Piezoelectric Effect in GaInN/GaN Heterostructure ... - Semantic Scholar

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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.
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, 1-501 Shiogamaguchi, Tempaku-ku, Nagoya 468-8502, Japan TEL +81-52-832-1151 (ex. 5064) FAX +81-52-832-1244 1.

Introduction

2.

Structural and optical properties of GaInN/GaN heterostructures

3.

4.

5.

2.1.

Crystal growth

2.2.

Structural properties

2.3.

Optical properties

Luminescence properties of GaInN quantum wells 3.1.

Theoretical piezoelectric field and transition energy

3.2.

Experiments

3.3.

Luminescence properties

Quantum-confined Stark effect in GaInN quantum wells 4.1.

Experiments

4.2.

Determination of piezoelectric field

4.3.

Determination of growth polarity

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

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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, GaInN3,4 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 diodes9,10 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]13-16 and the CdS/CdSe superlattice grown along [0001]17 have been investigated and understood as the “intrinsic”17 quantum confined Stark effect18 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

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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 (NH3) 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 350-600 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 680-780 oC 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

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the ternary alloys and the GaN simultaneously.19 Figure 2 shows the x-ray RSM around the ( 20 2 4 ) 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 Ga0.886In0.114N grown on thick GaN.21 On the other hand, Wu et al. found that a 270 nm Ga0.82In0.18N 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 Ga0.9In0.1N on GaN and 2 nm for Ga0.85In0.15N on GaN

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based on the theory

24

developed by Matthews and Blakeslee, 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

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Huck’s law, is described with elastic stiffness constants as follows:

 σ xx   σ yy  σ zz   σ yz  σ zx   σ zy 

 c 11     c 12   c 13   =   0   0      0  

c 12 c 11

c 13 c 13

0 0

0 0

0 0

c 13 0 0

c 13 0 0

0 c 44 0

0 0 c 44

0

0

0

0

0 0 0 − c 12 2

c 11

         

 ε xx   ε yy  ε zz ⋅  ε yz  ε zx   ε xy 

    ,     

(1)

where σij, ci, and εij 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 yy =

a

s

ε xy = 0 ,

− a ae

e

,

(2)

where as 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 ae 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:

2 c 13 ⋅ ε xx c 33 cs − ce (= ), ce ε yz = ε zx = 0 ,

ε zz = −

(4)

where cs is the c-axis lattice constant of the biaxially strained alloy, and ce is that of the fully relaxed alloy. Finally we obtain the following formula from Eqs. (2) and (4).

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c se − c e c a − ae = − 2 1 3 se , ce c33 ae

(5)

where cse and ase are the measured values from the x-ray diffraction. In addition, we obtain ce, ae, c13, and c33 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 N2 pulsed laser for extremely high intensity (200kW/cm2) 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