Wafer-Scale Synthesis and Optical Characterization of InP Nanowire Arrays for Solar Cells

Nanowire solar cells have the potential to reach the same efficiencies as the world-record III–V solar cells while using a fraction of the material. For solar energy harvesting, large-area nanowire solar cells have to be processed. In this work, we demonstrate the synthesis of epitaxial InP nanowire arrays on a 2 inch wafer. We define five array areas with different nanowire diameters on the same wafer. We use a photoluminescence mapper to characterize the sample optically and compare it to a homogeneously exposed reference wafer. Both steady-state and time-resolved photoluminescence maps are used to study the material’s quality. From a mapping of reflectance spectra, we simultaneously extract the diameter and length of the nanowires over the full wafer. The extracted knowledge of large-scale nanowire synthesis will be crucial for the upscaling of nanowire-based solar cells, and the demonstrated wafer-scale characterization methods will be central for quality control during manufacturing.


■ INTRODUCTION
Nanowires (NWs) are promising candidates for future solar cells. 1−3 They hold the potential to reach the high efficiencies of world-record III−V semiconductor technology while using only about 10% of the material. 4,5 Furthermore, NWs have unique advantages, such as the possibility to be integrated in polymers 6−9 to create flexible solar cells with high efficiencies. Due to their geometry, NWs are radiation hard, which makes them ideal candidates for space applications. 10,11 So far, the highest NW solar cell efficiencies have been reached by topdown processing, 12 which does not take full advantage of the possibilities that NWs enable, and bottom-up synthesis of epitaxial NW arrays. 13,14 Recently, there have been efforts to understand the efficiency-limiting factors of NW solar cells using electron-beam-induced current (EBIC) measurements among other techniques such as cathodoluminescence, 15 scanning photocurrent microscopy, 16 and conductive-probe atomic force microscopy 17 both on processed devices 18−21 and on single NWs. 22−26 However, to become a competitive photovoltaic technology, large-area NW solar cells are needed. Wafer-scale patterning necessary for NW synthesis has been shown by the use of nanoimprint lithography (NIL) 27 and displacement Talbot lithography (DTL). 28 Here, we demonstrate that wafer-scale synthesis of epitaxial InP NW arrays is feasible. In this work, we have used DTL to pattern 2 inch InP wafers. On one wafer, Sample 1, we defined five regions with different exposure doses to create NW arrays with different diameters. The other wafer, Sample 2, was patterned homogeneously. In order to characterize the material's quality of both samples, we measured photoluminescence (PL) and time-resolved photoluminescence (TRPL) with a PL mapper. The most direct method to measure the length of epitaxial NWs is cross-sectional scanning electron microscopy (SEM) imaging, for which the sample has to be cleaved. Therefore, NW arrays are often imaged by use of a tilted stage, which increases the uncertainty in the measurement. In addition, only small areas with high magnification can be characterized by the use of SEM, and it would be too time-consuming to investigate a full wafer. In situ reflectivity is a convenient method to control the NW length during synthesis, 29 but it gives information on a small central area of only about 1 mm 2 . By the creation of a simulated database that describes the reflectivity of NWs with a given diameter (D) and length (L), it is possible to extract those parameters from ex situ reflectivity measurements. This method has been used to measure the homogeneity across a small NW-array sample by time-consuming manual movement of the measurement spot over a 2 mm long line across the sample. 30 Here, we use a PL mapper equipped with a white light source to automatically measure several thousand reflectivity spectra and utilize such a database extraction method to extract maps of the NW diameter and length over the full 2 inch wafer.  Figure 1p,q shows photographs of Sample 1 with five areas with different DTL doses and the homogeneously patterned Sample 2, respectively. The clearly visible angle-dependent coloring of the wafer can be attributed to the diffraction grating effect of the periodic NW arrays. The DTL dose was increased in steps of 0.5 mJ/cm 2 from 2.5 to 4.5 J/cm 2 from left to right.

■ RESULTS AND DISCUSSION
The undercut that is created during development of the PMGI resist is dependent on the exposure time and is only 30 nm wide for the area with an exposure dose of 2.5 J/cm 2 (Figure 1a), while adjacent undercuts in the area that was exposed with 4.5 J/cm 2 almost merge together (Figure 1e). At 4.0 and 4.5 J/cm 2 (Figure 1d,e) second-order diffraction effects can be observed between the intended exposures but these are not transferred to the substrate after gold evaporation and liftoff. The hole size after DTL exposure and development is difficult to measure because the resist is affected by the electron beam of the SEM. It is more precise to measure the diameter of the gold particles after evaporation and liftoff. However, for NWs synthesized by the vapor−liquid−solid (VLS) mechanism, 31 it has to be considered that the NW diameter is determined by the interface area between the liquid seed particle and the substrate, which is dependent on the contact angle and the temperature-dependent solubility of the growth species in the seed particle.
In order to measure the homogeneity of the NW dimensions, we used a PL mapper equipped with a white light source and measured reflectance spectra of the NW arrays. Here, we performed the extraction of D and L similarly as in ref 30. That is, we created a database for modeled R(λ,D,L) for varying wavelength (λ), D, and L at a fixed period of 500 nm for the hexagonal array of nanowires. We varied D in the range from 0 to 500 nm in steps of 1 nm, L in the range from 0 to 10000 nm in steps of 1 nm, and λ mod in the range from 400 to 750 nm in steps of 5 nm. We chose this upper limit for λ mod , since at longer wavelengths the reflectance from the metal particle becomes more crucial for the optical response of the array. The lower limit of 400 nm is given by the lower limit of the measurements. Due to conveniently available tabulated refractive index values, 32 we modeled the metal as pure Au, whereas in reality it has formed a Au−In alloy. For the refractive index of InP, we used values from Glembocki and Piller. 33 The modeling was done using the Fourier modal method, 34 and the Au particle was assumed to be a hemisphere on top of the InP nanowires, which was modeled having a circular cross section. In the modeling, we assumed that the light is incident at a normal angle, since the measurements were performed with an objective of small numerical aperture (NA).
For the extraction of D and L from the measured spectrum R exp (λ) at a given position on the wafer, we calculated s(D,L) = ∑ i (R exp (λ i ) − R mod (λ i , D,L)) 2 , the sum of the square deviations between measured and modeled data, with λ i being the modeled wavelengths. In this calculation of s(D,L), we smoothed R exp over five measurement points, that is, over 2.8 nm in wavelength, and interpolated the smoothed R exp onto the modeled wavelengths λ i . We assigned those values that minimize this s(D,L) as extracted D and L. The model accurately fits the data obtained by mapping Samples 1 and 2, including the five separate areas on Sample 1 (Figure 2).
For Sample 1 we observe, as expected, a continuously increasing extracted D for increased DTL exposure doses ( Figure 2a) and, similarly, a decreasing extracted L ( Figure  2d). This wafer mapping demonstrates both homogeneous D and L within each of these five areas.  For all these points, we find that R exp and R mod corresponded well to each other in both spectral shape as well as in absolute value. Furthermore, the spectra between different positions vary noticeably, depending on both D and L, which allows for the simultaneous extraction of D and L. 30 In order to verify the lengths and diameters obtained from the above optical extraction, we characterized the nanowire length at the cross section of Sample 1 using SEM. Simultaneously, we measured the EBIC currents of at least five NWs from each of the different regions. The growth conditions had been optimized for 9 × 11 mm 2 substrates and an NW diameter of 200 nm. As seen from the EBIC measurements (Figure 3), the doping incorporation was not affected strongly by the substrate size or by the NW diameter. All across Sample 1 similar EBIC profiles were measured, although the highest currents were measured for 3.5 and 4.0 J/ cm 2 . This proves that all measured NWs, regardless of D and L, have a well-defined p−i−n junction suitable for further processing to NW solar cells. Table 1 gives D and L values of Sample 1 both extracted from reflectance maps (Figure 2g−k) and measured in the SEM: that is, from Figure 3. We find excellent agreement between the two measuring methods. The cross-sectional SEM was performed on a central horizontal line of the wafer, using several NWs of five different vertical positions. For the optical  Nano Letters pubs.acs.org/NanoLett Letter extraction, on the other hand, we analyzed the whole areas of the regions with different DTL exposures, excluding the outermost 1 mm. In Figure S1 we plot the extracted L against the extracted D on the basis of these 2939 measurement points. Note that we did not cleave the full wafer Sample 2 for accurate side-view SEM measurements, since it was used for later processing. Instead, on the basis of the verification of the extraction of D and L on Sample 1 with the optical method, we rely on this optical extraction for Sample 2.
In order to measure the homogeneity of the material's quality, we measured PL spectra over the samples in steps of 0.2 mm. The peak maxima and positions of the resulting PL maps are shown in Figure 4. Sample 1 demonstrates two effects. First, the PL intensity shows radial symmetry and peaks at the center of the wafer. Second, we notice an increased intensity not only toward the edge of the wafer but also toward the edges of the lithography-defined areas. Both effects complicate a direct comparison between the different areas, but the areas with higher DTL doses show higher PL intensities in comparison to the areas with lower DTL doses. Sample 2 exhibits a similar intensity distribution, but without the additional edge effect from lithography.
The peak position does not show such a pronounced radial dependence and is more homogeneous over the area of the wafer. Toward the edge of the wafer, but not toward lithography-defined edges, we measure a higher band gap. To explain this band gap variation, we note that InP NWs are known to be polymorphic and occur in both zincblende and wurtzite crystal structures, with band gaps at room temperature corresponding to 1.35 and 1.42 eV, respectively: 35 that is, 918 and 873 nm in corresponding photon wavelength. Furthermore, the top n segment tends to be more wurtzite than pdoped InP nanowires, for which it has been shown that Zn doping leads to a zincblende structure. 36 Additionally, most of the light absorption occurs at the tip of the NWs. 37 Therefore, we explain the blue-shifted peak position toward the edge of the wafer with an increase in NW length toward the edge, which is expected to increase the length of the n segment as well. Thus we expect, due to the longer n segment, relatively stronger absorption in the n segment than in the p segment toward the edge of the wafer and therefore relatively stronger wurtzite-type, blue-shifted PL at the edge of the wafer.
Additionally, Sample 1 shows that the blue shift in band gap is dependent on the NW diameter and is more prominent for thinner NWs. As the reflectance measurements only yield the total NW lengths, we used the EBIC measurements to estimate the lengths of the p, i, and n segments at the center of each region, as shown in Figure S2. The n segments of the NWs with the thinnest diameter are slightly longer than the n segments of the other NWs, but not long enough to explain the  Figure 2g−l for the corresponding reflectance spectra. Nano Letters pubs.acs.org/NanoLett Letter blue shift of the whole region. However, we note that a D value of 140 nm is actually optimized to absorb wavelengths from 600 to 650 nm. 38 Therefore, we modeled the diameterdependent axial absorption profiles of the 632 nm excitation laser, shown in Figure S3. Using the estimated segment lengths from the EBIC measurements, we calculated the absorption of the different segments of the p−i−n NWs. Due to the strong absorption of the laser wavelength, the relative absorption in the n segment in comparison to the p segment, for NWs with a D value of 140 nm, is about 100 times higher than for the thicker NWs, as can be seen in Table 2. Thus, for the smallest diameter region, we expect a much stronger relative photogeneration into the n segment in comparison to the p segment and hence more pronounced wurtzite type, blue-shifted photoluminescence. Furthermore, we have measured TRPL maps of both samples. Due to the increased measurement time, a larger step size of 1 mm was used to give a feasible time for the full mapping. Also with this larger step, the different areas of Sample 1 are clearly distinguishable. We used a biexponential decay to fit the TRPL kinetics. The decay curves consist of a fast initial decay with a short charge carrier lifetime τ 1 followed by a second decay with a longer charge carrier lifetime τ 2 . We did not observe significant differences over the sample area in the first initial decay. In order to illustrate the TRPL maps, Figure 5 shows the second, longer, charge carrier lifetime τ 2 for every measured decay curve.
The decay times of the TRPL kinetics show a trend similar to that in the PL intensity maps, with a longer τ 2 correlating with a higher PL intensity. Thus, (i) the carrier lifetime shows radial dependence that peaks toward the center of the wafer, (ii) the carrier lifetime increases toward the edges on both samples, and (iii) although the radial gradient dominates on Sample 1, we notice that the NWs with the largest diameter have a longer carrier lifetime than the NWs with the smallest diameter. Astonishingly, we measure carrier lifetimes that are 10 times longer than those of similar NW arrays with a sample size of 9 × 11 mm 2 that were homogeneously doped instead of having p−i−n junctions. 26 Long carrier lifetimes have been reported in mixed-phase InP NWs, 39,40 and it has been shown that the type II band offset between zincblende and wurtzite InP can increase recombination lifetimes. 41 However, we have studied similar NWs using transmission electron microscopy and observed mixed crystal phases even for homogeneously doped NWs; 42 consequently, it is not obvious that the type II band offset is the cause for the increase in the carrier lifetimes of the NWs discussed in this paper. Another beneficial factor for the lifetime is definitely the size of these samples, as the center of samples that are 9 × 11 mm 2 in size corresponds to an edge distance of 5 mm on the 2 inch wafer and we see here that τ 2 increases continuously toward the center of the 2 inch wafer. However, just such a sample-size effect does not explain the full increase in carrier lifetimes, and therefore the p−i−n junction clearly increases the carrier lifetime, presumably by separating charge carriers along the NW axis. This is expected to increase the carrier lifetime, since the separated excess carriers can then recombine only by diffusing back to the junction region with a very low concentration of electrons and holes. A quantitative analysis of the recombination in TRPL experiments has been shown with three-dimensional numerical simulations, 43 but the model has yet to be extended to take p− i−n junctions into account.

■ CONCLUSION
In conclusion, we have synthesized InP NW arrays on 2 inch wafers, which is crucial to fabricate solar cells with areas on the order of cm 2 , characterized them by optical methods, and compared the results to modeling results. We have studied the homogeneity of the material's quality across the wafer by measuring PL and TRPL maps. Furthermore, the NW diameter and length could be obtained by fitting reflectivity spectra to a calculated database. Cross-sectional SEM showed an excellent agreement with the dimensions obtained by these optical measurements. Finally, we measured EBIC on NWs from different areas of the wafers and showed that the dopants are homogeneously incorporated. This work paves the way for the fabrication of NW solar cells with an area of up to 2 inch wafers, and the methods we have used are applicable to 4 inch or even larger wafers.  Nano Letters pubs.acs.org/NanoLett Letter ■ ASSOCIATED CONTENT