Piezoelectric Effect in GaInN/GaN Heterostructure and Quantum Well Structure. T. Takeuchi, C. Wetzel, H. Amano, and Isamu Akasaki

Transcription

1 Piezoelectric Effect in GaInN/GaN Heterostructure and Quantum Well Structure T. Takeuchi, C. Wetzel, H. Amano, and Isamu Akasaki Department of Electrical and Electric Engineering, Meijo University, Shiogamaguchi, Tempaku-ku, Nagoya , Japan TEL (ex. 5064) FAX Introduction 2. Structural and optical properties of GaInN/GaN heterostructures 2.1. Crystal growth 2.2. Structural properties 2.3. Optical properties 3. Luminescence properties of GaInN quantum wells 3.1. Theoretical piezoelectric field and transition energy 3.2. Experiments 3.3. Luminescence properties 4. Quantum-confined Stark effect in GaInN quantum wells 4.1. Experiments 4.2. Determination of piezoelectric field 4.3. Determination of growth polarity 5. Orientation dependence of piezoelectric effect in GaInN/GaN heterostructures 5.1. Theoretical calculations 5.2. Piezoelectric field in GaInN/GaN heterostructures 5.3. Transition probability and energy of GaInN quantum wells 6. Conclusions 7. Acknowledgements 8. References 9. Figure captions 10. Tables 11. Figures 1

2 1. Introduction Group III nitride semiconductors have direct transition band structures with the band gap energies ranging from 1.9 ev for InN to 6.2 ev for AlN. Therefore, its applications to light emitters and detectors are expected in the visible and ultraviolet regions, which have not been demonstrated using the conventional III-V semiconductors, such as GaAs and InP. One of the biggest breakthroughs in the nitride research area is an insertion of a low-temperature-deposited buffer layer between a GaN layer and a sapphire substrate, which enables us to obtain a high quality (0001)-oriented GaN layer. 1,2 After that, the growth of high quality ternary alloys, GaInN 3,4 and AlGaN, 5,6 grown on the GaN were developed, leading to the realization of high quality heterostructures including quantum well (QW) structures. 7,8 It is well known that the heterostructure has played a key role in conventional III-V semiconductor devices. Actually, GaInN QW structures are unexceptionally used as active layers in high efficiency blue/green light emitting diodes 9,10 and ultraviolet laser diodes. 11,12 Accordingly, the investigation of optical properties of the GaInN QWs is significantly important in terms of practical applications as well as academic interests. The lattice constant of GaInN is larger than that of GaN, where the lattice mismatch is up to 10%. This is larger than that of the well-known GaInAs/GaAs system. An epitaxial GaInN layer grown on GaN is thus expected to be biaxially compressed and strained. In addition, group III nitride semiconductors have larger piezoelectric constants than the other III-V semiconductors. Then, large piezoelectric fields can be induced in the strained GaInN layers along polar directions, such as [0001]. Meanwhile, the optical properties of strained GaInAs QWs grown along [111] and the CdS/CdSe superlattice grown along [0001] 17 have been investigated and understood as the intrinsic 17 quantum confined Stark effect 18 caused by the internal piezoelectric fields. In this way, the optical properties of strained GaInN QWs grown along [0001] should be strongly affected by the piezoelectric effect. In this chapter, we describe the piezoelectric effect in GaInN/GaN heterostructures and QWs. We start with the structural and optical properties of GaInN/GaN heterostructures as well as those of AlGaN/GaN heterostructures in Section 2. We clarify the strain conditions of the ternary alloys grown on GaN, and describe a precise determination of the composition in the ternary alloys coherently grown on GaN by taking the strain into account. In section 3, we investigate the influence of piezoelectric fields on luminescence properties of strained GaInN QWs, such as excitation power dependence and well width dependence of the photoluminescence peak energy. The luminescence properties will be well explained by the intrinsic quantum confined Stark effect caused by the internal piezoelectric fields. We also discuss in Section 4 the extrinsic quantum confined Stark effect in GaInN QWs p-i-n 2

3 structures by applying the external voltage. Then, the direction and magnitude of piezoelectric fields in the GaInN QWs will be determined. In addition, the growth polarity of nitride epitaxial layers on sapphire substrates will be determined based on the direction of the piezoelectric fields. Finally, in Section 5, we theoretically calculate crystal orientation dependence of piezoelectric effects in GaInN/GaN heterostructures. This gives us potential controllability of the piezoelectric field in the biaxially strained nitride layers. 2. Structural and optical properties of GaInN/GaN heterostructures 2.1 Crystal growth We prepared samples using atmospheric pressure metalorganic vapor phase epitaxy (MOVPE). Triethyl-gallium (TMGa), triethiyl-aluminum (TMAl), and triethyl-indium (TMIn) were used as group III sources and ammonia (NH 3 ) was used as a group V source. We used sapphire (0001) C-face as substrates, and used a low-temperature-deposited AlN (LT-AlN) buffer layer between the sapphire and a GaN layer to obtain a high quality GaN layer. 1 Hydrogen was used as a carrier gas for the growth of LT-AlN, GaN, and AlGaN, while nitrogen was used for the growth of GaInN. 3 For prevention of the parasitic reaction between the group III and V sources, we supplied them to the substrate separately using a quartz flow channel. The substrate was heated with a SiC coated graphite susceptor by RF introduction. For the investigation of structural and optical properties of heterostructured ternary alloys, we grew GaInN/GaN and AlGaN/GaN heterostructures with various compositions in the ternary alloys. Figure 1 schematically shows the sample structure. After depositing the LT-AlN buffer layer on the sapphire substrate, about a 2 µm GaN layer was grown. Then, about a 40 nm GaInN layer or a AlGaN layer with its thickness in the range of nm was grown. All the layers were nominally undoped. In this experiment, the AlN molar fraction varied up to 0.25 by changing the ratio of TMAl to total group III sources up to 0.3 at the AlGaN growth. In the case of the GaInN alloys, the InN molar fraction varied up to 0.2 by changing the growth temperature in the range of o C as well as the ratio of TMIn to total group III sources up to 0.8 at the GaInN growth. 2.2 Structural properties Strain and relaxation in the ternary alloys grown on GaN were analyzed using x-ray diffraction. Here, reciprocal space mapping (RSM) measurements around asymmetrical diffraction were carried out so as to measure the a-axis and the c-axis lattice constants of both 3

4 the ternary alloys and the GaN simultaneously. 19 Figure 2 shows the x-ray RSM around the ( 20 24) diffraction from the GaInN layer with the InN molar fraction of 0.15 grown on GaN. The GaInN layer peak is aligned with the GaN peak in a vertical line to the q // [ 1010] axis. This clearly indicates that the a-axis lattice constants of both the GaInN and the GaN are the same, 3.182r0.001 Å, in contrast to a fully relaxed GaInN which has a larger a-axis lattice constant than GaN. In other words, the GaInN is coherently grown on the underlying GaN and under biaxial compression. The slight discrepancy of the a-axis lattice constant of bulk GaN (3.188r0.001 Å) 20 could be caused by the thermal stress originating from the difference in the thermal expansion coefficients between the GaN and the sapphire. Figure 3 shows the RSM of the AlGaN/GaN heterostructure with the AlN molar fraction of 0.1. This also indicates that the AlGaN has the same a-axis lattice constant as the underlying GaN, leading to the biaxial tension in the AlGaN layer. All the other samples showed the same evidence of this coherent growth. As the result of the RSM data, we can conclude that the relaxation mechanism, such as the generation of the misfit dislocation, should not exist in the strained GaInN and the strained AlGaN grown on the GaN within the parameters of this experiment. Romano et al. reported that no misfit dislocation was observed in a cross sectional TEM image of a 225 nm Ga In N grown on thick GaN. 21 On the other hand, Wu et al. found that a 270 nm Ga 0.82 In 0.18 N grown on GaN was partially relaxed from the analysis using Rutherford backscattering and x-ray diffraction. 22 Meanwhile, the theoretical critical thickness is 4 nm for Ga 0.9 In 0.1 N on GaN and 2 nm for Ga 0.85 In 0.15 N on GaN 23 based on the theory developed by Matthews and Blakeslee, 24 which shows reasonable agreement with experimental data of the GaInAs on GaAs. 25 The large discrepancy between the experimental results and the theoretical results indicates that it is hard to generate misfit dislocations in the wurtzite nitride materials compared to other III-V materials. 21 It is widely known that composition in ternary alloys can be determined from its lattice constant using Vegard s law. It is also well understood that, when an epitaxial layer is coherently grown on a lattice-mismatched substrate, the in-plain lattice of the epitaxial layer fits that of the substrate, but the lattice along the growth direction must be distorted due to the elastic deformation. 24 Therefore, we must take the lattice deformation into account to determine a precise composition of the strained ternary alloy using its lattice constant. Figure 4 schematically shows the lattice deformation in nitride ternary alloys coherently grown on GaN. The c-axis lattice constant of the strained GaInN should be larger than that of the relaxed GaInN, while that of the strained AlGaN should be smaller than that of the relaxed AlGaN. Here, we describe the determination of the composition in the biaxially strained nitride ternary alloy coherently grown on GaN. The relation between the stress and the strain in wurtzite structure, the so-called 4

5 Huck s law, is described with elastic stiffness constants as follows: σ σ σ σ σ σ xx yy zz yz zx zy = c c c c c c c c c c c c c 12 ε xx ε yy ε zz, ε yz zx ε ε xy (1) where σ ij, c i, and ε ij are the stress, the elastic constant, and the strain, respectively, in the strained layer. The lattice mismatch generally causes the biaxial strain in the strained layer coherently grown on the lattice-mismatched underlying layer. Thus, we can describe the xx, yy, and zz components of the strain using the lattice constants. ε xx = ε ε yy xy = = a s a 0, e a e, (2) where a s is the a-axis lattice constant of the biaxially strained alloy (it is the same as that of the underlying GaN in this case), and a e is that of the fully relaxed alloy, as schematically shown in Fig. 4. Since the alloy layer should have no stress along z-direction, we obtain the following equation: σ yz = σ zx = σ zz = 0. (3) Then, we obtain the zz, yz, and zx components of the strain from Eqs. (1) and (3) as follows: ε zz ε = ( = yz 2 c 13 c 33 c s c c e = ε zx = e ε ), 0, xx (4) where c s is the c-axis lattice constant of the biaxially strained alloy, and c e is that of the fully relaxed alloy. Finally we obtain the following formula from Eqs. (2) and (4). 5

6 c se c e c e = c c a se a e a e, (5) where c se and a se are the measured values from the x-ray diffraction. In addition, we obtain c e, a e, c 13, and c 33 from the interpolation between the values of GaN and those of InN as a function of the alloy composition. Finally, the alloy composition can be determined. Figure 5 shows the composition in the strained ternary alloys as a function of their lattice constants along c-axis. For comparison, the composition of the fully relaxed alloys is also plotted. In this calculation we used material parameters listed in Table 1. As shown in Fig. 5, the InN molar fraction of the strained GaInN layer is 61% of that of the relaxed GaInN layer with the same c-axis lattice constant. 32 The value is 73% in the case of the AlGaN layer. Romano et al. experimentally clarified that the difference in the case of the GaInN using Rutherford backscattering and x-ray diffraction is 69%, 21 which is close to our estimated value. As a result, it is indispensable to take the strain into account in order to precisely determine the composition of the strained nitride ternary alloy grown on GaN using its lattice constant. 2.3 Optical properties Here we discuss the molar fraction dependence of optical properties of the 40 nm strained GaInN in the GaInN/GaN heterostructure with the precise determination of the InN molar fraction. Photoreflection (PR) and photoluminescence (PL) spectroscopy were carried out at room temperature. 32 PR was performed using a Xe-arc lamp as a white light source in a near-to-perpendicular reflection configuration. A 40 mw 325 nm He-Cd laser was used as photomodulation in the PR measurements. PL was also performed using not only the He-Cd laser but also a N 2 pulsed laser for extremely high intensity (200kW/cm 2 ) excitation. The PL peak energy under the He-Cd laser was basically the same as the PL peak energy under the nitrogen laser in this experiment. Figure 6 shows the compositional dependence of the band gap energy from PR and the PL peak energy. A red shift of the PL peak was observed with respect to the PR band gap, which is attributed to the localization of the photocarriers into the electric field induced tailstates below the DOS band gap. Within the range 0<x<0.2 we can define the bowing parameter b in the following equation: 6

7 E ggainn = 3.4 (1 x ) x bx (1 x ). (6) We obtained best least-square-fit results of the PR data for b=2.6 ev and the PL data for b=3.2 ev. Note that these bowing parameters should include the band gap deformation due to the strain. Meanwhile, assuming that the deformation potential of GaInN is equal to that of GaN, we can estimate the bowing parameter of a relaxed GaInN using the following equation which was reported by Shikanai et al. 33 E g = ε zz ( ev ), (7) which is the relationship between the zz component of the strain (ε zz ) and the band gap of GaN at 10 K (E g ). As a result, we obtained 3.8 ev for the bowing parameter of a relaxed GaInN. Table 2 lists the reported experimental and theoretical values of the GaInN bowing parameter. Recent experimental data 19,32,36 in the composition range less than 0.2 were determined to be around 4 ev with the precise determination of the InN molar fraction considering the strain effect. These values are also in reasonable agreement with the recent theoretical data 36,38 within the compositional range under 0.2. The reasons that the previously reported values 29,30 are much smaller (1 ev) than the recent values are possibly explained by no consideration of the strain in the alloy layers 21,32 and the strongly compositional dependence of the bowing parameter theoretically predicted. 36,38 3. Optical properties of GaInN QWs 3.1 Theoretical calculations As we saw in the last section, GaInN is under in-plane biaxial strain in GaInN/GaN heterostructures where GaInN is coherently grown on GaN. In addition, the nitride materials have large piezoelectric constants. Therefore, large piezoelectric fields can be induced in the strained GaInN layer along a polar direction, such as [0001]. We describe here the influence of piezoelectric fields on luminescence properties of strained GaInN quantum wells, comparing experimental and theoretical results. We first summarize the reported piezoelectric constants and spontaneous polarization of nitride semiconductors in Table 3. There are a few experimentally 27,39,41,42 and theoretically 26,40 obtained piezoelectric constants. The experimental piezoelectric constants for AlN were obtained by Tsubouchi et al. using the fitting of surface acoustic wave phase velocity 7

8 and electromechanical coupling coefficient. 39 These are in agreement with the theoretical values predicted by both Bernerdini et al. 26 and by Shimada et al. 40 independently. On the other hand, the reported values for GaN vary widely. To our knowledge, the lowest value is the experimentally estimated one by Bykhovski et al. based on the piezoelectric constant e 14 which was extracted from the electron mobility data in an AlGaN/GaN heterostructure. 27 One of the largest values is the theoretically predicted one by Bernerdini et al. using the Berry-phase approach. 26 Further investigation is necessary to obtain more precise values. The comparison with the piezoelectric constants of other III-V 43 and II-VI 44 materials are shown in Table 4, where the piezoelectric constant for a wurtzite structure, e 31, is converted to e 14 for accurate comparison with that of a zincblende structure. The magnitude of the piezoelectric constants for nitride materials is much larger than that of other III-V materials, and the sign of the constants is the same as that of II-Vs, but the opposite of that of other III-Vs. Bernerdini et al. also predicted a large spontaneous polarization due to the reduced crystal symmetry in wurtzite structure, 21 as listed in Table 3. The magnitude of the spontaneous polarization corresponds to that of the piezoelectric polarization at a 1-2 % of stress. This indicates that we basically must consider this spontaneous polarization as well as the piezoelectric polarization for an estimation of the total polarization in wurtzite nitrides. The measurable field, however, could only depend on the difference of the total polarization across the interface. Since the spontaneous polarization in GaN and InN is almost identical, the spontaneous polarization could be neglected in GaInN/GaN, but not in GaN/AlGaN Thus, we here neglect the spontaneous polarization in the calculation of the total internal field in the strained GaInN/GaN heterostructure. Next, we calculate the piezoelectric fields in the strained GaInN coherently grown on GaN. We assume the growth orientation of these layers is (0001). In other words, the GaInN layer has the same a-axis lattice constant as the underlying GaN layer, resulting in biaxial strain perpendicular to [0001]. The relationship between a piezoelectric polarization and a strain in the case of a wurtzite structure is given by, P P P x y z = ε xx yy e ε zz e ε ε yz e 31 e 31 e ε zx ε xy, (8) where P i, e ij and ε ij are the piezoelectric polarization, the piezoelectric constant and the strain in 8

9 the strained GaInN layer, respectively. Here, the z direction is set parallel to the [0001] axis. As discussed in Section 2, all the strain components in this case are described as Eq. (2) and (4). The piezoelectric field along [0001] in the strained layer is given by E z = P z ε r ε o, (9) where ε r and ε o are the dielectric constant of the material and the permittivity of free space. We used two sets of piezoelectric constants reported by Bernerdini et al. 26 and Bykohvski et al. 27 in our calculations. All the other material parameters are listed in Table 2. Figure 7 shows the calculated magnitude of the piezoelectric field in the strained GaInN layer on GaN along (0001) as a function of the InN molar fraction. Note that in Fig. 7 the positive direction of the piezoelectric field is ( 0001) in the strained GaInN layer. It can be seen that the piezoelectric field in the strained GaInN is 0.85 or 1.7 MV/cm when the InN molar fraction is 10%, corresponding to about 1% of the compressive strain. This large piezoelectric field is mainly caused by the large piezoelectric constants as described before. We then calculated the transition energies of GaInN QWs with the calculated piezoelectric fields as a function of well width using the multi-step potential approximation approach developed by Ando and Itoh. 50 In this approach, the slope of the band line-up at the well layer was replaced by a flight of steps with atomic-order length. Because of some uncertainty of the effective masses and dielectric constants of GaInN, those of GaInN were assumed to be the same as those of GaN in this calculation, as listed in Table 2. We used 3.4(1-x)+1.9x-3.2x(1-x) ev as the band gap of the strained Ga 1-x In x N, which was described in Section 2. No excitonic effect was considered. Detailed result and discussion will be given later in comparison with the measured results Experimental We here grew strained GaInN QWs samples with various well and barrier thicknesses. The samples were grown on sapphire (0001) substrates by MOVPE. The structure consists of a 30 nm LT-AlN buffer layer, a 2 µm GaN layer and Ga 0.87 In 0.13 N/Ga 0.97 In 0.03 N multiple QWs as shown in Fig. 8. All the layers are undoped, and the InN molar fraction is 13% for well layers and 3% for barrier layers in all the samples. The well width, the barrier width and the number of layer periods of the samples are listed in Table 5. The compositions and the thicknesses of these layers were determined based on x-ray diffraction and growth time. For comparison, a 40 nm Ga 0.87 In 0.13 N single layer was also grown on a 2 µm GaN/30 nm LT-AlN buffer/sapphire (0001) 9

10 under the same growth conditions as the well layers in the QWs samples except for growth time. PL spectra were measured at 14K and room temperature (RT). A pulsed N 2 laser and a He-Cd laser were used for extremely high- (200 kw/cm 2 ) and relatively low- ( W/cm 2 ) intensity excitations, respectively Luminescence properties We first study excitation dependence of luminescence properties of strained GaInN QWs. 51 Figures 9(a) and 9(b) show 14K PL spectra of 10 periods of Ga 0.87 In 0.13 N(4.3 nm)/ga 0.97 In 0.03 N(4.3 nm) strained multiple QWs and those of the 40 nm Ga 0.87 In 0.13 N strained single layer at various excitation intensities of the He-Cd laser. As the excitation intensity increased, the PL peak of the GaInN strained QWs clearly showed a blue shift. This phenomenon can be explained as follows: Since the band line-up of the strained GaInN well layer was tilted by the piezoelectric fields, the transition energy of strained GaInN QWs becomes effectively smaller than without the field; this is the QCSE, as shown in Fig. 10(a). When the samples were irradiated with an excitation source, the piezoelectric fields in the strained GaInN well layer were partly screened by the photogenerated carriers, thus weakening the QCSE, as shown in Fig. 10(b). A further increase of the excitation intensity weakened the QCSE and increased the transition energy, whereby the blue shift occurred (Fig. 10(c)). This blue shift caused by the piezoelectric field was also observed in the (111)-oriented GaInAs QWs 14 and (0001)-oriented CdS/CdSe superlattice. 17 As a result, this excitation dependence indicates the evidence of the piezoelectric filed in the GaInN well layers. In contrast, almost no shift was observed in the PL spectra of the 40 nm GaInN strained layer on GaN with various excitation powers. The GaInN single layer was fully strained from the results of x-ray diffraction, therefore, the piezoelectric field should exist. Actually the Franz-keldysh oscillation was observed in the photoreflectance measurements of GaInN/GaN heterostructures, which clearly indicates the existence of the piezoelectric field in the GaInN. 52 In this manner, we observed in this experiment the Franz-Keldysh effect which causes a slight shift of the transition energy as compared with the QCSE, due to the lack of the quantum confinement. This could be the reason for almost no shift in the PL spectra of the 40 nm strained GaInN single layer. Next, we investigate well width dependence of PL peak energy of the strained GaInN QWs. 51 Figure 11 shows the measured RT-PL peak energies of the Ga 0.87 In 0.13 N strained QWs as a function of the well width. The calculated transition energy with the piezoelectric fields using the piezoelectric constants reported by Bernerdini et al. 26 (2.3 MV/cm) and by Bykovski et al. 27 (1.1MV/cm) are plotted for comparison. The calculated transition energy with no electric field is 10

11 also plotted. In Fig. 11, the PL peak energy of the GaInN strained QW under the He-Cd laser excitation becomes smaller linearly as the well width increases. Also, it becomes smaller than that of the 40 nm GaInN strained single layer when the well width is thicker than 4 nm. This tendency is in reasonable agreement with the theoretical calculations taking the piezoelectric fields into account. Note that the quantum size effect cannot explain this lower shift in PL peak energy of QWs in respect to that of the thick strained single layer. This phenomenon is attributed to the influence of internal fields due to the piezoelectric effect. The measured PL peak energy under the N 2 pulsed laser excitation showed a slightly lower shift and approached to that of the 40 nm GaInN strained single layer as the well width increased. These measured data are approximately equal to the transition energy calculated under the assumption without piezoelectric field, which indicates that the piezoelectric field could be completely screened by photogenerated carriers under the high excitation power. Therefore we conclude that the piezoelectric field greatly affects the luminescence properties and the properties are well explained as intrinsic QCSE without applying external voltage. Figure 12 shows the fitting results of PL peak energy as a function of well width between measured data and calculated data. A fitting parameter is the piezoelectric field in the calculation. In the case of the weak excitation, the piezoelectric field was determined to be 0.7 MV/cm. This magnitude is about 60% of the value using the piezoelectric constant measured by Bykovski et al. 27 and about 30% of the values of that predicted by Bernerdini et al. 26 To evaluate the value precisely by the fitting calculation, we should consider the degree of screening by photogenerated carriers and the influence of the local fluctuation of alloy composition at the GaInN layer. 53,54 We will also discuss the magnitude of the piezoelectric field in Section 4. J.S. Im et al. studied the influence of piezoelectric fields on the luminescence properties of Ga 0.95 In 0.05 N/GaN QWs in terms of PL decay time as well as PL peak wavelength. 55 They found that the PL decay time became longer and the PL peak energy became smaller as the well width was wider. Both results were simultaneously well explained by the calculated results considering the piezoelectric field of 0.35MV/cm. This result directly indicates that the piezoelectric field causes the spatial separation of the electron and hole wavefunctions. 4. Quantum confinement Stark effect in GaInN QWs 4.1 Experiment In this section, we identify the piezoelectric fields in strained GaInN QWs by studying the applied voltage dependence of the luminescence properties, the so-called extrinsic 11

12 quantum-confined Stark effect. 56 The strained GaInN/GaN quntum well p-i-n structures were used for this purpose. We used two different substrates, a LT-AlN buffer/sapphire (0001) and a 12 µm thick GaN on sapphire (0001) grown by hydride vapor phase epitaxy (HVPE). The sample structure consists of an n-gan (3 µm), undoped GaInN (3 nm)/gan (6 nm) 5 QWs, a p-algan (60 nm) and a p-gan (120 nm), as shown in Fig. 13. The two samples on the different substrates were separately grown by the MOVPE. The carrier concentrations of the n-gan, the p-algan, and the p-gan are 2x10 18, 2x10 17, and 1x10 18 cm -3, respectively, while the donor and acceptor concentrations, are 2x10 18 and 5x10 19 cm -3, respectively. In this structure, the direction of the built-in electric field points from substrate to growth surface. Using X-ray diffraction, we verified that the growth orientation of the samples is { 0001}, and the GaInN well layers and the p-algan layer have the same in-plane a-axis lattice constant as the n-gan layer. This indicates that these layers were under in-plane biaxial strain. Taking the strain into account, we determined that the InN molar fraction in the strained GaInN wells is 16% for the sample on the sapphire substrate and 15% for the sample on the HVPE grown GaN. We fabricated transparent electrodes as p-side contacts in order to measure PL spectra of the GaInN QWs through the electrodes. PL spectra were measured at room temperature under various applied voltages. When the applied voltage was changed from 4 to +2 V, we observed that the current through the devices varied from 5 to 700 µa. The current increased to 9 ma at the voltage of +3 V, and the electroluminescence was observed. A He-Cd laser with a power of 30 mw and spot size of 0.3 mm 2 was used as an excitation source Quantum confined Stark effect Figure 14 and 15 show the PL spectra of the GaInN/GaN QWs p-i-n structures on the sapphire and on the HVPE grown GaN under various applied voltages, respectively. Multiple peaks seen in the PL spectra must be attributed to interference fringes due to multiple reflection within the air/nitrides/sapphire system. 53 We eliminated this influence by dividing the PL spectra by calculated interference fringes based on the multiple reflection in the Fabry-Perot etalon. The best fitting results show clear single peaks in both Fig. 1 and 2, when we used the refractive index of 2.5, reflectivity from 0.04 to 0.11, and cavity length of 2.6 µm for the sapphire case and 13.4 µm for the HVPE grown GaN case, which are slightly different from our expected values. As a result, we observed a clear blue shift of the PL peak wavelength in the both substrate cases with an increase of the reverse applied voltage. In the typical QCSE, such as in GaAs/AlGaAs QWs 18, a red shift of transition wavelength is observed with increasing reverse voltages. This is due to an increase of the 12

13 internal field in the well layer, leading to a smaller effective band gap. Therefore, the blue shift in our case can be explained by a decrease of the internal field even with the increase of the reverse bias. In other words, this is interpreted to be a cancellation of the piezoelectric field by the reverse bias, similar to the case of GaInAs/GaAs QWs on GaAs (111). 15,16 Figure 16(a) shows the case that the piezoelectric field is set against the built-in and reverse bias field. When the reverse bias is increased, the band structure of the GaInN well approaches flat-band conditions, leading to the blue shift. On the other hand, in the case that the direction of piezoelectric field is the same as that of built-in field, the total internal field is monotonously increased with the increase of the reverse bias as shown in Fig.16(b). Therefore, we conclude that the direction of the piezoelectric field in the strained GaInN well layer is the opposite to those of the built-in/reverse bias field, which points from the growth surface to the substrate. Iychika et al. reported that blue shift of the PL peak wavelength of GaInN/GaN QWs under negative bias to the growth surface, resulted in the same direction of the piezoelectric field in the GaInN well layers as discussed here. 57 J.S. Im et al. also reported the same direction of the piezoelectric field by the PL decay measurement of two asymmetric QW samples, AlGaN/GaInN QW/GaN on substrate and GaN/GaInN QW/AlGaN on substrate. 58 They showed the difference of the almost 3 orders of magnitude in PL decay time, which can be explained by the different overlap of the electron and hole wavefunctions caused by the different barrier height at the triangular potential of AlGaN/GaInN or GaN/GaInN. In order to estimate the magnitude of the piezoelectric fields, we compared the measured PL peak energy with calculations as a function of the applied voltage. In the calculation, the total internal field (E total ) in the well layer is approximated as follows: 59 E V total bi = Ei V = Ei ( d u appl /( d u + dd) + E + dd) + E piezo piezo, N Lw, (10) where V bi, V appl, E piezo, and E i represent the built-in potential, the applied voltage, the piezoelectric field, and the internal field in the undoped and depletion regions, respectively. The positive direction of the electric fields is set from the substrate to the growth surface in Eq. 10. The thickness of the undoped region, depletion region, the well width, and the number of wells are represented as d u, d d, L w, and N, respectively. The built-in potential (3.3 V) was calculated from the carrier concentrations and the effective mass values. The thickness of the undoped region (51nm) and well width (3 nm) were obtained from the results of x-ray diffraction and the growth time. The depletion region thickness was calculated from the donor and acceptor concentrations, the built-in potential, and the applied voltage. This thickness varied from 89 to 13 nm with the applied voltage from 10 to +3 V. We used the piezoelectric field as a free 13

14 parameter for fitting to the experimental results. All the material parameters used in the calculations are listed in Table 2. Then we calculated the applied voltage dependence of the lowest transition energy between the conduction band and the valence band in GaInN/GaN QWs with the InN molar fractions of 15% and 16% using the multi-step potential approximation. 50 In this calculation we did not consider the screening effect of the piezoelectric field by carriers. Figure 17 shows a comparison between the experiments and the calculations. For negative applied voltages, the data can be well described assuming a piezoelectric field of 1.2 MV/cm for both Ga 0.84 In 0.16 N on the sapphire and Ga 0.85 In 0.15 N on the HVPE grown GaN. Here note that the minus sign of the piezoelectric fields indicates that the direction is from the growth surface to the substrate, which is consistent with that discussed above. For positive applied voltage, however, there is a discrepancy as large as 30 mev between the experiments and the calculations with a piezoelectric field of 1.2 MV/cm. At present we can not explain this discrepancy. The magnitude of the measured piezoelectric field here is about 40% of the calculated value using the piezoelectric constant predicted by Bernerdini et al. 26 and are very close to that using the piezoelectric constant measured by Bykhovski et al. 27 For more strict investigation, we need more accurate estimations of the built-in potential and the thickness of the depletion region, and should consider the influence of the compositional fluctuation in the GaInN layers. 53,54 Figure 18 shows summary of the comparison of some piezoelectric field derived from the optical measurements 51,52,55 with the theoretical data calculated in Section 3. It can be seen that the experimental data are slightly smaller than the calculated data using the piezoelectric constant experimentally derived from the mobility data by Bykhovski et al, 27 which is the lowest value in Table 2. This is not surprising because in the optical measurements the piezoelectric field should be partly screened by the photogenerated carriers. In this experiment PL intensity dramatically decreased as shown in Fig.19, while PL peak energy was blueshifted with the increase of the reverse voltage, that is, the decrease of the total field in the well layer. In general, the transition probability usually increases in this case because of an increase of the overlap integral between the wave function of the electron and that of the hole. The calculated transition probability in this case is also plotted in Fig.19. At the same time, however, we also observed that the photocurrent increased significantly, as shown in Fig.20. This indicates that, with the increase of the reverse voltage, photogenerated carriers contribute to the current transport rather than to the luminescence, resulting in the decrease of the PL intensity Growth polarity 14

15 GaN is typically grown along a [0001] polar direction on a LT-AlN buffer layer/sapphire substrate by MOCVD. 1 In this case, there are two polarities, such as A-face (Ga-face, (0001)) and B-face (N-face, ( 0001) ) as shown in Fig.21, where the bond starting from Ga to N, which are parallel to the c-axis, points in a positive direction. 45 The polarity greatly affects the chemical properties of the materials, such as etching properties. Thus, it is important to obtain the information on the polarity in terms of the control of the material fabrication. The determination of the growth polarity in nitride materials has been demonstrated by various techniques, as listed in Table 6. 56,57,60-68 It can be seen that the polarity greatly depended on the sample preparation. Here we determine the growth polarity of our materials by comparing the measured direction of piezoelectric and the theoretical directions. As we already discussed, the theoretical direction is ( 0001) in strained GaInN/GaN heterostructures using the sign of the piezoelectric constants reported by Bernerdini et al., 26 which is the same as that of II-VI materials. Meanwhile, the measured direction was determined to be from the substrates to the growth surface in this Section. Consequently, we can conclude that the growth polarity of both our nitride epilayers grown by MOVPE and HVPE are (0001), Ga-face. This result is consistent with all the other results of smooth GaN layers grown on sapphires using LT-buffer layers by MOVPE ,67,68 Iyechika et al. showed the same direction of the piezoelectric field in the strained GaInN as discussed above, but concluded that the polarity is N-face, assuming the opposite sign of the nitrides piezoelectric constant, which is the same as that of conventional III-Vs Orientation dependence of piezoelectric effect 5.1. Theoretical calculations As we discussed in the previous sections, the optical properties of strained nitride QWs are well explained by the QCSE which are caused by the internal piezoelectric fields. The new functional devices with an active use of the internal piezoelectric field have been reported in (111)-oriented GaInAs strained QWs. 69,70 This internal field, however, causes lower transition probability, resulting in lower efficiency of light emitting devices. In this way, the controllability of the internal piezoelectric field can expand further possibility of the band structure engineering, which leads to higher performance and/or novel functional devices. In zincblende strained QWs, such as a GaInAs/GaAs, there are several reports on crystal orientation dependence of the piezoelectric fields. 13,14 In these reports, (111) orientation has the largest longitudinal piezoelectric field, and (001) and (110) orientations have no field. This clearly 15

16 indicates the controllability of piezoelectric fields in strained layers by changing the crystal orientation. We here theoretically investigate the crystal orientation dependence of longitudinal piezoelectric fields induced in wurtzite strained GaInN/GaN heterostructures. 71 In order to study the orientation dependence of the piezoelectric effects, we first transformed the conventional coordinate system (x, y, z) into a new one (x, y, z ) using a rotation matrix, cos ϕ cos θ sin ϕ cos θ sin θ U = sin ϕ cos ϕ 0, (11) cos ϕ sin θ sin ϕ sin θ cos θ where ϕ and θ are the azimuth and the polar angles, respectively, as shown in Fig.22. The polar angle corresponds to the off angle from ( 0001 ). The piezoelectric tensor e i j k and stiffness coefficient tensor C i j k l in the new coordinate system are obtained after the transformation of the coordinate system as follows: 14 e i ' j ' k ' = U i ' iuj ' ju k ' keijk, C i ' j ' k ' l ' = U i ' i U j ' j U k ' k U l ' l C ijkl. (12) Here we consider wurtzite strained GaInN/GaN heterostructure grown along new z -direction. The GaInN layer should be under the in-plane biaxially compressive strain due to the lattice mismatch with the GaN. In general, there is difference in lattice mismatch between along a-axis and along c-axis in wurtzite heterostructures, resulting in an orientation dependence of the strain components. In the case of the Ga 1-x In x N/GaN, the magnitude of the lattice mismatch along a-axis is 11.1x% and that of c-axis is 11.0x%. The difference is so small that we neglect the orientation dependence of the strain. We, therefore, assume that the strain tensors of x x, y y and x y components in any crystal orientation are always equal to that in (0001) orientation as follows: ε ε x ' x ' x ' y ' = = ε ε y ' xy y ' = ε = 0, xx = ε yy = a s a e a e, (13) where a e and a s are the free-standing a-axis lattice constants of the GaInN layer and the underlying GaN layer, respectively. Using the same condition discussed in Section 2, Eq (1) and (3) in new coordinate system, we can determine the remaining three strain components of z z, 16

17 y z and z x. Finally the field along z -direction, the longitudinal piezoelectric field, in the strained GaInN layer is given by, E z P z ' ' =. (14) ε r ε o We use the piezoelectric constants experimentally derived in Section 4, which are equal to 40% of the values reported by Bernerdini et al. 26 and are very close to the value reported by Bykhovski et al. 27 Table 1 summarizes the material parameters used in our calculations. The orientation dependence of the dielectric constants was taken into account. In the calculation of the crystal orientation dependence of both the transition probability and the transition energy in 3 nm GaInN/GaN QWs, we also used the multiple step potential approximation. 50 We calculated the square of the overlap integral between the electron and hole wavefunctions for estimation of the transition probability Orientation dependence of piezoelectric field Figure 23 shows the longitudinal piezoelectric field in the strained GaInN layers as a function of the polar angle from ( 0001 ). Note that in Fig. 23 the positive direction of the field is set from the growth surface to the substrate. We found that the highest piezoelectric field with the order of MV/cm is induced in the strained GaInN layer grown along the [0001] direction. It is also seen that a larger piezoelectric field is induced along the [0001] direction with an increase of the InN molar fraction, which is due to the larger lattice mismatch with the underlying GaN. These values are more than 4 times larger than that of the (111)-oriented GaInAs/GaAs with the same In composition, 14 which is mainly due to about 2 times greater piezoelectric constants compared to those of arsenide materials. Meanwhile, no longitudinal piezoelectric field is induced in the case of the orientations with the off angles of 39 degrees or 90 degrees. The reason for the zero piezoelectric field generation in the case of 90 degrees is that the transformed piezoelectric constants of e 31, e 32, and e 33 are all zero. In the case of 39 degrees, the transformed piezoelectric constants have non-zero values, however, the summation of e ij ε kl for the z -direction is zero. Furthermore these results do not depend on the azimuth angle at all, i.e. the piezoelectric effect in wurtzite material shows monoaxial isotropic behavior along [0001], as the nitrides piezoelectric tensor itself indicates. As a result, examples of high symmetrical orientations with the off angles are ( 1120) and ( 1010) for 90 degrees, and ( 1124) and ( 1012) for 39 degrees. 17

18 S.H. Park and S.L. Chuang have already reported the theoretical orientation dependence of piezoelectric polarization in compressively and tesilely strained GaN in GaN/AlInN heterostructure. 72 The strain in the GaN was changed by varying the InN molar fraction in the unstrained AlInN. Their results also indicated the controllability of the piezoelectric polarization in wurtzite strained nitride by changing the growth orientation. They also pointed out that, in the case of the tensile strain, the sign of polarization does not depend on the angle in the range from 0 to 90 degrees Orientation dependence of transition probability and transition energy Figure 24 shows the transition probability of 3 nm GaInN QWs as a function of polar angle. The transition probability of the GaInN QWs with ( 0001 ) orientation is 2-5 times lower than that of the orientations with the off angles of 39 degrees or 90 degrees. In addition, with an increase of the InN molar fraction, a lower transition probability along (0001) orientation is observed. These are caused by the spatial separation between the electron and hole wavefunctions due to the large internal piezoelectric fields shown in Fig.23. Most of the nitride-based optical devices using strained GaInN QW reported so far have been grown along the [0001] direction. Therefore, we expect a significant increase of the light output power or decrease of the threshold current density by using the non- ( 0001 ) orientations, especially for the devices with a higher InN mole fraction, such as green or red light emitting diodes and laser diodes. Figure 25 shows the transition energy of 3 nm GaInN QW as a function of the polar angle. The QWs with the ( 0001 ) orientation shows the largest red shift, which is up to 200 mev in the case of the Ga 0.7 In 0.3 N QWs. This red shift is due to the intrinsic QCSE caused by the piezoelectric field. Accordingly, there is no red shift in case of the orientations with the off angles of 39 degrees and 90 degrees because of no piezoelectric field. This intrinsic QCSE leads to the blue shift of transition energy with increasing the excitation power in PL measurement 51 or increasing the current injection to light emitting diodes, 73 which is caused by the screening for the piezoelectric field by electron-hole pairs. Therefore, we also expect an improvement of the stability for the transition energy at any injection level by using these non- ( 0001 ) orientations. In our calculations shown in Fig. 24 and 25, the spontaneous polarization was not taken into account for the same reason described in Section 3. Concerning the orientation dependence on hole effective mass, there is a theoretical result which showed that the smallest hole effective mass of strained GaN with non- ( 0001 ) orientation is about half of that with ( 0001 ) orientation. 74 We have calculated the transition probability and energy using half the 18

19 value of the hole effective mass. The difference is 5% and 0.5% for the transition probability and the energy, respectively. Therefore, this orientation effect does not significantly affect our results. It should be noted that growth of high quality nitride layers has not been demonstrated on non- ( 0001 ) so far. We, however, point out that some growth facets during epitaxial lateral overgrowth, 75 such as ( 1011) (θ = 62 degrees) are applicable to the growth along high quality non- ( 0001 ) orientations. Figure 26 shows an example of the device structure including the GaInN QWs grown on V-grooved ( 1011) facets. In the ( 1011) orientation, the piezoelectric field can be reduced to 40% and the transition probability can be over 2 times higher, compared to the ( 0001 ) orientation. 6. Summary In this chapter, we described the piezoelectric effect in strained GaInN/GaN hererostructures and QWs. We clarified the strain in GaInN/GaN and AlGaN/GaN heterostructures using x-ray diffraction. The alloy layers were coherently grown on the underlying GaN, and were under the in-plane biaxial strain. Then we observed the influence of piezoelectric fields on luminescence properties of the strained GaInN QWs. A significant red shift of the PL peak wavelength was observed with an increase of the well width. The luminescence properties of the QWs are well explained by the QCSE caused by the internal piezoelectric field. We also identified the piezoelectric field in the strained GaInN well layers by measuring the PL peak energy of the QWs under various applied voltages. We observed a blue shift of the PL peak wavelength with increasing applied reverse voltage, which indicates that the applied reverse voltage cancels the internal piezoelectric field and its direction is from the growth surface to the substrate. From the direction of the piezoelectric field, the growth orientation of our sample was determined to be Ga-face. We finally performed a theoretical study of the crystal orientation dependence of the piezoelectric effects in wurtzite strained GaInN/GaN heterostructures. The result indicates the controllability of the piezoelectric field by changing the crystal orientation from zero to the order of MV/cm. Acknowledgments One of the authors (T.T.) is grateful to Dr. N. Yamada for their fruitful discussions and encouragement. This work was partly supported by the Ministry of Education, Science, Sports and Culture of Japan (High-Tech Research Center Project and contract nos , , 19

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