Growth History of Bulk lnGa1.As Crystals
Growth Problems in Bulk lnGa1As Crystals
Motivation of Present Work
The main objective of this study is to grow high-quality bulk InGaAs crystal using the MCZM method. By comparing the state of the strains and their distributions for different compositional profiles, the appropriate compositional profile can be selected for the MCZM growth process.
Outline of Thesis
In Chapter 2, the existence of strain in bulk InGaAs crystals grown by the two-step MCZM method was confirmed by Raman scattering (RS), photoluminescence (PL) and energy dispersive X-ray (EDX). To investigate the existence of strain in the crystal grown by the two-step MCZM method, Raman scattering (RS), photoluminescence (PL), and energy dispersive X-ray (EDX) experiments were performed.
Experimental Procedure
Although PL peak energy may be slightly shifted from the band gap energy of materials, PL spectrum is sharp enough to determine composition with high accuracy. Therefore, a combination of EDX measurement with the RS and PL measurements can be a good way to investigate the strain in bulk InaiAs mixed crystal under investigation.
Raman Results
Raman Spectra in lnGa1.As Crystal
TOGaAs Phonon Peaks and Lineshape Broadening
Comparison between Raman and EDX Results
The right-hand scale is adjusted to the left-hand scale using the compositional dependence of TOGS peak; TOGs(x x, which is reduced in several polycrystalline InGa 1As samples [15]. The right-hand scale is adjusted to the left-hand scale using the compositional dependence of TOGaAs phonon frequency: TO(x x, which is reduced in unstrained InGaiAs polycrystalline materials in ' a previous study [15].
Comparison between PL and EDX Results
Quantitative Amount of Strain
In order to investigate the compositional profile along the radial direction, Raman measurements along the diameter were also performed at several points along the length of the crystal. Thus, the experimental results show that there is a compositional variation along the crystal diameter and it increases while moving from the initial end to the rear end of the crystal. An approximate value of the axial strain can be calculated using one of the above equations.
In fact, several crack lines were observed at the end of the crystal, which may be due to the high value of stress accumulated at the end of the sample due to the gradual change in composition.
Summary
This strain value is large enough to explain the fracture mechanism in large InGaAs crystals grown by the MCZM method. In this chapter, strain models developed for a bulk mixed crystal system were used to quantify the amount of strain and their distribution for different compositional profiles in bulk InGaAs crystals grown by the two-step MCZM method. The residual strain caused by the compositional variation of mixed bulk crystals is a new issue and is very important for understanding the growth problems in the bulk mixed crystal system.
Although the above experimental techniques can be used to investigate the existence of deformation in a mass of mixed crystals, the amount of deformation cannot be measured with them.
One-dimensional Strain Model
To estimate not only the axial stress component but also the radial, tangential and shear stress components in the cylindrical bulk mixed crystal system with different compositional profiles, they further proposed an axially symmetric stress model [14]. Therefore, the issue of fracture related to composition change in InGaiAs bulk crystals grown by the MCZM method can be investigated using the axisymmetric strain model. Using the usual stress-strain relationship [31], the strain along the growth direction can be given by where E is Young's modulus and P is Poisson's ratio.
In order to determine other strain components along with the axial strain component for various compositional profiles in the crystals grown by the two-step MCZM method, axially symmetric strain model is discussed in the next section.
Axially Symmetrical Strain Model
The residual deformation caused by the composition variation in the mass of mixed crystals can be written [32] z. Since the residual strain in a bulk mixed crystal is related to compositional variation, the strain state depends entirely on its profile. The deformation phenomena in the epiplasts are not the same as those in the present massive mixed crystals.
Thus, epiplast deformation models cannot be used to evaluate deformations in a massive mixed crystal system.
Analytical Solution of Strains in Cylindrical Co-ordinates
Strain Distribution for the Profiles AF, BF and CF
The maximum amount of stresses evaluated in different radial positions of the crystal corresponding to the profiles AF, BF and CF are summarized in Table 3.2. It is then gradually reduced to zero at the end of the first step of the crystal's growth. It is then gradually reduced to zero at the end of the first growth step due to the homogeneity of the composition.
Consequently, this region of the crystal shows a drastic change in strain values for the AF profile, as shown in Fig. 1b.
Strain Distribution for the Profiles AE, BE and CE
The axially symmetric stress model is further used to estimate e, £ rr s0.1 and Er: for profiles AE, BE and CE. The stress distributions obtained for the compositional profiles AE, BE and CE are also shown by the solid, dotted and dashed lines, respectively. 3.4(a)-3.4(o) that the stress distributions for profiles AE, BE, and CE are almost similar to those of profiles AF, BF, and CF.
However, it is found that the amount of deformation is different along the radial direction for.
Strain Distribution for the Profiles AG, BG and CG
As shown in Table 3.3, the shear strain component r' is found to be zero along the growth axis of the crystal due to the axial symmetry of the composition. It is also found that the value of shear stress changes drastically at the end of the first stage growth process for the profile AG. In contrast, the shear strain changes gradually at the end of the first-stage growth process for profiles BG and 0G.
Furthermore, the distribution of the resulting radial strain is found to correspond to the shear strain for all the profiles.
Summary
In this chapter strain distributions have been investigated using the line diagram at three different radial positions of the crystal. In order to understand the spatial variation of the strain throughout the region of the crystal, two-dimensional mapping of the strain for different compositional profiles has been developed, which is presented in the next chapter. Since the line diagram is not suitable for understanding the spatial variation of strain, a two-dimensional mapping of strain and composition is developed here, which will enable us to explain the strain distributions precisely throughout the region of the crystal.
In this mapping system, color maps are constructed with a spatial resolution of 50 pm corresponding to the strain values evaluated along the radial and growth directions of the crystal.
Two-dimensional Mapping of Composition and Strain
Two-dimensional Composition and Strain Maps
- Maps for the Profiles AE, BE and CE
- Composition Maps
- Axial Strain Maps
- Radial Strain Maps
- Tangential Strain Maps
- Shear Strain Maps
- Resultant Radial Strain Maps
- Maps for the Profiles AG, BG and CG
- Composition Maps
- Axial Strain Maps
- Radial Strain Maps
- Tangential Strain Maps
- Shear Strain Maps
- Resultant Radial Strain Maps
- Maps for Profiles AF, BF and CF
- Composition Maps
- Axial Strain Maps
- Radial Strain Maps
- Tangential Strain Maps
- Shear Strain Maps
- Resultant Radial Strain Maps
4.6(a) it is found that 6 rr is the highest value for the AE profile at the periphery near the region with homogeneous crystal composition. Furthermore, the highest err'-e value for the BE profile is found at the periphery near the end of the crystal. For the BF and CF profiles, it is found that the strain values are much lower than those obtained for the AF profile.
In particular, strain values are almost negligible towards the end of the first growth stage for profiles BF and CF. For profiles AG, BG and CG, it is found that the strain values are highest near the nucleation end of the crystal. However, the highest strain values were found near the nucleation end of the crystal for profiles BF, BE and BG.
Selection of the Best Profile
Dependence of Strain with Crystal Length
Spatial variation of strains by changing the crystal length has been investigated here for the profile CF. Although the strain values are found to be independent of the crystal length, the accumulation rate of strain is higher for the shorter crystal than for the longer crystal. Thus, if the length of the crystal in the first step of the MCZM growth process is increased, the quality of the crystal can be improved.
4 MCM method, the dependence of load values with the crystal diameter has been further investigated in the next section.
Dependence of Strain with Crystal Diameter
The &, S'rr, and so,o, voltage components are slightly increased with the crystal length and diameter. However, if the diameter is increased from 15 mm to 20 mm, shear and resultant radial strains are increased for the same. COV distortion values are significantly reduced, even the crystal diameter is increased from 20 mm to 25 mm.
Larger diameter InGaAs crystals can be obtained if the crystal length is sufficiently increased during the first step growth of the two-step MCZM growth process.
Temperature Profiles
On the other hand, the slope of the estimated temperature profile corresponds to the proposed changes in the similar composition profile (OF) almost linearly in the first stage growth process, which is easily achievable. Thus, the proposed compositional profile leads to easily obtain growth parameters and therefore enables us to grow large-sized, high-quality InGaAs crystals using the two-step MCZM method.
Summary
It is also observed that the stress accumulation for the BF profile is higher at the end of the seed due to the large change in composition in this region. On the other hand, the change in strain is found to be gradual throughout the crystal for the CF profile. It is also found that if the crystal length in the first step of the MCZM growth process is increased sufficiently, the shear stress would be significantly reduced and larger diameter crystal growth would be possible with the MCZM growth technique.
In this thesis, the following research aspects were reported: (1) experimental investigation of residual deformation in bulk InaiAs mixed crystals grown by the MCZM method and thus to reveal the fracture issue, (2) analysis of deformation components for various composition profiles using an axially symmetric strain model, (3) development of two-dimensional composition and strain maps to investigate the spatial variations of composition and strain in bulk InGaAs crystals, (4) selection of best composition profile to solve the two-step crystal breakage problem -MCZM solvable growth process (5) investigate the dependence of strain values with the crystal length and diameter, (6) propose suitable growth parameters for the two-step MCZM growth method.
Conclusions and Suggestions
Suggestions of future Works
