In this thesis, a numerical simulation has been performed for the reduction of dislocation density in wuzrite InGaN and cubic lnGaAs heteroepitaxy with step-graded interlayers. An energy balance model has been developed to evaluate the misfit dislocation (MD) density in the stepwise structure of these heteroepitaxies.
Introduction 1-10
Dislocations Reduction and Thesis Motivation
As a result, fewer MDs as well as TDs could be generated in stepped intermediate layers. Although available theoretical works have been developed for no grading or linear and nonlinear grading, there is no such work on step-graded interlayers for wuzrite as well as cubic materials.
Objectives of the Thesis
The other parameters are defined in section 2.4.1 and have their appropriate values used at different slips for these materials, given in Appendix A. The in-plane misfit strain for i-layer can be calculated using Eq. 3.2) which was developed for a multilayer structure and the expressions of c, y and R have been published elsewhere [6]. The threading dislocation densities in the stepwise InGaN heteroepitaxy have been evaluated based on the numerical simulation of the reaction model developed in Chapter 3.
Synopsis of the Thesis
Fundamentals of Dislocation in Ill-V Semiconductors 11-30
- Different Models of Critical Thickness
- I Matthews and Blakeslee
- People and Bean
- Energy Balance Model .........................................................1 5
- Nucleation of Dislocations ................................................................ 1 8
- Dislocations Multiplication
- Graded Layer
- Slip Systems in Different Material Structure
- Wuzrite InGaN
- Cubic InGaAs
If the film is thin enough to remain coherent with the substrate, then the thin film in the plane parallel to the growth surface will adopt the in-plane lattice constant of the substrate. The stress applied to the film by the substrate in the plane of the interface between the two is the result of biaxial compression. The lattice constant of the film in the direction perpendicular to the growth direction will likewise be strained according to the elastic properties of the film.
The second force on misfit dislocation is due to the line tension, which acts as a restoring force resisting the motion of the dislocation. According to this model, the strain energy per unit area of the film-substrate interface. The thickness of the film is h, the slip plane is tilted by the angle cp from the normal to the interface.
During the growth, the mismatch and the lattice constant of the layer continuously change with the same or different rate in the linear and non-linear graded layer structure [3 1-34]. On the other hand, the misflt and the lattice constant of the epitaxial layer change stepwise for the step-graded layers [36-38]. A step-graded layer should relax the misaligned stress, mostly through the sliding motion of existing wire dislocations instead of the misaligned dislocation core.
Methods of Dislocations Reduction 31-51
MDs with Step-graded Interlayers
- Wuzrite InGaN Heteroepitaxy
- Cubic InGaAs Heteroepitaxy
In the above equation, h is the thickness of the epitaxial layer grown on the GaN substrate. The layer grown on the partially relaxed intermediate layer of thickness h will experience a mismatch stress, e,+ I) reduced by the residual stress Ej of the previous layer from Eq. The energy stored by the dislocation due to the wrong tension of the it interlayer can be written as.
Where the first term in parentheses is due to the edge component of the dislocation and the second term is to the screw component. The strain energy dissipated by this displacement per unit length of MD introduced by. The occurrence of the first misfit dislocation becomes feasible when this energy exceeds the dislocation energy given in Eq. 3.19) and the total energy stored by the system will be lower.
The grown layer over the partially relaxed layer of thickness h1 will experience a misfit strain less than the residual strain t' of the previous layer as expressed in Eq.
TDs with Step-graded Interlayers
A multiple critical thickness at different interlaces has been calculated in the case of stepped structure. Fig. 4.7 shows a comparison of the total generated edge type MI)s in all possible plans of the graded and ungraded structure. These figures show a comparison of total edge and mixed type MDs in the step-graded and non-graded structure.
The TD density in the top surface of a stepped structure is found to be extremely lower (less than one speck) than that of the structure without a stepped structure. Therefore, the TD reduction in stepwise structure can be improved by the MD blocking. The simulation of the stepwise lnGaAs interlayer was performed for a similar structure to InGaN heteroepitaxy.
4.17 (a) and (b) show total variation of different types of TD densities in the step-graded and non-graded structure. The behavior of overall TD density for the step-graded structure is shown in Fig. In determining TD density with increase of film thickness in step-graded InGaN and.
I Reaction Model for InGaN Heteroepitaxy
- Reaction Model for InGaAs 1-leteroepitaxy
Simulation Results and Discussion 52-72
Critical Thickness of InGaN/GaN and lnGaAs/GaAs System
- Critical Thickness at Different Slips
Dislocation Sources in Step-graded Heteroepitaxy
Estimation of the critical layer thickness for the old displacement of various propagation mechanisms is also an important issue for the proper design of the interlayer thickness in the scaled structure. Therefore, a gradual decrease of the misfit strain in the graded structure leads to greater critical thickness of these resources in the upper layers. In the case of scaled InGaN and InGaAs interconnects, a step increase of InGaN is more critical.
Further observation showed that the Frank-Read and spiral sources start generating after 108 and 60 hours, respectively, for a composition difference of 10% in each interlayer of the InGaN step structure. On the other hand, in the case of the stepped lnGaAs structure, the critical thicknesses of the Frank-Read and spiral sources are 191 and 103 nm, respectively, for a 10% increase in indium at each step. Thus, in a 1.5 tm staggered structure with 3 interlayers, each thickness of 200 nm with a composition difference of 0.1 will reduce their possibility of propagation in both heteroepitaxies.
Therefore, a relatively smaller number of MDs from these sources is expected in the proposed 1n04Ga06N/GaN and In04Ga0 6As/GaAs step heteroepitaxy using 3 interlayers.
MDs in Step-graded InGaN and InGaAs
- MDs Generation in Wuzrite InGaN
- MDs Generation in Cubic InGaAs
The total edge-type MDs at the InGaN epilayer are found to be 7.3x 10' and 1.72x 1012 cm'2 for step-graded and non-graded structure, respectively. The significant difference in dislocation density indicates that the stepped interlayers successfully reduce the dislocation between the GaN and InGaN interface and between the interlayers. The improvements of total mixed type MDs have also been calculated for the graded and ungraded structure and shown in Fig.
It reaffirms the significant improvement in the quality of the epilation due to the use of stepped intermediate layers. On the other hand, with the increase of the InGaN interlayer in the step structure, the composition gradually increases. The misaligned dislocation in InGaAs step heteroepitaxy was analytically evaluated using the energy balance model developed in Chapter 3.
The calculations have been made for a 1.5 trn step-graded structure with 3 InGaAs interlayers each with 200 nm thickness and 10% increase in composition at each interlayer.
TDs Reduction Using Step-graded Interlayer
- TDs in Wuzrite InGaN
13(a) and (b) represent the variation of TD density of mixed and screw type with specific number as a function of film thickness for the stepped structure. These figures show a decrease in the average edge, mixed, and helical TD densities of stepwise and stepless 11104Ga06N heteroepitaxy. Dislocation bending in the stepless structure occurs only very close to the InGa1N/GaN interface, while dislocation bending can be observed at every interface between InGaN interlayers of different compositions in the step structure.
As observed in various experimental works, the most nucleated sites for TDs are MDs which are remarkably lower in scale structure than scaleless ones. The TD densities of both species have extremely lower values in the upper part of the epilayer in the stepped structure than that of the unstepped layer. TD densities of 3.65x 1010 and l.64x 1010 cm 2 respectively for the mixed character and edge were calculated on the top surface per scale.
The step slope of TD at each interface promotes the reaction between them in the case of step layers.
Effect of Annihilation Radius
In this dissertation, the scaled interlayer technique for vuzrites as well as cubic heteroepitaxy is investigated through theoretical studies, mathematical modeling and numerical simulations. In addition to these, reaction models have been developed according to their crystal geometry and all possible burger vectors to observe the nature of TDs in scaled structures. It has been demonstrated that the introduction of scaled interlayers significantly reduces the MDs for InGaN as well as InGaAs heteroepitaxy.
In the case of step-graded 11104Ga06As heteroepitaxy with similar structure, this density decreased from 1. The above findings indicate the potential of step-graded interlayer technique for InGaN and lnGaAs heteroepitaxy. This simulation methodology can be used for other wuzrite as well as cubic material step-graded interlayer heteroepitaxy for future generation high performance electronic and optoelectronic devices.
This dissertation presented a theoretical analysis of the dislocation behavior and numerical simulations for scaled wuzrite inGaN and cubic lnGaAs heteroepitaxy.
Conclusions and Future Work 73-75
Future Work
In order to improve the current models, it would be interesting to consider the mechanism of generation of dislocations in multiple quantum wells to provide a theoretical critical thickness. Another possible direction would be to try to include in the model other possible relief mechanisms, such as V-pits. Modeling the reduction in thread dislocation density as described here was only a small step towards a model capable of quantitative predictions.
Future work may include further studies on the effects of different model parameters. Furthermore, using the knowledge gained from the 2D model, significant progress can be made by extending this model to 3D. Another important improvement in the direction of realism would be to consider significant optimization of the code used for simulations of reaction models.
This would involve the implementation of other higher accuracy numerical methods such as Runge-Kutta.
![Figure 1.1: The effect of dislocation density in InGaN single junction solar cell performance [23]](https://thumb-ap.123doks.com/thumbv2/filepdfnet/10907228.0/18.874.131.711.583.1004/figure-effect-dislocation-density-ingan-single-junction-performance.webp)
