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Shadowing and mask opening effects during selective-area vapor–liquid–solid growth of InP nanowires by metalorganic molecular beam epitaxy
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2013 Nanotechnology 24 475302 (http://iopscience.iop.org/0957-4484/24/47/475302) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 93.180.53.211 This content was downloaded on 07/02/2014 at 09:40
Please note that terms and conditions apply.
IOP PUBLISHING
NANOTECHNOLOGY
Nanotechnology 24 (2013) 475302 (7pp)
doi:10.1088/0957-4484/24/47/475302
Shadowing and mask opening effects during selective-area vapor–liquid–solid growth of InP nanowires by metalorganic molecular beam epitaxy A Kelrich, Y Calahorra, Y Greenberg, A Gavrilov, S Cohen and D Ritter Electrical Engineering Faculty, Technion-Israel Institute of Technology, Haifa 32000, Israel E-mail: [email protected]
Received 29 July 2013, in final form 23 September 2013 Published 31 October 2013 Online at stacks.iop.org/Nano/24/475302 Abstract Indium phosphide nanowires were grown by metalorganic molecular beam epitaxy using the selective-area vapor–liquid–solid method. We show experimentally and theoretically that the size of the annular opening around the nanowire has a major impact on nanowire growth rate. In addition, we observed a considerable reduction of the growth rate in dense two-dimensional arrays, in agreement with a calculation of the shadowing of the scattered precursors. Due to the impact of these effects on growth, they should be considered during selective-area vapor–liquid–solid nanowire epitaxy. (Some figures may appear in colour only in the online journal)
1. Introduction
(MOMBE), also referred to as chemical beam epitaxy (CBE). During SAE by MOVPE, lateral gas phase diffusion driven by concentration gradients parallel to the surface plays a dominant role in precursor supply to the growth front. By contrast, during SAE of conventional planar layers (not NWs) by MOMBE, precursors that contribute to growth must impinge upon the opening in the mask. Precursors impinging upon the dielectric mask re-evaporate/scatter and do not contribute to the growth [9]. A novel approach for growing III–V compound semiconductor NWs integrates the SAE and VLS techniques (SA-VLS) by placing metal catalysts into the mask openings [10]. The patterned mask provides defined positioning and prevents parasitic growth on the substrate, while the catalyst diameter (and consequently—NW diameter) is accurately defined by electron beam lithography and evaporated metal thickness [11]. As in conventional VLS, abrupt interfaces between the catalyst and the grown NW are obtained, while in pure SAE significant NW tip tapering is obtained [12]. Due to the lack of surface diffusion on the substrate, one can accurately predict the growth rate during SA-VLS
Epitaxial growth of semiconductor nanowires (NWs) is intensively explored for electronic, optoelectronic, energy conversion and sensor applications [1–4], as well as for basic physics studies [5]. The successful implementation of NW technology requires an understanding of NW growth mechanisms in order to achieve control of their dimensions, composition and crystal structure. A widely used approach for NW growth is based upon the vapor–liquid–solid mechanism (VLS) [6], where a catalyst particle, in most cases gold, forms a liquid alloy with the growth precursors and catalyzes crystal growth by precipitation from a supersaturated solution. An alternative approach is the catalyst-free selective area epitaxy (SAE) [7] method. During SAE, growth is restricted to lithographically defined openings in an inert mask, typically SiO2 or SiNx . One-dimensional (axial) NW growth is achieved by SAE along the h111i A or h111i B directions due to a low incorporation rate on the side facets [8]. The SAE approach is typically based upon metalorganic precursors during metalorganic vapor phase epitaxy (MOVPE) or metalorganic molecular beam epitaxy 0957-4484/13/475302+07$33.00
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c 2013 IOP Publishing Ltd Printed in the UK & the USA
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growth by MOMBE. Dalacu et al proposed an analytical model that predicts the growth rate of InP NWs [10]. They considered three components for the supply of precursors to the growing nanowire: direct impingement upon the catalyst, direct impingement upon the nanowire sidewalls, and indirect sidewall collection of the flux scattered from the mask layer. Assuming the cosine emission law of the reemitted flux from the mask layer onto the wire sidewall, the authors obtained the following expression: Z Leff Z ∞ dL 4L tan θ = 1+ +D dl dr dh πD 0 0 Z π/2 2lr2 cos φ 1 × dφ 2 2 (r + l ) π(D/2)2 0 2Leff 4L tan θ + (1) = 1+ πD D
along the radius in (1) as the opening radius, rop , yielding Z Leff Z ∞ dL = 1+D dl dr dh 0 rop Z π/2 2lr2 cos φ 1 × dφ 2 (r + l2 ) π(D/2)2 0 rop 2 2Leff 1 − arctan . (2) = 1+ D π Leff In our growth-system the metalorganic gases are injected perpendicular to the substrate, hence the second term in (1) is not included in (2). Since mask openings are typically small, it may be assumed that all precursors collected at the openings reach the NW base [16, 17]. The fraction of the flux that reaches the gold catalyst (out of the flux which is collected by the openings) is cosh−1 (L/Ldiff ),1 where Ldiff is the diffusion length along the side facets, which is assumed in our calculations to equal the above mentioned migration length, Lm . The contribution to the growth rate by the flux that impinges upon the openings is thus given by the ratio between the exposed opening area and NW cross section at the catalyst, multiplied by cosh−1 (L/Ldiff ). The resulting total growth rate is given by rop dL 2Leff 2 = 1+ 1 − arctan dh D π Leff " # 2 2rop 1 + −1 . (3) D cosh (L/Ldiff )
where Leff = min[L, Lm ], L is the wire length, and Lm is the migration length along the side facets. The parameter h in (1) stands for the equivalent planar layer thickness, D is the wire diameter, and θ is the angle between the incident precursor flux and the surface normal. The wire length is calculated by numerically integrating the growth rate given by (1) along the equivalent planar growth thickness. In this work, we theoretically and experimentally examine two subjects relevant to the SA-VLS method. First, we consider the influence of the mask opening size, which has two opposing effects on the growth rate. On one hand, with increasing opening size, precursor scattering from the mask is reduced, thus diminishing the contribution of the third and largest term in (1). On the other hand, precursors that impinge upon the openings may diffuse directly towards the growing NW. The combination of these two effects modifies the growth rate considerably. The second subject discussed in this work is shadowing of scattered precursors in dense two-dimensional arrays. The shadowing of direct beams is not a major concern during molecular beam epitaxy of nanowires, unless very dense arrays are grown and the precursor beams are not perpendicular to the substrate [13–15]. However, shadowing of scattered species turns out to be a significant effect during SA-VLS, regardless of the incidence angle between the molecular beams and the surface.
We demonstrate the effect of the mask opening on the obtained length of a NW in figure 1. We have plotted the original expression, which does not take the openings into account (1), and the results obtained with and without the contribution of the precursors that impinge directly into the openings. Note the large effect of the openings on the obtained nanowire length.
3. Experimental details Indium phosphide NWs were grown on epi-ready undoped (111)B InP substrates (Semiconductor Wafer Inc.) by a compact metalorganic molecular beam epitaxy system [19]. Before growth, the wafers were coated by a 15 nm thick SiNx mask layer by plasma-enhanced chemical vapor deposition (PECVD, Plasma-Therm 790) and then spin-coated with positive PMMA resist. The samples were electron beam patterned, developed and wet etched in buffered HF to produce circular openings in the mask with diameters of 70–130 nm. As in [10], the PMMA mask was not removed, and served as a lift-off mask for the gold particles. The thickness of the electron beam evaporated gold layer was 12 nm. A scanning electron microscope (SEM) image of the gold particles inside the mask openings is shown in figure 2.
2. Incorporation of the mask openings in the growth rate model As mentioned in section 1, the gold particle during the SA-VLS process is surrounded by an annular opening in the dielectric mask. This opening may be either deliberately defined in order to induce radial growth, or just a result of the isotropic wet-etches process. The opening reduces the available mask area for scattering of precursors towards the NW. The area close to the stem of the NW is most effective in supplying the precursors, and therefore although the annular opening area is quite small, the effect is substantial. This effect is easily modeled by setting the lower limit of integration
1 The diffusion process along the NW is analogous to diffusion along the
base of a bipolar transistor, see for example [18]. 2
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2.5 Eq. 3 Eq. 1 Eq. 2
Length [µm]
2
1.5
1
0.5
0 30
40
50
60
70
80
Diameter [nm]
Figure 1. Calculated NW length versus NW diameter for nominal planar growth of 82 nm at 450 ◦ C. The diameter of the opening is 40 nm larger than the diameter of the NW. The dotted line is after (1), which does not include the effect of the opening. The dashed line represents the reduction of the growth rate when the opening area does not contribute to TMI collection and scattering (2). The solid curve takes into account the collection of flux by the opening (3). The sidewall migration length is Lm = 700 nm. Figure 3. SEM image of InP nanowires grown from openings with varying diameter: 104 ± 4 nm for sample (a) versus 127 ± 4 nm for (b). The scale bar is 500 nm.
4. Results and discussion 4.1. Contribution of the annular opening to nanowire growth In order to evaluate the effect of the annular openings, two NW arrays went through identical processing, except for the SiN layer etching time. Figure 3 shows SEM images of the arrays grown at 420 ◦ C. Sample (b) was slightly over-etched, resulting in opening diameters of 127 ± 4 nm, compared to 104 ± 4 nm for sample (a). The diameter of the NWs, measured at the tip of the wire just below Au catalyst, was 67 ± 3 nm in both samples. It is evident from figure 3 that NWs grown from larger openings are significantly longer. A set of narrower NWs having a diameter of 51 ± 1 nm exhibited the same effect. The measured length of the NWs versus their annular opening diameters is plotted in figure 4(a). The major impact of the opening on the obtained length takes place during the initial stages of growth, illustrated in figure 4(b). At this stage, reflected precursors do not contribute to the growth and the precursors impinging into the opening significantly increase the growth rate. As the wire grows, the precursors reflected from the mask become the dominant source of material for growth, and the relative contribution of the opening area decreases. To model the growth rate, the migration length of indium precursors along the NW side facets [10] was obtained as a fitting parameter. The migration length results shown in table 1 agree quite well with SEM observations of the non-tapered NW region below the gold catalyst.
Figure 2. Plane view SEM image of a two-dimensional array of gold particles inside the SiNx openings prior to growth.
The precursors used during the MOMBE growth were trimethyl indium (TMI) and pre-cracked phosphine (PH3 ). Precise control of substrate temperature was achieved by a thermocouple in thermal contact with the sample holder. The sample was soldered to the holder using indium. The TMI flow rate corresponded to a planar growth rate of 110 nm h−1 on an InP(100) substrate at 500 ◦ C. The PH3 flow rate was 3 sccm and the growth temperature range was 420–480 ◦ C. The samples were first heated to the growth temperature under P2 flow, and then TMI was introduced to initiate growth. The TMI flux was perpendicular to the substrate surface. Growth duration was 50 min for all samples. Measurements of NW length, diameter and opening diameter, were performed by scanning electron microscopy (Hitachi S4700), with a 30◦ tilted view unless mentioned otherwise. As a result, the scale bar must be multiplied by two to obtain the nanowire length in the figures below. 3
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Table 1. Parameters used in NW growth model comparison. Growth temperature (◦ C)
TMI cracking efficiency [20] (%)
Migration length on the NW sidewall Lm (µm)
Exposed annular diameter (Dopening − Dwire ) (nm)
420 450 480
84 90 100
0.5 0.7 2.0
35 ± 4 40 ± 5 22 ± 4
the nanowire sidewalls. Additional data, obtained by TEM analysis, regarding the diameter and temperature dependence of NW tapering will be presented elsewhere. The modified model given by equation (3) fits quite well the experimental data. For all three samples, the planar growth rate was equivalent to 0.11 µm h−1 at 500 ◦ C on (100) InP. Lower TMI cracking efficiency were taken into consideration at 420 and 450 ◦ C [20]. All relevant parameters are summarized in table 1. Note the significant difference between the prediction given by (1) and the experimental data.
1.4
(a) 1.2
NW length [µm]
1
0.8
0.6
4.2. Shadowing of reflected precursors D = 51 nm D = 66 nm
0.4
0.2 80
90
100
110
120
Shadowing of the impinging molecular beams by neighboring nanowires in dense two-dimensional arrays during molecular beam epitaxy (MBE) was previously observed [13, 14] and analyzed [15]. During SA-VLS by MOMBE, a more pronounced shadowing effect of the reflected precursors from the mask area is expected. In a previous report no shadowing was observed, as only linear arrays were modeled [10]. Figure 6 shows a series of SEM images of nanowires grown at 450 ◦ C from a square array of gold particles. Array spacing varied between 300 and 1000 nm. It can be seen that the length of the NWs varies significantly with spacing, increasing by ∼25% for 1 µm pitch compared to 0.3 µm pitch. The experiment was repeated for four different sets of NWs with diameters of 53–70 nm. Every series was processed and grown simultaneously on the same substrate. A summary of the results is presented in figure 7. A significant growth rate enhancement is observed for a slight change from 0.3 to 0.5 µm of the array spacing. The same tendency continues in the 0.5–1 µm range, but when the pitch was increased from 1 to 2 µm a slight reduction of the growth rate and length uniformity were observed. The shadowing effect is more pronounced in thinner NWs due to their larger growth rate. As the growth rate varies considerably with NW diameter, special care was taken to measure accurately the NW diameters. Every data point in figure 7 was obtained by averaging the measured diameter of 15–20 NWs, obtaining a standard deviation of 1–2 nm. The opening diameters were verified to be similar in each set in order to eliminate the above-described influence on the growth rate. In order to evaluate the shadowing of the reflected precursors we have considered the flux impinging upon a single NW and divided the surface area into four categories: no shadowing, slight shadowing, considerable shadowing, and full shadowing, as schematically shown in figure 8. To simplify the calculations, we have considered the ‘slightly shadowed’ areas as not shadowed, and the ‘considerably
130
Opening diameter [nm]
(b)
Figure 4. (a) Nanowire length as a function of opening size for two different nanowire diameters. Growth performed at 420 ◦ C. The lines are based on equation (3), considering the relevant diameter. The error bars correspond to standard deviation. (b) Schematic illustration of opening size impact on nanowire growth. Possible mechanisms of precursor supply are presented.
The measured NW length versus their diameter for three samples grown at different temperatures is shown in figure 5. The wire-to-wire distance was 2 µm, in order to eliminate the shadowing effect described below. Some SEM images of typical nanowires are shown in the insets. The images reveal significant tapering of nanowires grown at 420 and 450 ◦ C, but no tapering of samples grown at 480 ◦ C, due to the much longer migration lengths along 4
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Figure 5. Nanowire length as a function of diameter for growth at 420, 450 and 480 ◦ C. Equivalent planar growth, considering TMI cracking efficiency, is 77, 83 and 92 nm, respectively. Error bars correspond to standard deviation. The insets show SEM images of typical InP nanowires, related to measured values by arrows. The scale bar in the insets is 100 nm.
Figure 6. SEM images of InP NWs grown at varying spacing at 450 ◦ C. The pitch is (a) 300 nm, (b) 500 nm, (c) 1000 nm. The insets show histograms of NW length based on measurements of 40 NWs in each array.
shadowed region is smaller. The growth rate is thus obtained by modifying (3) in the following manner Z L Z ∞ dL dl η(r) dr = 1+D dh rop 0 Z π/2 2lr2 cos φ 1 × dφ 2 2 ) π(D/2)2 (r + l 0 " # 2rop 2 1 + −1 (4) D cosh (L/Ldiff ) where 0 < η(r) < 1 is the unshaded fraction of the annular area at r. We have approximated the integral in (4) by dividing the area into a set of annuli, defined by neighboring NWs contributing to the shadowing effect Z Ldiff Z ∞ Z π/2 1 2lr2 cos φ D dl η(r) dr dφ 2 2 ) π(D/2)2 (r + l 0 rop 0 r r X 4Leff i i+1 ∼ ηri arctan − arctan (5) = π D L L i=0
Figure 7. Measured and calculated nanowire length as a function of array pitch for different nanowire diameters. The growth temperature is 450 ◦ C. Dashed lines connect the calculated values represented by solid data points. Measured values are represented by hollow data points with error bars corresponding to one standard deviation obtained by measuring at least 15 NWs of similar diameter.
where r0 = rop , and the following three ri values are indicated in figure 8. The fraction of the area between ri+1 and ri with line of sight to the central NW is denoted ηri . The sum is truncated when ηri = 0. The results of the calculation are shown in figure 7 together with experimental results. The model agrees very well with the experimental data for all wires separated by 0.3–1 µm, except the largest diameter of 70 nm. For the case of NWs with diameter larger than 60 nm the calculation
shadowed’ areas as fully shadowed. Nanowire diameter and pitch shown in figure 8 are equivalent to 60 nm and 300 nm, respectively, in order to show clearly the partially shadowed areas, but in most cases the relative area of the partially 5
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Acknowledgments The financial support of the Russell Berrie Nanotechnology Institute (RBNI) and of the Israel Ministry of Science and Technology (grant 38668) is highly appreciated. The fabrication was performed at the Micro-Nano Fabrication Unit (MNFU), Technion.
References [1] Li Y, Qian F, Xiang J and Lieber C M 2006 Nanowire electronic and optoelectronic devices Mater. Today 9 18–27 [2] Hochbaum A I and Yang P 2010 Semiconductor nanowires for energy conversion Chem. Rev. 110 527 [3] Wallentin J et al 2013 InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit Science 339 1057–60 [4] Cui Y, Wei Q, Park H and Lieber C M 2001 Nanowire nanosensors for highly sensitive and selective detection of biological and chemical species Science 293 1289–92 [5] Claudon J, Bleuse J, Malik N S, Bazin M, Jaffrennou P, Gregersen N, Sauvan C, Lalanne P and Gerard J-M 2010 A highly efficient single-photon source based on a quantum dot in a photonic nanowire Nature Photon. 4 174–7 [6] Wagner R S and Ellis W C 1964 Vapor–liquid–solid mechanism of single crystal growth Appl. Phys. Lett. 4 89–90 [7] Motohisa J, Noborisaka J, Takeda J, Inari M and Fukui T 2004 Catalyst-free selective-area MOVPE of semiconductor nanowires on (111) b oriented substrates J. Cryst. Growth 272 180–5 [8] Ikejiri K, Noborisaka J, Hara S, Motohisa J and Fukui T 2007 Mechanism of catalyst-free growth of GaAs nanowires by selective area MOVPE J. Cryst. Growth 298 616–9 [9] Kayser O 1991 Selective growth of InP/GaInAs in LP-MOVPE and MOMBE/CBE J. Cryst. Growth 107 989–98 [10] Dalacu D, Kam A, Austing D G, Wu X, Lapointe J, Aers G C and Poole P J 2009 Selective-area vapour–liquid–solid growth of InP nanowires Nanotechnology 20 395602 [11] Calahorra Y, Greenberg Y, Cohen S and Ritter D 2012 Catalyst design for native oxide based selective area InP nanowire growth 24th Int. Conf. on Indium Phosphide and Related Materials (Santa Barbara, CA, Aug. 2012) (Piscataway, NJ: IEEE) pp 265–8 [12] Poole P J, Dalacu D, Lapointe J, Mnaymneh K and Wu X 2011 Positioned growth and spectroscopy of InP nanowires containing single InAsP quantum dots 23rd Int. Conf. on Indium Phosphide and Related Materials (Berlin, May 2011) (Piscataway, NJ: IEEE) pp 1–4 [13] Sartel C, Dheeraj D, Jabeen F and Harmand J 2010 Effect of arsenic species on the kinetics of GaAs nanowires growth by molecular beam epitaxy J. Cryst. Growth 312 2073–7 [14] Czaban J A, Thompson D A and LaPierre R R 2008 GaAs core–shell nanowires for photovoltaic applications Nano Lett. 9 148–54 [15] Sibirev N V, Tchernycheva M, Timofeeva M A, Harmand J-C, Cirlin G E and Dubrovskii V G 2012 Influence of shadow effect on the growth and shape of InAs nanowires J. Appl. Phys. 111 104317 [16] Jensen L E, Bj¨ork M T, Jeppesen S, Persson A I, Ohlsson B J and Samuelson L 2004 Role of surface diffusion in chemical beam epitaxy of InAs nanowires Nano Lett. 4 1961–4
Figure 8. Scheme outlining the method used to evaluate the shadowing effect of precursors reflected from the mask. Yellow circles represent NWs locations. The first three radii in (5) are shown.
slightly underestimates the experimental data for inter-wire distances below 500 nm, probably due to the geometrical approximations made in our calculations. An interesting and yet unexplained observation is the reduction of the growth rate for the 2 µm pitch case for all diameters. An unexplained decrease of NW growth for larger pitch values was previously reported by Persson et al for VLS growth of patterned array of InAs NWs by CBE at large group-V/group-III ratios [21]. A gradual suppression of GaAs NW growth rate by MBE was also reported for an increasing inter-wire distance of 0.2–2 µm and attributed to an increased As/Ga ratio in the gold catalyst at higher pitches [22]. A full understanding of this phenomenon requires further studies. We finally note that the growth rate strongly depends upon array density during nonselective VLS growth of III–V semiconductor NWs, where substrate surface diffusion is the main source of group-III species [16, 21]. In this case, NWs compete over diffusing elements, growing faster as there is more collection area available. In SA-VLS, however, surface diffusion takes place only in the openings, and the only plausible interaction between NWs is the shadowing effect.
5. Conclusions We have demonstrated theoretically and experimentally the impact of the annular opening area size on indium phosphide nanowire growth rate by the selective area VLS method. The mask openings reduce mask area available for precursor scattering, but collect precursors that become available to radial or axial growth. The shadowing of scattered precursors in two-dimensional arrays was calculated. The calculation accounts for the observed reduction of growth rate in dense arrays. Overall, the modified growth model accurately predicts the growth rate of InP NWs by the SA-VLS method, thus paving the way for controllable device realization. 6
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[20] Heinecke H, Baur B, H¨oger R and Miklis A 1990 Growth of high purity InP by metalorganic MBE (CBE) J. Cryst. Growth 105 143–8 [21] Persson A, Froberg L, Jeppesen S, Bjork M and Samuelson L 2007 Surface diffusion effects on growth of nanowires by chemical beam epitaxy J. Appl. Phys. 101 034313 [22] Bauer B, Rudolph A, Soda M, Fontcuberta i Morral A, Zweck J, Schuh D and Reiger E 2010 Position controlled self-catalyzed growth of GaAs nanowires by molecular beam epitaxy Nanotechnology 21 435601
[17] Amano C, Rudra A, Grunberg P, Carlin J F and Ilegems M 1996 Growth temperature dependence of the interfacet migration in chemical beam epitaxy of InP on non-planar substrates J. Cryst. Growth 164 321–6 [18] Sze S M and Ng K K 2007 Physics of Semiconductor Devices 3rd edn (New York: Wiley) pp 243–52 [19] Hamm R, Ritter D and Temkin H 1994 Compact metalorganic molecular-beam epitaxy growth system J. Vac. Sci. Technol. A 12 2790–4
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Shadowing and mask opening effects during selective-area vapor–liquid–solid growth of InP nanowires by metalorganic molecular beam epitaxy
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2013 Nanotechnology 24 475302 (http://iopscience.iop.org/0957-4484/24/47/475302) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 93.180.53.211 This content was downloaded on 07/02/2014 at 09:40
Please note that terms and conditions apply.
IOP PUBLISHING
NANOTECHNOLOGY
Nanotechnology 24 (2013) 475302 (7pp)
doi:10.1088/0957-4484/24/47/475302
Shadowing and mask opening effects during selective-area vapor–liquid–solid growth of InP nanowires by metalorganic molecular beam epitaxy A Kelrich, Y Calahorra, Y Greenberg, A Gavrilov, S Cohen and D Ritter Electrical Engineering Faculty, Technion-Israel Institute of Technology, Haifa 32000, Israel E-mail: [email protected]
Received 29 July 2013, in final form 23 September 2013 Published 31 October 2013 Online at stacks.iop.org/Nano/24/475302 Abstract Indium phosphide nanowires were grown by metalorganic molecular beam epitaxy using the selective-area vapor–liquid–solid method. We show experimentally and theoretically that the size of the annular opening around the nanowire has a major impact on nanowire growth rate. In addition, we observed a considerable reduction of the growth rate in dense two-dimensional arrays, in agreement with a calculation of the shadowing of the scattered precursors. Due to the impact of these effects on growth, they should be considered during selective-area vapor–liquid–solid nanowire epitaxy. (Some figures may appear in colour only in the online journal)
1. Introduction
(MOMBE), also referred to as chemical beam epitaxy (CBE). During SAE by MOVPE, lateral gas phase diffusion driven by concentration gradients parallel to the surface plays a dominant role in precursor supply to the growth front. By contrast, during SAE of conventional planar layers (not NWs) by MOMBE, precursors that contribute to growth must impinge upon the opening in the mask. Precursors impinging upon the dielectric mask re-evaporate/scatter and do not contribute to the growth [9]. A novel approach for growing III–V compound semiconductor NWs integrates the SAE and VLS techniques (SA-VLS) by placing metal catalysts into the mask openings [10]. The patterned mask provides defined positioning and prevents parasitic growth on the substrate, while the catalyst diameter (and consequently—NW diameter) is accurately defined by electron beam lithography and evaporated metal thickness [11]. As in conventional VLS, abrupt interfaces between the catalyst and the grown NW are obtained, while in pure SAE significant NW tip tapering is obtained [12]. Due to the lack of surface diffusion on the substrate, one can accurately predict the growth rate during SA-VLS
Epitaxial growth of semiconductor nanowires (NWs) is intensively explored for electronic, optoelectronic, energy conversion and sensor applications [1–4], as well as for basic physics studies [5]. The successful implementation of NW technology requires an understanding of NW growth mechanisms in order to achieve control of their dimensions, composition and crystal structure. A widely used approach for NW growth is based upon the vapor–liquid–solid mechanism (VLS) [6], where a catalyst particle, in most cases gold, forms a liquid alloy with the growth precursors and catalyzes crystal growth by precipitation from a supersaturated solution. An alternative approach is the catalyst-free selective area epitaxy (SAE) [7] method. During SAE, growth is restricted to lithographically defined openings in an inert mask, typically SiO2 or SiNx . One-dimensional (axial) NW growth is achieved by SAE along the h111i A or h111i B directions due to a low incorporation rate on the side facets [8]. The SAE approach is typically based upon metalorganic precursors during metalorganic vapor phase epitaxy (MOVPE) or metalorganic molecular beam epitaxy 0957-4484/13/475302+07$33.00
1
c 2013 IOP Publishing Ltd Printed in the UK & the USA
Nanotechnology 24 (2013) 475302
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growth by MOMBE. Dalacu et al proposed an analytical model that predicts the growth rate of InP NWs [10]. They considered three components for the supply of precursors to the growing nanowire: direct impingement upon the catalyst, direct impingement upon the nanowire sidewalls, and indirect sidewall collection of the flux scattered from the mask layer. Assuming the cosine emission law of the reemitted flux from the mask layer onto the wire sidewall, the authors obtained the following expression: Z Leff Z ∞ dL 4L tan θ = 1+ +D dl dr dh πD 0 0 Z π/2 2lr2 cos φ 1 × dφ 2 2 (r + l ) π(D/2)2 0 2Leff 4L tan θ + (1) = 1+ πD D
along the radius in (1) as the opening radius, rop , yielding Z Leff Z ∞ dL = 1+D dl dr dh 0 rop Z π/2 2lr2 cos φ 1 × dφ 2 (r + l2 ) π(D/2)2 0 rop 2 2Leff 1 − arctan . (2) = 1+ D π Leff In our growth-system the metalorganic gases are injected perpendicular to the substrate, hence the second term in (1) is not included in (2). Since mask openings are typically small, it may be assumed that all precursors collected at the openings reach the NW base [16, 17]. The fraction of the flux that reaches the gold catalyst (out of the flux which is collected by the openings) is cosh−1 (L/Ldiff ),1 where Ldiff is the diffusion length along the side facets, which is assumed in our calculations to equal the above mentioned migration length, Lm . The contribution to the growth rate by the flux that impinges upon the openings is thus given by the ratio between the exposed opening area and NW cross section at the catalyst, multiplied by cosh−1 (L/Ldiff ). The resulting total growth rate is given by rop dL 2Leff 2 = 1+ 1 − arctan dh D π Leff " # 2 2rop 1 + −1 . (3) D cosh (L/Ldiff )
where Leff = min[L, Lm ], L is the wire length, and Lm is the migration length along the side facets. The parameter h in (1) stands for the equivalent planar layer thickness, D is the wire diameter, and θ is the angle between the incident precursor flux and the surface normal. The wire length is calculated by numerically integrating the growth rate given by (1) along the equivalent planar growth thickness. In this work, we theoretically and experimentally examine two subjects relevant to the SA-VLS method. First, we consider the influence of the mask opening size, which has two opposing effects on the growth rate. On one hand, with increasing opening size, precursor scattering from the mask is reduced, thus diminishing the contribution of the third and largest term in (1). On the other hand, precursors that impinge upon the openings may diffuse directly towards the growing NW. The combination of these two effects modifies the growth rate considerably. The second subject discussed in this work is shadowing of scattered precursors in dense two-dimensional arrays. The shadowing of direct beams is not a major concern during molecular beam epitaxy of nanowires, unless very dense arrays are grown and the precursor beams are not perpendicular to the substrate [13–15]. However, shadowing of scattered species turns out to be a significant effect during SA-VLS, regardless of the incidence angle between the molecular beams and the surface.
We demonstrate the effect of the mask opening on the obtained length of a NW in figure 1. We have plotted the original expression, which does not take the openings into account (1), and the results obtained with and without the contribution of the precursors that impinge directly into the openings. Note the large effect of the openings on the obtained nanowire length.
3. Experimental details Indium phosphide NWs were grown on epi-ready undoped (111)B InP substrates (Semiconductor Wafer Inc.) by a compact metalorganic molecular beam epitaxy system [19]. Before growth, the wafers were coated by a 15 nm thick SiNx mask layer by plasma-enhanced chemical vapor deposition (PECVD, Plasma-Therm 790) and then spin-coated with positive PMMA resist. The samples were electron beam patterned, developed and wet etched in buffered HF to produce circular openings in the mask with diameters of 70–130 nm. As in [10], the PMMA mask was not removed, and served as a lift-off mask for the gold particles. The thickness of the electron beam evaporated gold layer was 12 nm. A scanning electron microscope (SEM) image of the gold particles inside the mask openings is shown in figure 2.
2. Incorporation of the mask openings in the growth rate model As mentioned in section 1, the gold particle during the SA-VLS process is surrounded by an annular opening in the dielectric mask. This opening may be either deliberately defined in order to induce radial growth, or just a result of the isotropic wet-etches process. The opening reduces the available mask area for scattering of precursors towards the NW. The area close to the stem of the NW is most effective in supplying the precursors, and therefore although the annular opening area is quite small, the effect is substantial. This effect is easily modeled by setting the lower limit of integration
1 The diffusion process along the NW is analogous to diffusion along the
base of a bipolar transistor, see for example [18]. 2
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2.5 Eq. 3 Eq. 1 Eq. 2
Length [µm]
2
1.5
1
0.5
0 30
40
50
60
70
80
Diameter [nm]
Figure 1. Calculated NW length versus NW diameter for nominal planar growth of 82 nm at 450 ◦ C. The diameter of the opening is 40 nm larger than the diameter of the NW. The dotted line is after (1), which does not include the effect of the opening. The dashed line represents the reduction of the growth rate when the opening area does not contribute to TMI collection and scattering (2). The solid curve takes into account the collection of flux by the opening (3). The sidewall migration length is Lm = 700 nm. Figure 3. SEM image of InP nanowires grown from openings with varying diameter: 104 ± 4 nm for sample (a) versus 127 ± 4 nm for (b). The scale bar is 500 nm.
4. Results and discussion 4.1. Contribution of the annular opening to nanowire growth In order to evaluate the effect of the annular openings, two NW arrays went through identical processing, except for the SiN layer etching time. Figure 3 shows SEM images of the arrays grown at 420 ◦ C. Sample (b) was slightly over-etched, resulting in opening diameters of 127 ± 4 nm, compared to 104 ± 4 nm for sample (a). The diameter of the NWs, measured at the tip of the wire just below Au catalyst, was 67 ± 3 nm in both samples. It is evident from figure 3 that NWs grown from larger openings are significantly longer. A set of narrower NWs having a diameter of 51 ± 1 nm exhibited the same effect. The measured length of the NWs versus their annular opening diameters is plotted in figure 4(a). The major impact of the opening on the obtained length takes place during the initial stages of growth, illustrated in figure 4(b). At this stage, reflected precursors do not contribute to the growth and the precursors impinging into the opening significantly increase the growth rate. As the wire grows, the precursors reflected from the mask become the dominant source of material for growth, and the relative contribution of the opening area decreases. To model the growth rate, the migration length of indium precursors along the NW side facets [10] was obtained as a fitting parameter. The migration length results shown in table 1 agree quite well with SEM observations of the non-tapered NW region below the gold catalyst.
Figure 2. Plane view SEM image of a two-dimensional array of gold particles inside the SiNx openings prior to growth.
The precursors used during the MOMBE growth were trimethyl indium (TMI) and pre-cracked phosphine (PH3 ). Precise control of substrate temperature was achieved by a thermocouple in thermal contact with the sample holder. The sample was soldered to the holder using indium. The TMI flow rate corresponded to a planar growth rate of 110 nm h−1 on an InP(100) substrate at 500 ◦ C. The PH3 flow rate was 3 sccm and the growth temperature range was 420–480 ◦ C. The samples were first heated to the growth temperature under P2 flow, and then TMI was introduced to initiate growth. The TMI flux was perpendicular to the substrate surface. Growth duration was 50 min for all samples. Measurements of NW length, diameter and opening diameter, were performed by scanning electron microscopy (Hitachi S4700), with a 30◦ tilted view unless mentioned otherwise. As a result, the scale bar must be multiplied by two to obtain the nanowire length in the figures below. 3
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Table 1. Parameters used in NW growth model comparison. Growth temperature (◦ C)
TMI cracking efficiency [20] (%)
Migration length on the NW sidewall Lm (µm)
Exposed annular diameter (Dopening − Dwire ) (nm)
420 450 480
84 90 100
0.5 0.7 2.0
35 ± 4 40 ± 5 22 ± 4
the nanowire sidewalls. Additional data, obtained by TEM analysis, regarding the diameter and temperature dependence of NW tapering will be presented elsewhere. The modified model given by equation (3) fits quite well the experimental data. For all three samples, the planar growth rate was equivalent to 0.11 µm h−1 at 500 ◦ C on (100) InP. Lower TMI cracking efficiency were taken into consideration at 420 and 450 ◦ C [20]. All relevant parameters are summarized in table 1. Note the significant difference between the prediction given by (1) and the experimental data.
1.4
(a) 1.2
NW length [µm]
1
0.8
0.6
4.2. Shadowing of reflected precursors D = 51 nm D = 66 nm
0.4
0.2 80
90
100
110
120
Shadowing of the impinging molecular beams by neighboring nanowires in dense two-dimensional arrays during molecular beam epitaxy (MBE) was previously observed [13, 14] and analyzed [15]. During SA-VLS by MOMBE, a more pronounced shadowing effect of the reflected precursors from the mask area is expected. In a previous report no shadowing was observed, as only linear arrays were modeled [10]. Figure 6 shows a series of SEM images of nanowires grown at 450 ◦ C from a square array of gold particles. Array spacing varied between 300 and 1000 nm. It can be seen that the length of the NWs varies significantly with spacing, increasing by ∼25% for 1 µm pitch compared to 0.3 µm pitch. The experiment was repeated for four different sets of NWs with diameters of 53–70 nm. Every series was processed and grown simultaneously on the same substrate. A summary of the results is presented in figure 7. A significant growth rate enhancement is observed for a slight change from 0.3 to 0.5 µm of the array spacing. The same tendency continues in the 0.5–1 µm range, but when the pitch was increased from 1 to 2 µm a slight reduction of the growth rate and length uniformity were observed. The shadowing effect is more pronounced in thinner NWs due to their larger growth rate. As the growth rate varies considerably with NW diameter, special care was taken to measure accurately the NW diameters. Every data point in figure 7 was obtained by averaging the measured diameter of 15–20 NWs, obtaining a standard deviation of 1–2 nm. The opening diameters were verified to be similar in each set in order to eliminate the above-described influence on the growth rate. In order to evaluate the shadowing of the reflected precursors we have considered the flux impinging upon a single NW and divided the surface area into four categories: no shadowing, slight shadowing, considerable shadowing, and full shadowing, as schematically shown in figure 8. To simplify the calculations, we have considered the ‘slightly shadowed’ areas as not shadowed, and the ‘considerably
130
Opening diameter [nm]
(b)
Figure 4. (a) Nanowire length as a function of opening size for two different nanowire diameters. Growth performed at 420 ◦ C. The lines are based on equation (3), considering the relevant diameter. The error bars correspond to standard deviation. (b) Schematic illustration of opening size impact on nanowire growth. Possible mechanisms of precursor supply are presented.
The measured NW length versus their diameter for three samples grown at different temperatures is shown in figure 5. The wire-to-wire distance was 2 µm, in order to eliminate the shadowing effect described below. Some SEM images of typical nanowires are shown in the insets. The images reveal significant tapering of nanowires grown at 420 and 450 ◦ C, but no tapering of samples grown at 480 ◦ C, due to the much longer migration lengths along 4
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Figure 5. Nanowire length as a function of diameter for growth at 420, 450 and 480 ◦ C. Equivalent planar growth, considering TMI cracking efficiency, is 77, 83 and 92 nm, respectively. Error bars correspond to standard deviation. The insets show SEM images of typical InP nanowires, related to measured values by arrows. The scale bar in the insets is 100 nm.
Figure 6. SEM images of InP NWs grown at varying spacing at 450 ◦ C. The pitch is (a) 300 nm, (b) 500 nm, (c) 1000 nm. The insets show histograms of NW length based on measurements of 40 NWs in each array.
shadowed region is smaller. The growth rate is thus obtained by modifying (3) in the following manner Z L Z ∞ dL dl η(r) dr = 1+D dh rop 0 Z π/2 2lr2 cos φ 1 × dφ 2 2 ) π(D/2)2 (r + l 0 " # 2rop 2 1 + −1 (4) D cosh (L/Ldiff ) where 0 < η(r) < 1 is the unshaded fraction of the annular area at r. We have approximated the integral in (4) by dividing the area into a set of annuli, defined by neighboring NWs contributing to the shadowing effect Z Ldiff Z ∞ Z π/2 1 2lr2 cos φ D dl η(r) dr dφ 2 2 ) π(D/2)2 (r + l 0 rop 0 r r X 4Leff i i+1 ∼ ηri arctan − arctan (5) = π D L L i=0
Figure 7. Measured and calculated nanowire length as a function of array pitch for different nanowire diameters. The growth temperature is 450 ◦ C. Dashed lines connect the calculated values represented by solid data points. Measured values are represented by hollow data points with error bars corresponding to one standard deviation obtained by measuring at least 15 NWs of similar diameter.
where r0 = rop , and the following three ri values are indicated in figure 8. The fraction of the area between ri+1 and ri with line of sight to the central NW is denoted ηri . The sum is truncated when ηri = 0. The results of the calculation are shown in figure 7 together with experimental results. The model agrees very well with the experimental data for all wires separated by 0.3–1 µm, except the largest diameter of 70 nm. For the case of NWs with diameter larger than 60 nm the calculation
shadowed’ areas as fully shadowed. Nanowire diameter and pitch shown in figure 8 are equivalent to 60 nm and 300 nm, respectively, in order to show clearly the partially shadowed areas, but in most cases the relative area of the partially 5
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Acknowledgments The financial support of the Russell Berrie Nanotechnology Institute (RBNI) and of the Israel Ministry of Science and Technology (grant 38668) is highly appreciated. The fabrication was performed at the Micro-Nano Fabrication Unit (MNFU), Technion.
References [1] Li Y, Qian F, Xiang J and Lieber C M 2006 Nanowire electronic and optoelectronic devices Mater. Today 9 18–27 [2] Hochbaum A I and Yang P 2010 Semiconductor nanowires for energy conversion Chem. Rev. 110 527 [3] Wallentin J et al 2013 InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit Science 339 1057–60 [4] Cui Y, Wei Q, Park H and Lieber C M 2001 Nanowire nanosensors for highly sensitive and selective detection of biological and chemical species Science 293 1289–92 [5] Claudon J, Bleuse J, Malik N S, Bazin M, Jaffrennou P, Gregersen N, Sauvan C, Lalanne P and Gerard J-M 2010 A highly efficient single-photon source based on a quantum dot in a photonic nanowire Nature Photon. 4 174–7 [6] Wagner R S and Ellis W C 1964 Vapor–liquid–solid mechanism of single crystal growth Appl. Phys. Lett. 4 89–90 [7] Motohisa J, Noborisaka J, Takeda J, Inari M and Fukui T 2004 Catalyst-free selective-area MOVPE of semiconductor nanowires on (111) b oriented substrates J. Cryst. Growth 272 180–5 [8] Ikejiri K, Noborisaka J, Hara S, Motohisa J and Fukui T 2007 Mechanism of catalyst-free growth of GaAs nanowires by selective area MOVPE J. Cryst. Growth 298 616–9 [9] Kayser O 1991 Selective growth of InP/GaInAs in LP-MOVPE and MOMBE/CBE J. Cryst. Growth 107 989–98 [10] Dalacu D, Kam A, Austing D G, Wu X, Lapointe J, Aers G C and Poole P J 2009 Selective-area vapour–liquid–solid growth of InP nanowires Nanotechnology 20 395602 [11] Calahorra Y, Greenberg Y, Cohen S and Ritter D 2012 Catalyst design for native oxide based selective area InP nanowire growth 24th Int. Conf. on Indium Phosphide and Related Materials (Santa Barbara, CA, Aug. 2012) (Piscataway, NJ: IEEE) pp 265–8 [12] Poole P J, Dalacu D, Lapointe J, Mnaymneh K and Wu X 2011 Positioned growth and spectroscopy of InP nanowires containing single InAsP quantum dots 23rd Int. Conf. on Indium Phosphide and Related Materials (Berlin, May 2011) (Piscataway, NJ: IEEE) pp 1–4 [13] Sartel C, Dheeraj D, Jabeen F and Harmand J 2010 Effect of arsenic species on the kinetics of GaAs nanowires growth by molecular beam epitaxy J. Cryst. Growth 312 2073–7 [14] Czaban J A, Thompson D A and LaPierre R R 2008 GaAs core–shell nanowires for photovoltaic applications Nano Lett. 9 148–54 [15] Sibirev N V, Tchernycheva M, Timofeeva M A, Harmand J-C, Cirlin G E and Dubrovskii V G 2012 Influence of shadow effect on the growth and shape of InAs nanowires J. Appl. Phys. 111 104317 [16] Jensen L E, Bj¨ork M T, Jeppesen S, Persson A I, Ohlsson B J and Samuelson L 2004 Role of surface diffusion in chemical beam epitaxy of InAs nanowires Nano Lett. 4 1961–4
Figure 8. Scheme outlining the method used to evaluate the shadowing effect of precursors reflected from the mask. Yellow circles represent NWs locations. The first three radii in (5) are shown.
slightly underestimates the experimental data for inter-wire distances below 500 nm, probably due to the geometrical approximations made in our calculations. An interesting and yet unexplained observation is the reduction of the growth rate for the 2 µm pitch case for all diameters. An unexplained decrease of NW growth for larger pitch values was previously reported by Persson et al for VLS growth of patterned array of InAs NWs by CBE at large group-V/group-III ratios [21]. A gradual suppression of GaAs NW growth rate by MBE was also reported for an increasing inter-wire distance of 0.2–2 µm and attributed to an increased As/Ga ratio in the gold catalyst at higher pitches [22]. A full understanding of this phenomenon requires further studies. We finally note that the growth rate strongly depends upon array density during nonselective VLS growth of III–V semiconductor NWs, where substrate surface diffusion is the main source of group-III species [16, 21]. In this case, NWs compete over diffusing elements, growing faster as there is more collection area available. In SA-VLS, however, surface diffusion takes place only in the openings, and the only plausible interaction between NWs is the shadowing effect.
5. Conclusions We have demonstrated theoretically and experimentally the impact of the annular opening area size on indium phosphide nanowire growth rate by the selective area VLS method. The mask openings reduce mask area available for precursor scattering, but collect precursors that become available to radial or axial growth. The shadowing of scattered precursors in two-dimensional arrays was calculated. The calculation accounts for the observed reduction of growth rate in dense arrays. Overall, the modified growth model accurately predicts the growth rate of InP NWs by the SA-VLS method, thus paving the way for controllable device realization. 6
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[20] Heinecke H, Baur B, H¨oger R and Miklis A 1990 Growth of high purity InP by metalorganic MBE (CBE) J. Cryst. Growth 105 143–8 [21] Persson A, Froberg L, Jeppesen S, Bjork M and Samuelson L 2007 Surface diffusion effects on growth of nanowires by chemical beam epitaxy J. Appl. Phys. 101 034313 [22] Bauer B, Rudolph A, Soda M, Fontcuberta i Morral A, Zweck J, Schuh D and Reiger E 2010 Position controlled self-catalyzed growth of GaAs nanowires by molecular beam epitaxy Nanotechnology 21 435601
[17] Amano C, Rudra A, Grunberg P, Carlin J F and Ilegems M 1996 Growth temperature dependence of the interfacet migration in chemical beam epitaxy of InP on non-planar substrates J. Cryst. Growth 164 321–6 [18] Sze S M and Ng K K 2007 Physics of Semiconductor Devices 3rd edn (New York: Wiley) pp 243–52 [19] Hamm R, Ritter D and Temkin H 1994 Compact metalorganic molecular-beam epitaxy growth system J. Vac. Sci. Technol. A 12 2790–4
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