InP multiple quantum wells: interfacial roughness and photoexcited carrier relaxation

InP multiple quantum wells: interfacial roughness and photoexcited carrier relaxation

Journal of Luminescence 100 (2002) 259–267 Femtosecond laser spectroscopy of In0.53Ga0.47As/InP multiple quantum wells: interfacial roughness and pho...

409KB Sizes 3 Downloads 88 Views

Journal of Luminescence 100 (2002) 259–267

Femtosecond laser spectroscopy of In0.53Ga0.47As/InP multiple quantum wells: interfacial roughness and photoexcited carrier relaxation A. Nakamuraa,b,*, K. Tanasea, I. Yamakawaa, T. Yamauchib, Y. Hamanakaa, R. Ogac, Y. Fujiwarac, Y. Takedac a Department of Applied Physics, Nagoya University, Japan CREST, Japan Science and Technology Corporation (JST), Furocho, Chikus-ku, Nagoya 464-8603, Japan c Department of Materials Science and Engineering, Graduate School of Engineering, Nagoya University, Fur-cho, Chikusaku, Nagoya 464-8603, Japan b

Received 3 September 2002

Abstract Interfacial properties and relaxation dynamics of photoexcited carriers in In0.53Ga0.47As/InP multiple quantum wells (MQWs) have been investigated by means of cross-sectional scanning tunneling spectroscopy and optical spectroscopy methods (luminescence, absorption and pump–probe experiments). The MQW structure consists of 125 periods of 10nm-wide well layers and 40-nm-wide barrier layers on an InP(0 0 1) substrate. The observed interfacial roughness of the InGaAs-on-InP is 1–2 monolayers (ML), while that of the InP-on-InGaAs is 3–4 ML. The Stokes shift observed in luminescence and absorption spectra at 77 K corresponds well to the well-width distribution observed by the crosssectional STM. Differential absorption spectra measured by pump–probe spectroscopy show that relaxation of hot carriers in conduction and valence bands followed by exciton formation takes place in 17–30 ps depending on the excitation photon energy. The excitons formed at the band bottom are localized at thicker areas within a quantum well in B500 ps. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Femtosecond pump–probe spectroscopy; STM; Exciton dynamics; Hot electrons

1. Introduction The dynamics of intraband relaxation and exciton formation has been extensively investi*Corresponding author. Department of Applied Physics, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan. Tel.: +81-52-789-4450; fax: +81-52-789-5316. E-mail address: [email protected], [email protected] (A. Nakamura).

gated for both bulk crystals and quantum well (QW) structures of semiconductors. Cooling dynamics of hot carriers has been reported for III–V compound [1–5] and II–VI compound [6–8] semiconductors. Pump–probe spectroscopy showed that excitons in GaAs multiple quantum wells (MQWs) are formed with a time constant of 20 ps by the band-to-band excitation [9]. The relaxation dynamics of photoexcited carriers is governed by carrier–carrier interaction leading to

0022-2313/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 3 1 3 ( 0 2 ) 0 0 4 2 8 - 3

260

A. Nakamura et al. / Journal of Luminescence 100 (2002) 259–267

quasi-thermal equilibrium of the electron system and electron–phonon interaction accompanied by emission of optical and acoustic phonons. The kinetics depends on the excitation photon energy, the excitation power density and the temperature. In addition, resonant and nonresonant excitations with exciton states confined in QWs may change the formation dynamics of excitons. In MQW structures there exist fluctuations of QW thickness, and interfacial quality of heterojunctions is crucial for determination of the device performance. A Stokes shift of the exciton band seen in luminescence and absorption spectra has been understood in terms of localization of excitons due to the well-width fluctuation. Exciton relaxation in space within a well is also a subject of relaxation dynamics of photoexcited carriers. Interfacial roughness of MQWs has been investigated by means of cross-sectional transmission electron microscopy (TEM), and the well-width fluctuation has been indeed observed [10]. However, the study of interfacial properties of MQWs comparing optical and structural data for the same sample has not yet been performed. In the TEM measurement, we have to prepare specially thinned samples to look at heterojunctions of MQW structures, and such a preparing process may damage the structure. In addition, an observable area is restricted to the small area, though the high resolution on the atomic scale can be attained. Cross-sectional scanning tunneling microscopy (STM) is also a powerful technique to investigate interfacial roughness on the atomic scale [11–13]. The STM study on heterojunctions has an advantage over the TEM study, because we do not need a complex preparation process of samples, and we can use the same sample for optical and microscopy measurements. Moreover, a large area can be scanned with the atomic scale resolution, which enables us to collect statistical data. In this paper, we performed a systematic study of relaxation processes of photoexcited carriers and interfacial properties of In0.53Ga0.47As/InP MQWs using optical spectroscopy (luminescence, absorption and femtosecond pump–probe spectroscopy) and STM. We investigated overall behavior of intraband relaxation, exciton formation and

exciton localization comparing optical data and structural data of the QW interface. Interfacial roughness of the MQW structure grown by metalorganic vapor phase epitaxy (MOVPE) was measured by a cross-sectional STM for the same sample used in the optical measurements. The Stokes shift observed in luminescence and absorption spectra at 77 K corresponds well to the wellwidth distribution observed by the cross-sectional STM. Differential absorption spectra measured by pump–probe spectroscopy show that relaxation of hot carriers in conduction and valence bands followed by exciton formation takes place in 17–30 ps depending on the excitation photon energy. Localization of excitons at thicker areas within a QW is observed in a subnanosecond time region.

2. Experimental A MQW structure composed of 125 periods of 10-nm-wide In0.53Ga0.47As well layers and 40-nmwide InP barrier layers was grown on an InP (0 0 1) substrate by MOVPE. The composition x of In was chosen as x ¼ 0:53 to obtain lattice match with GaAs. The reactor pressure was fixed at 76 Torr and growth temperature was 6201C. Tertiarybutylphosphine (TBP) and trimethylindium (TMIn) were used for source-gases to grow InP buffer and barrier layers, and TMIn, triethylgallium (TEGa) and tertiarybutylarsin (TBAs) were used to grow InGaAs well layers. We used a standard source-gas flow sequence to prepare InGaAs/InP MQW structures. After the growth of the InP layer the surface was exposed to TBP for 0.5 s and then TBAs was supplied for 0.5 s before supplying TMIn and TEGa to grow an InGaAs layer. After the growth of the InGaAs layer TBAs was supplied for 0.5 s and then TBP was supplied for 0.5 s prior to supplying of TMIn for the growth of the InP layer. Cross-sectional STM measurements were carried out in an ultrahigh-vacuum chamber with a base pressure of 2  108 Pa using a scanning tunneling microscope JSTM-4610. A scan size of STM images was varied in the range 20  20 nm2– 6  6 mm2. Tungsten probe tips electrochemically etched were used. Samples were cleaved in situ to

A. Nakamura et al. / Journal of Luminescence 100 (2002) 259–267

create clean (1–10) surfaces with exposed heterojunctions. A sample bias voltage and a constant tunnel current were 3 V and 0.15 nA, respectively. Transient absorption spectra were measured by using an optical parametric amplifier based on a femtosecond Ti:saphire laser amplifier operating at 1 kHz and a polychromator equipped with an InGaAs photodiode array. The excitation photon energy was varied between 0.92 and 1.26 eV, and the bandwidth of the probe light was 0.75–1.05 eV. The laser pulse width was 100 fs, and the excitation density of electron–hole pairs was B5  1010 cm2. The details of the pump–probe spectroscopy are described in Ref. [5].

261

A brighter band is the In0.53Ga0.47As layer with a width of 10 nm. N and I indicate the In0.53Ga0.47As-on-InP interface (normal interface) and the InP-on-In0.53Ga0.47As interface (inverted interface), respectively. As shown in Fig. 2(b), a cross-sectional profile of the STM image along the A–A0 line indicates the periodic structure with a spacing of 0.59 nm corresponding to the lattice constant. Difference in height between the InP and In0.53Ga0.47As layers in the filled state image

3. Results and discussion 3.1. Interfacial properties of MQW Fig. 1 shows the cross-sectional STM image of the In0.53Ga0.47As/InP MQW structure with a scan size of 1480  890 nm2. As the sample bias voltage is negative, the picture indicates a filled state image. We see a black and white periodic structure with a period of 42 nm due to the MQW structure. White bands are identified as the In0.53Ga0.47As layer because of the band offset between the valence bands of InGaAs and InP. Shown in Fig. 2(a) is a zoom-in STM image of In0.53Ga0.47As/InP heterojunctions with a scan size of 28  20 nm2.

Fig. 1. Cross-sectional STM image of the In0.53Ga0.47As/InP MQW structure. The scan size is 1480 nm  890 nm and the gray scale is 0.84 nm.

Fig. 2. (a) Cross-sectional STM image of the In0.53Ga0.47As/ InP heterojunctions. The scan size is 28 nm  20 nm and the gray scale is 0.18 nm. N and I indicate the In0.53Ga0.47As-onInP interface (normal interface) and the InP-on- In0.53Ga0.47As (inverted interface), respectively. (b) Profile of the STM image along the A–A0 line. (c) The well-width variation with distance on the interface obtained from Fig. 2(a).

A. Nakamura et al. / Journal of Luminescence 100 (2002) 259–267

the well-width distribution ranges in 32 and 38 ML and the most probable value of the width is found to be 36 ML (10.5 nm).

3.2. Carrier dynamics Before discussing relaxation dynamics we investigate luminescence and absorption spectra comparing to the observed well-width fluctuation. Fig. 4 shows the absorption spectrum of the In0.53Ga0.47As/InP MQW at 4.2 K. Exciton absorption peaks due to the n ¼ 1 and 2 confined bands are clearly observed. 1hh and 1lh indicate the n ¼ 1 heavy- and light-hole excitons, respectively, and 2hh and 2lh indicate the n ¼ 2 heavyand light-hole excitons, respectively. We measured

Fig. 3. Histogram of the well-width. Vertical axis shows the total distance on the interface.

2.0

1 hh 1.5

2 hh

INTENSITY (arb.units)

reflects that the valence band edge of InGaAs is higher than that of InP. Let us discuss the observed interfacial roughness of the MQW structure. As seen in the height profile the In0.53Ga0.47As-on-InP interface (normal interface) is very sharp, showing the transition from InP to InGaAs within 1–2 monolayer (ML) in the [0 0 1] direction. 1 ML is equal to 0.293 nm for In0.53Ga0.47As. In the InP-on-In0.53Ga0.47As interface (inverted interface), however, the transition occurs within 3–4 ML. The larger roughness observed in the inverted interface can be interpreted considering the following growth mechanism influenced by the source-gas flow sequence. TBAs is supplied for 0.5 s before the growth of the InP layer, and then TBP is supplied to exchange arsenic for phosphorus. In this gas exchange period arsenic–phosphorous exchange may be insufficient, and As atoms remain at the sample surface because the desorption rate of As atoms on the InGaAs surface is low [14]. As a result, residual As atoms are incorporated in the InP layer when TMIn is supplied. On the other hand, the abrupt interface observed in the normal interface is interpreted in terms of difference in desorption rate between arsenic and phosphorus at the surface. Because of the high desorption rate of P atoms on the InP surface [14], there remain few P atoms when TBAs, TMIn and TMGa are supplied. In addition, cross incorporation of arsenic in the InP layer hardly occurs with the supply of TBAs, because the arsenic-ion radius is larger than phosphorus-ion radius. As a result, the normal interface becomes extremely sharp as seen in Fig. 2(a). We analyze distributions of well-width fluctuations at the heterointerface. We estimated average values of the roughness and the well size from two STM images with a 35  20 nm2 scan size; the roughness and well size on the normal interface are 1–2 ML and 31 nm, respectively, while they are 3–4 ML and 9 nm on the inverted interface. Fig. 2(c) shows the well-width variation with distance on the interface obtained from the STM image of Fig. 2(a). The well-width changes in the range 32–36 ML. From STM images taken at different areas of the cleaved surface, we created a histogram of the well-width. As shown in Fig. 3

OD

262

2 lh

1 lh

1.0 0.5 0 0.8

0.9

1.0 1.1 1.2 ENERGY (eV)

1.3

1.4

Fig. 4. Absorption spectrum of the In0.53Ga0.47As/InP MQWs at 4.2 K and spectra of the pump pulse lasers. 1hh(2hh) and 1lh(2lh) indicate the n ¼ 1ð2Þ heavy-hole and n ¼ 1ð2Þ light-hole exciton bands, respectively.

A. Nakamura et al. / Journal of Luminescence 100 (2002) 259–267

photoluminescence spectra at 4.2 and 77 K to compare with the absorption spectra. As shown in Fig. 5, the luminescence peaks shift to the lower energy side compared with the absorption peaks. The observed Stokes shifts are 9 and 3 meV at 4.2 and 77 K, respectively. To investigate the correspondence of the observed Stokes shift to the well-width fluctuation we calculated a gap energy between the n ¼ 1 conduction band and the n ¼ 1 heavy-hole band using a one-dimensional square well potential model with a finite barrier potential. The parameters used in calculation are listed in Table 1. We estimated an energy difference corresponding to the well-width between the most probable width (36 ML) and the largest width (38 ML). The energy difference corresponding to 2 ML is estimated to be 3.0 meV. This value is in good agreement with the Stokes shift observed at 77 K. The Stokes shift of 9 meV observed at 4.2 K corresponds to the width difference of 6 ML. However, such a large well (42 ML) is not observed in the STM images, which means that the density of the large well is not high, and areas (terraces) with the width of B42 ML exist locally at the interfaces. At 77 K the

Fig. 5. Luminescence spectra measured at 4.2 and 77 K. Solid and dotted arrows show the absorption peak energies at 4.2 and 77 K, respectively.

263

Table 1 Parameters used in calculation of energy levels of the In0.53Ga0.47As/InP MQW. They are taken from Ref. [15] unless noted below Name

In0.53Ga0.47As

a (nm) 0.5868a Eg (eV at 4.2 K) 0.8118b 0.043a me (m0 ) mlh (m0 ) 0.054a mhh (m0 ) 0.44a Bowing parameter (eV) 0.494c band offset DEc ¼ 0:39DEg d

GaAs InAs

InP

0.5653 1.5177 0.0665 0.087 0.475

0.5869 1.4230 0.079 0.12 0.45

0.6058 0.4180 0.023 0.025 0.41

a

Calculated by linear interpolation. Calculated using Vegard’s law. c Ref. [16]. d Ref. [17]. b

excitons trapped at such terraces are ionized to the thicker well areas (38 ML) with the relatively high density, and thus the luminescence comes from excitons localized at these area. At lower temperature most of excitons are trapped at the deep terraces (B42 ML), and the luminescence due to such trapped excitons is observed at 4.2 K. Let us now investigate relaxation dynamics of photoexcited carriers considering the existence of well-width fluctuation and terraces. Fig. 6 shows differential absorption spectra around the n ¼ 1 heavy-hole and light-hole exciton bands of the In0.53Ga0.47As/InP MQW at 4.2 K for various delay times between the pump and probe pulses. The photon energy of the pump pulse is 1.26 eV. The differential spectrum depicts the difference between the pumped and unpumped spectra. Bleaching of the 1hh and 1lh exciton bands is observed, and the absorption change increases with increase in delay time between 0.8 and 500 ps. After 500 ps the bleaching peak shifts to the lower energy side, and the red shift is as large as 4 meV at 1000 ps. This red shift is in agreement with the energy shift due to the well-width fluctuation by 2 ML. The variation of the red shift with time yields the time constant of B500 ps. Therefore, these results suggest that localization of excitons into the thicker well areas (38 ML) takes place in B500 ps. The exciton trapping dynamics into the deep terraces at low temperature cannot be observed in the differential spectrum because the

A. Nakamura et al. / Journal of Luminescence 100 (2002) 259–267

0.8ps

2ps 60ps

∆OD

500ps

1000ps

0.1

0.80

0.82

0.84

0.86

0.88

pump pulse for both exciton bands within the inhomogeneous broadening. The observed spectral shape of the differential spectrum indicates the broadening and peak shift of the exciton bands. Therefore, we fit the spectrum taking into account changes in the peak energy, the homogeneous width and the absorption area of the Lorentzian shape. The best-fitted curves are shown in Fig. 7 by the solid curves. The spectral change for various delay times is well reproduced by this fitting analysis. We discuss a time variation of the peak shift that reflects relaxation processes of photoexcited electron–hole pairs in the conduction and valence bands. Fig. 8 shows the energy shift DP of the 1hh exciton band as a function of delay time. DP exhibits a red shift at the early stage of the time

0.90

ENERGY (eV) Fig. 6. Differential absorption spectra around the n ¼ 1 exciton bands for various delay times at 4.2 K. The photon energy of the pump pulse is 1.26 eV.

4.2K OD

264

0.5

0 pump: 1.1 eV

0ps 0.2ps

2.0ps

∆OD

density of states of such terraces is too low to yield a detectable change in absorption. In the shorter time region the differential spectra reflect relaxation dynamics of photoexcited carriers and formation dynamics of excitons. Fig. 7 shows the absorption spectrum and the differential spectra when the 2lh exciton band is resonantly excited by the pump pulse (1.08 eV). In order to analyze the spectral behavior for various delay times, the spectral shape was fitted to the convolution of the Lorentian shape for homogeneous broadening (2.0 meV) and the Gaussian shape for inhomogeneous broadening (5.5 meV). The fitted absorption spectrum is shown by the solid curve in the upper panel of Fig. 7. In this analysis we assumed that the absorption spectrum consists of the 1lh and 1hh exciton bands and the band-to-band transition components associated with the heavy- and light-hole bands. To analyze the differential spectra we assumed that a spectral change in the Lorentzian shape is induced by the

-5.0ps

10ps

30ps

60ps

100ps

experiment fitting

0.05

0.80

0.82

0.84 0.86 ENERGY (eV)

0.88

0.90

Fig. 7. Absorption spectrum (upper panel) and differential absorption spectra for various delay times at 4.2 K. The photon energy of the pump pulse is 1.08 eV. Dashed and solid curves indicate fitted spectra by spectral shape analysis.

A. Nakamura et al. / Journal of Luminescence 100 (2002) 259–267 0.6 experiment ∆P ∆Pblue ∆Pred

0.3

∆P (meV)

∆ P (meV)

0.4

0.2 0.1

0.2 0.1 0 0

5 t (ps)

10

0 -0.1 0

20

40

60

80

100

DELAY TIME (ps)

Fig. 8. Time evolution of the peak shift DP extracted from the spectral fitting analysis (open circles). The solid curve indicates the best fitted result to the experiment, and the dotted and dashed curves indicate the red and blue shift components in the fitting analysis. Inset shows the time evolution in the time range 0–10 ps.

delay, and after B3 ps the shift changes to the blue shift. The blue shift increases with increase in delay time, and is saturated at B100 ps. The exciton energy shift results from the renormalization of the band gap, the screening of the Coulomb interaction and the exchange interaction [18,19]. The screening gives rise to a reduction of the exciton binding energy so that the exciton energy shifts to the higher-energy side. The renormalization of the band gap due to the many-body effect lowers the gap energy. The renormalization effect in the twodimensional system dominates the screening effect. The exchange effect yields a blue shift of the exciton resonance, and the shift is given by the following equation: DPB3:86pa22D Nex EB ;

of the free carrier density ðpNex Þ [19]. We show the best-fitted results by dotted (red shift) and dashed (blue shift) curves in Fig. 8. The time constants of the red shift and blue shift components are B400 fs and 27 ps, respectively. Since the red shift is ascribed to the band gap renormalization, the renormalization takes place in about 400 fs and decays as excitons are formed from free electrons and holes. As the blue shift due to the exchange interaction is proportional to the exciton density, the time evolution of the blue shift at the late stage indicates the formation of excitons from free carriers. Therefore, the time constant of 27 ps corresponds to the formation time of excitons for the excitation photon energy of 1.08 eV. The dependence of the formation time on the excitation photon energy was investigated by measuring differential absorption spectra for various photon energies shown in Fig. 4. The photon energies of 1.08 and 1.26 eV correspond to the resonant excitations of the 2hh and 2lh exciton bands, respectively. We show in Fig. 9 the formation time versus the excess energy measured from the 1hh exciton energy. The formation time increases monotonically from 17 to 30 ps with increasing the excess energy. This result indicates that the exciton formation process is not affected by the resonant excitation, and is governed by the excess energy of free carriers given by the photoexcitation. The excess energy is shared

40

30

ð1Þ

where a2D and EB are the Bohr radius and the binding energy, respectively, and Nex is the exciton density [19]. The observed time variation of DP was analyzed assuming two rise components corresponding to the red and blue shifts (time constants tR and tB ) and a decay component of the red shift. The time constant of the decay component is taken as 3tB ; because the red shift due to the band gap renormalization is proportional to the cube root

τex (ps)

0.5

265

20

10

0 0

100 200 300 400 EXCESS ENERGY (meV)

500

Fig. 9. Exciton formation time as a function of excess energy of photoexcited carriers. The solid curve is the guide for eyes.

266

A. Nakamura et al. / Journal of Luminescence 100 (2002) 259–267

among free carriers by mutual scattering of carriers, and as a result the electron system becomes hot compared to the phonon system. Hot carriers are relaxed to the band bottoms with emission of optical and acoustic phonons, and finally form excitons. When the excess energy is high, the time necessary for relaxation to the band bottoms becomes longer. As a result, the exciton formation time gets longer for the optical excitation with the higher photon energy. For the highest photon energy used in this study (1.26 eV) the saturation behavior of the excess energy dependence is observed, and the formation time coincides well with that observed for the bulk InGaAs crystal (B30 ps) [5]. With such excitations carriers are generated in the quasi-continuum states of the quantum confinement due to the barrier potential. Therefore, we have found that the exciton formation process in the QW exhibits a three-dimensional behavior when carriers are generated in the quasi-continuum states.

4. Conclusion We have investigated interfacial properties and overall behavior of intraband relaxation, exciton formation and exciton localization in In0.53Ga0.47As/InP MQWs using STM and optical spectroscopy methods. The MQW structure grown by MOVPE consists of 125 periods of 10-nm-wide well layers and 40-nm-wide barrier layers on an InP(0 0 1) substrate. Cross-sectional STM images of the MQW structure revealed that the interfacial roughness of the InGaAs-on-InP is 1–2 ML and that of the InP-on-InGaAs is 3–4 ML. Absorption spectra, luminescence spectra and time-resolved spectra in the time region of femtosecond to nanosecond were measured for the same sample used in the STM measurement. The Stokes shift observed in luminescence and absorption spectra at 77 K corresponds well to the energy difference due to the difference in the well-width between the most probable width and the largest width (2 ML). Differential absorption spectra measured by pump–probe spectroscopy show that relaxation of hot carriers in conduction and valence bands and formation of excitons take place in 17–30 ps.

The exciton formation time depends on the excess energy of photoexcited carriers, and is independent of the excitation condition resonant with the higher exciton state. The excitons formed at the band bottom are mobile in the QW, and then localized at the areas with the width thicker by 2 ML within the QW in B500 ps.

Acknowledgements This work is dedicated to the late Professor Shigeo Shionoya who has markedly contributed to progress of ultrafast laser spectroscopy in semiconductors. Professor Shionoya has encouraged the author (AN) to work in this field developing a novel technique.

References [1] R.F. Leheny, J. Shah, R.L. Fork, C.V. Shank, A. Migus, Solid State Commun. 31 (1979) 809. [2] C.V. Shank, R.L. Fork, R. Yen, J. Shah, B.I. Greene, A.C. Gossard, C. Weisbuch, Solid State Commun. 47 (1983) 981. [3] L. Roda, P. Lugli, T. Elsaesser, J. Shah, Phys. Rev. B 47 (1993) 4226. [4] K. Kash, J. Shah, Appl. Phys. Lett. 45 (1984) 401. [5] D. Nishiwaki, Y. Hamanaka, Y. Nonogaki, Y. Fujiwara, Y. Takeda, A. Nakamura, J. Lumin. 83–84 (1999) 49. [6] T. Tokizaki, H. Sakai, A. Nakamura, Phys. Rev.B 55 (1997) 15776. [7] T. Tokizaki, H. Sakai, G. Kogano, A. Nakamura, Jpn. J. Appl. Phys. 38 (1999) 3562. [8] F. Sasaki, T. Mishina, Y. Masumoto, Phys. Rev. B 46 (1992) 6750. [9] T.C. Damen, J. Shah, Y. Oberli, D.S. Chemla, J.E. Cumingham, J.M. Kuo, Phys. Rev. B 42 (1990) 7434. [10] A. Ourmazd, D.W. Taylor, J. Cumingham, C.W. Chu, Phys. Rev. Lett. 62 (1989) 933. [11] S.L. Skala, W. Wu, J.R. Tucker, J.W. Lyding, A. Seabaugh, E.A. Beam, D. Jovanovic, J. Vac. Sci. Technol. B 13 (1995) 660. [12] K-J. Chao, N. Liu, C-K. Shin, D.W. Gotthold, B.G. Streetman, Appl. Phys. Lett. 73 (1999) 2805. [13] H. Chen, H.A. McKay, R.M. Feenstra, G.C. Aers, P.J. Poole, R.L. Williams, S. Charbonneru, P.G. Piva, T.W. Simpson, I.V. Mitchell, J. Appl. Phys. 89 (2001) 4815. [14] S. Sudo, Y. Nakano, M. Sugiyama, Y. Shimogaki, H. Komiyama, K. Tada, Thin Solid Films 313 (1998) 604.

A. Nakamura et al. / Journal of Luminescence 100 (2002) 259–267 [15] O. Madelung, M. Schulz, H. Weiss (Eds.), Landolt– Bornstein New Series, Group 3, Vol. 17a, Springer, Berlin, 1982. [16] E. Kuphal, A. Pocker, A. Eisenbach, J. Appl. Phys. 73 (1993) 4599.

267

[17] S.R. Forrest, P.H. Schmidt, R.B. Wilson, M.L. Kaplan, Appl. Phys. Lett. 45 (1984) 1199. [18] S. Schmitt-Rink, C. Ell, J. Lumin. 30 (1985) 585. [19] S. Schmitt-Rink, D.S. Chemla, D.A.B. Miller, Phys. Rev. B 32 (1985) 6601.