Interplay of Surface Recombination and Diode Geometry for the

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Interplay of Surface Recombination and Diode Geometry for the Performance of Axial p-i-n Nanowire Solar Cells David J. Hill, Taylor S. Teitsworth, Earl T. Ritchie, Joanna M. Atkin, and James F. Cahoon ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b06577 • Publication Date (Web): 20 Sep 2018 Downloaded from http://pubs.acs.org on September 21, 2018

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Interplay of Surface Recombination and Diode Geometry for the Performance of Axial p-i-n Nanowire Solar Cells David J. Hill, Taylor S. Teitsworth, Earl T. Ritchie, Joanna M. Atkin, and James F. Cahoon* Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, 27599-3290, United States KEYWORDS. silicon nanowire, vapor-liquid-solid growth, photovoltaic, photodetector, optoelectronics, nanophotonics, ABSTRACT Nanowires (NWs) with axial p-i-n junctions have been widely explored as microscopic diodes for optoelectronic and solar energy applications, and their performance is strongly influenced by charge recombination at the surface. We delineate how the photovoltaic performance of these diodes is dictated not simply by the surface, however, but also by the complex and seemingly counterintuitive interplay of diode geometry—i.e. radius (R) and intrinsic length (Li)—with the surface recombination velocity (S). An analytical model to describe these relationships is developed and compared to finite-element simulations, which verify the accuracy and limitations of the model. The dependence of the dark saturation current (Io), internal quantum efficiency (IQE), short-circuit current (ISC), and open-circuit voltage (VOC) on both geometric and recombination parameters demonstrates that no single set of parameters produces optimal performance; instead, various tradeoffs in performance are observed. For instance, longer Li might be expected to produce higher ISC, yet at high values of S the ISC declines because of decreases in IQE. Moreover, longer Li produces a concurrent decline in VOC regardless of S due 1 ACS Paragon Plus Environment

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to increases in Io. We also find that ISC and VOC trends are radius-independent, yet Io is directly proportional to R, causing NWs with smaller R to display higher turn-on voltages. The analysis regarding the interplay of these parameters, verified by experimental measurements with various p-i-n geometries and surface treatments, provides clear guidance for the rational design of performance metrics for photodiode and photovoltaic devices.

Nanowires (NWs) have garnered substantial attention for the unique properties and technological applications that are made possible by their nanoscale radial dimensions and high anisotropy. The bottom-up vapor-liquid-solid (VLS) growth of NWs allows for precise dopant1-3 and morphological4-6 profiles to be encoded along the axial dimension, permitting the creation of various active and passive device elements.7,8 For instance, well-controlled syntheses can produce polytypic interfaces,9 compositional heterostructures,10,11 and plasmonic resonators12 with interfaces defined on the single- to sub-nanometer scale in the best cases. Perhaps the most fundamental device element is the p-n junction, and numerous reports on NW axial p-n or p-i-n junctions13-15 have enumerated the conditions for producing the structures in both group IV16-20 and III-V21-23 materials. Devices including light-emitting diodes,10,24 photodetectors,11,25,26 and solar cells19-21,23,27-30 have been demonstrated; however, the characteristics of these devices depends strongly on the geometry and precision of dopant profiles encoded during synthesis. A key challenge for p-n or p-i-n NWs has been precisely controlling the doping level and dopant profile in both axial and radial directions, and several techniques have been used to characterize these quantities. For instance, dopant elemental profiles can be reconstructed using atom-probe tomography31 and mapped using energy-dispersive x-ray spectroscopy in transmission electron microscopes.2,32 Photoluminescence and cathodoluminescence33 maps can

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reveal the composition and doping in direct-band gap materials while scanning photocurrent microscopy18,34,35 and electron beam induced current can map the position of junctions and charge carrier diffusion lengths.36 In addition, Kelvin probe force microscopy35,37-39 can map potential changes within the NW that result from the dopant profile, and electron holography can map potential changes and space charge regions within the NW.40,41 Scattering-scanning nearfield optical microscopy (s-SNOM),42 as used herein, can detect dopant profiles through local free-carrier terahertz absorption. In addition to the evaluation of dopant and electrostatic profiles, the photovoltaic (PV) performance of NW axial p-i-n junctions has been evaluated theoretically43-47 as well as in devices composed of single-NWs and large-area NW arrays. In devices, it has been shown that a reduction in surface recombination results in significantly improved performance, boosting both photocurrent and photovoltage.18,23,34,36,48,49 Though recombination may place an upper bound on device performance, it is not the sole determinant. It has been shown that in some cases, low values of the surface recombination velocity (S) of up to ~103 cm/s have a negligible effect on device performance.45,46 Moreover, the performance of p-i-n Si NWs has been observed to be strongly dependent on the diode geometry, with longer intrinsic regions corresponding to improved performance.20 In addition, the internal quantum efficiency (IQE) within the intrinsic region of NWs has been observed to be relatively weakly dependent on S.43 Here, we systematically explore the connection between diode geometry (i.e. radius and intrinsic length) and surface recombination, which together dictate nearly every PV parameter. We first discuss a theoretical analysis of the PV performance using an analytical model and finite-element simulations, finding that the analytical model can often be used as a predictive tool in place of computationally-expensive simulations. Second, we compare the predictions of PV performance


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to experimental device measurements on single NWs with various geometries and well-defined dopant profiles, as verified by s-SNOM. The results elucidate the complex and sometimes counterintuitive connection between surface recombination and diode geometry of NW p-i-n junctions, providing guidelines for the evaluation and design of high-performance devices. RESULTS AND DISCUSSION Theoretical Analysis. We consider the device physics of the axial p-i-n structure (inset of Figure 1A) in the limit where recombination within the depletion region dominates the overall recombination current of the diode. In this case, the dark saturation current, Io, can be expressed (see the Supporting Information) as: Io = qR2 WD ni ⁄2τ = qRLi ni S,

(1)

where q is elementary charge, R is the radius of the NW, WD is the depletion width, ni is the intrinsic carrier concentration at room temperature (~1.5 x1010 cm-3 for Si), and τ is the effective recombination lifetime for both electrons and holes in the depletion region.50 For NWs with relatively small R and non-negligible values of the surface recombination velocity S, τ can be expressed as τ = R/2S, assuming the same value of S for electrons and holes.18,51 Assuming the bulk Shockley-Read-Hall (SRH) lifetime is 1 µs or greater, this approximation for τ, which neglects bulk SRH recombination, should be nearly exact if the value of S is greater than ~50 cm/s for NWs ~250 nm or less in diameter. Moreover, we expect eq. 1 to be valid both for indirect bandgap materials such as Si NWs and for direct bandgap materials such as InP NWs. If we consider direct band-to-band radiative recombination, as shown in the Supporting Information, the ratio of the radiative recombination rate, Rr, to non-radiative surface recombination rate, Rs is given by Rr/Rs = BR(n + ni)/S, where n is the charge carrier concentration and B is the radiative recombination coefficient (e.g. B = 1.2 x 10-10 cm3/s for 4 ACS Paragon Plus Environment

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InP52). For both direct and indirect bandgap semiconductors, the surface recombination rate will far exceed the radiative recombination rate up to excess charge carrier densities of ~1017 cm-3 (Figure S1). Because the carrier density within the intrinsic region ranges from 1012-1015 cm-3 under typical conditions (Figure S2), direct recombination can be effectively neglected when considering the recombination characteristics in the intrinsic region of p-i-n devices, validating the use of eq. 1 for direct and indirect bandgap semiconductor NWs. In addition, in the limit of degenerately-doped n-type and p-type segments, WD in eq. 1 can be approximated as the length of the intrinsic segment, Li. Using these approximations results in the expression on the righthand side of eq. 1. Moreover, the value of S can be estimated from Io and the geometrical parameters R and Li by rearranging eq. 1 as: S = Io ⁄qRLi ni

.

(2) Interestingly, eq. 1 predicts that Io is directly proportional to R and Li while eq. 2 predicts that S is inversely proportional to both quantities. Thus, NWs with smaller radii or shorter Li should exhibit a smaller Io and thus relatively improved diode characteristics (e.g. a higher turnon voltage) if S is constant. To validate these expressions, we compare the predictions of eqs. 1-2 to a previously developed finite-element simulation43 that describes the full geometry and electrostatics of a p-i-n junction under the influence of drift, diffusion, charge-carrier generation, non-radiative recombination by surface and bulk SRH mechanisms, and radiative recombination for direct bandgap semiconductors (see Methods for details). Results for indirect bandgap Si NWs are displayed in the main text while results for direct bandgap InP NWs are shown in the Supporting Information. In Figure 1, simulated current-voltage (I-V) curves are shown for Si NW radii, R, ranging from 25 nm to 100 nm (Figure 1A) with fixed S and Li of 200 cm/s and 1 µm,


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respectively, and for Li ranging from 0.2 to 2.1 µm (Figure 1B) with fixed S and R values 2,000 cm/s and 110 nm, respectively. As expected from eq. 1, a higher turn-on voltage is observed for both smaller R and smaller Li. Under approximate 1-sun AM1.5G illumination, the simulated I-V curves (Figure 1C) at various Li show the same improved diode behavior as apparent in the dark, and the photocurrent shows a strong dependence on Li, as discussed later. Similar trends are observed for InP NW simulations (Figure S3), confirming that surface recombination dominates over radiative recombination in dictating NW behavior. Fits of the Si dark I-V curves in Figures 1A-B to the ideal diode equation were used to determine Io. The dependence of Io on R and Li is displayed in Figure 2A (circles and dashed lines), showing that Io increases approximately linearly with both R and Li, as expected from eq. 1 (solid lines in Figure 2A). Moreover, S can be calculated from eq. 2 using Io, and a comparison of the S values determined from eq. 2 relative to the S values used in various simulations is shown in Figure 2B. The results indicate that eqs. 1-2 correctly predict the values of both Io and S within a factor of ~2 or better for Si devices. The ratio of Io from simulations and from eq. 1 is plotted in Figure 2C as a function of R and Li. The ratio is relatively independent of R but is strongly dependent on Li, increasing toward unity for longer values. The trend can be explained by examining the spatial dependence of recombination within the depletion region for different Li, as shown in Figure 2D. As is apparent from this plot, the recombination width (i.e. the full width at half maximum (FWHM) of each curve in Figure 2D) is substantially less than, and does not scale linearly with, Li. For instance, at Li of 0.2, 0.6, and 1.4 µm, the recombination FWHM equals 19, 38, and 69 % of Li. This effect indicates that eq. 1 tends to overestimate Io because it overestimates the length of the intrinsic region that contributes to the overall dark saturation current of the diode. Similarly, eq. 2 underestimates the value of S because the recombination


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current is effectively divided over a larger area of the surface, lowering the calculated value. Nevertheless, because the difference between the values is a factor of two or less for Si devices, this analysis suggests that a dark I-V curve measurement should be sufficient to estimate Io and S in real devices using eqs. 1 and 2. Similar results for InP NWs (Figure S3) also show agreement within a factor of 2-3, highlighting the applicability of this analysis to both direct in indirect bandgap semiconductors. Under 1-sun illumination, the ISC varies greatly with Li, as apparent from the Si I-V curves in Figure 1C. ISC depends both on light absorption in the NW and the spatially-dependent internal quantum efficiency (IQE) of the p-i-n junction. To account for light absorption in a NW with radius R, the ideal short-circuit current density J ideal SC (assuming an IQE of unity) of a NW illuminated uniformly along its axial length can be calculated as the integral over the wavelength- and radius-dependent absorption efficiency (calculated from finite-element optical simulations) and the incident power density for simulated AM1.5G 1-sun illumination. The values and dependence of J ideal SC on R for Si NWs are illustrated in Figure S4, and the accuracy of these values has been verified in prior reports.53,54 However, for simplicity, we assume J ideal SC = 7 mA/cm2 for all Si calculations. To account for the spatially-dependent IQE, we assume a constant IQE value, φIQE, within the depletion region, WD, and an exponential decay elsewhere.43 Thus, ISC can be approximated as: ideal ISC = 2J ideal SC φIQE R WD + Ln + Lp = 2J SC φIQE R Li + Ln + Lp ,

(3) where Ln and Lp are the effective minority carrier diffusion lengths in the quasi-neutral n-type and p-type regions, respectively. On the right-hand side of eq. 3, we again assume that WD = Li. 7 ACS Paragon Plus Environment

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Thus, this expression predicts that the measured ISC should scale linearly with Li, as has been observed in previous reports of NW p-i-n devices,20 but it should also include an offset reflecting photocurrent generated outside of the depletion region if Ln and Lp are non-negligible. If recombination in the quasi-neutral regions is dominated by surface recombination, these quantities can be calculated by Ln,p = (Dp,nR/2S)1/2, with Dp,n the diffusion constant for electrons (Dn) or holes (Dp). However, in direct bandgap materials, Ln,p can be dictated by either radiative or surface recombination, depending on the surface recombination lifetime. When R is large and S is small, Ln,p will be dominated by radiative recombination, according to Ln,p = (Dp,n/BNA,D)1/2, where NA,D is the dopant concentration in either the p-type or n-type region. Thus, for a direct bandgap material, Ln,p can be smaller compared to an indirect bandgap material for the same values of R and S. However, at very small values of R, or when S is large (>105 cm/s), Ln,p will be dominated by surface recombination, according to Ln,p = (Dp,nR/2S)1/2. To evaluate the validity of eq. 3, in Figure 3A we plot the ISC of Si NW devices from simulated I-V curves as a function of Li at a fixed R of 110 nm and S ranging from 200 to 200,000 cm/s, as shown by the circles in Figure 3A. Predictions from eq. 3, assuming φIQE of unity, are also shown as the solid lines. The two calculations show reasonably good agreement, verifying eq. 3. ISC does exhibit a linear relationship with Li but with a constant offset that increases with lower values of S and extrapolates to a non-zero current at Li = 0. The non-zero current primarily reflects photocurrent generated in the quasi-neutral n-type and p-type segments but also photocurrent generated within the non-negligible depletion region. At low values of S, the small offset between the simulations and predictions of eq. 3 can be explained by the latter, highlighting the limitations of assuming WD = Li in eq. 3. At high values of S, in contrast, the simulations strongly deviate from the prediction of eq. 3, exhibiting a peak and decline at higher


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values of Li. This deviation originates from a non-uniform and non-unity value of φIQE, as discussed below. We observe similar trends from InP simulations (Figure S5A). To examine the magnitude and uniformity of IQE, we calculated the spatially-dependent IQE of Si NWs with various values of R, S, and Li, as shown in Figure 3B. For Li of 1.4 µm (Figure 3B, upper), the IQE of both large (220 nm) and small (68 nm) diameter wires exhibit high values of IQE within the intrinsic region when S = 2,000 cm/s (solid and dashed blue lines, respectively). However, when S = 200,000 cm/s, the IQE of the small diameter wire (dashed red line) is substantially lower than the larger (solid red line). For high S values, the spatial dependence of IQE with different Li (Figure 3B, lower) shows that for small Li, the average IQE of intrinsic region remains close to 99%. As Li increases to 2 µm, however, the average IQE drops to ~50% (Figure S4B). As a result, ISC does not scale linearly with Li at high values of S, and instead peaks and declines as Li increases, as shown by the data (purple circles) in Figure 3A. Overall, the results in Figure 3B show that the IQE within the intrinsic region is relatively independent of both Li and R for moderate to low values of S (> Ln+Lp, which would occur if S within the doped regions is substantially higher than S within the intrinsic region, as observed previously.57 All devices exhibit S near 1000 cm/s, which likely reflects only the value within the intrinsic region. As predicted (c.f. Figure 2A), Io increases with Li, while values for n and FF remain relatively constant. Note that previously reported axial p-i-n Si NW devices exhibited VOC values that substantially increased with increasing Li.20 This effect can be attributed to S values that strongly depend on Li as a result of the specific synthesis conditions used during NW growth.

Table 2. PV metrics oxidized/annealed axial p-i-n NW devices with various Li

a

Li (µm)

R (nm)

Sb (cm/s)

VOC (V)

Isc (pA)

JSCa (mA/cm2)

FF

0.5

110

1220

0.341

8.0

7.30

0.63

1.0

98

2050

0.310

15.3

7.82

0.61

η

n

Io (fA)

1.57

1.74

3.6

1.48

1.68

10.7

126 23.7 1.5 1450 0.318 6.26 0.62 1.48 1.69 b estimated using the intrinsic segment projected area; calculated using eq. 2.

14.8

(%)

To explore the IQE of the axial p-i-n NW devices, we measured the external quantum efficiency (EQE) spectra of devices as a function of wavelength under various bias conditions. Figure 6 displays the EQE spectra of an etched axial p-i-n NW with an intrinsic radius of 23 nm and S of 8300 cm/s, as calculated from eq. 2 using a measurement of Io from the dark I-V curve (Figure S8). Using the calculated value of S, the IQE of this device is not expected to be unity at an applied bias of zero; however, finite-element simulations of IQE (inset of Figure 6) indicate that a reverse bias of -5 V should be sufficient to nearly maximize IQE with the intrinsic region. The EQE spectrum progressively improves at -1 V and -5 V but shows no further improvement at lower values. This result is in good agreement with the IQE simulations. The spectra also 14 ACS Paragon Plus Environment

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highlight the potential photodetector applications of the p-i-n NWs. Because the spectral response of a NW strongly depends on diameter and polarization,53,54,58-61 selectively etching the intrinsic section of the NW controllably alters the absorption spectrum of the device. The EQE spectrum in Figure 6 exhibits peaks that reflect the optical modes of the intrinsic region. However, this etching process introduces surface defects, which increases S and tends to degrade photodetector performance. Nevertheless, our results show that near-unity IQE in the intrinsic region can be achieved under mild reverse bias. Thus, wavelength-tunable NW photodiodes can be created using modulation doping and etching, and surface recombination may be rendered inconsequential through the application of a reverse bias. CONCLUSIONS A combination of theoretical analysis, finite-element simulations, and experimental measurements on single-NW devices has been used to evaluate the effect of diode geometry and surface recombination on the PV performance of axial p-i-n junctions. The results reveal a direct analytical connection between the dark saturation current I0, surface recombination velocity S, and diode geometry (radius R and intrinsic length Li), thus allowing the prediction of I-V curves and PV metrics from the surface and geometrical parameters. Although the photocurrent (ISC) from devices is generally found to increase with increasing size of the diode (i.e. increasing Li), the photovoltage (VOC) is surprisingly found to remain constant or decrease, which can be attributed to increases in I0. In addition, the IQE of devices is found to be uniformly high within the intrinsic region regardless of S for short Li, but it is found to vary significantly with longer Li when S is high. Experimental measurements on single-NWs with well-defined geometry and dopant profile, as confirmed by s-SNOM measurements, confirm the theoretical predictions. This analysis on the interplay of surface recombination and geometry provides a framework for the


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rational design of higher performance axial p-i-n junctions for photodetector, solar energy, and solar fuel applications.

MATERIALS AND METHODS NW synthesis. NWs were grown in a home-built chemical vapor deposition system. Au catalysts of diameters 50−200 nm (BBI International) were immobilized on Si/SiO2 wafers with polylysine (Sigma-Aldrich) and cleaned in a UV-ozone cleaner. The substrate was then inserted into a 1 in. hot-wall tube furnace (Lindberg Blue M) and heated to the growth temperature. Silane (SiH4, Voltaix), diborane (B2H6, 1000 ppm in H2, Voltaix), and phosphine (PH3, 1000 ppm in H2, Voltaix) served as the precursors for the NWs. HCl (Matheson TriGas, 5 N) was used for chlorination, and H2 (Matheson TriGas, 5N semiconductor grade) was used as the carrier gas. NWs used in Figure 5A-B were grown at 650 °C and a total pressure of 20 Torr, with 0.5 sccm SiH4 and 3.2−3.6 sccm HCl, with a SiH4 partial pressure of ∼50 mTorr. NWs with varying intrinsic lengths, shown in Figure 5C, were grown at 510 °C and a total pressure of 20 Torr, with 2 sccm SiH4 and 4 sccm HCl, with a SiH4 partial pressure of ∼200 mTorr. The flow of H2 carrier gas was varied between 180 and 200 sccm, depending on the dopant gas flow, to maintain a constant SiH4 partial pressure. In p-type segments, the B2H6 flow rate was 15 sccm while ntype segments were grown with 20 sccm PH3. All gas flow rates were controlled and measured using model P4B mass-flow controllers from MKS Instruments. NW Etching. NWs were mechanically transferred onto Si/SiO2/Si3N4 substrates. The NW oxide was removed by etching in buffered hydrofluoric acid (Transene BHF Improved) for 10 s, and the substrate was subsequently washed in water and 2-propanol (Fischer Scientific). Any surface gold, which could impede etching, was removed by etching in a solution of 4:1:40


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(w/w/w) KI:I2:H2O and rinsing in water and 2-propanol. The oxide etch procedure was then repeated. The NW substrate was then immersed in the KOH etchant solution (20% w/w aq. KOH) at room temperature for times varying between 30 s and 4 min, depending on the diameter and intended etch depth. The substrate was quenched in acetic acid (2% v/v aq. AcOH) and rinsed in water and 2-propanol before being blown dry with N2. Electron Microscopy. SEM images were taken with an FEI Helios 600 Nanolab dualbeam system. Device Fabrication. An MMA/PMMA (MMA EL9, PMMA A2, Microchem) resist stack was spun onto Si/SiO2/Si3N4 wafers. Marker patterns were fabricated through electron beam lithography (EBL, Nanometer Pattern Generation System), thermal evaporation (Cr, 3nm; Au, 50 nm), and lift off. NWs were mechanically transferred onto the marker patterns and where appropriate, etched following the described procedure. The p-i-n NWs were then oxidized in a ULVAC MILA-5000 rapid thermal annealing system in 760 Torr O2 at 950 °C for 30 s. The annealing process was carried out in a 10% H2/90% N2 atmosphere at 760 Torr, ramping the temperature from 600 °C to 300 °C over 2 hrs. A resist stack was then spun on top of the NWs, and contacts were patterned using EBL. The NW oxide was etched with BHF and metal contacts were deposited (3 nm Ti, 300 nm Pd) using an electron beam evaporator (Thermionics VE-100) with a base pressure of ~9 x 10-8 Torr. Electrical Characterization. Light and dark current-voltage (IV) measurements were acquired using a Keithley 2636A SourceMeter in conjunction with Signatone micropositioners (S-725) and probe tips (SE-TL). Light measurements involved illumination from a Newport model 91191 (1 kW Xe lamp) solar simulator with an AM1.5G filter and was calibrated to 1-sun (100 mW/cm2) using a calibrated reference solar cell (Newport model 91150V). Power


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dependent measurements focused this light source to various sizes using a single lens. Photocurrent measurements were performed with the same SourceMeter and a supercontinuum laser (NKT Photonics, SuperK Extreme) operating at 78 MHz passing through a spectrograph (Princeton Instruments, SpectraPro SP-2300) with slits set at 1.5 mm. A Glan-Thomson polarizer (Thorlabs, GTH10M) was used to achieve polarization control. Measurements were taken at 5 nm increments, with light and dark measurements taken at each wavelength. Dark measurements were subtracted, and the photoresponse was corrected for the power spectrum of the illumination source, as measured by a calibrated silicon photodetector (Newport model 918D-SL-OD1). The pulsed source operates at 78 MHz, and the observed currents were ~10 pA, which equates to approximately one collected charge carrier per laser cycle. Thus, EQE spectra measured in this configuration should be equivalent to what would be measured in a continuous-wave configuration. Optical Simulations. Finite-element optical simulations were performed with COMSOL Multiphysics to evaluate optical resonances. Two-dimensional optical simulations were implemented using the total-field, scattered-field method. The background field was evaluated with a plane wave normally incident on the substrate using periodic boundary conditions on the two vertical boundaries, a perfectly matched layer (PML) on the lower boundary, and the plane wave source on the upper boundary. The scattered field was then solved after adding the NW to the simulation domain and replacing all boundaries with PMLs. Electrostatic Simulations. Finite-element simulations were performed with COMSOL Multiphysics to predict the current-voltage characteristics of axial p-i-n diodes using the model reported previously but without Auger recombination.43 Axially symmetric two-dimensional simulations were used to model the three-dimensional structure. The intrinsic region was varied


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from 200 nm to 2 µm, with 1 µm long p-type and n-type segments, doped at 2 x 1019 cm-3. A 10 nm dopant transition width was used. The models incorporated standard drift and diffusion physics with Shockley-Read-Hall (the recombination lifetime was fixed at 1 µs) and surface recombination mechanisms. For simulations under approximate 1-sun illumination (c.f. Figure 1C and Figure 3A,C,D), an additional uniform charge carrier generation term corresponding to a JSC value of 7 mA/cm2 was assumed. For comparisons between experiment and simulation in Figure 5B and Table 1, the experimental 1-sun I-V curves were fit to simulated dark I-V curves shifted by the experimental ISC value. For the analytical calculation of ISC for comparison to simulations, eq. 3 was modified to integrate only over the 1 µm length of the n-type and p-type segments used in the simulations. For calculation of IQE, a generation term of 6 mol·cm-3·s-1 was introduced stepwise in 5x5 nm2 areal elements of the cylindrically symmetric simulation domain. Ohmic metal contacts on both n- and p-type segments were assumed to be carrier selective to avoid recombination and narrow-base diode effects in the simulation. For InP NW simulations, a JSC value of 20 mA/cm2 was assumed, with ni = 1.3 x 107. Radiative recombination was also simulated, using B = 1.2 x 10-10 cm3/s.52 A generation rate of 12 mmol·cm-3·s-1 was used for the calculation of IQE. AFM Measurements. The near-field microscopy experiments were performed using a home-built infrared s-SNOM system based on a modified commercial AFM (Bruker Innova) as described in Ritchie et al.42 A vertically polarized CO2 laser (Access Lasers) at 10.6 µm wavelength is used as an excitation source. s-SNOM experiments were carried out with a homodyne interferometric scheme. The intensity of the near-field signal was demodulated at the third harmonic (n = 3) of the tapping frequency and used to construct an optical image simultaneously with the AFM topography. To allow for comparison of the near-field signal


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across samples, SiNWs were deposited onto Au-coated Si3N4 substrates and were normalized to the high-intensity signal from the gold surface. Near-field spatial resolution was determined from near-field approach curves to be ~10 nm. Several scans (2 × 2 µm, 256 × 256 pixels) were taken along the length of the wire to observe the doping profile. Doping assignments were determined by comparing section lengths to the dopant flow profile. The n-type sections were shown to have the highest near-field intensity, with p-type sections having a lower intensity, and intrinsic Si having the lowest. We observe an average n-type length of 342 ± 6.8 nm, p-type length of 790 ± 13 nm, and intrinsic Si length of 1730 ± 55 nm. ASSOCIATED CONTENT Supporting Information Available online. The supporting information includes the derivation of eq. 1, equations used for modeling of radiative and non-radiative recombination, Figures S1-S7, which show additional theoretical data on NW PV performance, and Figure S8, which shows experimental I-V curves for a NW photodetector. The authors declare no competing financial interests. AUTHOR INFORMATION Corresponding Author *Email: [email protected]. ACKNOWLEDGMENT This research was supported by the National Science Foundation (NSF) through grant DMR1555001. D.J.H. acknowledges an NSF graduate research fellowship, and J.F.C acknowledges a Packard Fellowship for Science and Engineering. This work made use of instrumentation at the Chapel Hill Analytical and Nanofabrication Laboratory (CHANL), a member of the North Carolina Research Triangle Nanotechnology Network (RTNN), which is supported by the NSF


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(ECCS-1542015) as part of the National Nanotechnology Coordinated Infrastructure (NNCI).

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(30) Wallentin, J.; Anttu, N.; Asoli, D.; Huffman, M.; Aberg, I.; Magnusson, M. H.; Siefer, G.; Fuss-Kailuweit, P.; Dimroth, F.; Witzigmann, B.; Xu, H. Q.; Samuelson, L.; Deppert, K.; Borgstrom, M. T. InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit. Science 2013, 339, 1057-1060. (31) Perea, D. E.; Allen, J. E.; May, S. J.; Wessels, B. W.; Seidman, D. N.; Lauhon, L. J. ThreeDimensional Nanoscale Composition Mapping of Semiconductor Nanowires. Nano Lett. 2006, 6, 181-185. (32) Kim, S.; Hill, D. J.; Pinion, C. W.; Christesen, J. D.; McBride, J. R.; Cahoon, J. F. Designing Morphology in Epitaxial Silicon Nanowires: The Role of Gold, Surface Chemistry, and Phosphorus Doping. ACS Nano 2017, 11, 4453-4462. (33) Li, Z.; Yang, I.; Li, L.; Gao, Q.; Chong, J. S.; Li, Z.; Lockrey, M. N.; Tan, H. H.; Jagadish, C.; Fu, L. Reducing Zn Diffusion in Single Axial Junction InP Nanowire Solar Cells for Improved Performance. Progress in Natural Science: Materials International 2018, 28, 178-182. (34) Dan, Y.; Seo, K.; Takei, K.; Meza, J. H.; Javey, A.; Crozier, K. B. Dramatic Reduction of Surface Recombination by In Situ Surface Passivation of Silicon Nanowires. Nano Lett. 2011, 11, 2527-2532. (35) Lysov, A.; Vinaji, S.; Offer, M.; Gutsche, C.; Regolin, I.; Mertin, W.; Geller, M.; Prost, W.; Bacher, G.; Tegude, F. J. Spatially Resolved Photoelectric Performance of Axial GaAs Nanowire pn-Diodes. Nano Res. 2011, 4, 987-995. (36) Zhong, Z. Q.; Li, Z. Y.; Gao, Q.; Li, Z.; Peng, K.; Li, L.; Mokkapati, S.; Vora, K.; Wu, J.; Zhang, G. J.; Wang, Z. M.; Fu, L.; Tan, H. H.; Jagadish, C. Efficiency Enhancement of Axial Junction InP Single Nanowire Solar Cells by Dielectric Coating. Nano Energy 2016, 28, 106-114. (37) Amit, I.; Jeon, N.; Lauhon, L. J.; Rosenwaks, Y. Impact of Dopant Compensation on Graded p-n Junctions in Si Nanowires. ACS Appl. Mater. Interfaces 2016, 8, 128-134. (38) Minj, A.; Cros, A.; Auzelle, T.; Pernot, J.; Daudin, B. Direct Assessment of p-n Junctions in Single GaN Nanowires by Kelvin Probe Force Microscopy. Nanotechnol. 2016, 27, 385202. (39) Sun, X. X.; Wang, X. Q.; Wang, P.; Sheng, B. W.; Li, M.; Su, J.; Zhang, J.; Liu, F.; Rong, X.; Xu, F. J.; Yang, X. L.; Qin, Z. X.; Ge, W. K.; Shen, B. Identifying a Doping Type of Semiconductor Nanowires by Photoassisted Kelvin Probe Force Microscopy as Exemplified for GaN Nanowires. Optical Materials Express 2017, 7, 904-912. (40) Darbandi, A.; McNeil, J. C.; Akhtari-Zavareh, A.; Watkins, S. P.; Kavanagh, K. L. Direct Measurement of the Electrical Abruptness of a Nanowire p-n Junction. Nano Lett. 2016, 16, 3982-3988. (41) He, K.; Cho, J. H.; Jung, Y.; Picraux, S. T.; Cumings, J. Silicon Nanowires: Electron Holography Studies of Doped p-n Junctions and Biased Schottky Barriers. Nanotechnol. 2013, 24, 115703. (42) Ritchie, E. T.; Hill, D. J.; Mastin, T. M.; Deguzman, P. C.; Cahoon, J. F.; Atkin, J. M. Mapping Free-Carriers in Multijunction Silicon Nanowires Using Infrared Near-Field Optical Microscopy. Nano Lett. 2017, 17, 6591-6597.


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(43) Christesen, J. D.; Zhang, X.; Pinion, C. W.; Celano, T. A.; Flynn, C. J.; Cahoon, J. F. Design Principles for Photovoltaic Devices Based on Si Nanowires with Axial or Radial pn Junctions. Nano Lett. 2012, 12, 6024-6029. (44) Huang, N.; Lin, C.; Povinelli, M. L. Limiting Efficiencies of Tandem Solar Cells Consisting of III-V Nanowire Arrays on Silicon. J. Appl. Phys. 2012, 112, 064321. (45) Yu, S.; Roemer, F.; Witzigmann, B. Analysis of Surface Recombination in Nanowire Array Solar Cells. J. Photonics Energy 2012, 2, 028002. (46) Chen, Y.; Kivisaari, P.; Pistol, M. E.; Anttu, N. Optimized Efficiency in InP Nanowire Solar Cells with Accurate 1D Analysis. Nanotechnol. 2018, 29, 045401. (47) Fernandes, C.; Shik, A.; Byrne, K.; Lynall, D.; Blumin, M.; Saveliev, I.; Ruda, H. E. Axial p-n Junctions in Nanowires. Nanotechnol. 2015, 26, 085204. (48) Zhang, P.; Liu, P.; Siontas, S.; Zaslavsky, A.; Pacifici, D.; Ha, J. Y.; Krylyuk, S.; Davydov, A. V. Dense Nanoimprinted Silicon Nanowire Arrays with Passivated Axial p-i-n Junctions for Photovoltaic Applications. J. Appl. Phys. 2015, 117, 125104. (49) Himwas, C.; Collin, S.; Rale, P.; Chauvin, N.; Patriarche, G.; Oehler, F.; Julien, F. H.; Travers, L.; Harmand, J. C.; Tchernycheva, M. In Situ Passivation of GaAsP Nanowires. Nanotechnol. 2017, 28, 495707. (50) Gray, J. L., The Physics of the Solar Cell. In Handbook of Photovoltaic Science and Engineering, 2nd ed.; Antonio Luque, S. H., Ed. Wiley: 2005; pp 61-112. (51) 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. High-Resolution Detection of Au Catalyst Atoms in Si Nanowires. Nat. Nanotechnol. 2008, 3, 168-173. (52) Liu, A.; Rosenwaks, Y. Excess Carriers Lifetime in InP Single Crystals: Radiative versus Nonradiative Recombination. J. Appl. Phys. 1999, 86, 430-437. (53) Cao, L.; Fan, P.; Barnard, E. S.; Brown, A. M.; Brongersma, M. L. Tuning the Color of Silicon Nanostructures. Nano Lett. 2010, 10, 2649-2654. (54) Kim, S. K.; Day, R. W.; Cahoon, J. F.; Kempa, T. J.; Song, K. D.; Park, H. G.; Lieber, C. M. Tuning Light Absorption in Core/Shell Silicon Nanowire Photovoltaic Devices through Morphological Design. Nano Lett. 2012, 12, 4971-4976. (55) Green, M. A. Solar Cell Fill Factors: General Graph and Empirical Expressions. Solid-State Electron. 1981, 24, 788-789. (56) Suzuki, E.; Takato, H.; Ishii, K.; Hayashi, Y. Evaluation of the Si-SiO2 Interface by the Measurement of the Surface Recombination Velocity S by the Dual-Mercury Probe Method. Jpn. J. Appl. Phys. 1990, 29, L2300-L2303. (57) Gabriel, M. M.; Grumstrup, E. M.; Kirschbrown, J. R.; Pinion, C. W.; Christesen, J. D.; Zigler, D. F.; Cating, E. E.; Cahoon, J. F.; Papanikolas, J. M. Imaging Charge Separation and Carrier Recombination in Nanowire p-i-n Junctions using Ultrafast Microscopy. Nano Lett. 2014, 14, 3079-3087. (58) Bronstrup, G.; Jahr, N.; Leiterer, C.; Csaki, A.; Fritzsche, W.; Christiansen, S. Optical Properties of Individual Silicon Nanowires for Photonic Devices. ACS Nano 2010, 4, 71137122.


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(59) Zhang, X.; Pinion, C. W.; Christesen, J. D.; Flynn, C. J.; Celano, T. A.; Cahoon, J. F. Horizontal Silicon Nanowires with Radial p-n Junctions: A Platform for Unconventional Solar Cells. J. Phys. Chem. Lett. 2013, 4, 2002-2009. (60) Cao, L.; White, J. S.; Park, J. S.; Schuller, J. A.; Clemens, B. M.; Brongersma, M. L. Engineering Light Absorption in Semiconductor Nanowire Devices. Nat. Mater. 2009, 8, 643-647. (61) Mokkapati, S.; Saxena, D.; Tan, H. H.; Jagadish, C. Optical Design of Nanowire Absorbers for Wavelength Selective Photodetectors. Sci. Rep. 2015, 5, 15339.

Figure captions:

Figure 1. Simulated I-V characteristics of axial p-i-n Si NW devices. (A) Simulated dark I-V curves for R ranging from 25 to 100 nm with S of 200 cm/s and Li of 1 µm. Inset: schematic of the geometrical and recombination parameters of an axial p-i-n junction. (B) Simulated I-V curves in the dark for R = 110 nm, Li ranging from 0.2 to 2.1 µm, and S of 2,000 cm/s. (C) Simulated I-V curves under 1-sun illumination for R = 110 nm, Li ranging from 0.2 to 2.1 µm, and S = of 2,000 cm/s.

Figure 2. Comparison of simulated and analytical Si PV metrics. (A) I0 as a function of R (blue) and Li (orange) from simulation (circles and dashed lines) and eq. 1 (solid lines) assuming S = 200 cm/s and Li = 1 µm (blue data) and S = 200 cm/s and R = 110 nm (orange data). (B) Correlation between S parametrized in finite-element simulations and S calculated from eq. 2 for R = 110 nm at six values of Li ranging from 0.2 to 2.1 µm. (C) Ratio of I0 from simulations and from eq. 1 as a function of Li (orange circles) and R (blue circles). The ratio is calculated from the corresponding data in panel A. (D) Recombination rate as a function of axial position at a bias of 0.4 V, with S = 200 cm/s and Li of 0.2 (purple), 0.6 (green), and 1.4 µm (orange).


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Figure 3. The effect of Li on Si PV metrics. (A) Comparison of analytically predicted (solid lines) ISC values and those extracted from simulations (circles) for R = 110 nm and S = 200 (blue), 2,000 (orange), 20,000 (yellow) and 200,000 (purple) cm/s. (B) Upper: Plot of IQE as a function of axial position at R of 110 nm (solid lines) and 34 nm (dashed lines) with S = 2000 cm/s (blue) and 200,000 cm/s (red); Lower: IQE vs. axial position with S = 200,000 cm/s, R = 110 nm, and Li of 1.4 (red), 1.2 (orange), 1.0 (yellow), 0.8 (green), 0.4 (blue), and 0.2 µm (purple). (C) Comparison of analytically predicted VOC values (lines) and those extracted from simulations (circles) for R = 110 nm and S = 200 (blue), 2,000 (orange), 20,000 (yellow) and 200,000 (purple) cm/s, when n = 2 (dashed lines) and n = 1.7 (solid lines). (D) Upper: Comparison of analytically predicted (solid lines) Pmax and those extracted from simulations (circles) for R = 110 nm and S = 200 (blue), 2,000 (orange), 20,000 (yellow) and 200,000 (purple) cm/s. Lower: Comparison of analytically predicted (solid lines) maximum power density (Pmax/2RLi) and those extracted from simulations (circles) for R = 110 nm and S = 200 (blue), 2,000 (orange), 20,000 (yellow) and 200,000 (purple) cm/s.

Figure 4. Geometrically-defined and degenerately-doped axial p-i-n Si NWs. (A) Schematic (upper) of an etched p-i-n junction, SEM images of an etched (middle) and diameter profile (lower) junction; scale bar, 500 nm. (B) AFM image of a p-i-n NW (upper), s-SNOM map of near-field signal in a p-i-n NW (middle), and a line trace of the s-SNOM signal (lower).

Figure 5. Axial p-i-n single-NW Si PV devices. (A) I-V curves of as-grown (blue) and treated (orange) devices in the dark. Inset, curves plotted on a log scale with linear fits (dashed lines). (B) Forward bias I-V curves of as-grown (solid blue) and treated (solid orange) devices under 1-


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sun illumination. Corresponding finite-element simulations are shown as dashed lines. (C) I-V curves of NW p-i-n devices under 1-sun illumination, with intrinsic segment lengths of 0.5 µm (black), 1 µm (red), and 1.5 µm (blue). Inset: I-V curves of these devices in the dark.

Figure 6. Etched p-i-n photodiode. EQE spectrum of an etched NW device under TE illumination and reverse bias conditions of 0 V (red), -1 V (yellow), and -5 V (green), and -10 V (blue). Inset, IQE vs. axial position, with S = 200,000 cm/s, R = 110 nm, and applied biases of 0 V (red), -1 V (yellow), and -5 V (green).


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C

ACS Nano

0.6 0.5

40 30

0.4 0.3

20

0.2

10

0.1

0 0

1

0.5 p

1

1.5

Li (μm) Li

2

00

2.5 n

0.5

1

1.5

2

2.5

1

1.5

2

2.5

Li (μm)

D 10-7

Pmax (mW)

IQE

0.8 0.6 0.4

10-8

10-9

0.2

Li = 0.2 μm 0.4 μm 0.6 μm 0.8 μm 1.4 μm 2.1 μm

1 0.8 IQE

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

50

S= 200 cm/s 2,000 cm/s 20,000 cm/s 200,000 cm/s

VOC (V)

A

0.6 0.4 0.2 0

102

Pmax / 2RLi (mW/cm2)

Page 31 of 34

101 100 10-1

ACS Paragon Plus Environment -1

-0.5 0 0.5 1 Axial position (μm)

10-2

0

0.5

Li (μm)

Li

A

ACS Nano i

p

Radius (nm)

1 2 3 100 4 50 5 60 7 B8 9 10 11 12 13 14 15 16 17 18 19 20 0 21 22

0.5

Page 32n of 34

1.0 1.5 Axial position (μm)

2.0 nm 100 75 50 25 1.4 1.0 0.6

ACS Paragon Plus Environment 0.5

1.0

1.5

Axial position (μm)

2.0

2.5

300

10-11

Current (pA)

200

Current (pA)

Current (pA)

1 2 3 4 5 6 7 8 9 B 10 11 12 13 14 15 16 17 18 19 20 21 C 22 23 24 25 26 27 28 29 30 31 32 33

ACS Nano

10-9

Current (A)

250 150

10-13

100

0.2

0.3 0.4 0.5 Bias (V)

50 0 -50 -100 -0.1

0

0.1

0.2 0.3 Bias (V)

0.4

0.5

0

0.1

0.2 0.3 Bias (V)

0.4

0.5

20 15 10 5 0 -5 -10 -15 -20 -0.1

40

30 20

Current (pA)

A

Page 33 of 34

10

30 20 10 0

-10

0

0

0.2 0.4 Bias (V)

-10 -20

ACS Paragon Plus Environment

-0.1

0

0.1

0.2 0.3 Bias (V)

0.4

1.0 0.8 EQE

1 2 3 4 5 6 7 8

0.6 0.4

1 -10ACS V Nano -5 V -1 V .6 0V

Page 34 of 34

IQE

1.2

.2 0 1 2 Axial position (μm)

0.2

ACS Paragon Plus Environment

0.0 400 450 500 550 600 650 700 750 Wavelength (nm)

Interplay of Surface Recombination and Diode Geometry for the

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