanowires as thin as 60 ...
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NANO LETTERS

Mapping Active Dopants in Single Silicon Nanowires Using Off-Axis Electron Holography

2009 Vol. 9, No. 11 3837-3843

Martien I. den Hertog,*,† Heinz Schmid,§ David Cooper,‡ Jean-Luc Rouviere,† Mikael T. Bjo¨rk,§ Heike Riel,§ Pierrette Rivallin,‡ Siegfried Karg,§ and Walter Riess§ INAC/SP2M/LEMMA, LETI, GEM Minatec, 17 rue des Martyrs, 38052 Grenoble Cedex 9, France, and IBM Research GmbH, Zurich Research Laboratory, Sa¨umerstrasse 4, 8803 Ru¨schlikon, Switzerland Received June 24, 2009; Revised Manuscript Received September 1, 2009

ABSTRACT We demonstrate that state-of-the-art off-axis electron holography can be used to map active dopants in silicon nanowires as thin as 60 nm with 10 nm spatial resolution. Experiment and simulation demonstrate that doping concentrations of 1019 and 1020 cm-3 can be measured with a detection threshold of 1018 cm-3 with respect to intrinsic silicon. Comparison of experimental data and simulations allows an estimation of the charge density at the wire-oxide interface of -1 × 1012 electron charges cm-2. Off-axis electron holography thus offers unique capabilities for a detailed analysis of active dopant concentrations in nanostructures.

The scaling of transistors and integrated circuits for future technology nodes poses huge challenges not only in terms of modeling, design, and fabrication but increasingly also regarding the available tools required for structural and compositional analysis of individual devices. Various techniques based on transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM)1,2 are readily available and very successfully employed, but do not yet provide the sensitivity for dopant profiling. While secondary ion mass spectroscopy3 has a high detection sensitivity, it lacks the needed spatial resolution. Alternative methods based on field ionization effects, such as atom probe tomography,4-7 can successfully map the 3D (dopant) atom distribution using a dedicated sample geometry. However, these methods are sensitive only to the chemistry of the structure, not the electronic properties. Therefore no information on the electrical activity of the dopant atoms is obtained. Electrical characterization tools with high spatial resolution, such as scanning spreading resistance microscopy,8 scanning capacitance microscopy,9 Kelvin force microscopy,10 or scanning tunneling microscopy,11 can provide information on the dopant distribution in the proximity of and/or on surfaces. However, no measurements of the active dopant concentration within a thin nanostructure with nanometer* To whom correspondence should be addressed. E-mail: martien.den-hertog@ grenoble.cnrs.fr. † INAC/SP2M/LEMMA, GEM Minatec. ‡ LETI, GEM Minatec. § IBM Research GmbH. 10.1021/nl902024h CCC: $40.75 Published on Web 09/25/2009

 2009 American Chemical Society

scale spatial resolution have so far been demonstrated. Here we show that by employing high-performance off-axis electron holography and using samples that are free from structural defects, the active doping concentration and profile in nanoscale devices can be measured. Electron holography has been successfully used to map active dopant distributions in semiconductor devices that are several hundreds of nanometer thick12-14 and in a ∼200 nm diameter core-shell nanowire.15 To date, however, off-axis electron holography has not yet been applied to sub-100 nm structures with modulated doping profiles as the signal-tonoise ratio in the reconstructed phase images would be too low to detect, since averaging over large areas is not possible in circular nanowire structures. The excellent mechanical and electrical stability of state of the art TEMs, such as the FEI TITAN that was used in this work, allow holograms to be acquired for very long periods, which leads to a high phase resolution in the phase images. Off-axis electron holography is a TEM-based technique that uses a biprism (charged wire) to interfere an object wave that has passed through the sample and a reference wave that has only traversed through vacuum. From the interference pattern (known as electron hologram), an amplitude and phase image of the specimen can be reconstructed. In the absence of magnetic fields and diffraction contrast, the phase difference ∆φ between electrons that have passed through vacuum and electrons that have traversed the specimen is related to the crystal potential, or mean inner potential (MIP) V (x, y, z), by

∆φ ) CE

∫ V(x, y, z)dz t

0

(1)

where CE is an interaction constant (7.29 × 106 rad V-1 m-1 at 200 kV) that depends on the acceleration voltage, and t is the thickness of the sample in the beam direction z. The builtin potential of a p-n junction can be calculated using the classical formula16 (valid only in the absence of other charges, as they will modify the location of valence and conduction bands with respect to the Fermi level) Vbi )

( )

NAND kT ln e n2i

(2)

where k is the Boltzmann constant, ni is the intrinsic carrier concentration of silicon, and NA and ND are the acceptor and donor concentrations, respectively. Using eq 1, the phase difference across a p-n junction for a specimen of known thickness can be converted into the difference in MIP (equal to the built-in potential) and then, in principle, into an active dopant concentration using eq 2. A comparison of simulated data and experimental results have shown that a significant portion of the sample does not contribute to the phase signal. This so-called inactive layer,12 whose extent strongly depends on the dopant concentration, can be more than 100 nm thick.17 For this reason specimens studied by electron holography need to be thicker than twice the inactive layer thickness but smaller than 500 nm. The two factors that contribute to the inactive layer are specimen damage from focused ion beam (FIB) milling during sample thinning12 and surface depletion effects.16,18 During FIB milling, structural defects are introduced at and below the surface, severely compromising the sample quality. Moreover, surface depletion effects can occur in semiconducting samples in the presence of interfacial and oxide layers. Such defects at the oxide interface and within the oxide can both act as trap states for charges.19-21 In addition, charges can be created by bombardment with high-energy electrons,21,22 and therefore experimental results must be compared with simulations that take the actual sample geometry and charge distribution into account. This is particularly important for nanoscale structures, where surface properties can dramatically modify the potential profile in the sample. By using silicon nanowires (SiNWs) grown by the vapor-liquid-solid (VLS) method,23 minimal sample preparation is needed and therefore the crystal is not damaged during this stage. Moreover, these sample geometries allow an undisturbed passage of the reference beam. Two samples of axially modulation doped SiNWs were studied (for the growth details, see the Supporting Information). The SiNWs on sample A contained five 200 nm long n-doped (phosphorus) segments (ND ) 1020 cm-3) separated by equally long intrinsic regions. In this sample, gold clusters were present predominantly on the doped regions24 and small thickness variations could sometimes be observed at the junctions. The SiNWs on sample B were grown epitaxially on a lightly doped (1015 cm-3 p-type) 〈111〉 silicon wafer and contained three 150 nm long n-doped (phosphorus) 3838

Figure 1. Schematic, STEM image, and retrieved phase information of a modulation-doped SiNW. (A) Schematic of a SiNW with 63 nm diameter. The indicated doping concentrations have been estimated from transport measurements.25 (B) HAADF STEM image. (C) Phase image with enhanced color scale revealing four n-doped (phosphorus) regions. (D) Line profile along the dotted line in panel C. The average of the four peaks has been estimated and used to draw the dotted line as a guide to the eye to show the reduced phase signal of the first doped region next to the catalyst particle.

regions with ND of 1020, 1019, and 1018 cm-3 separated by intrinsic segments. Doping concentrations were determined from electrical transport measurements on individual, homogenously doped wires.25 In sample B, a uniform distribution of small gold clusters was present everywhere on the SiNW surface.26,27 Sample B was prepared for TEM observation such that the SiNWs remained attached to the substrate in the vertical 〈111〉 direction (details of the TEM sample preparation are described in the Supporting Information). Both SiNW samples were studied with the native oxide (3 nm) left on the surface. Figure 1 shows a schematic illustration of a SiNW from sample A with the hemispherical gold tip on the left side, and the axially n-doped segments, each doped to ND ) 1020 cm-3 (as estimated from transport measurements25). The corresponding high angle annular dark-field (HAADF) STEM image is shown below (Figure 1B). The phase image reconstructed from the original hologram is shown in Figure 1C, with contrast levels enhanced for better visibility. A line profile made along the reconstructed phase image is shown in Figure 1D. The image and line scan clearly reveal the differently doped regions of the SiNW, showing the four segments of higher phase change values that correspond to the four doped segments, alternated by intrinsic segments. Nano Lett., Vol. 9, No. 11, 2009

The line scan also reveals that the four peaks do not have the same intensity as would be expected. The intensity of the four peaks decreases linearly toward the tip of the SiNW with the peak closest to the tip (to the left in Figure 1D) exhibiting an additionally reduced phase shift. Potential sources of the differences in the observed phase shift are geometrical variations along the length of the SiNW and effects related to the presence of Au on the tip as well as along the SiNW. These effects will be analyzed and discussed later. At this stage, we note that the phase shift induced by the phosphorus dopant atoms in the volume of a 63 nm diameter SiNW gives rise to a detectable phase shift between the reference and the object wave. To explore the detection limit of our measurement setup, SiNWs were used that contained regions with three different donor concentrations, ranging from ND ) 1020 cm-3 down to 1018 cm-3 (as estimated from transport measurements25), from sample B. Figure 2A shows a schematic illustration of a SiNW from sample B with axially n-doped segments. The corresponding experimental electron hologram of a 56 nm diameter SiNW is reproduced below in Figure 2B. The reconstructed phase image with contrast levels enhanced for better visibility is displayed in Figure 2C, and the experimental and the simulated phase profiles are shown in Figure 2D. The experimental phase profile permits all three doped segments within the intrinsic SiNW to be located. However, the magnitudes of the phase shifts do not correlate exactly to the doping concentrations. In addition, as observed in the previous experiment, the signal of the doped segment closest to the Au particle is reduced. An explanation could be that carriers present in the first doped region flow into the gold catalyst or create a buildup of charge near the catalyst interface, due to the difference in work function, thereby effectively reducing or masking the dopant-related potential in the first doped region. Potential simulations (for details, see Supporting Information) were performed for a cylindrical nanowire with different negative charge quantities present at the oxide-silicon interface ranging from 0 to -2 × 1012 e.c. (electron charges) cm-2. The best match between the recorded phase contrast and simulation is obtained using a negative interface charge density of -1 × 1012 e.c. cm-2, which is in excellent agreement with the charge density at the oxide-SiNW interface deduced from transport measurements.25 Simulations without interface charges yielded a step in phase over the junction of less than 0.1 rad. However the measured phase shift, which is approximately equal to the calculated step in phase according to eq 2, is much larger and around 0.35 rad. This discrepancy can be explained by the large depletion width of roughly 1 µm16 in the intrinsic region, which is much longer than the length of the intrinsic segment (200 nm). The depletion width of 1 µm (without interface charge) is reduced to 50 nm if a negative charge density of -1 × 1012 e.c. cm-2 is present. In accordance, the visibility of the lowest doped segment (ND ) 1018 cm-3) depends more sensitively on the amount of charge present at the oxide interface than the higher doped segments, owing to the increased depletion width. In Figure 2e, a vertical phase profile across the nanowire is shown, as indicated by the Nano Lett., Vol. 9, No. 11, 2009

Figure 2. Schematic, off-axis electron hologram and retrieved phase information of a modulation-doped SiNW. (A) Schematic of a SiNW that contains three n-doped (phosphorus) regions of varying doping concentration, 1020, 1019, and 1018 cm-3. The indicated doping concentrations have been estimated from transport measurements.25 All segments are 150 nm long. (B) Off-axis hologram of the SiNW. (C) phase image of the nanowire with modified contrast levels showing the differently doped regions. (D) Phase profile extracted across the center of the nanowire shown in panel C as indicated by the dotted line, averaged over 3.5 nm. Simulations of the phase-profile at the center of this structure with zero (0), -1 × 1011 (O), -1 × 1012 ()), and -2 × 1012 e.c. cm-2 charge (×) at the wire oxide-interface are plotted for comparison. (E) Phase profile made perpendicular across the nanowire in panel C as indicated by the dashed line. The phase offset in this figure is arbitrary and was chosen so that the profile would fall only on positive phase values, since holography can only measure a phase difference.

dashed line in Figure 2c. Clearly the phase signal increases in the vacuum when going away from the nanowire, indicating electric fields in the vacuum that could be caused by the negative charge present in the oxide, in support of the presence of negative surface charges. Comparison of the experimental phase gradient with simulated phase gradients in the vacuum as a function of interface charge quantity allow an independent estimation of the charge density of -1 × 1012 e.c. cm-2. However this correlation is not sufficiently precise to decouple the effect of surface charge from the effect of doping concentration.28 Future work involving in 3839

Figure 3. Phase change over junctions with different n-doping concentration. The phase change (y-axis) over an n+-i junction (on the x-axis the n-doping concentration) is calculated from simulations for a nanowire with a diameter of 60 nm including 3 nm oxide at the surface. The simulations were performed with zero charge (0), which is equal to the calculated step in phase using eq 2, with -1 × 1011 (O), -1 × 1012 ()), and 2 × 1012 e.c. cm-2 charge (0) with the p-doped intrinsic silicon of NA ) 1015 cm-3. Lines are drawn to guide the eye.

situ biasing of the SiNWs will be needed to decouple these effects. Figure 3 shows the results of simulations in which the phase change is plotted as a function of doping concentrations for various surface charges. The step in phase at a n+-p junction with varying n-doping concentrations and lightly p-doped silicon (1015 cm-3) is calculated for a nanowire diameter of 56 nm, either using eq 2, which is equal to the simulation with zero interface charge; or by simulations including varying negative sheet charge concentrations. The phase measurement sensitively depends on the interface charge and doping concentration of the sample. Furthermore, as clearly revealed in Figure 3, the phase change becomes strongly nonlinear if the interface charge is above ∼ -1 × 1012 e.c. cm-2, which explains the experimental results of Figure 2D. A doping concentration of ∼1018 cm-3 will be difficult to measure with respect to intrinsic silicon if the interface charges are equal to -2 × 1012 e.c. cm-2 since the step in phase over the junction is only 0.1 rad, which is comparable to the phase noise that will be discussed in the next section. It can be seen from Figure 3 that due to the presence of surface charges (equal to or above -1 × 1012 e.c. cm-2) regions with 1017 at. cm-3 n-doping cannot be distinguished from a neighboring intrinsic region. This is independent of the phase noise, which will be discussed in more detail below, but due to the depleting effect of the surface charges on lowly doped regions. Such low doping concentrations can only be detected at a reduced interface charge density (equal to or below -1 × 1011 e.c. cm-2). However it should be noted that the depletion width is not included in Figure 3 and increases for a decreasing interface charge quantity going from ∼300 nm (intrinsic -1017 at. cm-3 n-doping) with an interface charge quantity of -1 × 1011 e.c. cm-2 to ∼1 µm in the absence of surface charges. 3840

Figure 4. Effect of Au clusters on the phase measurement. (A) Schematic and (B) bright-field image of a SiNW. The indicated doping concentrations have been estimated from transport measurements.25 (C) Phase image of the nanowire shown in panel B with enhanced color scale showing one doped region in the center. With the exception of the oxide bump indicated, no thickness changes were observed; however, gold clusters are present everywhere on the faceted surfaces. The crystallographic growth direction of the nanowire was 〈111〉.

If the length of the doped region is below the depletion width the phase change given in Figure 3 will also be reduced, jeopardizing the detection of the doped region. The experimental data in Figure 1D and Figure 2D show significant fluctuations in the phase signal. In what follows, we examine potential sources of this variability, focusing on material impurities and thickness changes. It was shown that the surface of a SiNW can be faceted and covered with 1-1.5 monolayers of gold during growth26,27,29,32 and that this gold layer can lead to the nucleation of gold clusters with a thickness of approximately 2 nm and a diameter of 3 nm.26,27,29,30 We have investigated the contribution of Au clusters to the phase shift. Figure 4A displays the schematic of the SiNW with the positions of the doped sections, and Figure 4B the corresponding bright-field TEM image. The image reveals that the SiNW is of uniform diameter and exhibits a uniform coverage of Au clusters that are visible as black spots. The reconstructed phase image of this SiNW with enhanced color scale is shown in Figure 4C, where the highly doped region in the center is clearly visible. Calculations show that these Au clusters can increase the phase shift locally by 0.1-0.2 rad. However, because of the spatial resolution of ∼10 nm, the signals from local material or thickness variations such as gold clusters will be spread out in the reconstructed phase image and will not be detectable here because of the rather homogeneous distribution of Au clusters. Nevertheless, traces of gold at the surface affect the precision of the phase measurements and are likely to constitute a significant source of background noise, considering that the phase sensitivity of our experimental setup is approximately 0.01 rad.13 It can be seen from the fluctuations present on the phase signal in Figures 1D and 2D that phase variations below approximately 0.08 rad will be difficult to detect in these nanowires due to the significant amount of sample induced noise, regardless of the intrinsically high phase resolution of the experimental setup. From eq 1 it is clear that variations in sample thickness will directly influence the phase signal and might compromise the measurement of the dopant-induced phase signal. We noticed that, depending on growth conditions, the SiNWs Nano Lett., Vol. 9, No. 11, 2009

mental profile. These results clearly show that the recorded phase signal is primarily due to doping contrast. The thickness variations along the SiNW observed here lead to measurement errors that are smaller than the signal from the doping and, importantly, that can be compensated if the sample geometry is known. We note that despite the same doping concentration, the step in phase measured across the left junction is smaller than that across the right junction, and speculate that this variation could be due to contributions from thickness variations not detected in the BF image (backside of sample) and/or the nonuniform presence of gold clusters on the doped region, as was observed in STEM images (Supporting InformationFigure S1). Having addressed the sensitivity of the phase measurement on the thickness variation it seems that the origin of the observed slope of the phase in Figure 1d is a convoluted effect of the variations of the thickness, the influence of the gold catalyst, and the gold coverage on the doped regions (since it is known that the gold migration can also be influenced by the size of the nanowire27).

Figure 5. Influence of thickness changes on the measured step in phase. (A) Schematic of a detail of a NW. The indicated doping concentrations have been estimated from transport measurements.25 (B) BF-TEM image of a nanowire. (C) Phase image with enhanced color scale of the same nanowire. The segments vary slightly in diameter. The diameter of each segment, as obtained from calibrated BF-TEM images, is indicated in nanometers. (D) Phase profile extracted across the nanowire shown in panels B and C as indicated by the dotted line (solid line), calculated phase profile showing the phase signal that would be due to the thickness change as indicated in panel C (O) and the phase change corrected for the measured thickness changes (0). The nanowire was studied on carbon film. The crystallographic growth direction of the nanowire was 〈112〉.

from sample A can exhibit axial thickness changes. It is therefore critical to know the sample thickness accurately. We now demonstrate that the observed phase signal is indeed dominated by the dopant atoms and not by thickness variations. Figure 5A schematically illustrates a SiNW from sample A and the positions of the doped sections that have a slightly larger diameter than the intrinsic regions. The thickness change along the single crystalline nanowire was measured using calibrated bright-field (BF) images as shown in Figure 5B. The diameters of the SiNW across the segments are 63.8, 63.1, and 64.7 nm, respectively. Figure 5C shows the reconstructed phase image of the SiNW with enhanced color scale, in which the two highly doped regions are visible. The corresponding phase profile across the SiNW sample is shown in Figure 5D (solid line), together with a calculated phase signal based on the measured thickness difference and the corrected phase signal, which was obtained by subtracting the trace caused by thickness variations from the experiNano Lett., Vol. 9, No. 11, 2009

It is not only the doping concentration that is of interest, but also the abruptness of the junction, especially for devices based on tunneling, such as tunneling field-effect transistors.31 In the following, we investigate whether the junction abruptness can be extracted from a comparison of the experimental phase profiles with simulated ones that include the depletion width W,16 that is, the spatial region in which the potential changes over the junction. To compare the experimental phase profile with the simulation of abrupt and nonabrupt junctions, a simplified sample structure as shown in Figure 6a was used. Here, the nonabrupt junctions are modeled as a low-doped (1018 cm-3) region of length L inserted between the heavily doped and the intrinsic regions. An abrupt junction thus corresponds to setting L ) 0. Simulations using multiple low doped regions with gradually increasing doping concentrations (1016, 1017, and 1018 cm-3) inserted between the intrinsic and the heavily doped regions resulted in similar results as for the insertion of only one low-doped (1018 cm-3) region, because the low-doped regions (1016 and 1017 cm-3) are fully depleted due to the surface charges (Figure 3), justifying the use of this simple model. In Figure 6B, the experimental phase profile across a 1019 cm-3 doped region is shown together with the simulated potential profiles for junctions with L ) 0, 30, and 60 nm, including a surface charge of -1 × 1012 e.c. cm-2. In the simulation, the length of the heavily doped zone (inserted between the 2 low doped regions) was 100, 70, and 20 nm for L ) 0, 30, and 60 nm, respectively, to allow superposition of the depletion regions on both sides of the doped zone with the experimental data. The simulated data only show very small differences between the phase profiles for L ) 0, 30, and 60 nm, which is attributed to depletion effects from the oxide charges that affect the low-doped (L) and the intrinsic regions. The distance between the experimental and simulated profiles was calculated as a function of L, which shows a best agreement for L ) 30 nm (see Supporting Information); however, given the discussed fluctuations in the experimental phase profile, 3841

this reason, a correct interpretation of the data is possible only by comparison with simulated potential profiles, which allowed estimation of a negative interface charge density of -1 × 1012 e.c. cm-2. An estimate of the doping abruptness smaller than 30 nm/decade was extracted, but there is a great uncertainty on this value due to sample induced noise. We expect that measurements of the phase profile and the extraction of the doping concentration can be improved using samples with reduced and uniform surface charge layers that are free from strong phaseshifting impurities such as gold clusters. We also anticipate that quantitative measurements of the doping concentration in nanostructures will be possible in the near future using off-axis electron holography in combination with in situ biasing14 of the specimen.

Figure 6. Evaluation of junction abruptness. (A) Schematic of the simulated nonabrupt junction with L ) 30 nm. In the simulation, the length of the heavily doped zone (inserted between the 2 lowly doped regions) was 100, 70, and 20 nm for L ) 0, 30, and 60 nm, respectively, to allow superposition of the depletion regions on both sides of the doped zone with the experimental data. (B) Simulations of the phase profile at the center of the nanowire structure shown in panel A compared with an experimental profile of the junction (solid line). The simulation was performed with -1 × 1012 e.c. cm-2 sheet charge. Also shown are simulated phase profiles of the abrupt junction ()) and of two nonabrupt junctions including L ) 30 nm of 1018 cm-3 (0) and L ) 60 nm of 1018 cm-3 doped silicon (O) between the highly doped and the intrinsic silicon. The depletion width W is indicated for L ) 0.

a conservative estimate of the junction abruptness of the 56 nm diameter SiNW is somewhere between 30 and 60 nm. If L becomes much larger than 60 nm, the junction consist only of a 1018 at cm-3 doped region Therefore it can be seen from Figure 6 that if L would be much larger than 60 nm the phase step over the junction would decrease and the phase profile would be shaped like a parabola. The simulated steps in phase over an n+-n junction (ND 1019 cm-3 - ND 1017 cm-3) and over an n+-p- (ND 1019 cm-3 - NA 1015 cm-3) are the same because of surface charges. Therefore an uncertainty on the number of decades over the junction (two to four) is present as well as an uncertainty on the length L (30-60 nm). Combining both uncertainties we find that the variations in the observed potential indicate a doping profile with an abruptness below 30 nm/dec but no better than 7.5 nm/dec Note that the latter number is below the spatial resolution present in our experiments (10 nm), which is not a limitation because only junctions of more than one decade were considered and the depletion width in these NWs is generally larger than the length of the junction. More quantitative results seem possible if sample induced noise, which is mainly due to gold clusters, can be reduced. In conclusion, we have shown that active doping concentrations as low as 1018 cm-3 can be detected in a 60 nm diameter silicon nanowire as well as the position of the junctions. The amount of charge at the oxide interface strongly influences the observed potential. For 3842

Acknowledgment. We acknowledge Yann-Michel Niquet, Aurelien Lherbier and Silvain Barraud for fruitful discussions concerning simulations. This work was partially supported by research funding from the European Community under the FP6-Marie Curie Host Fellowships for Early Stage Research Training (EST) “CHEMTRONICS” Contract Number MEST-CT-2005-020513 and the EU program NODE 015783. Supporting Information Available: This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Voyles, P.; Muller, D.; Grazul, J.; Citrin, P.; Gossmann, H. Nature 2002, 416, 826. (2) Molina, S.; Sanchez, A.; Beltran, A.; Sales, D.; Ben, T.; Chisholm, M.; Varela, M.; Pennycook, S.; Galindo, P.; Papworth, A.; Goodhew, P.; Ripalda, J. Appl. Phys. Lett. 2007, 91, 263105. (3) Zelsacher, R.; Wood, A.; Bacher, E.; Prax, E.; Sorschag, K.; Krumrey, J.; Baumgart, J. Microelectron Reliab. 2007, 47, 1585. (4) Tsong, T.; et al. ReV. Sci. Instrum. 1982, 53, 1442. (5) Hoummada, K.; Mangelinck, D.; Cadel, E.; Perrin-Pellegrino, C.; Blavette, D.; Deconihout, B. Microelectron. Eng. 2007, 84, 2517. (6) Blavette, D.; Cadel, E.; Fraczkiewicz, A.; Menand, A. Science 1999, 286, 2317. (7) Perea, D.; Lensch, J.; May, S.; Wessels, B.; Lauhon, L. Appl. Phys. A: Mater. Sci. Process. 2006, 85, 271. (8) Eyben, P.; Janssens, T.; Vandervorst, W. Mater. Sci. Eng., B 2005, 124-125, 45. (9) Biberger, R.; Benstetter, G.; Schweinboeck, T.; Breitschopf, P.; Goebel, H. Microelectron. Reliab. 2008, 48, 1339. (10) Ligowski, M.; Moraru, D.; Anwar, M.; Mizuno, T.; Jablonski, R.; Tabe, M. Appl. Phys. Lett. 2008, 93, 142101. (11) Berthe, M.; Stiufiuc, R.; Grandidier, B.; Deresmes, D.; Delerue, C.; Stie´venard, D. Science 2008, 319, 436. (12) Rau, W.; Schwander, P.; Baumann, F.; Ho¨ppner, W.; Ourmazd, A. Phys. ReV. Lett. 1999, 82, 2614. (13) Cooper, D.; Truche, R.; Rivallin, P.; Hartmann, J.; Laugier, F.; Bertin, F.; Chabli, A. Appl. Phys. Lett. 2007, 91, 143501. (14) Twitchett, A.; Dunin-Borkowski, R.; Broom, R.; Midgley, P. J. Phys.: Condens. Matter 2004, 16, S181. (15) Chung, J.; Rabenberg, L. Appl. Phys. Lett. 2006, 88, 013106. (16) Sze, S. Semiconductor DeVices Physics and Technology; John Wiley & Sons: New York, 1985. (17) Cooper, D.; Ailliot, C.; Truche, R.; Barnes, J.; Hartmann, J.; Bertin, F. J. Appl. Phys. 2008, 104, 064513. (18) Twitchett-Harrison, A.; Yates, T.; Newcomb, S.; Dunin-Borkowski, R.; Midgley, P. Nano Lett. 2007, 7, 2020. (19) Eades, W.; Swanson, R. J. Appl. Phys. 1985, 58, 4267. (20) Angermann, H. Appl. Surf. Sci. 2008, 254, 8067. (21) Nicollian, E.; Brews, J. MOS (Metal Oxide Semiconductor) Physics and Technology; John Wiley & Sons: New York, 1982. (22) Fazzini, P.; Merli, P.; Pozzi, G.; Ubaldi, F. Phys. ReV. B. 2005, 72, 085312. Nano Lett., Vol. 9, No. 11, 2009

(23) Wagner, R.; Ellis, W. Trans. Met. Soc. AIME 1965, 233, 1053. (24) Pan, L.; Lew, K.; Redwing, J.; Dickey, E. J. Cryst. Growth 2005, 277, 428. (25) Bjo¨rk, M.; Schmid, H.; Knoch, J.; Riel, H.; Riess, W. Nat. Nanotechnol. 2009, 4, 103. (26) Hannon, J.; Kodambaka, S.; Ross, F.; Tromp, R. Nature 2006, 440, 69. (27) den Hertog, M.; Rouviere, J.; Dhalluin, F.; Desre´, P.; Gentile, P.; Ferret, P.; Oehler, F.; Baron, T. Nano Lett. 2008, 8, 1544. (28) The phase gradient in the vacuum in proximity of an entirely intrinsic nanowire with a negative sheet charge density of-1 × 1012 e.c. cm-2 has been simulated and is found to be similar to the measured phase gradient shown in Figure 2E. Simulations also predict the existence of phase variations in the vacuum around the doped regions. Such

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(29) (30) (31) (32)

variations were only rarely observed and if so were of reduced intensity. These results will be published in the Institute of Physics Conference Series in 2009. den Hertog, M.; Rouviere, J.; Dhalluin, F.; Gentile, P.; Ferret, P.; Ternon, C.; Baron, T. Inst. Phys. Conf. Ser. 2007, 1, 217. Popescu, R.; Muller, E.; Wanner, M.; Gerthsen, D.; Schowalter, M.; Rosenauer, A.; Bottcher, A.; Loffler, D.; Weis, P. Phys. ReV. B 2007, 76, 235411. Reddick, W. M.; Amaratunga, A. J. Appl. Phys. Lett. 1995, 67, 495. Ross, F. M.; Tersoff, J.; Reuter, M. C. Phys. ReV. Lett. 2005, 95, 146104.

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