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Nucleation of GaN nanowires grown by plasma-assisted molecular beam epitaxy: The effect of temperature
Journal of Crystal Growth 334 (2011) 177–180
Contents lists available at SciVerse ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Nucleation of GaN nanowires grown by plasma-assisted molecular beam epitaxy: The effect of temperature Rafael Mata a,b, Karine Hestroffer b, Jorge Budagosky a, Ana Cros a, Catherine Bougerol b, Hubert Renevier c, Bruno Daudin b,n a
Materials Science Institute, University of Valencia, P.O. Box 22085, E46071 Valencia, Spain CEA-CNRS group ) Nanophysique et Semiconducteurs* , Institut Ne´el/CNRS-Univ., J. Fourier and CEA Grenoble, INAC, SP2M, 17 rue des Martyrs, 38 054 Grenoble, France c Laboratoire des Mate´riaux et du Ge´nie Physique, Grenoble INP-MINATEC, 3 parvis L. Ne´el, 38016 Grenoble, France b
a r t i c l e i n f o
abstract
Article history: Received 18 May 2011 Received in revised form 10 August 2011 Accepted 13 August 2011 Communicated by K. Deppert Available online 22 August 2011
The growth of GaN nanowires by means of plasma assisted molecular beam epitaxy directly on Si(1 1 1) has been investigated as a function of temperature. Statistical analysis of scanning electron microscopy pictures taken for different growth temperatures has revealed that density, diameter, length and length dispersion of nanowires were strongly dependent on temperature. Length dispersion, in particular, was found to be significant at high temperature. These features have been assigned to the different duration of the nucleation process with temperature, namely to the dependence with temperature of the time necessary for the size increase of the three-dimensional precursors up to a critical value. & 2011 Elsevier B.V. All rights reserved.
Keywords: A1. Nanostructures A1. Nucleation A3. Molecular beam epitaxy B2. Semiconducting III–V materials
1. Introduction The current interest in III-nitride nanowires (NWs) relies to a large extent on their excellent structural and optical properties, making them an alternative to their dislocation-plagued twodimensional counterparts. Among the various growth techniques used upto date to grow such wires, plasma-assisted molecular beam epitaxy (PA-MBE) is particularly attractive as it does not require the use of catalysts, which are a potential source of impurity contamination [1]. As a further advantage with respect to 2D material, NWs can be grown on (1 1 1) Si. GaN NWs grown using PA-MBE are usually found to be vertically aligned, especially when using a thin AlN buffer layer deposited on (1 1 1) Si, a favorable situation for the growth of axial heterostructures [2]. As a matter of fact, the demonstration that GaN/InGaN or GaN/AlGaN NWs’ heterostructures could be used to achieve light emitting diodes (LEDs) in the visible [3–5] and UV [6] range has been made recently. Nevertheless, compared to the standard 2D LEDs, additional difficulties specific to NW arrays are faced: for instance, processing of NW LED structures requires a planarization step, in order to optimize the upper electrode. This step is expected to be greatly eased if the height distribution of NWs is narrow enough,
n
Corresponding author. Tel.: þ33 438 783 750; fax: þ33 438 785 197. E-mail address: [email protected] (B. Daudin).
0022-0248/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2011.08.015
which raises the issue of precisely controlling the growth process. However, despite the practical importance of such an issue, it appears that growth studies dealing with the nucleation and height control of NWs are relatively scarce in literature [7–15]. It has to be emphasized that the role of the AlN buffer layer optionally deposited on Si(1 1 1) before growth of GaN NWs to ensure a better verticality [2] cannot be neglected. As a matter of fact, it has been found that the final density of GaN NWs could be correlated to the grain size of the AlN buffer layer [11]. Then, with the prospect of dealing with intrinsic nucleation mechanisms uninfluenced by the presence of a buffer layer, we address in this article the issue of nucleation processes of GaN NWs grown directly on Si(1 1 1) as a function of temperature. Based on the statistical processing of scanning electron microscopy (SEM) pictures, it will be shown that the density of NWs as well as their diameter and length variability strongly depends on growth temperature, suggesting that they are governed by a kineticallydriven process. By contrast, the size of 3D precursors is temperature-independent, suggesting that it is not governed by kinetics but rather related to the relaxation of their elastic energy.
2. Experiment and results The samples studied have been grown by plasma-assisted molecular beam epitaxy (PA-MBE) on 2-in Si(1 1 1) wafers. Prior to growth
178
R. Mata et al. / Journal of Crystal Growth 334 (2011) 177–180
the substrates were cleaned with a hydrofluoric acid solution and thermally outgassed for 15 min at 300 1C until the 7 7 reconstruction of the Si(1 1 1) surface was observed. Growth of GaN NWs was performed in N-rich condition with a Ga/N ratio of 1/3. In order to ensure NW growth reproducibility, reflection high energy electron diffraction (RHEED) was used to determine the Si surface temperature by measuring the Ga desorption transient from the 7 7 Si(1 1 1) reconstructed surface, following its exposure to a Ga flux. Such an exposure results in the formation of a self-regulated Ga amount on the Si surface, independent of flux/exposure time fluctuations in the 740–860 1C growth temperature range [16]. Then measuring the Ga desorption transient leads to the determination of a reproducible relationship between the Ga desorption time and the temperature indicated by the thermocouple in mechanical contact with the rear face of the Si wafer. As the thermocouple measurement is biased by direct thermal radiation from the heater filament, a correction was further applied by observing the appearance/disappearance of the 7 7 reconstruction, which was set at 860 1C [17]. Finally, this two-steps procedure provided a relationship between the Ga desorption transient and the surface temperature (see inset of Fig. 1). In a next stage, the dependence of the NW density as a function of the transient desorption time was studied, eventually
Temperature (°C)
Nanowires density (108/cm2)
1000 800 600
870 840 810 780 750
400
10 1 Ga desorption time (s)
200 0 780
790
800 810 Temperature (°C)
820
830
Fig. 1. GaN nanowire density as a function of the corrected temperature. Inset: substrate temperature (as read by the thermocouple in contact to the rear face of the (1 1 1) Si wafer) as a function of Ga desorption time from the Si surface.
leading to the density–temperature relationship as shown in Fig. 1 where each experimental point corresponds to a single sample. For each single sample, the NW density was measured in the center of the wafer. The GaN deposition time was 90 min. In agreement with the results recently obtained using a pyrometer to measure the temperature [14], Fig. 1 reveals that GaN NWs’ density is drastically decreasing between 780 and 805 1C and falls down to zero above 805 1C, consistent with the rapid increase of the decomposition of GaN in MBE environment above 800 1C, which has been observed by Grandjean and coworkers [18]. In a next stage of the experiments reported in the present work and with the purpose of investigating NW nucleation and morphology as a function of temperature on a single sample, advantage was taken of the marked temperature gradient from the center of the 2 in silicon wafer towards the edge, depending on the mechanical design of the substrate holder. For this purpose, two types of samples were grown: sample #1 consists of GaN NWs, which were grown during 3 h in order to study the evolution of their dispersion length as a function of density/ temperature. Sample #2 was grown under the same conditions but the growth time was limited to 20 min in order to analyze the first stages of the nucleation process as a function of temperature. The morphological characteristics of samples #1 and #2 were analyzed by means of top-view and cross section Scanning Electron Micrographs (SEM) (ZEISS Ultra 55 microscope) taken at regular intervals along the wafer radius. Fig. 2(a–c) shows representative SEM images of sample #1 taken at three different positions of the wafer. Consistent with data of Fig. 1, a decrease of NWs’ density is observed as growth temperature increases. Moreover, changes in diameter and length are observed, both of them decreasing for the higher temperatures. Fig. 2(d–f) shows similar SEM micrographs from sample #2. Due to the short growth time of sample #2 the onset of NW formation has only taken place in low temperature regions (Fig. 2(d), close to the wafer edge). Regions closer to the wafer center, at higher temperatures, present the formation of small islands, namely the 3D precursors, which are formed in a nucleation stage prior to the steady state growth of NWs [11,12]. A clear decrease in density for higher substrate temperature is observed. Based on a detailed statistical analysis of the SEM pictures, diameter, length and length dispersion of NWs were determined as a function of temperature. In practice, images with less than 20 wires have been excluded from the analysis. Results are plotted in Fig. 3, which show the length and the length dispersion of the NWs as a function of temperature. NW length remains almost constant in most of the temperature range studied, with a rapid
Fig. 2. SEM micrographs of sample #1 taken in cross section (top) and top view (middle) from the sample edge (a, lower temperature), and two regions closer to the wafer center (b, c, higher temperature). Bottom: similar top view SEM micrographs of sample #2 taken from the sample edge (d, lower temperature), and two regions closer to the wafer center (e, f, higher temperature).
R. Mata et al. / Journal of Crystal Growth 334 (2011) 177–180
350
Mean length (nm)
300 250
100
200 150
50
Length dispersion (nm)
150
100 50 775
780
785 790 795 Temperature (°C)
800
0 805
Fig. 3. Variation of the mean length (dots) and of the length dispersion (triangles) of GaN NWs as a function of temperature. Lines are guides to the eyes.
28
#1
Mean diameter (nm)
#2 24 20 16 12 8 770
780
790 Temperature (°C)
800
810
Fig. 4. Variation of the mean diameter of the NWs (dots) and precursor islands (triangles) as a function of temperature. Lines are guides to the eyes.
decrease for temperatures larger than 790 1C, associated to the rapid increase in GaN decomposition rate in this temperature range [18]. Length dispersion increases with temperature, with a marked increase in the high temperature range. Similar statistical analysis for the diameter of samples #1 and #2 is shown in Fig. 4. The NWs’ diameter dependence with temperature is almost linear, with a marked decrease as the temperature is raised, reaching a value of E12 nm at the higher temperatures. Interestingly, it is found that the diameter of 3D precursor islands is almost constant (about 12 nm) and independent of temperature, increasing only slightly for the lowest temperatures, where NWs have already formed, which is assigned to the reduced nucleation delay in the low temperature range. This suggests that precursors have to reach a critical size before turning into NWs, consistent with data reported by Consonni and coworkers [19]. It also indicates that this critical size is not governed by nucleation kinetics. Indeed, it has been previously demonstrated that NW 3D precursors grown on Si(1 1 1) covered by a thin AlN buffer layer are plastically relaxed, consistent with the observation of misfit dislocations at the interface between the 3D precursor and the thin AlN buffer layer [11,12]. As shown by Furtmayr and coworkers, when no AlN buffer layer is used, the absence of wetting layer rather evidences that nucleation of GaN islands is of Volmer–Weber type [20]. Actually, the data of Landre´ and coworkers [11] as well as those presented here furthermore
179
suggest that with or without AlN buffer layer the 3D precursor size is governed by the elastic strain relaxation mechanism and not by kinetic considerations. More precisely, a detailed analysis of the NW nucleation process by X-ray diffraction performed in situ on NWs grown in an MBE machine connected to a synchrotron beam line at the European synchrotron research facility in Grenoble (France) is reported in Ref. [11]. The presence of three regimes has been established, namely a first stage corresponding to the nucleation of a wetting layer on the thin AlN buffer layer followed by a second stage associated with the size increase of 3D NW precursors, and finally a third stage corresponding to the steady state NW growth. Depending on Ga flux and substrate temperature, it was established that the duration of the second stage corresponding to precursor size increase ranged from a few seconds to almost one hour. During this stage, the amount of GaN deposited was found to vary as At2 þ d, t being the growth time. The exponent, 2þ d, of this supralinear regime was found to be in the range of 1.9–2.3, depending on Ga flux. According to the model developed by Osipov [21], this implies that the twodimensional size increase of NW precursors in the stage immediately following the deposition of the wetting layer is not isotropic but characterized by a rapid increase of the island diameter/perimeter till reaching a critical size associated with misfit dislocation formation at the AlN/GaN interface [11,12]. These results lead to the conclusion that the 3D precursor nucleation process, which depends on the areal density of Ga adatoms, will be controlled by both temperature and Ga flux. As the critical size of precursors giving rise to NW growth is only governed by an elastic energy relaxation process, this implies that the time spreading of the onset of steady-state NW growth will reflect the duration of the 3D precursor nucleation process till reaching their critical size. Consequently, a length dispersion of the NWs will be observed, as it is actually, associated to the duration of the 3D precursor nucleation process, which indeed increases with temperature. This qualitatively supports the hypothesis that at low temperature all 3D precursor islands are almost simultaneously formed and will reach the critical size for plastic relaxation at the same time, giving place to the continuous growth of NWs with the same length. On the contrary, at high temperature, the decrease in nucleation probability and the drastic increase in GaN dissociation rate both lead to a marked increase of the time elapsed between the formation of the first precursor having reached its critical size and the formation of the last one. Then, the onset of steady state growth of NWs is significantly scattered, reflecting the time duration of the precursor nucleation process and leading to the growth of wires with different lengths, presenting a much larger dispersion than those grown at lower temperature. Interestingly, it is worth noting that at low temperature, although it can be safely assumed that all 3D precursor islands are almost simultaneously formed, a NW length dispersion of about 12 nm is still observed (see Fig. 2a). This residual size dispersion is assigned to fluctuations inherent to the growth process itself. As a matter of fact, it is well known that GaN NWs is governed to a large extent by Ga diffusion in the basal plane and along the NWs’ side walls [16]. Then, random nucleation of NWs combined to shadow effects may lead to fluctuations in the amount of Ga atoms reaching the top of individual NWs, resulting in a residual size dispersion of about 5% in the present growth conditions.
3. Conclusion In summary, it appears on one hand that GaN NWs’ growth proceeds through the formation of 3D precursor islands, for which
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critical size before turning into NWs is independent of the growth temperature. However, on the other hand, both nucleation probability and size increase of these 3D precursor islands, which are kinetically driven processes, depend on growth temperature through the temperature dependence of Ga adatom density/ diffusion and of GaN dissociation rate. Then, as a consequence of the statistical nature of the nucleation process and of its marked temperature dependence, it is expected that the nucleation of 3D GaN precursors of NWs till reaching their critical size is actually occurring during a time span, the duration of which increases with growth temperature. This leads to a marked temperature dependence of the length dispersion of GaN NWs grown catalyst-free by MBE on Si(1 1 1). For practical applications requiring NWs with reduced length dispersion, the present study suggests to disconnect the nucleation stage, which should be performed at low/moderate temperature, from the steady-state growth stage, which could be performed at higher temperature in order to optimize structural/optical properties.
Acknowledgments This work has been supported by the funding awarded by the Ministry of Science and Innovation of Spain, FEDER (MAT2009010350). Support of French national research agency (ANR) program BONAFO is acknowledged. We are grateful to Y. Cure´ for technical assistance during experiments. References ˜ oz, [1] E. Calleja, M.A. Sanchez-Garcia, F.J. Sanchez, F. Calle, F.B. Naranjo, E. Mun U. Jahn, K. Ploog, Physical Review B 62 (2000) 16826.
[2] R. Songmuang, O. Landre´, B. Daudin, Applied Physics Letters 91 (2007) 251902. [3] A. Kikuchi, M. Kawai, M. Tada, K. Kishino, Japanese Journal of Applied Physics 43 (2004) L1524. [4] H.M. Kim, Y.H. Cho, H.S. Lee, S.I. Kim, S.R. Ryu, D.Y. Kim, T.W. Kang, K.S. Chung, Nano Letters 4 (2004) 1059. [5] A.-L. Bavencove, G. Tourbot, E. Pougeoise, J. Garcia, P. Gilet, F. Levy, B. Andre, G. Feuillet, B. Gayral, B. Daudin, Le Si Dang, Physica Status Solidi A 207 (2010) 1425. [6] H. Sekiguchi, K. Kishino, A. Kikuchi, Electronics Letters 44 (2008) 151. [7] K.A. Bertness, A. Roshko, L.M. Mansfield, T.E. Harvey, N.A. Sanford, Journal of Crystal Growth 300 (2007) 94. ¨ [8] R. Calarco, R.J. Meijers, R.K. Debnath, T. Stoica, E. Sutter, H. Luth, Nanoletters 7 (2007) 2248. [9] K.A. Bertness, A. Roshko, L.M. Mansfield, T.E. Harvey, N.A. Sanford, Journal of Crystal Growth 310 (2008) 3154. [10] J. Ristic, E. Calleja, S. Fernandez-Garrido, L. Cerutti, A. Trampert, U. Jahn, K.H. Ploog, Journal of Crystal Growth 310 (2008) 4035. [11] O. Landre´, C. Bougerol, H. Renevier, B. Daudin, Nanotechnology 20 (2009) 415602. [12] V. Consonni, M. Knelangen, L. Geelhaar, A. Trampert, H. Riechert, Physical Review B 81 (2010) 085310. [13] S. Ferna´ndez-Garrido, J. Grandal, E. Calleja, M.A. Sa´nchez-Garcı´a, D. Lo´pezRomero, Journal of Applied Physics 106 (2009) 126102. [14] Santino D. Carnevale, Jing Yang, Patrick J. Phillips, Michael J. Mills, Roberto C. Myers, Nanoletters 11 (2011) 866. [15] V. Consonni, M. Knelangen, A. Trampert, L. Geelhaar, H. Riechert, Applied Physics Letters 98 (2011) 071913. [16] O. Landre´, R. Songmuang, J. Renard, E. Bellet-Amalric, H. Renevier, B. Daudin, Applied Physics Letters 93 (2008) 183109. [17] T. Suzuki, Y. Hirabayashi, Japanese Journal of Applied Physics 32 (1993) L610. [18] N. Grandjean, J. Massies, F. Semond, S. Yu Karpov, R.A. Talalaev, Applied Physics Letters 74 (1854) 1999. [19] V. Consonni, M. Hanke, M. Knelangen, L. Geelhaar, A. Trampert, H. Riechert, Physical Review B 83 (2011) 035310. [20] F. Furtmayr, M. Vielemeyer, M. Stutzmann, J. Arbiol, S. Estrade´, F. Peiro, J.R. Morante, M. Eickhoff, Journal of Applied Physics 104 (2008) 034309. [21] A.V. Osipov, Thin Solid Films 227 (1993) 111.
Contents lists available at SciVerse ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Nucleation of GaN nanowires grown by plasma-assisted molecular beam epitaxy: The effect of temperature Rafael Mata a,b, Karine Hestroffer b, Jorge Budagosky a, Ana Cros a, Catherine Bougerol b, Hubert Renevier c, Bruno Daudin b,n a
Materials Science Institute, University of Valencia, P.O. Box 22085, E46071 Valencia, Spain CEA-CNRS group ) Nanophysique et Semiconducteurs* , Institut Ne´el/CNRS-Univ., J. Fourier and CEA Grenoble, INAC, SP2M, 17 rue des Martyrs, 38 054 Grenoble, France c Laboratoire des Mate´riaux et du Ge´nie Physique, Grenoble INP-MINATEC, 3 parvis L. Ne´el, 38016 Grenoble, France b
a r t i c l e i n f o
abstract
Article history: Received 18 May 2011 Received in revised form 10 August 2011 Accepted 13 August 2011 Communicated by K. Deppert Available online 22 August 2011
The growth of GaN nanowires by means of plasma assisted molecular beam epitaxy directly on Si(1 1 1) has been investigated as a function of temperature. Statistical analysis of scanning electron microscopy pictures taken for different growth temperatures has revealed that density, diameter, length and length dispersion of nanowires were strongly dependent on temperature. Length dispersion, in particular, was found to be significant at high temperature. These features have been assigned to the different duration of the nucleation process with temperature, namely to the dependence with temperature of the time necessary for the size increase of the three-dimensional precursors up to a critical value. & 2011 Elsevier B.V. All rights reserved.
Keywords: A1. Nanostructures A1. Nucleation A3. Molecular beam epitaxy B2. Semiconducting III–V materials
1. Introduction The current interest in III-nitride nanowires (NWs) relies to a large extent on their excellent structural and optical properties, making them an alternative to their dislocation-plagued twodimensional counterparts. Among the various growth techniques used upto date to grow such wires, plasma-assisted molecular beam epitaxy (PA-MBE) is particularly attractive as it does not require the use of catalysts, which are a potential source of impurity contamination [1]. As a further advantage with respect to 2D material, NWs can be grown on (1 1 1) Si. GaN NWs grown using PA-MBE are usually found to be vertically aligned, especially when using a thin AlN buffer layer deposited on (1 1 1) Si, a favorable situation for the growth of axial heterostructures [2]. As a matter of fact, the demonstration that GaN/InGaN or GaN/AlGaN NWs’ heterostructures could be used to achieve light emitting diodes (LEDs) in the visible [3–5] and UV [6] range has been made recently. Nevertheless, compared to the standard 2D LEDs, additional difficulties specific to NW arrays are faced: for instance, processing of NW LED structures requires a planarization step, in order to optimize the upper electrode. This step is expected to be greatly eased if the height distribution of NWs is narrow enough,
n
Corresponding author. Tel.: þ33 438 783 750; fax: þ33 438 785 197. E-mail address: [email protected] (B. Daudin).
0022-0248/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2011.08.015
which raises the issue of precisely controlling the growth process. However, despite the practical importance of such an issue, it appears that growth studies dealing with the nucleation and height control of NWs are relatively scarce in literature [7–15]. It has to be emphasized that the role of the AlN buffer layer optionally deposited on Si(1 1 1) before growth of GaN NWs to ensure a better verticality [2] cannot be neglected. As a matter of fact, it has been found that the final density of GaN NWs could be correlated to the grain size of the AlN buffer layer [11]. Then, with the prospect of dealing with intrinsic nucleation mechanisms uninfluenced by the presence of a buffer layer, we address in this article the issue of nucleation processes of GaN NWs grown directly on Si(1 1 1) as a function of temperature. Based on the statistical processing of scanning electron microscopy (SEM) pictures, it will be shown that the density of NWs as well as their diameter and length variability strongly depends on growth temperature, suggesting that they are governed by a kineticallydriven process. By contrast, the size of 3D precursors is temperature-independent, suggesting that it is not governed by kinetics but rather related to the relaxation of their elastic energy.
2. Experiment and results The samples studied have been grown by plasma-assisted molecular beam epitaxy (PA-MBE) on 2-in Si(1 1 1) wafers. Prior to growth
178
R. Mata et al. / Journal of Crystal Growth 334 (2011) 177–180
the substrates were cleaned with a hydrofluoric acid solution and thermally outgassed for 15 min at 300 1C until the 7 7 reconstruction of the Si(1 1 1) surface was observed. Growth of GaN NWs was performed in N-rich condition with a Ga/N ratio of 1/3. In order to ensure NW growth reproducibility, reflection high energy electron diffraction (RHEED) was used to determine the Si surface temperature by measuring the Ga desorption transient from the 7 7 Si(1 1 1) reconstructed surface, following its exposure to a Ga flux. Such an exposure results in the formation of a self-regulated Ga amount on the Si surface, independent of flux/exposure time fluctuations in the 740–860 1C growth temperature range [16]. Then measuring the Ga desorption transient leads to the determination of a reproducible relationship between the Ga desorption time and the temperature indicated by the thermocouple in mechanical contact with the rear face of the Si wafer. As the thermocouple measurement is biased by direct thermal radiation from the heater filament, a correction was further applied by observing the appearance/disappearance of the 7 7 reconstruction, which was set at 860 1C [17]. Finally, this two-steps procedure provided a relationship between the Ga desorption transient and the surface temperature (see inset of Fig. 1). In a next stage, the dependence of the NW density as a function of the transient desorption time was studied, eventually
Temperature (°C)
Nanowires density (108/cm2)
1000 800 600
870 840 810 780 750
400
10 1 Ga desorption time (s)
200 0 780
790
800 810 Temperature (°C)
820
830
Fig. 1. GaN nanowire density as a function of the corrected temperature. Inset: substrate temperature (as read by the thermocouple in contact to the rear face of the (1 1 1) Si wafer) as a function of Ga desorption time from the Si surface.
leading to the density–temperature relationship as shown in Fig. 1 where each experimental point corresponds to a single sample. For each single sample, the NW density was measured in the center of the wafer. The GaN deposition time was 90 min. In agreement with the results recently obtained using a pyrometer to measure the temperature [14], Fig. 1 reveals that GaN NWs’ density is drastically decreasing between 780 and 805 1C and falls down to zero above 805 1C, consistent with the rapid increase of the decomposition of GaN in MBE environment above 800 1C, which has been observed by Grandjean and coworkers [18]. In a next stage of the experiments reported in the present work and with the purpose of investigating NW nucleation and morphology as a function of temperature on a single sample, advantage was taken of the marked temperature gradient from the center of the 2 in silicon wafer towards the edge, depending on the mechanical design of the substrate holder. For this purpose, two types of samples were grown: sample #1 consists of GaN NWs, which were grown during 3 h in order to study the evolution of their dispersion length as a function of density/ temperature. Sample #2 was grown under the same conditions but the growth time was limited to 20 min in order to analyze the first stages of the nucleation process as a function of temperature. The morphological characteristics of samples #1 and #2 were analyzed by means of top-view and cross section Scanning Electron Micrographs (SEM) (ZEISS Ultra 55 microscope) taken at regular intervals along the wafer radius. Fig. 2(a–c) shows representative SEM images of sample #1 taken at three different positions of the wafer. Consistent with data of Fig. 1, a decrease of NWs’ density is observed as growth temperature increases. Moreover, changes in diameter and length are observed, both of them decreasing for the higher temperatures. Fig. 2(d–f) shows similar SEM micrographs from sample #2. Due to the short growth time of sample #2 the onset of NW formation has only taken place in low temperature regions (Fig. 2(d), close to the wafer edge). Regions closer to the wafer center, at higher temperatures, present the formation of small islands, namely the 3D precursors, which are formed in a nucleation stage prior to the steady state growth of NWs [11,12]. A clear decrease in density for higher substrate temperature is observed. Based on a detailed statistical analysis of the SEM pictures, diameter, length and length dispersion of NWs were determined as a function of temperature. In practice, images with less than 20 wires have been excluded from the analysis. Results are plotted in Fig. 3, which show the length and the length dispersion of the NWs as a function of temperature. NW length remains almost constant in most of the temperature range studied, with a rapid
Fig. 2. SEM micrographs of sample #1 taken in cross section (top) and top view (middle) from the sample edge (a, lower temperature), and two regions closer to the wafer center (b, c, higher temperature). Bottom: similar top view SEM micrographs of sample #2 taken from the sample edge (d, lower temperature), and two regions closer to the wafer center (e, f, higher temperature).
R. Mata et al. / Journal of Crystal Growth 334 (2011) 177–180
350
Mean length (nm)
300 250
100
200 150
50
Length dispersion (nm)
150
100 50 775
780
785 790 795 Temperature (°C)
800
0 805
Fig. 3. Variation of the mean length (dots) and of the length dispersion (triangles) of GaN NWs as a function of temperature. Lines are guides to the eyes.
28
#1
Mean diameter (nm)
#2 24 20 16 12 8 770
780
790 Temperature (°C)
800
810
Fig. 4. Variation of the mean diameter of the NWs (dots) and precursor islands (triangles) as a function of temperature. Lines are guides to the eyes.
decrease for temperatures larger than 790 1C, associated to the rapid increase in GaN decomposition rate in this temperature range [18]. Length dispersion increases with temperature, with a marked increase in the high temperature range. Similar statistical analysis for the diameter of samples #1 and #2 is shown in Fig. 4. The NWs’ diameter dependence with temperature is almost linear, with a marked decrease as the temperature is raised, reaching a value of E12 nm at the higher temperatures. Interestingly, it is found that the diameter of 3D precursor islands is almost constant (about 12 nm) and independent of temperature, increasing only slightly for the lowest temperatures, where NWs have already formed, which is assigned to the reduced nucleation delay in the low temperature range. This suggests that precursors have to reach a critical size before turning into NWs, consistent with data reported by Consonni and coworkers [19]. It also indicates that this critical size is not governed by nucleation kinetics. Indeed, it has been previously demonstrated that NW 3D precursors grown on Si(1 1 1) covered by a thin AlN buffer layer are plastically relaxed, consistent with the observation of misfit dislocations at the interface between the 3D precursor and the thin AlN buffer layer [11,12]. As shown by Furtmayr and coworkers, when no AlN buffer layer is used, the absence of wetting layer rather evidences that nucleation of GaN islands is of Volmer–Weber type [20]. Actually, the data of Landre´ and coworkers [11] as well as those presented here furthermore
179
suggest that with or without AlN buffer layer the 3D precursor size is governed by the elastic strain relaxation mechanism and not by kinetic considerations. More precisely, a detailed analysis of the NW nucleation process by X-ray diffraction performed in situ on NWs grown in an MBE machine connected to a synchrotron beam line at the European synchrotron research facility in Grenoble (France) is reported in Ref. [11]. The presence of three regimes has been established, namely a first stage corresponding to the nucleation of a wetting layer on the thin AlN buffer layer followed by a second stage associated with the size increase of 3D NW precursors, and finally a third stage corresponding to the steady state NW growth. Depending on Ga flux and substrate temperature, it was established that the duration of the second stage corresponding to precursor size increase ranged from a few seconds to almost one hour. During this stage, the amount of GaN deposited was found to vary as At2 þ d, t being the growth time. The exponent, 2þ d, of this supralinear regime was found to be in the range of 1.9–2.3, depending on Ga flux. According to the model developed by Osipov [21], this implies that the twodimensional size increase of NW precursors in the stage immediately following the deposition of the wetting layer is not isotropic but characterized by a rapid increase of the island diameter/perimeter till reaching a critical size associated with misfit dislocation formation at the AlN/GaN interface [11,12]. These results lead to the conclusion that the 3D precursor nucleation process, which depends on the areal density of Ga adatoms, will be controlled by both temperature and Ga flux. As the critical size of precursors giving rise to NW growth is only governed by an elastic energy relaxation process, this implies that the time spreading of the onset of steady-state NW growth will reflect the duration of the 3D precursor nucleation process till reaching their critical size. Consequently, a length dispersion of the NWs will be observed, as it is actually, associated to the duration of the 3D precursor nucleation process, which indeed increases with temperature. This qualitatively supports the hypothesis that at low temperature all 3D precursor islands are almost simultaneously formed and will reach the critical size for plastic relaxation at the same time, giving place to the continuous growth of NWs with the same length. On the contrary, at high temperature, the decrease in nucleation probability and the drastic increase in GaN dissociation rate both lead to a marked increase of the time elapsed between the formation of the first precursor having reached its critical size and the formation of the last one. Then, the onset of steady state growth of NWs is significantly scattered, reflecting the time duration of the precursor nucleation process and leading to the growth of wires with different lengths, presenting a much larger dispersion than those grown at lower temperature. Interestingly, it is worth noting that at low temperature, although it can be safely assumed that all 3D precursor islands are almost simultaneously formed, a NW length dispersion of about 12 nm is still observed (see Fig. 2a). This residual size dispersion is assigned to fluctuations inherent to the growth process itself. As a matter of fact, it is well known that GaN NWs is governed to a large extent by Ga diffusion in the basal plane and along the NWs’ side walls [16]. Then, random nucleation of NWs combined to shadow effects may lead to fluctuations in the amount of Ga atoms reaching the top of individual NWs, resulting in a residual size dispersion of about 5% in the present growth conditions.
3. Conclusion In summary, it appears on one hand that GaN NWs’ growth proceeds through the formation of 3D precursor islands, for which
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critical size before turning into NWs is independent of the growth temperature. However, on the other hand, both nucleation probability and size increase of these 3D precursor islands, which are kinetically driven processes, depend on growth temperature through the temperature dependence of Ga adatom density/ diffusion and of GaN dissociation rate. Then, as a consequence of the statistical nature of the nucleation process and of its marked temperature dependence, it is expected that the nucleation of 3D GaN precursors of NWs till reaching their critical size is actually occurring during a time span, the duration of which increases with growth temperature. This leads to a marked temperature dependence of the length dispersion of GaN NWs grown catalyst-free by MBE on Si(1 1 1). For practical applications requiring NWs with reduced length dispersion, the present study suggests to disconnect the nucleation stage, which should be performed at low/moderate temperature, from the steady-state growth stage, which could be performed at higher temperature in order to optimize structural/optical properties.
Acknowledgments This work has been supported by the funding awarded by the Ministry of Science and Innovation of Spain, FEDER (MAT2009010350). Support of French national research agency (ANR) program BONAFO is acknowledged. We are grateful to Y. Cure´ for technical assistance during experiments. References ˜ oz, [1] E. Calleja, M.A. Sanchez-Garcia, F.J. Sanchez, F. Calle, F.B. Naranjo, E. Mun U. Jahn, K. Ploog, Physical Review B 62 (2000) 16826.
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