Secondary-ion-mass spectrometry and high ...

Secondary-ion-mass spectrometry and high-resolution x-ray diffraction analyses of GaSb–AlGaSb heterostructures grown by molecular beam epitaxy C. Gerardi, C. Giannini, L. De Caro, L. Tapfer, Y. Rouillard et al. Citation: J. Vac. Sci. Technol. B 19, 836 (2001); doi: 10.1116/1.1372926 View online: http://dx.doi.org/10.1116/1.1372926 View Table of Contents: http://avspublications.org/resource/1/JVTBD9/v19/i3 Published by the AVS: Science & Technology of Materials, Interfaces, and Processing

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Secondary-ion-mass spectrometry and high-resolution x-ray diffraction analyses of GaSb–AlGaSb heterostructures grown by molecular beam epitaxy C. Gerardi,a) C. Giannini, L. De Caro, and L. Tapferb) Centro Nazionale Ricerca e Sviluppo Materiali (PASTIS-CNRSM), Strada Statale 7 ‘‘Appia’’ 72100 Brindisi, Italy

Y. Rouillard,c) B. Jenichen, L. Da¨weritz, and K. H. Ploog Paul-Drude-Institut fu¨r Festko¨rperelektronik, Hausvogteiplatz 5-7, 10117 Berlin, Germany

共Received 11 August 2000; accepted 26 March 2001兲 Secondary-ion-mass spectrometry and high-resolution x-ray diffraction are used to investigate Alx Ga1⫺x Sb/GaSb heterostructures (0.2⬍x⬍1) grown by molecular beam epitaxy. We show that the AlCs⫹ and GaCs⫹ intensities, obtained by using caesium cluster secondary-ion-mass spectrometry mode, vary linearly with the relative concentrations, and therefore, allows us to evaluate quantitatively the aluminum and gallium contents in the epitaxial layers. Intermixing of Ga/Al species at the GaSb/AlSb interfaces could be clearly detected by secondary-ion-mass spectrometry and is also confirmed by high-resolution x-ray diffraction. The intermixing is the result of a particular mechanism in order to minimize the strain energy, and occurs prior to the lattice relaxation, which generates structural defects taking place. The analyses also give evidence of a constant arsenic contamination 共⬃0.5%兲 both in the GaSb buffer and in the Alx Ga1⫺x Sb layers. In fact, As contamination occurs if the molecular beam epitaxy chamber has been used previously for the growth of As-compound materials. We show that the signal obtained by using the caesium cluster secondary-ion-mass spectrometry mode AsCs⫹ is nearly unaffected by the changes of the Al content throughout the total structure 共matrix effects兲 contrary to what occurs for single As ions. © 2001 American Vacuum Society. 关DOI: 10.1116/1.1372926兴

I. INTRODUCTION AlGaSb material attracts great attention due to the optoelectronic device applications in the 1.3–1.55 ␮m infrared range corresponding to the wavelength interval of low losses in the optical fibers communication field.1–4 Very recently, growing attention was directed toward these materials because of their superior performances compared to the quaternary GaInAsP heterostructures. However, the accurate control of the epitaxial growth process of this material system is still the subject of extensive research both from a scientific as well as a technological point of view.5 For microstructural and microanalytical characterization of heterostructures, secondary-ion mass spectrometry 共SIMS兲 is a suitable and highly accurate technique, even more so if used in combination with a complementary technique such as high-resolution x-ray diffraction 共HRXRD兲.6 In addition, good depth resolution 共1–2 nm兲 can be achieved by SIMS using low energy sputtering in order to minimize the ion beam induced relocation effects. In some cases, this resolution can be sufficiently high and accurate to quantify the spreading of interdiffusion at the heterostructure interfaces.7 Moreover, extensive use of cluster caesium analysis 共commonly known as MCs⫹ 兲 performed by analyzing the molecua兲

Present address: ST Microelectronics, Central R&D, Stradale Primosole 50, Catania, Italy. b兲 Electronic mail: [email protected] c兲 Present address: CEM2, Universite` Montpellier II, Place Euge`ne Bataillon, Montpellier, France. 836

J. Vac. Sci. Technol. B 19„3…, MayÕJun 2001

lar ion clusters, which are formed after the sample is bombarded with the caesium atoms, demonstrated that in several cases SIMS can achieve a high accuracy 共about ⫾2%8兲 in the determination of major element concentrations by reducing or eliminating the matrix effects. In this work, we investigate GaSb/Alx Ga1⫺x Sb/GaSb heterostructures grown on 共100兲GaSb substrates by molecular beam epitaxy 共MBE兲 combining high-resolution and caesium cluster SIMS with HRXRD. We show that the use of caesium cluster SIMS allows us to minimize the matrix effects and, consequently the AlCs⫹ and GaCs⫹ intensities vary linearly with the relative concentrations. Therefore, a quantitative evaluation of the Al and Ga contents in the layers is possible. In addition, we monitored the As contamination and we found that the incorporation of As in the epitaxial layers is almost independent from the Al concentration. A pronounced Ga–Al interdiffusion effect has also been detected by SIMS analyses performed both with the MCs⫹ scheme and by using a low energy oxygen primary beam 共2 keV兲 that allows us to reach a better depth resolution by minimizing the collisional effects. II. EXPERIMENT The investigated Alx Ga1⫺x Sb heterostructures were grown by MBE at a growth temperature of 470 °C and a constant growth rate of 1 ␮m/h. The V/III flux ratio was kept constant at the value of 2. A detailed description of the growth procedure has been given elsewhere.9 It is very im-

1071-1023Õ2001Õ19„3…Õ836Õ7Õ$18.00

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Gerardi et al.: SIMS and high-resolution XRD analyses

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portant to note, that nonintentional incorporation of As in the antimonide materials occurs if the group III antimonides are grown in the same MBE chambers that were used previously for the growth of group III arsenides. In fact this contamination has been observed and reported by several authors.10–13 Under this condition we cannot neglect this aspect since previously our MBE chamber has been also used for the growth of group III arsenide materials. The typical layer sequence of the investigated heterostructures comprises a 共100兲GaSb substrate, a 1-␮m-thick GaSb buffer, a 150-nm-thick Alx Ga1⫺x Sb (0.2⬍x⬍1), and a GaSb cap layer of about 5 nm thickness. In addition, we examined a multilayer consisting of a 共100兲GaSb substrate and three AlGaSb layers of different Al content. Here, the AlSb layer is grown first directly on the GaSb substrate in order to prevent oxidation of the Al-rich layer after the whole sample is exposed to air. SIMS analyses were carried out on a CAMECA ims 4 f instrument using either O⫹ 2 ions of 2 or 5.5 keV energy or 5.5 keV Cs⫹ ions with off-normal impacting angles of 55° 共2 keV兲 and 42° 共5.5 keV兲, respectively. The three different conditions were chosen in order to improve the depth resolution, to better detect the arsenic signal, and to reduce the matrix effects. The quantification of Al and Ga was performed by the above mentioned caesium cluster analysis. The arsenic contamination was detected by analyzing either the single As⫹ ions or the AsCs⫹ clusters. The primary beam currents were chosen in the range of 20–60 nA. The secondary ions were collected through an aperture that delimited the analyzed area in the center of the eroded area 共250⫻250 ␮m2兲. For high-resolution measurements 共2 keV O⫹ 2 兲 the analyzed area was a circle 8 ␮m in diameter in order to avoid artifacts due to bottom crater rounding. For the cesium cluster analysis, used for the quantitative analysis, the diameter of the analyzed section was about 60 ␮m in diameter. The erosion rate was estimated by measuring the sputtered depth in the different matrices by using a stylus profilometer 共TENCOR-alphastep兲. HRXRD analysis was performed by means of a multicrystal x-ray diffractometer and using a Cu target 共Cu K ␣ radiation兲 as an x-ray source. A four-crystal channel-cut Ge 共220兲 crystal is used as a monochromator and collimator. The x rays impinging on the sample surface have a divergence of 12 arc sec and the wavelength dispersion is estimated to be 2.5⫻10⫺5 . The diffracted x-ray intensity is measured by a proportional counter.

FIG. 1. SIMS depth profiles on a GaSb/Alx Ga1⫺x Sb/GaSb heterostructure with nominal mole fraction x⫽0.2. Measurements are performed by using a 5.5 keV, 42° caesium beam, and monotoring AlCs⫹ , GaCs⫹ , and AsCs⫹ ions, respectively.

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III. RESULTS AND DISCUSSION A. Quantitative analysis of arsenic and chemical composition of the epilayers

The SIMS profiles of Al, Ga, and As elements recorded by the caesium cluster mode on a GaSb/Alx Ga1⫺x Sb/GaSb heterostructure with x⫽0.2 are shown in Fig. 1. The transient region at the sample surface in which the SIMS signal is not stabilized takes a great part of the cap layer which has a thickness comparable with the projected range of the implanted caesium ions. The presence of a significant As con-

tamination can be clearly detected throughout the whole epitaxial structure. The As is incorporated into the GaSb buffer layer as well as in the Alx Ga1⫺x Sb layer which, in fact, results in a ternary GaAsy Sb1⫺y and quaternary Alx Ga1⫺x Asy Sb1⫺y compound, respectively. Using x-ray diffraction we measured via Vegard’s rule 共which states a linear relationship between lattice constant and mole fraction of a crystalline compound semiconductor兲14 the As content in the buffer layer which was 0.5 at. %. As it can be observed, there is a 14% increase in the arsenic signal intensity from the buffer GaAs layer into the Alx Ga1⫺x Sb layer. However, this signal intensity increase cannot be attributed to a difference in the erosion rate between the GaSb and the Alx Ga1⫺x Sb (x⫽0) matrix only. It is very likely that a small matrix effect could still exist passing from the GaSb matrix (x⫽0) to the Alx Ga1⫺x Sb matrix (x⫽0). Nevertheless, the very small variations in the arsenic intensity for the Alx Ga1⫺x Sb layers in the mole fraction range 0.2⬍x⬍1 of the investigated samples can be ascribed to the changes in the sputter yield related to the different aluminum content of the epitaxial layers. Figure 2 shows the measured erosion rate versus the Al content in the epilayers. On the contrary, in the analysis of the single arsenic ions, the different Alx Ga1⫺x Sb layers show strong differences in the As intensity clearly caused by matrix effects induced by the increase of the aluminum concentration. Figures 3共a兲 and 3共b兲 compare the arsenic profiles obtained as As⫹ and AsCs⫹ for three Alx Ga1⫺x Sb layers with x⫽0.2, 0.6, and 1, respectively. The analysis with caesium clusters shows that the arsenic contamination is almost constant throughout the thickness of the epitaxial layers with almost the same level

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FIG. 2. Erosion rate vs aluminum content in Alx Ga1⫺x Sb epitaxial layers for different x as determined experimentally by using 5.5 keV Cs⫹ ions.

of the nominal GaSb buffer. In summary, SIMS analyses demonstrate a constant As incorporation in the whole heterostructure yielding a GaSb/Alx Ga1⫺x As/GaSb GaAsy Sb1⫺y /Alx Ga1⫺x Asy Sb1⫺y /GaAsy Sb1⫺y structure. The actual stoichiometry of the epilayers was determined by means of HRXRD.14 Figures 4 and 5 show the 共400兲 experimental 共A兲 and simulated 共B兲 HRXRD spectra of the samples with a nominal AlSb mole fraction of x⫽0.6 and x⫽1, respectively. The experimental curves 共A兲 were simulated 共B兲 by using the dynamical theory of x-ray diffraction for distorted crystals.15 The GaSb buffer peaks are located at a higher diffraction angle with respect to the GaSb substrate peaks indicating a reduced lattice parameter for the buffer layer unit cell. The reduction of the lattice parameter can be explained by the incorporation of As atoms in the host lattice, i.e., Sb atoms are partially substituted by As atoms.9 The angular separation between buffer layer and substrate peaks allows us to determine the strain and, consequently, the Sb:As ratio in the buffer by applying Vegard’s rule.14 In addition, it is possible to determine the Sb content in the epilayer quaternary compound by using the As content determined from the strain field of the GaSb buffer layer. The analysis is based on the constant As incorporation into the whole structure as observed by SIMS. Experimental and simulated x-ray patterns are in excellent agreement. It is important to note that all the heterostructures investigated here are pseudomorphic, i.e., the in-plane strain of the epitaxial layers is zero, as confirmed by asymmetric diffraction measurements performed around the 共135兲 and 共335兲 reciprocal lattice points. Considering the lattice mismatch of f ⫽0.0065 between AlSb (a⫽0.613 53 nm) and GaSb (a ⫽0.609 593 nm) a critical thickness h c of about 20 nm can be expected from the Matthews–Blakeslee as well as from the Dodson–Tsao model.16 Our findings show, however, that the critical thickness is above 150 nm, which is in agreement

FIG. 3. SIMS profiles for three different GaSb/Alx Ga1⫺x Sb/GaSb heterostructures of different mole fraction x 共No. 791: x⫽0.2, No. 799: x⫽0.6, ⫹ No. 797: x⫽1兲 as obtained by O⫹ 2 bombardment–As secondary ions 共a兲 and Cs⫹ bombardment–AsCs⫹ secondary ions detection 共b兲, respectively.

with the experimental value of h c ⫽154 nm reported by Villaflor and Kimafe.17 The appearance of the interference fringes due to the finite thickness of the quaternary epitaxial layer indicates the good structural quality of the epilayers. In the case of lattice relaxation no interference fringes would be observed because the structural defects destroy the long distance lattice periodicity. The chemical composition values of the Alx Ga1⫺x Asy Sb1⫺y epilayers used for the x-ray simulation are summarized in Table I. In fact, even the sample with a nominal AlSb mole fraction x⫽1 共Fig. 5兲 was treated as a quaternary compound because of the Ga interdiffusion detected by SIMS as will be discussed in Sec. III B. B. Ga–Al intermixing at GaSbÕAlSb interfaces

The SIMS depth profiles of Ga and Al recorded on the sample with a nominal AlSb mole fraction x⫽1 are shown in Fig. 6. A pronounced tail on the gallium signal extending

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FIG. 4. Experimental 共A兲 HRXRD pattern close to the 共400兲GaSb reciprocal lattice point of the heterostructure grown onto the 共100兲GaSb substrate and consisting of a nominally pure GaSb buffer layer 共1 ␮m thick兲, a Alx Ga1⫺x Sb epitaxial layer 共nominal mole fraction x⫽0.6兲, and a 5-nmthick GaSb cap layer. The simulated x-ray diffraction pattern 共B兲 is obtained by using a dynamical diffraction model and the appropriate thickness, lattice strain, and chemical composition parameters 共see the text兲.

FIG. 5. Experimental 共A兲 high-resolution x-ray diffraction pattern close to the 共400兲GaSb reciprocal lattice point of the heterostructure grown onto the 共100兲GaSb substrate and consisting by a nominally pure GaSb buffer layer 共1 ␮m thick兲, a nominally pure AlSb epitaxial layer, and a 5-nm-thick GaSb cap layer grown on 共100兲GaSb. The simulated x-ray diffraction pattern 共B兲 is obtained considering: 共i兲 a 0.5% contamination of As in the GaSb buffer and the AlGaSb epitaxial layer and 共ii兲 a Ga interdiffusion from the GaSb cap layer in the AlGaSb epilayer, which results in a Ga contamination of about 9.3%.

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from the cap layer into the AlSb layer can be well observed 共see arrow in Fig. 6兲. The Ga distribution gradient within the AlSb layer was taken into account in the chemical analysis performed by HRXRD 共see Table I兲. In order to investigate the Ga–Al intermixing at the heterointerface we also analyzed a multilayer structure consisting of the three Alx Ga1⫺x Sb layers with different Al concentrations. The nominal layer sequence, schematically shown in the inset of Fig. 7, is the following: on a 共100兲GaSb substrate a 150-nm-thick AlSb layer is grown directly without the buffer layer, followed by a 150-nm-thick Al0.6Ga0.4Sb and a 150-nm-thick Al0.3Ga0.7Sb layer. Figure 7 shows the symmetrical 共400兲 x-ray diffraction pattern of the multilayer structure. The three AlGaSb layer peaks correspond to the different lattice mismatch, i.e., different Al content, and are well observed at a lower diffraction angle with respect to the GaSb substrate peak. In this sample structure no GaSb buffer layer has been grown and, therefore, the As-contaminated GaSb buffer peak is not observed. Nevertheless, on the basis of the results discussed in Sec. III A, it is reasonable to assume a constant and uniform 0.5% contamination of As also in this multilayer structure. The diffraction peaks A, B, and C in Fig. 7 correspond to an Al concentration of 0.27, 0.57, and 1, respectively.

Due to the low matrix effect, the SIMS signals vary almost linearly with the concentrations in the layers. The Al, Ga, and Sb depth profiles recorded with 5.5 keV Cs⫹ are shown in Fig. 8. The quantitative Al profile is shown in Fig. 9. It has been obtained from the raw profiles of Fig. 8, using the calibration factors obtained from the x-ray diffraction measurements 共see data in Table I兲 on the heterostructures composed of a single epitaxial layer and by normalizing the Al intensity to the Sb intensity 共both the signal intensities change兲. Contrary to what occurs for the layers with x⫽0.26 and 0.57, a nonTABLE I. Chemical compositions of the Alx Ga1⫺x Asy Sb1⫺y epilayers as determined from x-ray simulations. Elements Sample No.

Al

Ga

Sb

As

791 800 799 796 797

0.147 0.291 0.473 0.675 0.907

0.853 0.709 0.527 0.325 0.093

0.995 0.9943 0.9948 0.9939 0.9946

0.005 0.0057 0.0052 0.0061 0.0054


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FIG. 6. SIMS depth profiles on the sample with a nominally pure AlSb 共mole fraction x⫽1兲 epilayer sandwiched between a GaSb buffer and thin GaSb cap layer grown onto 共100兲GaSb 共see Table I兲.

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FIG. 8. SIMS depth profiles in the cesium cluster mode of Al, Ga, and Sb, recorded on a heterostructure consisting of three layers of AlGaSb with nominal mole fraction x⫽0.3, 0.6, and 1, respectively, deposited onto a 共100兲GaSb substrate.

uniform concentration is observed in the layer with x⫽1. We attribute this variation to the intermixing effects involving Ga and Al. Also by reducing the primary beam energy in order to minimize the ion beam collision effects, the broadening of the Al signal at the interfaces is still evident. In fact, Fig. 9

FIG. 7. Symmetrical 共400兲 high-resolution x-ray diffraction pattern of the three-layer heterostructure with different Al content. The peaks labeled by A, B, and C refer to the AlGaSb layers with AlSb mole fraction 0.26, 0.57, and 1, respectively. The As concentration is constant within all three layers and is about 0.5%.

FIG. 9. Quantitative Al profile is obtained from the raw profiles 共Fig. 8兲 and by using the calibration factors obtained from x-ray diffraction experiments 共Table I兲. The arrow indicates the Al depletion at the interface at which the Ga interdiffusion is particularly evident.


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plots the Al profile, as recorded on the same multilayer with 2 keV O⫹ 2 , showing the persistence of the intermixing effect. For the layer with the nominal x Al⫽1 we can clearly observe a reduced Al concentration close to the upper interface at a depth 380–400 nm from the sample surface 共marked by the arrow in Fig. 9兲. Problems related to interdiffusion and/or segregation effects have been widely reported in III–V semiconductor alloys, in particular for the InGaAs/GaAs system. These phenomena affect the optical properties because of the modification induced on the potential profile by the changes in the interface shape and in addition may also be the origin of a structural deterioration and defect generation at the heterointerfaces. Modifications of the potential profile of AlGaSb–GaSb quantum wells have been observed as the growth temperature is raised, but it is not clear what the cause of this effect is. Segregation of Al or Ga or other interdiffusion mechanisms have been argued. Here, the problem is different with respect to the InGaAs/GaAs structure, where the difference of binding energy and the compressive biaxial strain work in the same direction as a driving force to induce an accumulation of indium at the surface. In the AlGaSb/GaSb system the binding energy difference between GaSb and AlSb should favor the Ga migration, while the strain associated with the incorporation of Al would promote the Al migration.4 It is well known that at heterointerfaces of highly mismatched materials a compositional gradient is formed in order to minimize the strain energy. Here, the intermixing of the chemical species is a competitive mechanism to the generation of structural defects in order to reduce the lattice strain.18 Consequently, the high lattice strain is reduced by forming thin layers of different chemical composition and by subsequent generation of structural line defects.19 In fact, the critical thickness of AlSb grown on 共100兲GaSb is 14 nm as experimentally determined, but a gradual lattice relaxation up to a layer thickness of 100 nm has been observed.16 In our samples, the AlSb layer thickness is about 150 nm, i.e., beyond the critical thickness. Therefore, it is very likely that this gradual relaxation is associated with the Ga–Al intermixing at the GaSb/AlSb interface observed by SIMS. It should also be mentioned that the pronounced Ga–Al intermixing has been observed by SIMS only in GaSb/AlSb, indicating that only in this case is the lattice mismatch high enough to promote the group-III intermixing. Our findings are also in agreement with the far-infrared reflection measurements on GaSb/AlSb superlattices that could be explained only by considering a Ga/Al intermixing at the heterointerfaces.20 Actually, we directly detect by high-resolution profiling that the intermixing for the GaSb/AlSb system occurs in the substrate temperature range 570–600 °C. In particular, Ga strongly diffuses towards the substrate direction when GaSb is deposited onto AlSb layers changing the matrix to a ternary AlGaSb compound close to the GaSb/AlSb interface.

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IV. CONCLUSIONS We analyzed the chemical composition of MBE-grown GaSb/Alx Ga1⫺x Sb/GaSb heterostructures by using SIMS experiments. In addition, we investigated the chemical distribution at AlGaSb/GaSb heterointerfaces. By means of the caesium cluster spectrometry we obtained secondary ion yields which are negligibly affected by the matrix effects and, therefore, in combination with HRXRD experiments, we could determine the actual relative concentration of Al and Ga. These results demonstrate that the caesium cluster spectrometry is very effective for an accurate characterization of the GaSb–AlGaSb system. We found a constant 0.5% arsenic contamination throughout the GaAsy Sb1⫺y /Alx Ga1⫺x Asy Sb1⫺y /GaAsy Sb1⫺y heterostructures independently from the Al/Ga content in the epitaxial layers. The As contamination must be taken into account in the MBE growth of AlGaSb, if the same growth chamber has also been used for the growth of As-based heterostructures. Finally, SIMS profiling reveals a strong Ga diffusion in the AlSb at the GaSb/AlSb interface and an Al diffusion towards the GaSb. We interpret this finding considering a particular mechanism to reduce the lattice strain at the GaSb/AlSb interface rather than a diffusion phenomenon. Here, the intermixing of Ga and Al at the heterointerfaces is promoted in order to reduce the lattice strain and to minimize the strain energy. However, further investigations, in particular by employing high-resolution transmission electron microscopy, are necessary to clarify and understand this experimental evidence.

ACKNOWLEDGMENTS The authors would like to thank A. Cappello and A. Sacchetti for their valuable technical assistance during SIMS and XRD measurements, respectively. This work has been supported by the Volkswagen-Stiftung, Hannover, Germany. AQ. G. Milnes and A. Y. Polyakov, Solid-State Electron. 36, 803 共1993兲. H. Xie and W. I. Wang, Appl. Phys. Lett. 63, 776 共1993兲. 3 H. Temkin and W. T. Tsang, J. Appl. Phys. 55, 1413 共1984兲. 4 J. Massies, M. Leroux, Y. Martinez, P. Vennegues, and S. Lau¨gt, J. Cryst. Growth 160, 211 共1996兲. 5 P. S. Dutta, H. L. Bath, and V. Kumar, J. Appl. Phys. 81, 5821 共1997兲. 6 C. Gerardi, C. Giannini, A. Passaseo, and L. Tapfer, J. Vac. Sci. Technol. B 15, 2037 共1997兲. 7 C. Gerardi, Surf. Interface Anal. 25, 397 共1997兲. 8 Y. Gao, J. Appl. Phys. 64, 3760 共1988兲. 9 Y. Rouillard, B. Jenichen, L. Da¨weritz, K. Ploog, C. Gerardi, C. Giannini, L. DeCaro, and L. Tapfer, J. Cryst. Growth 204, 263 共1999兲. 10 M. Yano, M. Ashida, A. Kawaguchi, and M. Inoue, J. Vac. Sci. Technol. B 7, 199 共1989兲. 11 Y. Rouillard, B. Lambert, Y. Toudic, M. Baudet, and M. Gauneau, J. Cryst. Growth 156, 30 共1995兲. 12 N. Bertru, R. Klann, A. Mazuelas, O. Brandt, K. H. Ploog, and S. Gaillard, Appl. Phys. Lett. 69, 2237 共1996兲. 13 C. Bocchi, A. Bosacchi, C. Ferrari, S. Franchi, P. Franzosi, R. Magnanini, and L. Nasi, J. Cryst. Growth 165, 8 共1996兲. 14 L. De Caro, C. Giannini, and L. Tapfer, J. Appl. Phys. 79, 4101 共1996兲. 15 L. Tapfer, III–V Quantum System Research, edited by K. H. Ploog 共The Institution of Electrical Engineers, UK, 1995兲, Chap. 8. 16 H.-J. Gossmann, G. P. Schwartz, B. A. Davidson, and G. J. Gualtieri, J. 1 2


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