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Localized exciton dynamics in InGaN quantum well structures
Applied Surface Science 190 (2002) 330–338
Localized exciton dynamics in InGaN quantum well structures Shigefusa F. Chichibua,*, Takashi Azuhatab, Hajime Okumurac, Atsushi Tackeuchid, Takayuki Sotae, Takashi Mukaif a Institute of Applied Physics, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan Department of Materials Science and Technology, Hirosaki University, 3 Bunkyo-cho, Hirosaki, Aomori 036-8561, Japan c Power Electronics Research Center, National Institute of Advance Industrial Science and Technology (AIST), Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan d Department of Applied Physics, Waseda University, 3-4-1 Ohkubo, Shinjuku, Tokyo 169-8555, Japan e Department of Electrical, Electronics and Computer Engineering, 3-4-1 Ohkubo, Shinjuku, Tokyo 169-8555, Japan f Nichia Corporation, Nitride Semiconductor Research Laboratory, 491 Oka, Kaminaka, Anan, Tokushima 774-8601, Japan b
Abstract InGaN multiple quantum well laser diode (LD) wafer that lased at 400 nm was shown to have the InN mole fraction, x, of only 6% in the wells. Nanometer-probe compositional analysis showed that the fluctuation of x was as small as 1% or less, which is the resolution limit. However, the wells exhibited a Stokes-like shift (SS) of 49 meV and an effective localization depth E0 was estimated by time-resolved photoluminescence (TRPL) measurement to be 35 meV at 300 K. Since the effective electric field due to polarization in the wells is estimated to be as small as 286 kV/cm, SS is considered to originate from an effective bandgap inhomogeneity. Because the well thickness fluctuation was insufficient to produce SS or E0, the exciton localization is considered to be an intrinsic phenomenon in InGaN material. Indeed, bulk cubic In0.1Ga0.9N, which does not suffer any polarization field or thickness fluctuation effect, exhibited an SS of 140 meV at 77 K and similar TRPL results. The origin of the localization is considered to be due to the large bandgap bowing and In clustering in InGaN material. Such shallow and low density localized states are leveled by injecting high density carriers under the lasing conditions for the 400 nm LDs. # 2002 Elsevier Science B.V. All rights reserved. PACS: 78.66.Fd; 78.40.-q; 78.47.þp Keywords: InGaN; Localized exciton; Exciton dynamics; Cubic InGaN
1. Introduction Inx Ga1x N quantum wells (QWs) are attracting attention because they serve as an active region [1–3] of UV to visible light emitting diodes (LEDs) and purple laser diodes (LDs). Since they exhibit an efficient emission with external quantum efficiency, Zext, *
Corresponding author. Tel.: þ81-298-53-5289; fax: þ81-298-53-5205. E-mail address: [email protected] (S.F. Chichibu).
up to 20% at 470 nm in spite of large threading dislocation (TD) density up to 1010 cm2 [4], optical properties of InGaN QWs have been investigated intensively. Internal electric field, F, due to spontaneous and piezoelectric polarization [5,6] has been shown to modify the QW energy states through quantum-confined Stark effect (QCSE) [7]; redshift of the emission peak compared to unperturbed QW resonance energy [5,8] and reduction of electron–hole wavefunction overlap (oscillator strength) [6,9]. Coulomb screening due to carrier injection [5,8] or impurity doping
0169-4332/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 ( 0 1 ) 0 0 9 0 7 - 2
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[9] recovers the overlap. A predominant reason for the efficient emission has been proposed [8,9] to be due to short quasi-diffusion length [10] of carriers, which is caused by the presence of quantum-disk (Q-disk)-size [11] effective bandgap inhomogeneity [8–10,12] or quantum dots (QDs) [13–15]. However, degree of the compositional fluctuation and structural quality of practical InGaN multiple quantum well (MQW) LD structures exhibiting the lasing wavelengths between 390 and 410 nm, which are proper wavelengths to obtain low threshold current density and long-lived cw lasers, are not fully understood yet. In this article, results of structural and compositional analyses on InGaN MQW LD structure that lased at around 400 nm are shown in addition to the results of static and time-resolved (TR) photoluminescence (PL) spectroscopy to clarify the spontaneous emission mechanisms in terms of QW exciton [7,16] localization due to large bandgap bowing in InGaN alloys. To exclude the disturbance due to F and thickness fluctuation effect usually seen in hexagonal QW structures, bulk cubic In0.1Ga0.9N film and MQWs were also examined.
2. Experimental Inx Ga1x N MQW LD wafer that lased at 400 nm was grown by two-flow metal organic vapor phase epitaxy on sapphire (0 0 0 1) substrates. It consisted of a 30 nm thick GaN low temperature nucleation layer, a 3.5 mm thick GaN:Si template, a 0.16 mm thick InGaN compliance layer, a 0.3 mm thick AlGaN:Si cladding, a 0.1 mm thick GaN:Si waveguide, an MQW, a 20 nm thick AlGaN:Mg electron-overflow blocking layer, a 0.1 mm thick GaN:Mg, a 0.3 mm thick AlGaN:Mg and a 0.18 mm thick GaN:Mg layer. The MQW consisted of 10 periods of 2.3 nm thick InGaN wells and 5.8 nm thick InGaN barriers. Each layer thickness was measured using a high-resolution H-9000UHR 300 keV transmission electron microscope (HR-TEM). High-resolution X-ray diffraction (HR-XRD) measurements were carried out using an X’Pert-MRD system. Nanometer-probe compositional analysis was carried out using a KEVEX DELTA energy dispersive X-ray microanalysis (EDX) equipped on HB501 field emission scanning TEM. The probe diameter, acceleration energy and current were
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1 nm, 100 kV and 109 A, respectively. The accumulation duration was 50 s. TEM observation and EDX measurement were done by TORAY Research. The TEM specimen was carefully prepared to suppress damages like artificial In segregation. Static PL and photoluminescence excitation (PLE) measurements were carried out on the wafer while electroluminescence (EL), photovoltaic (PV) and electroreflectance (ER) measurements were carried out on a processed wafer. Static PL was excited by the 325.0 nm line of a cw He–Cd laser (12 mW) and dispersed by a 67 cm focal-length grating monochromator (McPHERSON 207). PLE spectra were measured by monitoring the lower energy tail of a broad PL band. TRPL was excited either by a 600 ps pulse of a N2 laser or a 100 fs pulse of a frequency-doubled Ti:sapphire laser. A standard streak-camera acquisition technique was employed to analyze the signal. To compare the decay dynamics between hexagonal (h-) and cubic (c-) InGaN, a 170 nm thick c-In0.1Ga0.9N film and a 5-period-MQW having 5 nm thick c-In0.1Ga0.9N wells and 10 nm thick c-GaN barriers were grown by r.f. molecular-beam epitaxy (RF-MBE) using metallic Ga and In, and N2 plasma source (SVT-4.5) on a 300 nm thick c-GaN template. They were grown on a 7 mm thick 3C–SiC (0 0 1) layer on Si (0 0 1), which has been prepared by chemical vapor deposition [17]. Typical residual electron density n is estimated to be of the order of 1017 cm3 or smaller. The structure of the samples was also characterized by HR-XRD. Inclusion of the hexagonal phase was negligible and the c-InGaN layers were confirmed by reciprocal lattice mapping method to be pseudomorphically grown on relaxed c-GaN templates.
3. Results and discussion 3.1. Structural and optical properties of h-InGaN MQW LD wafer The MQW LD structure had atomically flat and abrupt interfaces, as shown in HR-TEM bright-field images in Fig. 1. The upper limit of the thickness fluctuation (sum of the two interfaces) of InGaN wells is not greater than two monolayers (2 ML; 0.52 nm) over a few micrometers considering possible defocusing effects.
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Fig. 1. HR-TEM micrograph of h-InGaN MQW region. Nanometerprobe EDX was carried out at each point (A–E) in the figure.
Well-resolved superlattice (SL) satellite peaks due to InGaN MQW are found in the HR-XRD pattern, as shown in Fig. 2. The entire structure is confirmed to be pseudomorphically grown on the GaN template. The alloy compositions are calculated from the lattice constants obtained from the XRD pattern shown in Fig. 2 based on the quasi-cubic approximation, ezz ¼ 2ðC13 =C33 Þexx , where ezz (exx) is the strain along the c-axis (a-axis), and C13 and C33 are the elastic stiffness constants. The values used are the same as those used in Ref. [18]. Note that those values of alloys are
Fig. 2. HR-XRD pattern of the InGaN MQW LD structure that lased at 400 nm.
assumed to obey the Vegard’s law. The AlN mole fraction in the AlGaN cladding layers is thus obtained as 14% and average InN mole fraction in the InGaN MQW is only 3%. The SL period is calculated to be 8.5 nm, which nearly agrees with the TEM result of 8.1 nm. Nanometer-probe EDX was carried out at each point marked in Fig. 1. The AlN mole fraction in the AlGaN blocking layer on top of the MQW is 22%, as shown by spot ‘‘A’’ in Fig. 1. The value in the cladding layers is approximately 15% (not in Fig. 1), which agrees with the value obtained from the XRD data. The InN mole fraction x in the barriers is approximately 2.1% and that of the wells is 5.1– 5.9%. However, the latter variation nearly agrees with the detection limit of 1%. The result means that the compositional inhomogeneity in the well is very small. If we assume average x as 5.5% for the wells, total average x in the MQW is calculated to be 3.1% considering their thickness. The value agrees with the XRD result being 3%. Optical spectra of the MQW at 300 K are summarized in Fig. 3. A transition structure at 3.42 eV is due to the GaN waveguide layer. Recently, the bowing parameter, b, of Inx Ga1x N alloys has been reported to be very large [19–21] and vary with x [21]. Using the value of b(x) [21], bandgap energies of bulk In0.02Ga0.98N and In0.055Ga0.945N are calculated to be 3.27 and 3.04 eV, respectively. Both values are consistent with the experimental ones being 3.33 and 3.158 eV considering the
Fig. 3. Electroreflectance (ER), electroluminescence (EL), photovoltaic (PV), and photoluminescence excitation (PLE) spectra of the In0.06Ga0.94N MQW LD structure measured at 300 K.
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Eme ¼ 3:17 eV approximately coincides with the QW resonance energy obtained from the ER spectrum (3.158 eV). However, the increase of the decay time would also be explained by the field screening effect [24]. Therefore, effective field strength must be estimated. 3.2. Estimation of the effective field in h-InGaN wells
Fig. 4. Time-integrated PL spectrum and the emission lifetime as a function of detection photon energy at 300 K of the In0.06Ga0.94N MQW LD structure. The inset shows the PL intensity as a function of time after excitation.
effect of compressive biaxial stress and quantum-size effect. Therefore, the transition structures at 3.158 and 3.33 eV are assigned as being due to excitonic resonances in the In0.06Ga0.94N wells and In0.02Ga0.98N barriers, respectively. Thus, the wells are revealed to have the thickness L ¼ 2:3 nm and x ¼ 0:055. In spite of very small compositional inhomogeneity determined above, the spontaneous EL peak energy is 3.109 eVand the Stokes-like shift (SS) is 49 meV even at 300 K. Origin of the SS is either the field effect [22] or effective bandgap inhomogeneity [8,9], which will be discussed later. The luminescence decay time increases from 800 ps to 2.2 ns with decreasing detection photon energy from 3.2 to 3 eV, as shown in Fig. 4. The peak energy shifts to the lower energy with time, though the data are not shown here. Since this behavior is characteristic of localized excitons [23] in an exponential-tail density-of-states (DOS) gðEÞ ¼ expðE=E0 Þ, where E0 represents the localization depth, the relation between the PL lifetime tPL and emission energy E is fitted using tPL ðEÞ ¼ tr =f1 þ exp½ðE Eme Þ=E0 g, where Eme is the energy similar to the mobility edge and tr the radiative or effective lifetime. E0 is obtained as 35 meV, which is a bit smaller than SS (49 meV). The value of E0 increases monotonically with decreasing measurement temperature, the result means that the tail states are not filled by thermal energy at 300 K.
In InGaN wells with InGaN barriers, the spontaneous polarization can be nearly neglected [6] and the piezoelectric field, FPZ, dominates total effective F. The strength of FPZ is calculated using the relation, FPZ ¼ Pz;PZ =er;k e0 , where er,k and e0 are the relative dielectric constant along the z-axis and the dielectric constant in vacuum, respectively. Pz,PZ is the piezoelectric polarization along the z-axis, which can be expressed as Pz;PZ ¼ 2e31 exx þ e33 ezz , where eij are the piezoelectric constants and eij are the strain. The value of FPZ in the In0.06Ga0.94N well is thus calculated to range from 1.1 MV/cm [6] to 160 kV/cm [22] depending on the values of eij [6,22]. Since the values of eij reported to date scatter an order of magnitude, effective fields F in h-InGaN have been investigated experimentally using following three approaches. (i) Static PL, PLE and TRPL signals from In0.1Ga0.9N QW structures have been measured as a function of well thickness L [9,25] to demonstrate that QCSE controlled the PL peak energy under low excitation conditions especially for L larger than 3 nm. Indeed, the PL peak shifted to the higher energy under high excitation conditions. However, the amount of the shift is remarkably small for thinner wells, and high excitation PL peak energies nearly agreed with the low excitation ones for L smaller than 3 nm. The strength of F has been estimated by calculating confined energy levels and wavefunctions in the In0.1Ga0.9N wells as functions of F, L and doping density n in the barriers by variational method neglecting exciton binding energy within the Hartree approximation solving the Schro¨ dinger equation and Poisson equation simultaneously and self-consistently. The value of F has been estimated to be about 350– 400 kV/cm for x ¼ 0:1, which nearly agreed with previous reports [22].
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Fig. 5. Emission and absorption edge energies of 3 nm thick Inx Ga1x N QWs. The bandgap of unstrained bulk InGaN estimated after Ref. [21] is also plotted.
(ii) Static and dynamic optical processes in a series of 3 nm thick Inx Ga1x N QWs with various x were investigated. The PL peak energy of the QWs showed the redshift and the full width at half maximum (FWHM) increased simultaneously with increasing x. The PL peak energy and average bandgap, which was defined as the energy where the PLE/PV signal decreased to its half the maximum or the transition energy in the ER spectrum, of the wells are plotted as a function of x in Fig. 5. Bandgap energies of unstrained bulk Inx Ga1x N alloys, which were calculated using the relation Eg ðxÞ ¼ 3:42x þ 1:89ð1 xÞ bðxÞxð1 xÞ, where Eg(x) is the energy gap and b(x) the composition-dependent bowing parameter of Inx Ga1x N [21], are also plotted in Fig. 5. It should be noted that the energy gap of Inx Ga1x N alloys cannot be fitted by quadratic dependence on x [21]. The effective bandgap of the Inx Ga1x N QWs for x < 0:15 is remarkably higher than the bulk bandgap. This is reasonable since both the compressive biaxial strain in InGaN and the quantum size effect increase the bandgap, and the field effect F is not so serious for the QWs with x < 0:10 and L < 3 nm [25]. The emission peak energy is higher than the bulk bandgap for x < 0:12. However, the emission peak energy of the QWs is smaller than the bulk bandgap for x > 0:15,
indicating that F plays a certain role in the wells even for L ¼ 3 nm. Note that x ¼ 0:15 corresponds to the practical blue SQW LEDs. The strength of F for each x was estimated by calculating confined energy levels and wavefunctions in the 3 nm thick Inx Ga1x N wells as functions of bulk bandgap given above, F and doping density n in the barriers by variational method. The results are consistent with the result of the approach (i). (iii) PL spectra of the 2.5 nm thick In0.25Ga0.75N amber SQW LED wafer has been measured as a function of external bias [26]. The PL from the QW has been excited by the 488.0 nm line of a cw Arþ laser to selectively excite the well. Takeuchi et al. [27] have also used this method to determine the direction and strength of FPZ in In0.16Ga0.84N QWs, and have found a blue shift of the PL peak with increasing reverse bias. Their conclusion that FPZ pointed from the surface to the substrate seemed to be valid considering a Ga-face growth during MOVPE. The PL peak of the amber LED wafer has shifted to the higher energy by up to 110 meV by changing the external bias from þ2 to 10 V [26]. By solving again the Schro¨ dinger equation and Poisson equation simultaneously and self-consistently to fit the peak energy shift, F has been estimated to be 1.4 MV/cm. The value is close to the one estimated from the strain and piezoelectric constants reported by Wetzel et al [22]. Using the results of (i)–(iii), the strength of F in Inx Ga1x N QWs was correlated with x [28]. As has been shown, F (FPZ) naturally increases monotonically with increasing x. The value of F for the In0.06Ga0.94N QWs is nearly 286 kV/cm. In that case a potential drop across the 2.3 nm thick well is as small as 66 meV, which is smaller than the band discontinuity between the wells and barriers (172 meV). It should be mentioned that the electron quantized energy level is flat within the well due to larger conduction band discontinuity, and the QW may belong to the CASE II in Refs. [9,25]. In this case, luminescence peak must be close to the absorption edge if there is no in-plane potential fluctuation. Therefore, the field effect is not so strong in the current In0.06Ga0.94N MQW LD wafer.
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Since FWHM of the EL peak is approximately 75 meV and SS is 49 meV (65% of FWHM of the EL), as shown in Fig. 3, QW excitons are considered to localize [8,23] at certain potential minima [9,10] even at 300 K. The concept of exciton localization can explain why InGaN QWs exhibit high Zext against the large TD density especially for larger x (larger strain) [1,3]. 3.3. Origin of exciton localization A simple calculation indicates that effective bandgap inhomogeneity due to 2 ML thickness fluctuation (0.52 nm) for the well with L ¼ 2:3 nm and x ¼ 0:06 is nearly 20 meV, which should be leveled by thermal energy at 300 K. However, there still remain SS ¼ 49 meV and E0 ¼ 35 meV at 300 K. Therefore, the QW should have other localization mechanisms like In compositional inhomogeneity [8]. In order to exclude the localization effect due to thickness fluctuation and the field effect due to FPZ, optical properties of the bulk c-In0.1Ga0.9N film were investigated. The c-In0.1Ga0.9N film exhibits a large SS of 280 meV compared to 100 meV for h-In0.1Ga0.9N [28], indicating that compositional fluctuation in cInGaN is larger than that in h-InGaN materials presumably due to difficulties in growing metastable cubic nitrides. Its luminescence decay time increases with decreasing detection photon energy. TRPL signals monitored at particular wavelengths from a 170 nm thick c-In0.1Ga0.9N film at 10 K are shown in Fig. 6(a). All signals show a non-exponential decay similar to the case for h-InGaN [9,30]. Two analyses are carried out as follows. One model assumes a presence of exponentially decreasing localized band-tail states due to an effective bandgap inhomogeneity [23]. Another assumes a presence of disordered quantum nanostructures [31] like closely spaced self-formed QDs or Q-disks. At first, PL lifetime tPL is plotted as a function of emission photon energy E in Fig. 6(b), together with the time-integrated PL spectrum. The lifetime is defined as the longer decay component when the decay curve is fitted assuming a double exponential decay. As shown, tPL increases with decreasing emission photon energy. The relation between tPL and E is analyzed in the same manner as described in Section 3.1. The fitting curve reasonably reproduces the
Fig. 6. (a) TRPL signals monitored at particular wavelengths from 170 nm thick c-In0.1Ga0.9N/c-GaN at 10 K, (b) PL lifetime tPL as a function of emission photon energy E and (c) ln{ln[I0/I(t)]} vs. ln(t) relation.
experimental data giving the values of E0 ¼ 109 meV, eVand tr ¼ 495 ps. It should be noted that tPL at 10 K is an order of magnitude shorter than that of h-InGaN QWs, which means that tr in h-InGaN QWs is considered to be made longer by the wavefunction separation due to QCSE. Next, ln{ln[I0/I(t)]} vs. ln(t) relation is plotted in Fig. 6(c), where I(t) is the PL intensity at time t and I0 is I(0). Chen et al. [31] have analyzed PL decay curve from disordered low-dimensional semiconductors to propose that above relation can be approximated by a straight line; IðtÞ ¼ I0 exp½ðt=tÞb , which has been defined as ‘‘stretching exponential’’ decay where b is the scaling parameter that is related to the dimensionality of the localized centers and t the delocalized lifetime. Obviously, the data can be approximated by the straight line, as shown in Fig. 6(c) giving t ¼ 149 ps and b ¼ 0:65.
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Both models seem to qualitatively fit the data. In addition, PL peak energies of the films show a weak redshift of 20 meV with increasing temperature from 10 to 300 K, as is the case with h-InGaN QWs [29]. Note that the amount of the bandgap shift between 10 and 250 K in c-GaN is 64 meV [32]. Since the crystal homogeneity of cubic materials is worse than that of hexagonal polytype, the data shown here are not the representatives of h-InGaN device structures. However, the carrier/exciton localization is considered to be an universal phenomenon in InGaN materials because h-InGaN also exhibits certain SS [8,9,28, 30], large bandgap bowing, increasing tPL with decreasing energy and small PL peak shift with increasing temperature. Therefore, the emission is assigned as being due to the recombination from certain localized states. Bellaiche et al. [21] have predicted natural resonant hole wavefunction localization at In site in GaN:In and have attributed this to be the origin of exciton localization. This seems plausible. However, localization of holes is insufficient to explain the improved Zext against the presence of large number of TDs and of FPZ, since electrons injected from the barrier are free. Also, their prediction [21] that PL intensity of Inx Ga1x N would decrease with increasing x due to drastic decrease of the momentum matrix element for low x conflicts with general experimental findings that Zext increases with increasing x [3].
Fig. 7. PL lifetime tPL, radiative lifetime tr and non-radiative lifetime tnr of the emission from c-In0.1Ga0.9N/c-GaN MQW structure. The latter two are deduced from tPL and the PL intensity as a function of temperature.
Fig. 7 shows the radiative lifetime tr and non-radiative lifetime tnr of the emission from c-In0.1Ga0.9N/cGaN MQW structure, which are deduced from the PL decay time tPL and the PL intensity as a function of temperature, T, using the relation Zint ¼ 1=ð1 þ tr =tnr Þ, where Zint is an internal quantum efficiency. To simplify, Zint is set unity at low temperature since non-radiative recombination process is generally frozen at low temperature. At the moment, there is no evidence that this assumption is valid for c-InGaN. However, it can be recognized that tr is nearly constant below 100 K but increases linearly or slightly superlinearly with T above 150 K. Therefore, the DOS from which the emission originates seems to change from zero dimension (0D) to two or three dimension (2D or 3D) with increasing T [33,34]. Indeed, the well thickness (5 nm) is rather larger than the free exciton Bohr radius (3.4 nm) and the wavefunction confinement is weak. Note here that the PL still shows a stretching-exponential decay even at 300 K. The origin of the exciton localization [8] universally seen in InGaN is thus considered to be the local potential minima [8–10] due to non-random alloy compositional fluctuation or a combination of this and the hole localization mentioned above. The size of the lateral localization has been estimated to be smaller than 50 nm [10] and thus we have concluded it to Q-disk size, but the size can be even smaller than the size of structural QDs [21], as revealed from temperature-independent tr shown in Fig. 7. It should be noted that even though the compositional fluctuation is only 1%, electrons can be localized due to the large [19–21] and composition-dependent [21] bandgap bowing of InGaN alloys. For example, the bandgap energies of h-Inx Ga1x N bulk crystals are calculated to be 3.059 eV for x ¼ 0:05 and 2.990 eV for x ¼ 0:06 using the value of bðx ¼ 0:055Þ ¼ 6 eV [21]. The energy difference between the two (69 meV) exceeds the value of SS being 49 meV of the 400 nm h-InGaN LD. Thus the compositional inhomogeneity might be smaller than 1%. Since the threshold carrier density of the LD action is estimated to be of the order of 1019–1020 cm3 and the bandgap renormalization is obvious, such shallow localization depth (35 meV at 300 K) is easily filled up under the lasing conditions for the 400 nm LD wafer at 300 K. This delocalization can explain the decrease of quantum efficiency under high excitation conditions.
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4. Conclusions In0.06Ga0.94N MQW LD structure that lased at 400 nm was shown to have atomically flat interfaces and very small compositional inhomogeneity. However, excitons were confirmed to be localized within the DOS which might have an exponential-tail type distribution. Although the dimensionality of the localization is not yet resolved, the variation of tr for cInGaN implied that lateral confinement is weak at 300 K. Q-disks might be responsible. However, such shallow and low density localized states would be leveled under high excitation conditions. The spontaneous emission was assigned as being due to the recombination of localized excitons while the stimulated emission seemed to come from the continuum states energetically higher than the mobility edge.
Acknowledgements The authors are grateful to Dr. Alex Zunger and Dr. M. Sugawara for stimulating discussions. They wish to thank Dr. Y. Ishida, N. Ohtake, T. Kuroda, M. Sugiyama and T. Kitamura for help in experiments. They are thankful to Professor F. Hasegawa for continuous encouragements. This work was supported in part by the Ministry of Education, Science, Sports, and Culture of Japan (Grant-in-Aid for Scientific Research No. 11750268), Ogasawara Foundation for the Promotion of Science and Engineering and Casio Science Promotion Foundation. They wish to thank partial financial support by AFOSR/AOARD. References [1] S. Nakamura, G. Fasol, The Blue Laser Diode, Springer, Berlin, 1997. [2] I. Akasaki, H. Amano, Jpn. J. Appl. Phys. 36 (1997) 5393. [3] T. Mukai, M. Yamada, S. Nakamura, Jpn. J. Appl. Phys. 38 (1999) 3976. [4] F. Ponce, D. Bour, Nature 386 (1997) 351. [5] T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano, I. Akasaki, Jpn. J. Appl. Phys. 36 (1997) L382. [6] F. Bernardini, V. Fiorentini, Phys. Rev. B 57 (1998) R9427; F. Bernardini, V. Fiorentini, Phys. Stat. Sol. (b) 216 (1999) 391.
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Localized exciton dynamics in InGaN quantum well structures Shigefusa F. Chichibua,*, Takashi Azuhatab, Hajime Okumurac, Atsushi Tackeuchid, Takayuki Sotae, Takashi Mukaif a Institute of Applied Physics, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan Department of Materials Science and Technology, Hirosaki University, 3 Bunkyo-cho, Hirosaki, Aomori 036-8561, Japan c Power Electronics Research Center, National Institute of Advance Industrial Science and Technology (AIST), Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan d Department of Applied Physics, Waseda University, 3-4-1 Ohkubo, Shinjuku, Tokyo 169-8555, Japan e Department of Electrical, Electronics and Computer Engineering, 3-4-1 Ohkubo, Shinjuku, Tokyo 169-8555, Japan f Nichia Corporation, Nitride Semiconductor Research Laboratory, 491 Oka, Kaminaka, Anan, Tokushima 774-8601, Japan b
Abstract InGaN multiple quantum well laser diode (LD) wafer that lased at 400 nm was shown to have the InN mole fraction, x, of only 6% in the wells. Nanometer-probe compositional analysis showed that the fluctuation of x was as small as 1% or less, which is the resolution limit. However, the wells exhibited a Stokes-like shift (SS) of 49 meV and an effective localization depth E0 was estimated by time-resolved photoluminescence (TRPL) measurement to be 35 meV at 300 K. Since the effective electric field due to polarization in the wells is estimated to be as small as 286 kV/cm, SS is considered to originate from an effective bandgap inhomogeneity. Because the well thickness fluctuation was insufficient to produce SS or E0, the exciton localization is considered to be an intrinsic phenomenon in InGaN material. Indeed, bulk cubic In0.1Ga0.9N, which does not suffer any polarization field or thickness fluctuation effect, exhibited an SS of 140 meV at 77 K and similar TRPL results. The origin of the localization is considered to be due to the large bandgap bowing and In clustering in InGaN material. Such shallow and low density localized states are leveled by injecting high density carriers under the lasing conditions for the 400 nm LDs. # 2002 Elsevier Science B.V. All rights reserved. PACS: 78.66.Fd; 78.40.-q; 78.47.þp Keywords: InGaN; Localized exciton; Exciton dynamics; Cubic InGaN
1. Introduction Inx Ga1x N quantum wells (QWs) are attracting attention because they serve as an active region [1–3] of UV to visible light emitting diodes (LEDs) and purple laser diodes (LDs). Since they exhibit an efficient emission with external quantum efficiency, Zext, *
Corresponding author. Tel.: þ81-298-53-5289; fax: þ81-298-53-5205. E-mail address: [email protected] (S.F. Chichibu).
up to 20% at 470 nm in spite of large threading dislocation (TD) density up to 1010 cm2 [4], optical properties of InGaN QWs have been investigated intensively. Internal electric field, F, due to spontaneous and piezoelectric polarization [5,6] has been shown to modify the QW energy states through quantum-confined Stark effect (QCSE) [7]; redshift of the emission peak compared to unperturbed QW resonance energy [5,8] and reduction of electron–hole wavefunction overlap (oscillator strength) [6,9]. Coulomb screening due to carrier injection [5,8] or impurity doping
0169-4332/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 ( 0 1 ) 0 0 9 0 7 - 2
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[9] recovers the overlap. A predominant reason for the efficient emission has been proposed [8,9] to be due to short quasi-diffusion length [10] of carriers, which is caused by the presence of quantum-disk (Q-disk)-size [11] effective bandgap inhomogeneity [8–10,12] or quantum dots (QDs) [13–15]. However, degree of the compositional fluctuation and structural quality of practical InGaN multiple quantum well (MQW) LD structures exhibiting the lasing wavelengths between 390 and 410 nm, which are proper wavelengths to obtain low threshold current density and long-lived cw lasers, are not fully understood yet. In this article, results of structural and compositional analyses on InGaN MQW LD structure that lased at around 400 nm are shown in addition to the results of static and time-resolved (TR) photoluminescence (PL) spectroscopy to clarify the spontaneous emission mechanisms in terms of QW exciton [7,16] localization due to large bandgap bowing in InGaN alloys. To exclude the disturbance due to F and thickness fluctuation effect usually seen in hexagonal QW structures, bulk cubic In0.1Ga0.9N film and MQWs were also examined.
2. Experimental Inx Ga1x N MQW LD wafer that lased at 400 nm was grown by two-flow metal organic vapor phase epitaxy on sapphire (0 0 0 1) substrates. It consisted of a 30 nm thick GaN low temperature nucleation layer, a 3.5 mm thick GaN:Si template, a 0.16 mm thick InGaN compliance layer, a 0.3 mm thick AlGaN:Si cladding, a 0.1 mm thick GaN:Si waveguide, an MQW, a 20 nm thick AlGaN:Mg electron-overflow blocking layer, a 0.1 mm thick GaN:Mg, a 0.3 mm thick AlGaN:Mg and a 0.18 mm thick GaN:Mg layer. The MQW consisted of 10 periods of 2.3 nm thick InGaN wells and 5.8 nm thick InGaN barriers. Each layer thickness was measured using a high-resolution H-9000UHR 300 keV transmission electron microscope (HR-TEM). High-resolution X-ray diffraction (HR-XRD) measurements were carried out using an X’Pert-MRD system. Nanometer-probe compositional analysis was carried out using a KEVEX DELTA energy dispersive X-ray microanalysis (EDX) equipped on HB501 field emission scanning TEM. The probe diameter, acceleration energy and current were
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1 nm, 100 kV and 109 A, respectively. The accumulation duration was 50 s. TEM observation and EDX measurement were done by TORAY Research. The TEM specimen was carefully prepared to suppress damages like artificial In segregation. Static PL and photoluminescence excitation (PLE) measurements were carried out on the wafer while electroluminescence (EL), photovoltaic (PV) and electroreflectance (ER) measurements were carried out on a processed wafer. Static PL was excited by the 325.0 nm line of a cw He–Cd laser (12 mW) and dispersed by a 67 cm focal-length grating monochromator (McPHERSON 207). PLE spectra were measured by monitoring the lower energy tail of a broad PL band. TRPL was excited either by a 600 ps pulse of a N2 laser or a 100 fs pulse of a frequency-doubled Ti:sapphire laser. A standard streak-camera acquisition technique was employed to analyze the signal. To compare the decay dynamics between hexagonal (h-) and cubic (c-) InGaN, a 170 nm thick c-In0.1Ga0.9N film and a 5-period-MQW having 5 nm thick c-In0.1Ga0.9N wells and 10 nm thick c-GaN barriers were grown by r.f. molecular-beam epitaxy (RF-MBE) using metallic Ga and In, and N2 plasma source (SVT-4.5) on a 300 nm thick c-GaN template. They were grown on a 7 mm thick 3C–SiC (0 0 1) layer on Si (0 0 1), which has been prepared by chemical vapor deposition [17]. Typical residual electron density n is estimated to be of the order of 1017 cm3 or smaller. The structure of the samples was also characterized by HR-XRD. Inclusion of the hexagonal phase was negligible and the c-InGaN layers were confirmed by reciprocal lattice mapping method to be pseudomorphically grown on relaxed c-GaN templates.
3. Results and discussion 3.1. Structural and optical properties of h-InGaN MQW LD wafer The MQW LD structure had atomically flat and abrupt interfaces, as shown in HR-TEM bright-field images in Fig. 1. The upper limit of the thickness fluctuation (sum of the two interfaces) of InGaN wells is not greater than two monolayers (2 ML; 0.52 nm) over a few micrometers considering possible defocusing effects.
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Fig. 1. HR-TEM micrograph of h-InGaN MQW region. Nanometerprobe EDX was carried out at each point (A–E) in the figure.
Well-resolved superlattice (SL) satellite peaks due to InGaN MQW are found in the HR-XRD pattern, as shown in Fig. 2. The entire structure is confirmed to be pseudomorphically grown on the GaN template. The alloy compositions are calculated from the lattice constants obtained from the XRD pattern shown in Fig. 2 based on the quasi-cubic approximation, ezz ¼ 2ðC13 =C33 Þexx , where ezz (exx) is the strain along the c-axis (a-axis), and C13 and C33 are the elastic stiffness constants. The values used are the same as those used in Ref. [18]. Note that those values of alloys are
Fig. 2. HR-XRD pattern of the InGaN MQW LD structure that lased at 400 nm.
assumed to obey the Vegard’s law. The AlN mole fraction in the AlGaN cladding layers is thus obtained as 14% and average InN mole fraction in the InGaN MQW is only 3%. The SL period is calculated to be 8.5 nm, which nearly agrees with the TEM result of 8.1 nm. Nanometer-probe EDX was carried out at each point marked in Fig. 1. The AlN mole fraction in the AlGaN blocking layer on top of the MQW is 22%, as shown by spot ‘‘A’’ in Fig. 1. The value in the cladding layers is approximately 15% (not in Fig. 1), which agrees with the value obtained from the XRD data. The InN mole fraction x in the barriers is approximately 2.1% and that of the wells is 5.1– 5.9%. However, the latter variation nearly agrees with the detection limit of 1%. The result means that the compositional inhomogeneity in the well is very small. If we assume average x as 5.5% for the wells, total average x in the MQW is calculated to be 3.1% considering their thickness. The value agrees with the XRD result being 3%. Optical spectra of the MQW at 300 K are summarized in Fig. 3. A transition structure at 3.42 eV is due to the GaN waveguide layer. Recently, the bowing parameter, b, of Inx Ga1x N alloys has been reported to be very large [19–21] and vary with x [21]. Using the value of b(x) [21], bandgap energies of bulk In0.02Ga0.98N and In0.055Ga0.945N are calculated to be 3.27 and 3.04 eV, respectively. Both values are consistent with the experimental ones being 3.33 and 3.158 eV considering the
Fig. 3. Electroreflectance (ER), electroluminescence (EL), photovoltaic (PV), and photoluminescence excitation (PLE) spectra of the In0.06Ga0.94N MQW LD structure measured at 300 K.
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Eme ¼ 3:17 eV approximately coincides with the QW resonance energy obtained from the ER spectrum (3.158 eV). However, the increase of the decay time would also be explained by the field screening effect [24]. Therefore, effective field strength must be estimated. 3.2. Estimation of the effective field in h-InGaN wells
Fig. 4. Time-integrated PL spectrum and the emission lifetime as a function of detection photon energy at 300 K of the In0.06Ga0.94N MQW LD structure. The inset shows the PL intensity as a function of time after excitation.
effect of compressive biaxial stress and quantum-size effect. Therefore, the transition structures at 3.158 and 3.33 eV are assigned as being due to excitonic resonances in the In0.06Ga0.94N wells and In0.02Ga0.98N barriers, respectively. Thus, the wells are revealed to have the thickness L ¼ 2:3 nm and x ¼ 0:055. In spite of very small compositional inhomogeneity determined above, the spontaneous EL peak energy is 3.109 eVand the Stokes-like shift (SS) is 49 meV even at 300 K. Origin of the SS is either the field effect [22] or effective bandgap inhomogeneity [8,9], which will be discussed later. The luminescence decay time increases from 800 ps to 2.2 ns with decreasing detection photon energy from 3.2 to 3 eV, as shown in Fig. 4. The peak energy shifts to the lower energy with time, though the data are not shown here. Since this behavior is characteristic of localized excitons [23] in an exponential-tail density-of-states (DOS) gðEÞ ¼ expðE=E0 Þ, where E0 represents the localization depth, the relation between the PL lifetime tPL and emission energy E is fitted using tPL ðEÞ ¼ tr =f1 þ exp½ðE Eme Þ=E0 g, where Eme is the energy similar to the mobility edge and tr the radiative or effective lifetime. E0 is obtained as 35 meV, which is a bit smaller than SS (49 meV). The value of E0 increases monotonically with decreasing measurement temperature, the result means that the tail states are not filled by thermal energy at 300 K.
In InGaN wells with InGaN barriers, the spontaneous polarization can be nearly neglected [6] and the piezoelectric field, FPZ, dominates total effective F. The strength of FPZ is calculated using the relation, FPZ ¼ Pz;PZ =er;k e0 , where er,k and e0 are the relative dielectric constant along the z-axis and the dielectric constant in vacuum, respectively. Pz,PZ is the piezoelectric polarization along the z-axis, which can be expressed as Pz;PZ ¼ 2e31 exx þ e33 ezz , where eij are the piezoelectric constants and eij are the strain. The value of FPZ in the In0.06Ga0.94N well is thus calculated to range from 1.1 MV/cm [6] to 160 kV/cm [22] depending on the values of eij [6,22]. Since the values of eij reported to date scatter an order of magnitude, effective fields F in h-InGaN have been investigated experimentally using following three approaches. (i) Static PL, PLE and TRPL signals from In0.1Ga0.9N QW structures have been measured as a function of well thickness L [9,25] to demonstrate that QCSE controlled the PL peak energy under low excitation conditions especially for L larger than 3 nm. Indeed, the PL peak shifted to the higher energy under high excitation conditions. However, the amount of the shift is remarkably small for thinner wells, and high excitation PL peak energies nearly agreed with the low excitation ones for L smaller than 3 nm. The strength of F has been estimated by calculating confined energy levels and wavefunctions in the In0.1Ga0.9N wells as functions of F, L and doping density n in the barriers by variational method neglecting exciton binding energy within the Hartree approximation solving the Schro¨ dinger equation and Poisson equation simultaneously and self-consistently. The value of F has been estimated to be about 350– 400 kV/cm for x ¼ 0:1, which nearly agreed with previous reports [22].
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Fig. 5. Emission and absorption edge energies of 3 nm thick Inx Ga1x N QWs. The bandgap of unstrained bulk InGaN estimated after Ref. [21] is also plotted.
(ii) Static and dynamic optical processes in a series of 3 nm thick Inx Ga1x N QWs with various x were investigated. The PL peak energy of the QWs showed the redshift and the full width at half maximum (FWHM) increased simultaneously with increasing x. The PL peak energy and average bandgap, which was defined as the energy where the PLE/PV signal decreased to its half the maximum or the transition energy in the ER spectrum, of the wells are plotted as a function of x in Fig. 5. Bandgap energies of unstrained bulk Inx Ga1x N alloys, which were calculated using the relation Eg ðxÞ ¼ 3:42x þ 1:89ð1 xÞ bðxÞxð1 xÞ, where Eg(x) is the energy gap and b(x) the composition-dependent bowing parameter of Inx Ga1x N [21], are also plotted in Fig. 5. It should be noted that the energy gap of Inx Ga1x N alloys cannot be fitted by quadratic dependence on x [21]. The effective bandgap of the Inx Ga1x N QWs for x < 0:15 is remarkably higher than the bulk bandgap. This is reasonable since both the compressive biaxial strain in InGaN and the quantum size effect increase the bandgap, and the field effect F is not so serious for the QWs with x < 0:10 and L < 3 nm [25]. The emission peak energy is higher than the bulk bandgap for x < 0:12. However, the emission peak energy of the QWs is smaller than the bulk bandgap for x > 0:15,
indicating that F plays a certain role in the wells even for L ¼ 3 nm. Note that x ¼ 0:15 corresponds to the practical blue SQW LEDs. The strength of F for each x was estimated by calculating confined energy levels and wavefunctions in the 3 nm thick Inx Ga1x N wells as functions of bulk bandgap given above, F and doping density n in the barriers by variational method. The results are consistent with the result of the approach (i). (iii) PL spectra of the 2.5 nm thick In0.25Ga0.75N amber SQW LED wafer has been measured as a function of external bias [26]. The PL from the QW has been excited by the 488.0 nm line of a cw Arþ laser to selectively excite the well. Takeuchi et al. [27] have also used this method to determine the direction and strength of FPZ in In0.16Ga0.84N QWs, and have found a blue shift of the PL peak with increasing reverse bias. Their conclusion that FPZ pointed from the surface to the substrate seemed to be valid considering a Ga-face growth during MOVPE. The PL peak of the amber LED wafer has shifted to the higher energy by up to 110 meV by changing the external bias from þ2 to 10 V [26]. By solving again the Schro¨ dinger equation and Poisson equation simultaneously and self-consistently to fit the peak energy shift, F has been estimated to be 1.4 MV/cm. The value is close to the one estimated from the strain and piezoelectric constants reported by Wetzel et al [22]. Using the results of (i)–(iii), the strength of F in Inx Ga1x N QWs was correlated with x [28]. As has been shown, F (FPZ) naturally increases monotonically with increasing x. The value of F for the In0.06Ga0.94N QWs is nearly 286 kV/cm. In that case a potential drop across the 2.3 nm thick well is as small as 66 meV, which is smaller than the band discontinuity between the wells and barriers (172 meV). It should be mentioned that the electron quantized energy level is flat within the well due to larger conduction band discontinuity, and the QW may belong to the CASE II in Refs. [9,25]. In this case, luminescence peak must be close to the absorption edge if there is no in-plane potential fluctuation. Therefore, the field effect is not so strong in the current In0.06Ga0.94N MQW LD wafer.
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Since FWHM of the EL peak is approximately 75 meV and SS is 49 meV (65% of FWHM of the EL), as shown in Fig. 3, QW excitons are considered to localize [8,23] at certain potential minima [9,10] even at 300 K. The concept of exciton localization can explain why InGaN QWs exhibit high Zext against the large TD density especially for larger x (larger strain) [1,3]. 3.3. Origin of exciton localization A simple calculation indicates that effective bandgap inhomogeneity due to 2 ML thickness fluctuation (0.52 nm) for the well with L ¼ 2:3 nm and x ¼ 0:06 is nearly 20 meV, which should be leveled by thermal energy at 300 K. However, there still remain SS ¼ 49 meV and E0 ¼ 35 meV at 300 K. Therefore, the QW should have other localization mechanisms like In compositional inhomogeneity [8]. In order to exclude the localization effect due to thickness fluctuation and the field effect due to FPZ, optical properties of the bulk c-In0.1Ga0.9N film were investigated. The c-In0.1Ga0.9N film exhibits a large SS of 280 meV compared to 100 meV for h-In0.1Ga0.9N [28], indicating that compositional fluctuation in cInGaN is larger than that in h-InGaN materials presumably due to difficulties in growing metastable cubic nitrides. Its luminescence decay time increases with decreasing detection photon energy. TRPL signals monitored at particular wavelengths from a 170 nm thick c-In0.1Ga0.9N film at 10 K are shown in Fig. 6(a). All signals show a non-exponential decay similar to the case for h-InGaN [9,30]. Two analyses are carried out as follows. One model assumes a presence of exponentially decreasing localized band-tail states due to an effective bandgap inhomogeneity [23]. Another assumes a presence of disordered quantum nanostructures [31] like closely spaced self-formed QDs or Q-disks. At first, PL lifetime tPL is plotted as a function of emission photon energy E in Fig. 6(b), together with the time-integrated PL spectrum. The lifetime is defined as the longer decay component when the decay curve is fitted assuming a double exponential decay. As shown, tPL increases with decreasing emission photon energy. The relation between tPL and E is analyzed in the same manner as described in Section 3.1. The fitting curve reasonably reproduces the
Fig. 6. (a) TRPL signals monitored at particular wavelengths from 170 nm thick c-In0.1Ga0.9N/c-GaN at 10 K, (b) PL lifetime tPL as a function of emission photon energy E and (c) ln{ln[I0/I(t)]} vs. ln(t) relation.
experimental data giving the values of E0 ¼ 109 meV, eVand tr ¼ 495 ps. It should be noted that tPL at 10 K is an order of magnitude shorter than that of h-InGaN QWs, which means that tr in h-InGaN QWs is considered to be made longer by the wavefunction separation due to QCSE. Next, ln{ln[I0/I(t)]} vs. ln(t) relation is plotted in Fig. 6(c), where I(t) is the PL intensity at time t and I0 is I(0). Chen et al. [31] have analyzed PL decay curve from disordered low-dimensional semiconductors to propose that above relation can be approximated by a straight line; IðtÞ ¼ I0 exp½ðt=tÞb , which has been defined as ‘‘stretching exponential’’ decay where b is the scaling parameter that is related to the dimensionality of the localized centers and t the delocalized lifetime. Obviously, the data can be approximated by the straight line, as shown in Fig. 6(c) giving t ¼ 149 ps and b ¼ 0:65.
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Both models seem to qualitatively fit the data. In addition, PL peak energies of the films show a weak redshift of 20 meV with increasing temperature from 10 to 300 K, as is the case with h-InGaN QWs [29]. Note that the amount of the bandgap shift between 10 and 250 K in c-GaN is 64 meV [32]. Since the crystal homogeneity of cubic materials is worse than that of hexagonal polytype, the data shown here are not the representatives of h-InGaN device structures. However, the carrier/exciton localization is considered to be an universal phenomenon in InGaN materials because h-InGaN also exhibits certain SS [8,9,28, 30], large bandgap bowing, increasing tPL with decreasing energy and small PL peak shift with increasing temperature. Therefore, the emission is assigned as being due to the recombination from certain localized states. Bellaiche et al. [21] have predicted natural resonant hole wavefunction localization at In site in GaN:In and have attributed this to be the origin of exciton localization. This seems plausible. However, localization of holes is insufficient to explain the improved Zext against the presence of large number of TDs and of FPZ, since electrons injected from the barrier are free. Also, their prediction [21] that PL intensity of Inx Ga1x N would decrease with increasing x due to drastic decrease of the momentum matrix element for low x conflicts with general experimental findings that Zext increases with increasing x [3].
Fig. 7. PL lifetime tPL, radiative lifetime tr and non-radiative lifetime tnr of the emission from c-In0.1Ga0.9N/c-GaN MQW structure. The latter two are deduced from tPL and the PL intensity as a function of temperature.
Fig. 7 shows the radiative lifetime tr and non-radiative lifetime tnr of the emission from c-In0.1Ga0.9N/cGaN MQW structure, which are deduced from the PL decay time tPL and the PL intensity as a function of temperature, T, using the relation Zint ¼ 1=ð1 þ tr =tnr Þ, where Zint is an internal quantum efficiency. To simplify, Zint is set unity at low temperature since non-radiative recombination process is generally frozen at low temperature. At the moment, there is no evidence that this assumption is valid for c-InGaN. However, it can be recognized that tr is nearly constant below 100 K but increases linearly or slightly superlinearly with T above 150 K. Therefore, the DOS from which the emission originates seems to change from zero dimension (0D) to two or three dimension (2D or 3D) with increasing T [33,34]. Indeed, the well thickness (5 nm) is rather larger than the free exciton Bohr radius (3.4 nm) and the wavefunction confinement is weak. Note here that the PL still shows a stretching-exponential decay even at 300 K. The origin of the exciton localization [8] universally seen in InGaN is thus considered to be the local potential minima [8–10] due to non-random alloy compositional fluctuation or a combination of this and the hole localization mentioned above. The size of the lateral localization has been estimated to be smaller than 50 nm [10] and thus we have concluded it to Q-disk size, but the size can be even smaller than the size of structural QDs [21], as revealed from temperature-independent tr shown in Fig. 7. It should be noted that even though the compositional fluctuation is only 1%, electrons can be localized due to the large [19–21] and composition-dependent [21] bandgap bowing of InGaN alloys. For example, the bandgap energies of h-Inx Ga1x N bulk crystals are calculated to be 3.059 eV for x ¼ 0:05 and 2.990 eV for x ¼ 0:06 using the value of bðx ¼ 0:055Þ ¼ 6 eV [21]. The energy difference between the two (69 meV) exceeds the value of SS being 49 meV of the 400 nm h-InGaN LD. Thus the compositional inhomogeneity might be smaller than 1%. Since the threshold carrier density of the LD action is estimated to be of the order of 1019–1020 cm3 and the bandgap renormalization is obvious, such shallow localization depth (35 meV at 300 K) is easily filled up under the lasing conditions for the 400 nm LD wafer at 300 K. This delocalization can explain the decrease of quantum efficiency under high excitation conditions.
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4. Conclusions In0.06Ga0.94N MQW LD structure that lased at 400 nm was shown to have atomically flat interfaces and very small compositional inhomogeneity. However, excitons were confirmed to be localized within the DOS which might have an exponential-tail type distribution. Although the dimensionality of the localization is not yet resolved, the variation of tr for cInGaN implied that lateral confinement is weak at 300 K. Q-disks might be responsible. However, such shallow and low density localized states would be leveled under high excitation conditions. The spontaneous emission was assigned as being due to the recombination of localized excitons while the stimulated emission seemed to come from the continuum states energetically higher than the mobility edge.
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