GaN-based quantum dots

GaN-based quantum dots

Available online at Physica E 16 (2003) 244 – 252 GaN-based quantum dots Li Jiawei∗ , Ye Zhizhen...

518KB Sizes 2 Downloads 140 Views

Available online at

Physica E 16 (2003) 244 – 252

GaN-based quantum dots Li Jiawei∗ , Ye Zhizhen, N.M. Nasser State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou 310027, China Received 1 November 2001; accepted 11 October 2002

Abstract During the last few years e3cient light emitting devices have been developed from UV to IR in the III-N system, opening up a very large application 7eld. The problem with the present III-N emitters is the high defect (dislocation) density in the material produced to date. One approach to eliminate the in9uence of dislocations on light emitting structures is to use zero-dimensional quantum dot (QD) structures in the active part of the material. In this article, we will review the growth mode, methods and the types of III-N QDs achieved in the last few years and the applications of QDs in devices will be introduced 7nally. ? 2002 Elsevier Science B.V. All rights reserved. Keywords: GaN; Quantum dot; Growth; Application

1. Introduction Investigations of semiconductor quantum dots (QDs) have been very extensive, particularly in the last decade [1,2]. Compared with bulk (three-dimensional or 3D) materials and quantum well (QW) (two-dimensional or 2D) structures, QD is the prototype of zero-dimensional system. In brief, the electronic states in QD are spatially localized and the energy is fully quanti7ed. Due to the quantization, the atomic-like density of states near the band gap is higher than 3D and 2D systems, which can lead to a higher e3ciency for optical transitions. This is the most dazzling advantage of QDs for potential applications in light emitting and detecting devices. In addition, the QDs system is more stable against thermal perturbation. Furthermore, QDs strongly localize the carriers and inhibit their migration toward non-radiative centers such as dislocations. These ∗

Corresponding author.

properties have been achieved in many material systems such as group-VI (e.g., Ge/Si), III–V (e.g., InAs/GaAs) and II–VI (e.g., CdSe/ZnSe) [3]. III-nitride semiconductors are currently of great interest for applications in optical devices in the visible and ultraviolet (UV) energy range when GaN(3:4 eV) is alloyed with InN(1:9 eV) and AlN(6:2 eV) [4]. The progress of blue laser diodes (IDs) or blue– green light-emitting diodes (LEDs) are extremely remarkable in recent years [5–7]. High-power and long-lifetime InGaN multi-quantum well lasers have already been achieved [7]. In order to improve the performance of these devices and develop new optoelectronic devices, there is considerable interest now for studying III-nitride QD structures because of their unique physical phenomena. For instance, it is predicted that the use of III-nitride QDs in the active region of a laser could lead to a lower threshold current density due to the reduction of the density of states, since hitherto the lowest room-temperature threshold current density for a semiconductor laser has been obtained for a InAs QD (laser 26 A=cm2 ) [8].

1386-9477/03/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 9 4 7 7 ( 0 2 ) 0 0 6 6 9 - 0

L. Jiawei et al. / Physica E 16 (2003) 244 – 252


Fig. 1. Schematic diagram of the three possible growth modes: Frank-van der Merwe, Volmer-Weber, and Stranski-Krastinov (Ref. [10]).

2. Growth 2.1. Growth mode There are three diLerent modes in the equilibrium theory of material growth. As schematically shown in Fig. 1 [9,10], Frank-Van der Merwe mode represents a layer-by-layer or 2D growth. Volmer-Weber mode corresponds to island or 3D growth. Stranski-Krastanov (S-K) mode is 2D growth of a few monolayers, called wetting layer, followed by 3D island formation. The last mode is the one most relevant to the growth of semiconductor QDs that include the so-called strain-induced transition due to the large lattice or the surface energy mismatch between thin 7lms and substrates. In a lattice-mismatched system, the bulk elastic energy in the epilayer induced by strain plays an important role. Since it increases with layer thickness, a strain relaxation is expected when the layer thickness is increased beyond a critical value. In this case, the stress 7eld tends to force the atoms to coalesce. The strain energy can be partially released by the formation of islands through elastic relaxation, without any dislocations in the islands. The spontaneous growth of QDs by either 3D or S-K mode is known as the self-organized or self-assembled growth. In the researches of InGan/GaN QDs by Kim [11] and Damilano et al. [12], the process of the 2D–3D transition can be noticed clearly. Fig. 2(a) – (f) shows the AFM images of morphological evolution of InGaN thin 7lms grown at 800◦ C, which are dependent on

the growth times (thickness) from 0 to 3600 s. Typical surface shape for n-type GaN, including steps, terraces, and surface dislocations, is shown in Fig. 2(a). The small surface dislocations observed are 37 nm in size and 0.5 –1 nm in height. The density of surface dislocations is 4 –5 × 109 cm−2 , which shows good agreement with the dislocation density measured by TEM. Many of them lie along the step boundaries. As the nominal thickness of InGaN 7lms increase as from 0.15 (Fig. 2(b)) to 1.15 (Fig. 2(d)) nm, one can clearly see the 2D (corresponding to wetting layer) to 3D (self-assembled QD) transition, which is direct evidence of S-K growth mode of InGaN epilayer. For the case of QDs shown in the InGaN 7lm with the thickness of 0.57 and 1:15 nm, the average lateral size and height of dots are 73, 2 and 78, 3:7 nm, respectively. Widmann et al. [13] have studied the growth of GaN QDs on AlN and found the same phenomenon. In Fig. 3, the growth of GaN on the AlN layer is followed by re9ection high-energy electron diLraction (RHEED). During the 7rst 10 s of growth, no diLraction spots are observed: the growth remains 2D. After 10 s, a transition occurs: the roughness increases abruptly, and at the same time the lattice parameter rises towards a value closer to that of relaxed GaN. This behavior is assigned to island formation, following the completion of two monolayers critical thickness, corresponding to the 7rst 10 s of the growth. Before the transition, the growing GaN layer is strained and 2D. After the transition, the strain is relaxed elastically through the free surface of the


L. Jiawei et al. / Physica E 16 (2003) 244 – 252

Fig. 2. AFM images of InGaN 7lms with the growth time (nominal thickness) of (a) 0 s (0 nm), (b) 3 s (0.15 nm), (c) 12 s (0.57 nm), (d) 24 s (1.15 nm), (e) 48 s (2.3 nm), and (f) 3600 s (400 nm). Scan areas are 4 × 4 m2 (Ref. [11]).

Fig. 3. Variation, as a function of time, of the in-plane lattice parameter deduced from the spacing between the RHEED streaks (dots) and of the 3D character of the growth, deduced from the intensity of a Bragg diLraction spot (black line). Growth rate is 0:25 ML=s.

islands. This relaxation is not complete, since the variation is only 1.5% instead of 2.5%, as would be expected if GaN were totally relaxed on AlN. The size of the island might be of importance for whether all or only part of the strain is relaxed. This process of elastic strain relaxation through 3D islanding after completion of a thin 2D wetting layer is typical of a S-K growth mode. After island formation, one can observe that the roughness, as well as the lattice parameter, decreases. This is assigned to the

coalescence of the islands, which smoothes the surface. The free surface of the islands is reduced during their coalescence, and therefore the layer is strained again, leading to a decrease of the in-plane lattice parameter. The GaN relaxation process during the 7rst stages of growth is temperature dependent. At high temperature, the 2D–3D transition occurs, but after the island coalescence, the growth remains three 3D. At lower temperature, the transition is almost absent, and the layer remains two 2D and strained.

L. Jiawei et al. / Physica E 16 (2003) 244 – 252


In a word, III-nitride QDs follow a typical S-K growth mode mainly relating to the strain caused by the mismatch between QDs and substrate materials. 2.2. Growth methods The great majority of III-nitride QDs are grown by molecular beam epitaxy (MBE) and metalorganic chemical vapor deposition (MOCVD), since the high quality GaN and correlative devices have been carried out by these methods. The details will be displayed when we introduce the main types of GaN-based QDs in the next paragraph. Other growth methods such as laser ablation and reactive radio-frequency (r.f.) sputtering were also reported [14] but we do not want to introduce them here. 3. Types of III-Nitride QDs 3.1. InGaN quantum dots The InGaN alloy is presently used in the active region of high-brightness blue and green light emitting diodes (LEDs) and 0:4 m laser diodes (LDs). It is a singular semiconductor compound as its direct band gap covers the whole, visible spectrum from 0.36 to 0:65 m. Another peculiarity concerns the high e3ciency of InGaN/GaN quantum well (QW) heterostructures though they contain a huge density of dislocations. It has been proposed that in the case of MOCVD, InGaN alloy is inhomogeneous: In-rich clusters being formed. The latter induce deep potentials in the three dimensions (3D) that give rise to the formation of QDs. These objects trap the carriers and increase the radiative e3ciency because once the carriers are localized they can no longer diLuse toward the dislocations that are non-radiative recombination centers. Damilano et al. [15] have grown InGaN/GaN heterostructures by MBE on c-plane sapphire substrates. The growth of Ga1−x Inx N (x ¿ 12%) alloy has been extensively studied. The samples are grown on sapphire (0 0 0 1) substrates by MBE using ammonia as B-precursor and standard eLusion cells for the evaporation of group-III elements (Ga, In, Al). The active N species are produced by the pyrolysis of the NH3 molecules on the growing surface. A low temperature GaN buLer layer is deposited before the

Fig. 4. Schematic representation of the presence of small In-rich clusters regardless of the growth mode: Frank van der Merve (2D) and Stranski-Karstanov (2D–3D).

growth of a few m thick GaN template. The usual growth conditions for GaN are a substrate temperature of 800◦ C, an ammonia 9ux of 50 sccm, and a growth rate of 1 m=h. The InGaN layer are grown at 500 –550◦ C. They also use a very large NH3 9ux (200 sccm). At low V/III ratio, the growth undergoes a S-K transition giving rise to the formation of 3D islands. On the other hand, a high V/III ratio promotes the 2D layer-by-layer growth regime. The optical properties of Ga1−x Inx N (x ¿ 12%)=GaN heterostructures made from either a 3D InGaN layer or 2D InGaN layer are similar. This indicates that the mechanism responsible for the peculiar optical properties is intrinsically due to self-assembled QDs that may arise from In clustering in the InGaN alloy (see Fig. 4) regardless of the growth technique. Varying the InGaN layer thickness and keeping the In composition constant (16 ± 2)%, the InGaN/GaN QD heterostructures can cover the whole visible spectrum. Fig. 5 displays the 300 K PL spectra of InGaN samples that contain only one plane of QDs. The blue (451 nm), green (532 nm), red (656 nm) PL spectra correspond to InGaN thickness of 1.5, 3, and 5 nm, respectively. The strong PL intensity at 300 K despite the huge density of dislocations suggests a high radiative e3ciency. 3.2. GaN quantum dots Recently, GaN QDs in AlN matrix were grown by MBE on silicon (1 1 1) substrates [16]. The samples


L. Jiawei et al. / Physica E 16 (2003) 244 – 252

Fig. 5. Room temperature PL spectra of GaInN/GaN QD heterostructures for diLerent GaInN thicknesses: 1:5 nm (blue), 3 nm (green–yellow), 5 nm (red).

were grown in a RIBER growth system. The Nitrogen active species was NH3 . A double 7lament cell and a cold-lip cell were used for Ga and Al evaporation, respectively. Si(1 1 1) substrates were prepared in situ by rapid thermal annealing up to 900◦ C in order to remove the native oxide. When decreasing the temperature below 830◦ C, RHEED indicates a clear O thick AlN buLer 7 × 7 reconstruction. Then, a 300 A layer is deposited onto silicon at 900◦ C before the growth of a ≈ 1 m thick GaN template at 800◦ C. A 0:3 m thick AlN layer is further depsoited at 900◦ C. The variation of the in-plane lattice parameter measured in situ by RHEED indicates that this AlN is fully relaxed. This is an important point because the diLerence between GaN and AlN lattice parameters is at the origin of the GaN QD formation by strain induced 2D–3D transition. At the usual GaN growth temperature (∼ 800◦ C), no 2D–3D growth transition is observed when GaN is continuously deposited onto a relaxed AlN template. The growth remains 2D and the lattice mismatch-induced strain begins to be plastically relaxed after a critical thickness of 12 monolayers (ML) [17]. However, GaN islanding is observed under growth interruption for thicknesses larger than 3 ML: the RHEED pattern becomes instantaneously spotty with well de7ned (10 –13) facets. This indicates that the 2D–3D transition is kinetically hindered

Fig. 6. Room temperature photoluminescence spectra corresponding to diLerent sizes of GaN quantum dots. The corresponding Gaussian 7t of the spectra is shown in the inset. The peak energy shifts from 3.18 to 2:13 eV when increasing the QD size.

during growth. Such a QD formation process allows one to easily control the QD size by simply varying the amount of GaN deposited. The constraint is to deposit more than 3 ML to get islanding and less than 12 ML to avoid plastic relaxation. Fig. 6 displays the room temperature PL spectra of diLerent GaN/AlN QD size samples. The PL energies vary from 3.18 to 2:13 eV corresponding to GaN nominal thickness ranging from 5 to 12 ML. This energy range covers almost the whole visible spectrum although the room temperature band gap energies are 3.4 and 6:2 eV for unstrained GaN and AlN. This fact can be explained by the presence of a very strong electric 7eld in QDs due to both piezoelectric and spontaneous polarization effects [18,19]. The relationship between the integrated photoluminescence intensity and the QD stacked layer number was reported in Fig. 7. This allows to estimate the optimum QD stacking for which the PL intensity saturates: for 100 QD layers, the PL intensity reaches ∼ 95% of the expected maximum value for an exciton wavelength at 244 nm. The PL intensity of samples with 40 QD planes despite grown on Si(111) or c-plane sapphire substrate is equivalent, whereas the dislocation density is higher when GaN is grown on Si(111) than on sapphire. This is the con7rmation that the QD density is much larger than the dislocation

L. Jiawei et al. / Physica E 16 (2003) 244 – 252

Fig. 7. Variation of the integrated photoluminescence intensity as a function of the QD stacked layer number. The solid squares correspond to samples grown on silicon (1 1 1) and the open square to a sample grown on sapphire (0 0 0 1).

density for both cases, and that localization in the dots is an e3cient way of 7ltering non-radiative paths due to dislocations. 3.3. AlGaN quantum dots Hirayama et al. [20] have demonstrated the 7rst fabrication of self-assembling AlGaN QDs on AlGaN surfaces using MOCVD. The QDs were fabricated using a growth mode change from 2D step-9ow growth to 3D island formation by modifying the surface energy balance of AlGaN with a Si anti-surfactant. Contrary to S-K growth mode, the QD formation using this method is based on the surface energy balance. Then, this method is especially useful for QD formation on the interfaces of small lattice mismatch system. The formation of AlGaN QDs on AlGaN surfaces is relatively di3cult in comparison with the cases of GaN or InGaN QDs, because AlGaN easily forms a 7lm on GaN or AlGaN surfaces due to large surface energy of AlGaN. The use of Si anti-surfactant was not enough to obtain a growth mode control to 3D nano-scale dot formation in high growth temperature. In addition to the use of anti-surfactant, they reduced the growth temperature of AlGaN QDs in order to control the migration of precursors on AlGaN surface.


The structures were grown, at 76 Torr on the Si-face of an on-axis 6H-SiC(0001) substrate, by a conventional horizontal-type MOVPE system. As precursors ammonia (NH3 ), tetraethylsilane (TESi), trimethylaluminium (TMAl), and trimethylgallium (TMGa) were used with H2 as carrier gas. N2 gas was also independently supplied by a separate line and mixed with the H2 just before the substrate susceptor. Typical gas 9ows were 2 standard liters per minute (SLM), 2SLM, and 0.5SLM for NH3 ; H2 , and N2 , respectively. The molar 9uxes of TMG and TMA of Al0:38 Ga0:62 N growth for buLer and capping layers were 38 and 13 mol=min, respectively. At this condition, the growth rate was approximately 2:5 m=h. The molar 9uxes of TMG and TMA of Al0:05 Ga0:95 N growth for fabrication of QD structure were 7.2 and 0:47 mol=min, respectively. The growth rate used for QD formation was approximately 0:4 m=h. In order to achieve a surface suitable for growth of AlGaN QDs, 7rst an approximately 400-nm-thick Al0:38 Ga0:62 N buLer layer was deposited on a 6H-SiC substrate at 1140◦ C. The buLer layer was found to provide a step-9ow grown surface as con7rmed by atomic force microscopy (AFM). Prior to the Alx Ga1−x N dot growth, TESi was intentionally supplied for the deposition of silicon anti-surfactant modifying the surface properties at 1140◦ C. Then the sample was cooled to the Alx Ga1−x N dot growth temperature, i.e., around 900◦ C. The Alx Ga1−x N QDs were grown by a short supply of TMAl/TMGa using H2 as carrier gas. The equivalent layer thickness, based on the growth rate, was determined to be 3 nm. This resulted in a 3D nano-scale island growth which was not observed in the case without any silicon dose. Then an approximately 5-nm-thick Al0:38 Ga0:62 N capping layer was grown on Alx Ga1−x N QDs. Fig. 8(a) – (d) shows the AFM images just after the growth of Al0:05 Ga0:95 N on Si-deposited surfaces. The growth temperature Tg and the Si-dose amount are 1100◦ C and 0:04 mol; 1100◦ C and 0:2 mol; 900◦ C and 0:04 mol, and 900◦ C and 0:2 mol for Fig. 8(a), (b), (c) and (d), respectively. Three-dimensional growth is seen in the samples using anti-surfactant. For high growth temperature of 1100◦ C, nano-scale dot structures were not obtained as shown in Fig. 8(a) and (b). Therefore, the surface energy control by using Si anti-surfactant was not enough to obtain a growth mode change to 3D nano-scale QD formation


L. Jiawei et al. / Physica E 16 (2003) 244 – 252

Fig. 8. AFM images just after the growth of Al0:05 Ga0:95 N on Si deposited surfaces. The growth temperature Tg and the Si-dose amount are (a) 1100◦ C and 0:04 mol, (b) 1100◦ C and 0:2 mol, (c) 900◦ C and 0:04 mol, and (d) 900◦ C and 0:2 mol.

L. Jiawei et al. / Physica E 16 (2003) 244 – 252

for AlGaN. On the other hand, the AlGaN dot was controlled to nano-scale structure by reducing the QD growth temperature to 900◦ C as seen in Fig. 8(c) and (d). The average lateral size and the height of fabricated AlGaN dots grown at 900◦ C were estimated to be approximately 20 and 6 nm, respectively, by AFM views. The dot density is found to be controlled from 5 × 1010 cm−2 down to 2 × 109 cm−2 by increasing the dose of Si anti-surfactant from 0.04 to 0:2 mol. Using the same method (Si as anti-surfactant), GaN and InGaN QD on AlGaN surfaces have also been obtained successfully [21,22]. Peter [23] and Kuball et al. [24] have reported the optical properties and resonant Raman scattering of GaN QDs, respectively. 4. Application for light emitters III-nitrides (III-N) form a novel interesting materials system for light emitters, covering the entire photon energy region from UV to IR. During the last few years e3cient light emitting diodes (LEDs) have been developed from blue to yellow in the III-N system, opening up a very large application 7eld. More recently more demanding laser diodes (LDs) in the violet region have been developed, and now are also commercially available. Large application volumes are projected for such lasers, e.g. for DVD disk players or printing/copier applications. The problem with the present III-N emitters is the high defect (dislocation) density in the material produced to date. In LEDs the dislocation density is typically 109 –1010 cm−2 , while for lasers this density needs to be reduced considerably, at present to a level of about 106 –107 cm−2 . The reason for the high defect density is that no GaN substrates have been developed, instead the III-N structures are grown on foreign substrates (typically sapphire) with a very large lattice mismatch. The development of GaN substrates has just begun, but it will take many years before they are commercially available, therefore innovative solutions are needed to diminish or eliminate the deleterious in9uence of dislocations on heteroepitaxially grown III-N device structures. One approach to eliminate the in9uence of dislocations on light emitting structures is to use


zero-dimensional quantum dot (QD) structures in the active part of the material. Provided the injected carriers in the structure can be e3ciently captured into the QDs, the recombination will be radiative, and largely independent of parasitic nonradiative recombination at dislocations. III-N QD structures are investigated for light emitting applications in the UV range. The visible range LEDs now on the market give a rather good e3ciency based on the principle of localization of carriers (excitons) in rather strong localization potentials inside an InGaN MQW structure before recombination, so that the nonradiative recombination at dislocations can be largely avoided. In the UV region, attempts have been made to use QWs with GaN as the active region material, but because of a more limited localization at RT the e3ciency remains much worse than with InGaN LEDs. Therefore the QD approach, using GaN QDs, seems promising, and interesting preliminary results have been reported in PL data. The presence of very strong polarisation 7elds in the III-N material structures has been shown to aLect the QW PL emission dramatically, so that the upward energy shift due to the QD con7nement is completely oLset, and a wide range of energies downshifted from the GaN band gap can be obtained in such QD structures. Regarding LDs, despite the successful realization of blue LDs by Nakamura et al., serious problems are still to be overcome, related to the lack of an adapted substrate. In particular, a reduction in the number of crystallographic defects is highly desirable in order to improve the lifetime and to reduce the threshold current of the LDs. This is partly achieved through the recent development of lateral overgrowth for GaN, which leads to the reduction of the dislocation density by several orders of magnitude. Alternatively, the realization of devices with quantum dots (QDs) in the active layer appears promising, based on the theoretical prediction of a low threshold current and of a weak temperature dependence of the threshold current. Furthermore, due to the reduced size of the QDs, they are expected to be virtually perfect, with most crystallographic defects out of the dots, which should result in a decrease in non radiative recombination. Temperature-dependent PL performed on diLerent InGaN/GaN heterostructures is a clear evidence of the higher radiative e3ciency of QDs compared to true QWs [25].


L. Jiawei et al. / Physica E 16 (2003) 244 – 252

Acknowledgements This work has been supported under the auspices of the National Key Project for basic research on “basic problems of information function materials” (G2000068306). References [1] A.D. YoLe, Adv. Phys. 50 (2001) 1. [2] D. Bimberg, M. Grundmann, N. Ledentsov, Quantum Dot Heterostructures, Wiley, Chichester, 1999. [3] J.M. Gerard, O. Cabrol, B. Sermage, Appl. Phys. Lett. 68 (1996) 3123. [4] S. Nakamura, G. Fasol, The Blue Laser Diode, Springer, Heidelberg, 1997. [5] S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimoto, H. Kiyoku, Jpn. J. Appl. Phys. 36 (1997) L1059. [6] S. Nakamura, T. Mukai, M. Senoh, Appl. Phys. Lett. 64 (1994) 1687. [7] S. Nakamura, M. Senoh, S. Nagahama, Appl. Phys. Lett. 69 (1996) 3034. [8] G.T. Liu, A. Stintz, H. Li, Electron. Lett. 35 (1999) 1163. [9] V.A. Shchukin, D. Bimberg, Rev. Mod. Phys. 71 (1999) 1125. [10] D.J. Eaglesham, M. Cerullo, Phys. Rev. Lett. 64 (1990) 1943.

[11] K.S. Kim, C.-H. Hong, W.-H. Lee, MRS-000232. [12] B. Damilano, N. Grandjean, J. Massies, F. Semond, Appl. Surf. Sci. 164 (2000) 241. [13] F. Widmann, B. Daudin, G. Feuillet, et al., MRS V 2, Article 20. [14] T.J. Goodwin, V.L. Leppert, H. Risbud, et al., Appl. Phys. Lett. 70 (1997) 3122. [15] B. Damilano, N. Gradjean, J. Massies, et al., Phys. Stat. Sol. (A) 180 (2000) 363. [16] B. Damilano, N. Gradjean, F. Semond, et al., Phys. Stat. Sol. (B) 216 (1999) 451. [17] B. Damilano, N. Gradjean, F. Semond, et al., Appl. Phys. Lett. 75 (1999) 962. [18] F. Bernardini, V. Fiorentini, D. Vanderbilt, Phys. Rev. B 56 (1997) R10024. [19] F. Widmann, J. Simon, B. Daudin, et al., Phys. Rev. B 58 (1998) R15989. [20] H. Hirayama, Y. Aoyagi, S. Tanaka, MRS Internet J. Nitride Semicond. Res. 4s1 (1999) G9.4. [21] S. Tanaka, S. Iwai, Y. Aoyagi, Appl. Phys. Lett. 69 (1996) 4096. [22] H. Hirayma, S. Tanaka, P. Ramvall, et al., Appl. Phys. Lett. 72 (1998) 1736. [23] P. Ramvall, P. Riblet, S. Nomura, et al., J. Appl. Phys. 87 (2000) 3883. [24] M. Kuball, J. Gleize, Satoru Tanaka, et al., Appl. Phys. Lett. 78 (2001) 987. [25] N. Grandjean, B. Damilano, J. Massies, et al., Solid State Commun. 113 (2000) 495.