Letter pubs.acs.org/NanoLett
Direct Determination of Minority Carrier Diffusion Lengths at Axial GaAs Nanowire p−n Junctions Christoph Gutsche,*,†,§ Raphael Niepelt,*,‡,§ Martin Gnauck,‡ Andrey Lysov,† Werner Prost,† Carsten Ronning,‡ and Franz-Josef Tegude† †
Solid State Electronics Department and CeNIDE, University of Duisburg-Essen, Lotharstrasse 55, 47048 Duisburg, Germany Institute of Solid State Physics, Friedrich-Schiller-Universität, Max-Wien-Platz 1, 07743 Jena, Germany
‡
S Supporting Information *
ABSTRACT: Axial GaAs nanowire p−n diodes, possibly one of the core elements of future nanowire solar cells and light emitters, were grown via the Au-assisted vapor−liquid−solid mode, contacted by electron beam lithography, and investigated using electron beam induced current measurements. The minority carrier diffusion lengths and dynamics of both, electrons and holes, were determined directly at the vicinity of the p−n junction. The generated photocurrent shows an exponential decay on both sides of the junction and the extracted diffusion lengths are about 1 order of magnitude lower compared to bulk material due to surface recombination. Moreover, the observed strong diameter-dependence is well in line with the surface-to-volume ratio of semiconductor nanowires. Estimating the surface recombination velocities clearly indicates a nonabrupt p−n junction, which is in essential agreement with the model of delayed dopant incorporation in the Au-assisted vapor−liquid−solid mechanism. Surface passivation using ammonium sulfide effectively reduces the surface recombination and thus leads to higher minority carrier diffusion lengths. KEYWORDS: Nanowire, p−n-junction, diffusion length, solar cell, electron beam induced current, surface passivation
N
For highly doped n-type Si nanowires, Allen et al. reported hole diffusion lengths from 25 up to 80 nm for nanowires 30 to 100 nm in diameter, respectively. This is a 100- to 1000-fold decrease compared to bulk material.24 A thin layer of amorphous silicon, forming core−shell structures reduces the surface recombination and hole diffusion lengths up to 500 nm were observed.14 On the contrary, a value of 2000 nm was determined for n-type Si nanowires with a huge diameter of 900 nm, which anyway represents bulklike behavior.19 Others have investigated the minority carrier diffusion lengths in CdS nanowires18 and PbS nanowire field effect transistors.17 Concerning III−V materials the ambipolar diffusion lengths of homogeneous GaAs nanowires, axial AlGaAs/GaAs, and InGaAs/GaAs nanowire heterostructures were studied with and without AlGaAs capping using cathodoluminescence.22,23 All nanowires were nonintentionally doped and the ambipolar diffusion lengths ranged from 100 to 900 nm, the shortest for uncapped GaAs.22 Hole diffusion lengths were found to be 1200 nm for n-type GaN/AlGaN core−shell nanowires from 200 to 800 nm diameter20,21 and revealed a strong decrease in the uncapped case.20
anowires are considered as potential building blocks for future energy harvesting applications such as solar cells.1−6 The nanowire approach enables the growth of highly mismatched heterostructures7,8 giving the freedom to stagger multiple axial p−n junctions perfectly matching the solar spectrum in a tandem solar cell.9,10 In addition, the enhanced light collection efficiency11,12 as well as the highly reduced material consumption13 with respect to conventional thin film devices makes nanowires quite attractive for the development of photovoltaics. Contrary to the commonly used Si, III−V compounds are often direct semiconductors implying largely enhanced absorption coefficients and have bandgaps spanning a wide spectral range. On the other hand, the high density of surface states in combination with a large surface-to-volume ratio can drastically reduce minority carrier diffusion lengths and lifetimes, respectively.14,15 Since the active p−n junction absorption length is comprised of the depletion region and the minority carrier diffusion lengths, a detailed knowledge of the latter is required for device optimization. Basically, there are many ways to determine diffusion lengths in semiconductors.16 Time-resolved scanning photocurrent microscopy (SPCM),17 SPCM combined with a near-field scanning optical microscope (NSOM),14,18,19 a combined atomic force microscope (AFM)/NSOM system,20,21 cathodoluminescence (CL),22,23 and electron beam-induced current (EBIC)24 have been used on nanowires for this purpose. Nevertheless, only few investigations are available up to now. © 2012 American Chemical Society
Received: November 23, 2011 Revised: February 14, 2012 Published: February 24, 2012 1453
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where I0 is the maximal intensity, x is the distance from the junction and Lp and Ln are the minority carrier diffusion length for electrons and holes following
Minority carrier lifetimes that are directly correlated to the diffusion lengths have been investigated for GaAs nanowires with and without AlGaAs capping by photoluminescence25−28 and terahertz spectroscopy,15 respectively. The obtained values ranged from 5 ps (uncapped, Au-assisted, room temperature)15 to 2.5 ns (capped with AlGaAs, self-assisted, room temperature)25 depending on the synthesis method and measurement temperature. Breuer et al. revealed that a drastically reduced minority carrier lifetime might be attributed to the incorporation of Au into the nanowire, which then acts as nonradiative recombination center.25 However, all of the previously mentioned studies neither included the effect of intentional doping nor obtained the minority carrier diffusion lengths directly from the most relevant device for semiconductor nanowires: directly at the p−n junction. Furthermore, no results regarding the minority carrier diffusion lengths in GaAs nanowires have been reported so far. Thus, a detailed study on the diameter-dependent diffusion lengths of both, electrons and holes, in vapor−liquid−solid (VLS) grown axial GaAs nanowire p−n junctions29 is presented in this work (for additional details on the growth process see Supporting Infomation). The use of EBIC directly at the p−n junction allows visualizing the depletion region, determining the minority carrier diffusion length on both sides of the p−n junction, estimating the respective surface recombination velocities, and studying the effect of surface passivation with ammonium sulfide in vicinity of the active device. EBIC is widely used for visualization of sites of enhanced recombination, like dislocations or stacking faults,30,31 as well as for monitoring the carrier dynamics near a junction to investigate the carrier diffusion process.32 In the geometry investigated in this study, displayed in Figure 1a, the decrease of the induced current with
Li =
(2)
with Di and τi as the respective diffusion coefficient and carrier recombination lifetime. Scanning a nanowire with an axial p−n junction allows to extract both electron and hole diffusion lengths on the respective p- and n-type side of the junction simultaneously, like depicted in Figure 1c. Instead of using EBIC, the minority carrier diffusion length can also be determined by photocurrent measurements within a microphotoluminescence (μ-PL) or NSOM setup; however, the use of an electron beam results in a far better spatial resolution. It is important that the device is investigated under low injection conditions (LIC) for such kind of analysis, which means that the amount of excess carriers excited in the sample has to be small versus the doping level.33 If LIC are not fulfilled, one measures a diffusion length of both minority and majority carriers, also defined as ambipolar diffusion length. To verify that LIC occur in our experiments, the concentration of excess carriers Δp is evaluated and compared to the doping level. For bulk material the value of Δp can be derived analytically by comparing the activation volume and the deposited energy E0. In case of nanostructures, the distribution of energy in the sample is strongly connected to the sample structure. Therefore, Monte Carlo simulations applying the Casino v3.2 code34 were used to determine the energy distribution inside an irradiated GaAs nanowire lying on a GaAs/SiN substrate. With E0 that is distributed inside a volume V the excess carrier generation rate G0 can be estimated35 G0 ≈
E0 1 3Eg V
(3)
expresses the amount of carriers excited per volume by a single electron. The energy distribution E0/V provided by the Monte Carlo code depends on the choice of spatial resolution for the simulation. Here, the simulation was conducted for volume cells of 4 nm edge length. A larger choice of simulation cell size would lead to a more uniform energy distribution. However, if the cell size is not small enough compared to the carrier diffusion length, the distribution will be smeared out and a reasonable conclusion on the injection regime following G0 is not possible. For a certain electron beam current IB, a known excess carrier lifetime τexc, and uniform generation, Δp can be estimated via
Figure 1. (a) EBIC measurement setup scheme using single axial nanowire p−n junctions. (b) Schematic band diagram of the respective p−n diode. During the measurement, both majority and minority carriers can diffuse to the junction. Only the respective minority carriers are collected, whereas the majority carriers of both sides are repulsed. (c) EBIC signal along the wire axis. The minority carrier diffusion lengths of both, electrons and holes, are extracted by analyzing the exponential decay of the current signal.
Δp ≈
G0 IB τexc e
(4)
where e is the elementary charge. In Figure 2, Δp is displayed for a nanowire with 200 nm diameter and typical electron current (IB = 40 pA) and acceleration voltage (E0 = 10 keV) used in this study. With the minority carrier lifetimes estimated from the EBIC profiles, Δp was found to be always orders of magnitude below the doping level. For the evident nonuniform excess carrier generation, the outdiffusion of carriers from the simulated volume element is neglected in eq 4. Thus, Δp shown in Figure 2 represents an upper bound on the excess carrier concentration and LIC are assured. The dependence between the measured minority carrier diffusion length and the nanowire diameter allows extracting the surface recombination velocities. As the diameter of our
increasing distance to the junction gives direct access to the minority carrier diffusion length in axial GaAs nanowire p−n diodes. As it is shown in Figure 1b, only minority carriers of both sides contribute to the induced current when reaching the junction region. Analyzing the decay of the EBIC signal along the nanowire, one obtains an exponentially decreasing current signal following
I = I0e−x / L
Di τi
(1) 1454
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Figure 2. Distribution of Δp in a nanowire with 200 nm diameter for typical electron current density and acceleration voltage values determined using Casino v3.234 and the minority carrier lifetimes estimated from the EBIC profiles. The concentration of excess carriers Δp is always orders of magnitude below the doping levels, which are (a) 1.6 × 1019 cm−3 in the p-type and (b) 1 × 1018 cm−3 in the n-type region of the nanowire.
samples is way below the bulk diffusion lengths (Lp, Ln > 1 μm),36−38 the determined value Li has to be interpreted as an effective diffusion length L*i =
Di τ*i
(5)
with the diffusion coefficient Di (Dp = 200 cm2/s, Dn = 10 cm2/s)39 and an effective lifetime τ*i that is governed by the surface recombination velocity S of the nanowires.24 This parameter τ*i is connected with S and the bulk lifetime τB via
1 1 4S = + τ*i τB d
Figure 3. EBIC signal measured under varying applied voltages. (a) EBIC images of an axial GaAs p−n nanowire (vertical) showing that the signal strength strongly increases with increasing applied voltage. (b) The ascending slope of the EBIC signal does not show any bias dependence for reverse bias voltage up to 0.5 V (green bars) but flattens for higher voltages (red bars). Forward bias also changes the slope significantly (black curve).
(6)
whereby d denotes the nanowire diameter.14 The relation above is only valid to certain values of S; for details, see Supporting Information. EBIC measurements were carried out on four different nanowire p−n diodes with diameters ranging from approximately 100 to 300 nm. Identical I−V characteristics have been recorded before and after the EBIC measurements to exclude any damage effects caused by the electron beam. Apart from the choice of the right electron beam conditions, it is necessary to check if the collected current is really driven by diffusion and not by electrical drift along the nanowire. Thus, the same nanowire diode was repeatedly measured under varying applied bias voltages. From Figure 3 it is evident, that the EBIC signal strength depends on the applied voltage. However, the estimated diffusion lengths did not show any bias dependence for a bias between 0 and −0.5 V, which implies that drift currents are negligible in this voltage range. In contrast, the diffusion lengths change when applying a reverse bias of −1 V or higher, as clearly demonstrated in Figure 3. The determined effective minority carrier diffusion lengths of both, electrons and holes, are plotted in Figure 4 and show a monotonically increasing behavior with increasing nanowire diameter. The nanowire diffusion lengths are significantly small and about 10-fold lower compared to minority carrier diffusion lengths of GaAs bulk crystals or thin layers.36−38 The observed diameter dependence proves the strong influence of the nanowire surface. As illustrated in Figure 5, Fermi-level pinning
in the GaAs midgap causes a band−banding at the nanowire surface and hence a surface depletion space charge layer dspc,p,n =
2ε0εrφs,p,n qNA,D
(7)
where ε0 denotes the vacuum permittivity, εr is the dielectric constant, φs,p,n is the surface potential of p- or n-type GaAs, and NA,D are the respective carrier concentrations. Therefore, large fractions of the locally generated carriers will be moved toward the surface by the internal electric field and recombine with surface states instead of contributing to the measured EBIC signal. The expected dependency of the diffusion lengths as a function of the nanowire diameter are also shown in Figure 4 for different values of S. Here, the diameter d in eq 6 was replaced by an effective diameter d*. The value of d* was determined by subtracting the expected surface depletion layer thickness dspc,p,n from the measured diameter. The curves have been fitted to the measured values by adjusting S. The resulting surface recombination velocities (Sp = 4 × 106 cm/s, Sn = 3 × 105 cm/s) are comparable to values measured in GaAs bulk samples.40,41 The value S is almost identical to the bulk value40 for the p-type side of the nanowire (NA = 1.6 × 1019 cm−3);42 whereas, for the n-type side S is 1 order of magnitude smaller41 than expected for an estimated carrier concentration of ND = 1 × 1018 cm−3.43 As the nanowire surface on both sides of the 1455
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First, large fractions of the locally generated carriers will recombine at the uncapped GaAs surface. Second, traces of Au that are incorporated into the semiconductor nanowire might act as recombination center and further reduce the carrier lifetimes.25 Third, the incorporation of doping atoms has a strong impact on the carrier lifetime, especially for p-type material.46 For p-GaAs bulk samples τp decreases about 3 orders of magnitude if the carrier concentration increases from nonintentionally doped (nid) to NA = 1 × 1019 cm−3. Taking this into account, the calculated values are in essential agreement with the results reported for nid GaAs nanowires by Parkinson et al..15 As the EBIC signal might also depend on the carrier generation volume inside the nanowire, we conducted measurements at acceleration voltages between 5 and 10 kV to vary the extent of the excited volume. No effect on the diffusion length was visible, proving that the observed diameter dependence of the diffusion length is not an effect related to the dimensions of the excitation volume, which is consistent with literature.24 Since the dramatic reduction of minority carrier diffusion lengths in GaAs nanowires compared to GaAs bulk material is strongly related to the large number of surface states, an effective surface passivation should help to increase Ln and Lp like already shown in the case of Si and GaN nanowires.14,21 In Figure 6 the comparative EBIC linescans along a p−n GaAs nanowire before and after a passivation process using aqueous ammonium sulfide47 (for details see Supporting Information) are displayed. The diffusion lengths increase after the passivation procedure while the I−V characteristic of the device remains unchanged (inset of Figure 6). Although the
Figure 4. Measured minority carrier diffusion lengths for p−n GaAs nanowires as a function of nanowire diameter. The dashed lines are showing the theoretical progression of the diameter dependence for the stated surface recombination velocities. For the calculation depletion layers with 29.6 nm (n-type) and 6.8 nm (p-type) width have been taken in account.
Figure 5. Fermi-level pinning in the GaAs midgap for the (left) p- and (right) n-type nanowire region, respectively. The band−banding at the nanowire surface is visible in the corresponding band diagrams below. It causes a surface depletion space charge layer dspc,p,n like sketched in the schematic nanowire cross sections.
junction was always treated identically, our EBIC measurements point to a lower doping level on the n-type side compared to our previous estimations.43 In the region near the junction, where the EBIC measurements were conducted, this might effectively be the case due to the synthesis method of the nanowires. During VLS nanowire growth, the Au seed particle acts as a delay element for the dopant atoms. Although the type of dopants is switched from p to n rapidly, it still takes some time to reach a high doping level in the n-doped part, which finally leads to an axially graded dopant profile in the vicinity of the p−n junction. Therefore, this result is in agreement with previous investigations using spatially resolved photoluminescence and Kelvin probe force microscopy.44,45 It perfectly fits to the picture of delayed dopant incorporation in the Au-assisted VLS mechanism. According to eq 5 and the diffusion coefficients Di in bulk material39 the corresponding carrier lifetimes can be calculated to τ*p ≈ 1 fs and τ*n ≈ 0.5 ps, respectively. This very low lifetimes compared to literature25−28 can be interpreted as follows:
Figure 6. EBIC scans at a single nanowire p−n junction before and after the passivation treatment using ammonium sulfide. Directly after the treatment the signal shows a different slope, referring to an increased minority carrier diffusion length. After 4 days, slope and diffusion length have dropped down to their initial values. The I−V curve of the device remains unchanged (inset).
values for L obtained on passivated structures are still far below the bulk values, this experiment clearly shows the importance of an effective nanowire surface passivation. The relatively weak but measured effect can be explained by the design of the study. First of all, the ammonium sulfide passivation is known to be 1456
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(6) Goto, H.; Nosaki, K.; Tomioka, K.; Hara, S.; Hiruma, K.; Motohisa, J.; Fukui, T. Appl. Phys. Express 2009, 2, 035004. (7) Messing, M. E.; Wong-Leung, J.; Zanolli, Z.; Joyce, H. J.; Tan, H. H.; Gao, Q.; Wallenberg, L. R.; Johansson, J.; Jagadish, C. Nano Lett. 2011, 11 (9), 3899−3905. (8) Wallentin, J.; Persson, J. M.; Wagner, J. B.; Samuelson, L.; Deppert, K.; Borgström, M. T. Nano Lett. 2010, 10, 974. (9) Sun, K.; Kargar, A.; Park, N.; Madsen, K. N.; Naughton, P. W.; Bright, T.; Jing, Y.; Wang, D. IEEE J. Sel. Top. Quantum Electron. 2011, DOI: 10.1109/JSTQE.2010.2090342. (10) Borgström, M. T.; Wallentin, J.; Heurlin, M.; Fält, S.; Wickert, P.; Leene, J.; Magnusson, M. H.; Deppert, K.; Samuelson, L. IEEE J. Sel. Top. Quantum Electron. 2010, 99, 1. (11) Garnett, E.; Yang, P. Nano Lett. 2010, 10, 1082. (12) Diedenhofen, S. L.; Vecchi, G.; Algra, R. E.; Hartsuiker, A.; Muskens, O. L.; Immink, G.; Bakkers, E. P. A. M.; Vos, W. L.; Rivas, J. G. Adv. Mater. 2009, 21, 973. (13) Kupec, J.; Stoop, R. L.; Witzigmann, B. Opt. Express 2010, 18, 27589. (14) Dan, Y.; Seo, K.; Takei, K.; Meza, J. H.; Javey, A.; Crozier, K. B. Nano Lett. 2011, 11, 2527. (15) Parkinson, P.; Joyce, H. J.; Gao, Q.; Tan, H. H.; Zhang, X.; Zou, J.; Jagadish, C.; Herz, L. M.; Johnston, M. B. Nano Lett. 2009, 9, 3349. (16) Davidson, S. M. J. Microsc. 1977, 110, 177. (17) Graham, R.; Miller, C.; Oh, E.; Yu, D. Nano Lett. 2011, 11, 717. (18) Gu, Y.; Romankiewicz, J. P.; David, J. K.; Lensch, J. L.; Lauhon, L. J.; Kwak, E. S.; Odom, T. W. J. Vac. Sci. Technol., B 2006, 24, 2172. (19) Kelzenberg, M. D.; Turner-Evans, D. B.; Kayes, B. M.; Filler, M. A.; Putnam, M. C.; Lewis, N. S.; Atwater, H. A. Nano Lett. 2008, 8, 710. (20) Baird, L.; Ang, G. H.; Low, C. H.; Haegel, N. M.; Talin, A. A.; Li, Q.; Wang, G. T. Physica B 2009, 404, 4933. (21) Baird, L.; Ong, C. P.; Cole, R. A.; Haegel, N. M.; Talin, A. A.; Li, Q.; Wang, G. T. Appl. Phys. Lett. 2011, 98, 132104. (22) Gustafsson, A.; Bolinsson, J.; Sköld, N.; Samuelson, L. Appl. Phys. Lett. 2010, 97, 072114. (23) Bolinsson, J.; Mergenthaler, K.; Samuelson, L.; Gustafsson, A. J. Cryst. Growth 2011, 315, 138. (24) 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, 168. (25) Breuer, S.; Pfüller, C.; Flissikowski, T.; Brandt, O.; Grahn, H. T.; Geelhaar, L.; Riechert, H. Nano Lett. 2011, 11, 1276. (26) Kang, J. H.; Gao, Q.; Joyce, H. J.; Tan, H. H.; Jagadish, C.; Kim, Y.; Guo, Y.; Xu, H.; Zou, J.; Fickenscher, M. A.; Smith, L. M.; Jackson, H. E.; Yarrison-Rice, J. M. Cryst. Growth Des. 2011, 11, 3109. (27) Joyce, H. J.; Gao, Q.; Tan, H. H.; Jagadish, C.; Kim, Y.; Fickenscher, M. A.; Perera, S.; Hoang, T. B.; Smith, L. M.; Jackson, H. E.; Yarrison-Rice, J. M.; Zhang, X.; Zou, J. Adv. Funct. Mat. 2008, 18, 3794. (28) Demichel, O.; Heiss, M.; Bleuse, J.; Mariette, H.; Fontcuberta i Morral, A. Appl. Phys. Lett. 2010, 97, 201907. (29) Regolin, I.; Gutsche, C.; Lysov, A.; Blekker, K.; Li, Z.-A.; Spasova, M.; Prost, W.; Tegude, F.-J. J. Cryst. Growth 2011, 315, 143. (30) Wittry, D. B.; Kyser, D. F J. Appl. Phys. 1964, 35, 2439. (31) Holt, D. B. Quantitative Scanning Electron Microscopy; Holt, D. B., Muir, M. D., Grant, P. R., Boswarva, I. M., Eds.; Academic Press: New York/London, 1974. (32) Higuchi, H.; Tamura, H. Jpn. J. Appl. Phys. 1965, 4, 316. (33) Cavalcoli, D.; Cavallini, A. Mater. Sci. Eng., B 1994, 24, 98. (34) Demers, H.; Poirier-Demers, N.; Couture, A. R.; Joly, D.; Guilmain, M.; de Jonge, N.; Drouin, D. Scanning 2011, 33, 135. (35) Klein, C. A. J. Appl. Phys. 1968, 39, 4. (36) Wright, D. R.; Oliver, P. E.; Prentice, T.; Steward, V. W. J. Cryst. Growth 1981, 55, 183. (37) Hwang, C. J. J. Appl. Phys. 1969, 40, 3731. (38) Casey, H. C.; Miller, B. I.; Pinkas, E. J. Appl. Phys. 1973, 44, 1281. (39) Joshi, R.; Grondin, R. O. Appl. Phys. Lett. 1989, 54, 2438.
unstable to air, whereat the stability depends on the used method.48,49 Furthermore, the above measurements were taken 10 h after the passivation process, and continuous EBIC measurements on the same device showed that the initial values of the diffusions length were reached after about 4 days. A measurement directly after the passivation was not possible for us, but should clearly reveal a much stronger effect. Permanently stable alternatives are given by the combined (NH4)2S/SiN50 or (NH4)2S/BCB2 passivations. Besides, there are no standard processing parameters for ammonium sulfide passivation of GaAs nanowires and further improvement can be expected by process optimization. In summary, the minority carrier diffusion lengths of both, electrons and holes, have been directly determined in axial GaAs nanowire p−n junctions using electron beam induced current measurements. The extracted nanowire diffusion lengths demonstrated a clear diameter dependence and a significant decrease compared to bulk values that can be attributed to the strong influence of the nanowire surface. The nanowire surface recombination velocities were estimated on both sides of the p−n junction, revealing an excellent agreement with bulk data if an axially smeared out p−n junction is taken into account. Moreover, the corresponding minority carrier lifetimes indicate a strong doping-related decrease. However, surface passivation with ammonium sulfide increases the minority carrier diffusion lengths. These results will guide the further improvement of semiconductor nanowire solar cells.
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ASSOCIATED CONTENT
S Supporting Information *
Additional details on methods used including nanowire growth, measurement equipment, a supporting mathematical derivation for the main text, and experimental details on the applied ammonium sulfide passivation process. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: (C.G.)
[email protected]; (R.N.) raphael.
[email protected]. Author Contributions §
These authors contributed equally to this manuscript.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors gratefully acknowledge the partial financial support by the Ziel2 project “Nanowire solar cells and light emitters (Nasol)” funded by the European Commission and “Nano IIIV PIN” project of Federal Ministry of Science and Technology.
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REFERENCES
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