Comparison of Three E-Beam Techniques for Electric Field Imaging

Letter pubs.acs.org/NanoLett

Comparison of Three E‑Beam Techniques for Electric Field Imaging and Carrier Diffusion Length Measurement on the Same Nanowires F. Donatini,†,‡ Andres de Luna Bugallo,†,‡ Pierre Tchoulfian,†,‡,§ Gauthier Chicot,†,‡ Corinne Sartel,∥ Vincent Sallet,∥ and Julien Pernot*,†,‡,⊥ †

Université Grenoble Alpes, F-38000 Grenoble, France CNRS, Institut NEEL, F-38042 Grenoble, France § CEA, LETI, Minatec Campus, F-38054 Grenoble, France ∥ Groupe d’Etude de la Matière Condensée (GEMAC), CNRS Université de Versailles St. Quentin, Université Paris-Saclay, 78035 Versailles Cedex, France ⊥ Institut Universitaire de France, 103 Boulevard Saint-Michel, F-75005 Paris, France ‡

ABSTRACT: Whereas nanowire (NW)-based devices offer numerous advantages compared to bulk ones, their performances are frequently limited by an incomplete understanding of their properties where surface effect should be carefully considered. Here, we demonstrate the ability to spatially map the electric field and determine the exciton diffusion length in NW by using an electron beam as the single excitation source. This approach is performed on numerous single ZnO NW Schottky diodes whose NW radius vary from 42.5 to 175 nm. The dominant impact of the surface on the NW properties is revealed through the comparison of three different physical quantities recorded on the same NW: electron-beam induced current, cathodoluminescence, and secondary electron signal. Indeed, the space charge region near the Schottky contact exhibits an unusual linear variation with reverse bias whatever the NW radius. On the contrary, the exciton diffusion length is shown to be controlled by the NW radius through surface recombination. This systematic comparison performed on a single ZnO NW demonstrates the power of these complementary techniques in understanding NW properties. KEYWORDS: Nanowire, cathodoluminescence, electron beam induced current, voltage contrast, Schottky, ZnO

S

On the other hand, some of us have previously demonstrated how scanning cathodoluminescence (CL) maps the SCR thanks to exciton dissociation in the ZnO NW Schottky diodes.11 These techniques offer attractive resolution to delineate the SCR where an intense electric field holds. However, electric field values cannot be directly evaluated inside this area because the EBIC signal is not proportional to the electric field and no CL signal is emitted. Secondary electron voltage contrast (VC) must therefore be recorded because it was helpfully used to evaluate the electric field and to infer the doping levels in the NW pn junction under different reverse biases.4,12 All these complementary techniques are powerful tools for investigating NW properties but have not yet been applied to the same object in order to confirm the reliability of the determined parameters. In the present work, we report the visualization of the effects of the electric field, induced by a SCR, by performing CL, EBIC, and VC on numerous single ZnO NW devices in the vicinity of a Schottky contact. On the basis of the analysis of high spatial resolution mapping, the exciton diffusion length

ince the beginning of the 2000s, the emergence of nanowires has introduced some new possibilities for building high-performance devices as for example, gas sensors, photovoltaic cells, or light-emitting diodes. Nanowires are attractive systems thanks to their large surface-to-volume ratio making them good candidates not only for devices but also to study low-dimensional physics (0D or 1D system, topological insulator).1 However, the electronic properties of NW are often not understood and/or uncontrolled due to the strong influence of the surface states on the NW electrostatic properties or physical quantities like the minority carrier or exciton diffusion lengths. Recently, research groups have developed efficient nanoscale probes to measure such properties in NW. Spatially resolved electrical current mapping with local injection of electron−hole pairs or excitons, for example, electron beam induced current (EBIC) and scanning photocurrent (SPC), yields characteristic lengths such as the space charge region (SCR) width or exciton/minority carrier diffusion length at a pn junction2−6 or at a Schottky contact.7,8 Moreover, the possibility to connect and bias single NWs opens the route to new investigation of the electric field influence on the optical9 and transport10 properties of single wires. © XXXX American Chemical Society

Received: November 18, 2015 Revised: March 24, 2016

A

DOI: 10.1021/acs.nanolett.5b04710 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters

Figure 1. (a) Schematic of the EBIC and the CL setup used on a single 175 nm radius ZnO nanowire Schottky diode with the Schottky contact on the left and the ohmic contact on the right. (b) Magnified view near the Schottky contact. In the given example, the e-beam is impinging on the neutral region (green area) and is far from the space charge region (red area) induced by the Schottky contact. (c) Near Schottky contact imagings of a 175 nm radius NW at 10 V reverse bias. Top: SEM image. Middle: near band edge polychromatic CL image (red color is used for the CL signal and yellow is the edge of the wire measured by SEM). Bottom: EBIC image (orange color is used for the EBIC signal and yellow is the edge of the wire measured by SEM). (d) Transverse profiles of the SEM, CL, and EBIC measurements at the crossing point of (e). (e) Axial profiles along NW axis of the CL and EBIC measurements (symbols) and simulations (lines). (f) Space charge region width WCL measured by CL and exciton diffusion length measured by CL (LDCL) and EBIC (LDEBIC) versus reverse bias voltage.

200 ps,13,14 the average density of generated hot electron hole pairs is estimated to be around 1016 cm−3, 2 orders of magnitude below the measured doping level of our ZnO NWs.15 In this low injection regime and due to the large free exciton binding energy in ZnO (Eb = 60 meV), the hot electron hole pairs mainly create excitons even at room temperature. Indeed, from the mass action law16 and assuming a doping level of 3 × 1018 cm−3,15 the exciton population is estimated to be more than ten times larger than the electron−hole pair concentration at room temperature. Therefore, in the following only excitons will be considered in the discussion. These excitons are subjected to various physical processes, whose extent depends on the e-beam location along the wire axis. For an electron beam in the neutral region and far away from the Schottky contact (schematically shown in the example of Figure 1b), the excitons diffuse and then recombine. The recombination process is both nonradiative and radiative because ZnO is a direct band gap semiconductor. The emitting photons collected by the polychromatic detection (intense near the band edge emission and the weak defect band) induces the CL signal shown in red at the middle of Figure 1c. In contrast, no EBIC current is induced as inferred from the black color at the bottom of Figure 1c. Close to the Schottky contact, the excitons can diffuse toward or are generated within the SCR. If the local electric field is high enough, the electrons and the holes are separated and drift apart toward the neutral region

and SCR width are determined following an established procedure. We evaluate the critical impact of the nanowire radius by carrying out the measurements on NWs with radius ranging from 42.5 to 175 nm under different reverse biases (from 0 to 40 V). The exciton diffusion length is found to be completely controlled by surface recombination processes. An unusual SCR width dependence versus reverse bias is observed for all NW radii. This property is discussed and compared using a finite element calculation. This work demonstrates the power of a comparative analysis using CL, EBIC, and VC on a same NW. Experimental methods using e-beam excitation are schematically described in Figure 1a,b. Room-temperature scanning electron microscope (SEM), CL, and EBIC mapping measurements were complementarily performed on several single ZnO nanowire Schottky diodes with a radius ranging from 42.5 to 175 nm. Figure 1c from top to bottom shows an SEM image of a single ZnO NW Schottky diode with a 175 nm radius and its corresponding CL and EBIC mappings under 10 V reverse bias, respectively. To achieve high spatial resolution as well as low carrier injection in wires, the electron beam parameters were 30 kV for the acceleration voltage, 35 pA for the current, and a few nanometers for the e-beam diameter. According to Monte Carlo, simulation (CASINO software, Université de Sherbrooke), the energy loss in the NW by the incident electrons would be about few percent.11 Assuming an exciton lifetime of B


Letter

Nano Letters

Figure 2. Scanning electron microscopy (top) and near band edge polychromatic cathodoluminescence image for four different reverse bias voltages (5, 10, 15, and 20 V) of single Schottky ZnO nanowires with different radii (r): (a) r = 42.5 nm, (b) r = 100 nm, and (c) r = 170 nm.

where IEBIC is the EBIC current, x is the distance from the Schottky contact, and LDEBIC the exciton diffusion length from EBIC experiment. Figure 1c,e shows an example of CL and EBIC maps and profiles when applying 10 V reverse voltage. The full set of measurements was made between 0 and 40 V using 10 V steps. For both techniques, and applying the same methodology described above, WCL, LDCL, and LDEBIC values were determined as shown in Figure 1 f. LDCL and LDEBIC values are within 10% and are independent of the applied voltage, whereas the SCR width WCL presents a linear behavior dependence. Since the CL signal clearly delineates W and is moreover an optical signal that is not sensitive to bias current and internal current amplification, CL was exclusively used for W and diffusion length measurements. As an example, Figure 2 shows the CL mapping (on the Schottky side) recorded at room temperature and under bias conditions for NW having 42.5, 100, and 170 nm radii. The results of measured LDCL on many different NW radius devices are reported in Figure 3. The exciton diffusion length is strongly dependent on the NW radius r and ranged between 91 to 289 nm. However, no bias

and the Schottky contact, respectively. Exciton dissociation by the electric field can occur via two different mechanisms. First, to field-dissociate a free exciton, the electric field must provide in ZnO at least a potential drop of Eb = 60 meV across the effective Bohr radius ab = 1.8 nm. Thus, direct field dissociation occurs in ZnO for an electric field larger than 3.3 × 105 V/cm. Second, exciton impact ionization should appear for lower electric field values.17 In that case, the exciton gets ionized by a carrier having enough kinetic energy induced by the electric field. The exciton dissociation and electron hole drift under SCR electric field induce an EBIC signal and an extinction of the CL signal. Both CL and EBIC signals are therefore complementary ways to map out the SCR. Figure 1d,e shows that the scan line profiles extracted from CL and EBIC map images perpendicular to the wire growth axis (d) are scan lines along the dashed green line of (c), and along the wire growth axis (e). In order to determine the exciton diffusion length (LD) and the SCR width (W), LDCL and WCL values are first obtained by fitting the normalized CL intensity profile using eq 111 ⎡ ⎤ 2 ICL(x > WCL) = ⎢1 − ((x − W )/ L ) ⎥ ( − ( x − W )/ L ) CL DCL CL DCL ⎣ ⎦ e +e (1)

where ICL is the cathodoluminescence signal intensity, x is the distance from the Schottky contact, LDCL and WCL are, respectively, the exciton diffusion length and SCR width determined from CL experiment. In Figure 1e, the fitting limits used for exciton diffusion on CL and EBIC images are marked by dashed black lines (corresponding to the dashed white lines of Figure 1c). They delineate the most interesting region where excitons can either diffuse to the neutral region or into the SCR. Between these two limits, the normalized CL and EBIC profiles are complementary signals. The SCR width is delineated more accurately using a CL profile rather than an EBIC profile because within this region the CL emission is fully inhibited, whereas the EBIC signal is not constant. Finally, the WCL value is then used in the EBIC equation (eq 2) to extract LDEBIC:18 IEBIC(x > WCL) =

Figure 3. Exciton diffusion length versus ZnO nanowire radius determined by cathodoluminescence measurement (symbols) at T = 300 K. The diffusion length is strongly dependent on the radius of the nanowire. The lines represent the diffusion length using the surface recombination model with a surface recombination velocity S of 2 × 104 cm/s (full line), 1.3 × 104 cm/s (dashed line), 3 × 104 cm/s (dotted line), and a near surface space charge width dspc= 22 nm.

2 e

((x − WCL)/ L DEBIC)

+ e(−(x − WCL)/ LDEBIC) (2) C


Letter

Nano Letters voltage dependence was observed as illustrated in Figure 1f. Because the bias voltage enables sweeping of the area probed by the diffusion length along the NW, it can be concluded that the surface recombination process described below is identical all along the NW. The surface recombination model described by Allen et al.7 has been used here to evaluate the effective exciton diffusion length LD* using a surface depleted space charge width dspc due to Fermi level pinning at the NW surface3 L D* =

Dτ *

(3)

1 1 2S = + τ* τB r − dspc

(4)

with D = 1.5 cm /s as the diffusion coefficient, τ* is the effective lifetime, τB = 10 ns the exciton bulk lifetime,19 and S is the surface recombination velocity of the nanowire. By adjusting S and ddspc from the experimental fit, S values were deduced between 1.3 × 104 to 3.0 × 104 cm/s with a space charge region dspc= 22 nm. The best agreement is obtained for S = 2.0 × 104 cm/s. LD* versus r dependence measured here can be described with a simple model having surface recombination velocity S value independent to the NW radius. As illustrated on Figure 3, an S deviation induced an L*D deviation. As an example from the simulation, for S varying from 1.3 × 104 to 3.0 × 104 cm/s, the corresponding LD* values vary between 177 and 261 nm for a 150 nm radius NW. Also, we conclude than even a reasonable variation of S around an average value is enough to describe the LD* dispersion. No very strong Sdependence versus radius is needed to fit our data with this model in opposition to ref 8 where the authors did not take into account the near surface radial depletion. It must be noticed that the recombination of carriers in ZnO NW involved additional steps compared to GaAs.3 After electron−hole pair creation, the excitons are rapidly formed before diffusing in the NW. Excitons can be ionized under an electric field which can have two different origins: (i) the SCR induced by the Schottky barrier or (ii) the SCR induced by the Fermi level pinning at the surface (see below). In that latter case, the induced electric field is radially oriented. Generated electrons and holes are spatially separated by the electric field and the hole minority carrier recombines or drift-diffuses to the Schottky electrode. Obviously, only the axial electric field from the Schottky barrier will be efficient to transport holes to Schottky contact and so create an EBIC current. A pinning of the Fermi level at the surface is generally observed in ZnO NW due to oxygen atoms adsorbed at the surface, leading to an acceptor level at 0.9 eV below the conduction band.20 These species are probably at the origin of the dspc = 22 nm deduced from the fit and in good agreement with a simulation of radial SCR length for a NW doping level of ∼1018 cm−3 and a density of oxygen absorbed atoms of 2 × 1012 cm−2 (see Figure 4 and finite element calculation). This fixed charge value induces a 0.75 eV upward band bending at the NW near surface. Moreover, this dspc = 22 nm is compatible with Figure 1d where no CL and EBIC signals are observed on the sides of the NW and with four probe electrical measurements made on the same set of NW.15 The effective lifetime of the exciton is completely governed by the NW surface with values ranging between 50 to 170 ps for an NW radius ranging from 42.5 to 175 nm, to compare with a 10 ns exciton bulk lifetime.19 The surface recombination velocity writes S = σvthNt where σ is the capture cross section of the 2

19

Figure 4. The 3D finite element calculations of a 100 nm radius ZnO Schottky diode. Top: cross section at half height of the circular ZnO NW used in the calculations (red, Schottky metal; blue, n-type ZnO with Nd = 1018 cm−3; and black, surrounding vacuum). The nanowire is lying on a SiO2 substrate. Bottom: cross section mapping at half height of the NW of the space charge region for reverse bias voltage ranging from 0 to 20 V. The color scale represents the ionized donor density inside the NW. The white color corresponds to a full donor ionization (N+d = 1018 cm−3), whereas the dark color represents the neutral region (N+d = 0 cm−3). Nt = 2 × 1012 cm−2 acceptor traps have been introduced at the surface of the NW and are at the origin of the near surface axial space charge region all along the NW. The axial space charge region extension versus reverse bias is much lower than the linear one measured experimentally by CL and EBIC (30 nm/V). The radial space charge region extension due to the acceptor states at the surface is in good agreement with the dspc = 22 nm value inferred from the diffusion length versus bias radius fit.

recombination center, vth is the thermal hole velocity, and Nt is the recombination center density. Assuming that the oxygen atoms adsorbed at the surface are at the origin of the recombination centers, that is, Nt = 2 × 1012 cm−2 and evaluating vth, the recombination center capture cross section σ can be inferred and is equal to σ = 10−15 cm2. This capture cross section is in reasonable agreement with an attractive center for holes, that is, oxygen atoms acceptor adsorbed at the surface. More unexpectedly, W linearly extends versus bias voltage with a 30 nm/V slope whatever the radius, as shown in Figure 2. Contrary to the exciton diffusion length, W extension versus bias is not radius dependent. Square root bias dependence is expected with bulk material due to the presence of a threedimensional (3D) SCR (with a homogeneous doping level). Hayden et al.2 and others11 have reported comparable experimental results for CdS and ZnO NWs. A linear SCR extension versus bias voltage is predicted if there is 2D electron gas depletion21 and has even been experimentally observed.22 However, this low-dimensional system does not correspond to our experimental situation. D


Letter

Nano Letters

Figure 5. (a) SE contrast profile measured versus the distance from the Schottky contact edge (x = 0) along the 175 nm radius NW axis for reverse bias of 20 V (green circles), 30 V (pink circles), and 40 V (blue circles). Inset gives the depletion width measured from VC profiles versus reverse bias (dashed line corresponds to a 30 nm/V slope line to guide the eyes). (b) CL, EBIC, and VC profile versus the distance from the Schottky contact edge under a reverse bias of 20 V. A linear drop voltage is observed from the VC contrast, confirming the space charge region extension measured by CL and EBIC.

delineates the same space charge extension as for the CL and EBIC profiles and allows the determination of the electric field at the NW surface. All of the experiments performed in this work, that is, CL, EBIC, and VC, confirm that the electric field distribution in the NW cannot be satisfactorily described by a system including only the ZnO NW, Schottky metal, SiO2 substrate, and vacuum. We need to take into account the specific situation of NW where the surface interaction with external species can produce some strong modifications of the electrostatic properties in the whole wire. Figure 6 compares the near surface electric field (a

In order to understand the origin of this unusual linear dependence, finite element calculations (nextnano, see details in Experimental Details) were performed using the doping parameters determined on the same set of NWs by electrical transport measurement.15 Because of the high residual n-type doping level of these NW (>1018cm−3), the axial SCR is expected to extend no more than 200 nm outside of the Schottky contact toward the ohmic contact under a reverse bias of 20 V (see Figure 4). A 150 nm extension takes place in the core of the wire. The calculated SCR corresponds to the intense electric field region created by the ionized donors, where direct dissociation or impact ionization could occur. The simulation of the SCR extension does not match our experimental 600 nm extension at 20 V, even when taking into account the low screening due to the surrounding vacuum. However, this simulation partially takes into account the high sensitivity of the ZnO surfaces to their surrounding environment (here only oxygen acceptors in neutral area) but nothing specific inside the high electric field region. In order to investigate the surface properties of the NW, the voltage contrast (VC) was extracted from SEM images of NWs under different reverse biases. The VC is defined as the subtraction of secondary electron (SE) signals with and without reverse bias and calibrated with the biases applied voltage as shown in Figure 5a). The VC signal gives the potential below the surface (a few nm). As in ref 4, the calibration of VC in V was done using the continuity property of the potential from the Schottky electrode to the ohmic contact. Considering the VC signal only in the ZnO region close to the Schottky contact Figure 5a, two major elements can be deduced from the experimental data. First, the SCR extends linearly at 30 nm/V as shown in inset of Figure 5a versus reverse bias (the SCR is delineated where the VC signal vanished). Second, the potential decreases linearly from the Schottky contact toward the neutral part of the NW. This means that the electric field parallel to the NW growth axis is constant up to the neutral part of the NW, where it drops sharply. Assuming the whole voltage drops in the ZnO material, the near surface electric field value is 3.3 × 105 V/cm. This value is identical to that of the free exciton dissociation field. The VC technique is complementary to the EBIC and CL measurements, as shown in Figure 5b. The VC contrast profile

Figure 6. Near-surface electric field along the horizontal axis of the 100 nm radius ZnO NW Schottky diode for a reverse bias of 20 V: finite element calculations (full line) and extracted from the fit of the voltage contrast measurement (dotted line).

few nm in depth) along the NW axis estimated from the VC profile of Figure 5 under 20 V reverse bias to the one calculated from the finite element calculations of Figure 4 with a 100 nm radius ZnO NW Schottky diode. We can see a clear difference between the simulation and the experiment. As observed on the simulated curve, an intense electric field is expected near the Schottky contact with a strong decrease toward the neutral part of the NW. This intense electric field due to negative ionized donors located near the Schottky contact (see Figure 4) extends outside the NW and certainly modifies the adsorption properties of the species on the NW surface. The adsorption of the species, which provokes upward (oxygen) or downward (hydrogen) band bending23 at the surface, could completely change the distribution of the charges in the NW and thus, the spatial distribution of the electric field. For example, H atom E


Letter

Nano Letters adsorption at the surface of ZnO is known to transfer an electron to the semiconductor, creating an electron accumulation layer. The adsorption of residual H atoms from the microscope chamber to the NW surface could be enhanced by the local electric field induced by the bulk ionized donors. In that case, the positive charge, located in the bulk SCR and induced by the ionized donors, could be partially compensated by the electron transferred from the H atoms. Some of the bulk donor charge state then becomes neutral. The positive charge induced by the H+ ions is exclusively located on the (1010̅ ) surface of the NW and not in the core of the NW. This space charge is then 2D and in good agreement with a linear depletion versus bias, as described by Achoyan et al.21 Using the equation from ref 21, we can evaluate the concentration of 2D sheet density at the surface of the NWs from the space charge extension 30 nm/V to be around 1012 cm−2. To sum up, cathodoluminescence, electron beam induced current, and secondary electron voltage contrast signals have been complementarily used to map the space charge region and measure the exciton diffusion length on the same Schottky diode ZnO NWs. The extracted values have been compared in order to demonstrate the reliability of the three different ebeam techniques. NWs with radii ranging between 42.5 and 175 nm have been analyzed. The exciton diffusion length is found to be strongly radius dependent and completely governed by the surface recombination processes. However, the spatial extension of the space charge region near the Schottky contact versus bias voltage is found to be independent to the NW radius with a slope of 30 nm/V. The voltage contrast demonstrates that the potential drops linearly from the Schottky contact to the neutral region, corresponding to a constant electric field at the surface of the NWs. Finite element calculation has been performed and compared with experiments. The results have been discussed in terms of ZnO NW surface interaction with its surrounding environment. Experimental Details. Nanowire Growth Conditions. ZnO nanowire samples were grown on A-plane sapphire substrates by metal organic chemical vapor deposition in a horizontal reactor operating at a reduced pressure of 50 Torr. Diethylzinc (DEZn) and nitrous oxide (N2O) were used as zinc and oxygen sources respectively, whereas helium was used as a carrier gas. The ZnO nanostructure NWs were grown at a temperature of 875 °C, using an oxygen/zinc molar ratio in the range of [750−1150], favoring 1D growth, that is, to ensure the formation of vertically aligned nanowires with a high aspect ratio. Four NW samples with lengths ranging from 4 to 8 μm and with radii ranging from 42.5 to 175 nm were studied. Nanowire Contact Processing. Schottky diodes were made from single ZnO NWs dispersed on Si/SiO2 substrate using an original hybrid fabrication process combining e-beam lithography and CL imaging, as described in ref 24. These diodes were fabricated using a double run of this specific e-beam lithography with Ti/Au and Ni/Au metallizations as an Ohmic and Schottky contact, respectively. The electrical access to the ZnO NWs was carried out using a field emission scanning electron microscope, FEI Inspect F50, equipped with a fourprobe nanomanipulators. A typical current voltage characteristic at room temperature of a NW having a162 nm radius is shown on Figure 7. The I−V characteristic is rectifying and the strong current−voltage slope at low voltage is certainly due to the high doping of the sample, which induces tunnel effect at the Schottky interface.

Figure 7. Current voltage characteristics measured at room temperature of a Schottky diode performed with a 162 nm radius single NW.

SEM, CL, and EBIC Experimental Details. SEM, CL, and EBIC mappings on single NW Schottky diodes were carried out at 300 K with the e-beam current and energy set to 35 pA and 30 keV, respectively. No e-beam current dependence has been observed for e-beam current ranging from 35 to 250 pA. However, in this work 35 pA e-beam current was used in order to preserve the NW from repeated charge injection. The high ebeam energy setting first allows the best resolution on secondary electron images for a long working distance around 16 mm (due to the parabolic mirror inserted between the end of the e-gun and the sample) and second the most localized ebeam probe in the volume of the nanowire across the diameter. The weak e-beam current minimizes the degradation of the NW over time and insures the weak injection conditions even if the electron−hole pair creation is not dominant compared to the exciton formation at room temperature in ZnO material. In order to obtain the best signal-to-noise ratio for the EBIC measurements, the e-beam was modulated at 30 kHz using a homemade electrostatic beam-blanking system and the EBIC current was measured using a lock-in amplifier. For each single NW Schottky diode, SEM, CL, and EBIC images were acquired consecutively under the same e-beam modulation but without the use of a lock-in-amplifier for SEM and CL images. Finite Element Calculations. In order to simulate the electrostatic properties of the ZNO NWs, Poisson’s equation was solved using a 3D finite element calculation (nextnano3). Khanal and Wu25 demonstrated the importance of using a 3D grid mesh, instead of a 1D or 2D mesh, in the case of a semiconducting NW surrounded by different dielectric materials (here, air and SiO2). Here, we assume a circular ZnO wurzite NW with a c-growth axis along the horizontal direction. A doping level of 1018 cm−3 was introduced in the calculations, in accordance with electrical measurements performed on the same set of NWs n-type ZnO.15 An omega-shaped Schottky metal with a 0.5 eV barrier height surrounded the ZnO NW on the left side, whereas a symmetrical ohmic contact was considered on the right. A semi-infinite SiO2 substrate sustained the NW. A sheet density of 2 × 1012 cm−2 with a negative surface charge (acceptor levels) was considered on the NW surface. Bias voltage was applied to the Schottky electrode with bias voltage ranging from 0 to 40 V. F


Letter

Nano Letters

■

(22) Reuter, D.; Werner, C.; Wieck, A. D.; Petrosyan, S. Appl. Phys. Lett. 2005, 86 (16), 162110. (23) Hu, Y.; Liu, Y.; Li, W.; Gao, M.; Liang, X.; Li, Q.; Peng, L.-M. Adv. Funct. Mater. 2009, 19 (15), 2380−2387. (24) Donatini, F.; Dang, Le Si Nanotechnology 2010, 21, 375303. (25) Khanal, D. R.; Wu, J. Nano Lett. 2007, 7 (9), 2778−2783.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors acknowledge the Nanofab team at Institut Néel for the use of their facilities and their technical assistance. The authors acknowledge Le Si Dang, Maxime Richard, and Martien Den Hertog from Institut Néel for fruitful discussions. This research was partially supported by the French National Research Agency within the MADFIZ Project (No. ANR-11NANO-013).

■

REFERENCES

(1) Elm, M. T.; Uredat, P.; Binder, J.; Ostheim, L.; Schäfer, M.; Hille, P.; Müßener, J.; Schörmann, J.; Eickhoff, M.; Klar, P. J. Nano Lett. 2015, 15 (12), 7822−7828. (2) Hayden, O.; Zheng, G.; Agarwal, P.; Lieber, C. M. Small 2007, 3 (12), 2048−2052. (3) Gutsche, C.; Niepelt, R.; Gnauck, M.; Lysov, A.; Prost, W.; Ronning, C.; Tegude, F.-J. Nano Lett. 2012, 12 (3), 1453−1458. (4) Tchoulfian, P.; Donatini, F.; Levy, F.; Dussaigne, A.; Ferret, P.; Pernot, J. Nano Lett. 2014, 14 (6), 3491−3498. (5) Lavenus, P.; Messanvi, A.; Rigutti, L.; Bugallo, A. D. L.; Zhang, H.; Bayle, F.; Julien, F. H.; Eymery, J.; Durand, C.; Tchernycheva, M. Nanotechnology 2014, 25 (25), 255201. (6) Tchernycheva, M.; Neplokh, V.; Zhang, H.; Lavenus, P.; Rigutti, L.; Bayle, F.; Julien, F. H.; Babichev, A.; Jacopin, G.; Largeau, L.; Ciechonski, R.; Vescovi, G.; Kryliouk, O. Nanoscale 2015, 7 (27), 11692−11701. (7) Allen, J. E.; Hemesath, E. R.; Perea, D. E.; Lensch-Falk, J. L.; Li, Z. Y.; Yin, F.; Gass, M. H.; Wang, P.; Bleloch, A. L.; Palmer, R. E.; Lauhon, L. J. Nat. Nanotechnol. 2008, 3 (3), 168−173. (8) Soudi, A.; Dhakal, P.; Gu, Y. Appl. Phys. Lett. 2010, 96 (25), 253115. (9) Müßener, J.; Teubert, J.; Hille, P.; Schäfer, M.; Schörmann, J.; de la Mata, M.; Arbiol, J.; Eickhoff, M. Nano Lett. 2014, 14 (9), 5118− 5122. (10) Chen, G.; McGuckin, T.; Hawley, C. J.; Gallo, E. M.; Prete, P.; Miccoli, I.; Lovergine, N.; Spanier, J. E. Nano Lett. 2015, 15 (1), 75− 79. (11) Hwang, J.-S.; Donatini, F.; Pernot, J.; Thierry, R.; Ferret, P.; Dang, L. S. Nanotechnology 2011, 22 (47), 475704. (12) Lu, Y.-J.; Lu, M.-Y.; Yang, Y.-C.; Chen, H.-Y.; Chen, L.-J.; Gwo, S. ACS Nano 2013, 7 (9), 7640−7647. (13) Reparaz, J. S.; Güell, F.; Wagner, M. R.; Hoffmann, A.; Cornet, A.; Morante, J. R. Appl. Phys. Lett. 2010, 96 (5), 053105. (14) Reparaz, J. S.; Callsen, G.; Wagner, M. R.; Güell, F.; Morante, J. R.; Torres, C. M. S.; Hoffmann, A. APL Mater. 2013, 1 (1), 012103. (15) Bugallo, A. D. L.; Donatini, F.; Sartel, C.; Sallet, V.; Pernot, J. Appl. Phys. Express 2015, 8 (2), 025001. (16) Im, J. S.; Moritz, A.; Steuber, F.; Härle, V.; Scholz, F.; Hangleiter, A. Appl. Phys. Lett. 1997, 70 (5), 631−633. (17) Pedrós, J.; Takagaki, Y.; Ive, T.; Ramsteiner, M.; Brandt, O.; Jahn, U.; Ploog, K. H.; Calle, F. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 75 (11), 115305. (18) The Electrical Characterization of Semiconductors; Orton, J. W., Blood, P., Eds.; Academic Press: New York, 1992; pp 23−27. (19) Noltemeyer, M.; Bertram, F.; Hempel, T.; Bastek, B.; Polyakov, A.; Christen, J.; Brandt, M.; Lorenz, M.; Grundmann, M. J. Mater. Res. 2012, 27 (17), 2225−2231. (20) Soudi, A.; Hsu, C.-H.; Gu, Y. Nano Lett. 2012, 12 (10), 5111− 5116. (21) Achoyan, A. S.; Yesayan, A.; Kazaryan, M.; Petrosyan, S. G. Semiconductors 2002, 36 (8), 903−907. G


Comparison of Three E-Beam Techniques for Electric Field Imaging

Recommend Documents