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Numerical modeling of structure formation during GaInN thin films production.
Leonid Sakharov Introduction. Since a demonstration of principal possibilities of producing of violet InGaN/GaN laser diodes by Nakamura [1] and their commercial presentations by Nichia Corporation in 1999 [2] the process of production of quality GaN films is in the focus of efforts for improving their efficiency. These laser diodes have a number of potential applications such as optical storage, printing, full-color displays, chemical sensors and in medical devices [3]. For example the data capacity of digital versatile disks (DVDs) can be increased from 4.7 to more than 15 gigabytes by using violet InGaN lasers instead of red. The problem of production high quality monocrystal thin (thick) films of GaInN is far from ultimate solution. Specific difficulties of producing GaN low defect films are high equilibrium pressure of nitrogen at the temperatures of crystal structure formation and mismatch in crystallographic parameters with most of relatively cheap monocrystal substrates like sapphire or silicon. A development of reliable technology deposition of GaN based monocrystal films directly on silicon will open broad way for direct integration of GaN-based devices light emitting with conventional Si electronics. A numerical simulation of technologies processes permits to save time and materials durind the optimization of technology comparable with pure trial-and-error approach. The formation of grain structure of the film during high temperature crystallization and difference
in thermal expansions of substrate and film that materializing into lattice stress during cooling down,
according to our point of view, are two most important contributors of the device independent defects
in the deposited thin films. In this proposal a major attention will be concentrated on the farther development of: - Monte-Carlo simulation of film structure formation during crystallization; - Temperature dependence of relative expansiion and strength;is planning to be used for improving predictability of the model. Formation crystal structure during thin film deposition. Several parameters contribute in the formation of grains structure of films on the stage of crystallization: - the deposition rate of the material of the film itself; - primary and secondary nucleation rates on the substrate and film itself; - vertical and tangent components of the fillm growth rate. Analytical solutions of distribution grains on deposited film by size, crystalline structure and their orientation exist only for special situations when one of the parameters is playing dominate role [4]. For example if tangent component of crystal growth much higher then vertical one and nucleation rate small it's reasonable to expect a formation of grains with very large size. In case of small or none energy barrier of nucleation the film growth can be characterized as an ideal epitaxial. A real situation at most represents some intermediate combination of these growth parameters. The problem is appeared to be even more complex if one takes into account the fact that there are very limited number of publications devoted to the direct systematic observation of temperature dependence of crystal growth rates and nucleation for most prospect in semiconductor materials that in the spite of its extraordinary technical difficulty is considered as priority research initiative [5]. In the proposed project the approach of creation of eclectic numerical model based on two relatively independent micro and macro level algorithms for the simulations of the growth of depositing films is supposed to be realized. On the micro level stimulatory Monte-Carlo model of the surface reaction during crystal growth that is in general already developed by the author of this proposal in the program LeoCrystal [6] is supposed to be chosen as a template for the building up macro level for the calculation of the crystal grain structure of the deposited film. The Monte Carlo algorithm permits to calculate a frequency of two dimension nucleation and growth rates by taken as initial parameters thermodynamical, microstructure and kinetic characteristics of the phase transition. To apply this algorithm to the specific case of film deposition the special adjustments related to the gas phase transport, substrate-film interaction for differently oriented nucleus, original defects concentration on the substrate need to be implemented. Other addition to the program will take these parameters produced for the growth of different lattice oriented grains on the substrate as initials and simulate on the large scale the grains growth with output in the distribution of grains sizes and crystallographic orientations. Because of lack of experimental data about surface energy and own thermal frequency of vibration of structure elements the comparison with the experimental data has to be interactive process of finding best fit of model's output for different combination of these micro parameters with morphology of actual films. The broadest range of deposition temperatures and raw material partial pressure in gas (plasma) phase and substrate materials are planning to be used for films producing and comparison its microcrystalline structure with the developed model. The series of numerical experiments will be used for the determination of best time-temperature-pressure conditions of the deposition leading to the producing optimal in sense of electro optical characteristic grain structure of the films. Imperfection in deposited films as a result of differences between thermal expansions of substrate and film materials. The deposition of the films has to be done at the high enough temperatures these are needed for forming crystal structure that is usually sited around 700 - 800oC with following cooling down to the room temperature. The mismatch in thermal expansion of the film and the substrate are contributing to the establishing of local stresses in the film that later in a process can be resolved in cracks. There are several criteria for estimation of the compatibility of substrate and film materials based on the comparison of their thermal expansion coefficients. The most detail considerations are taken into account the fact that thermal expansion coefficients themselves have temperature dependence as well. We propose to take into account the temperature dependence of the material strength as well. In the publication of the author of the proposal [6] was presented relative simple method of calculation of temperature dependence of theoretical strength of the crystalline materials on the base of the elasticity module, thermal expansion coefficient at low temperature, temperature of melting and temperature dependence of thermocapacity. The perception of the method is the approximation of the molecule interaction energy potential on the base known mechanical and thermodynamical constants of material. This method permits also to calculate of temperature dependence of the thermal expansion of materials. As the condition of the crack film one can assume the situation when the local extension stress in the film forced by the interaction with substrate is overcoming a critical strength for the material at any given temperature during the cooling procedure. Both of the parameters - theoretical strength and length misbalance are increasing during this process. It's reasonable to expect that most damaging temperature interval producing most defects could be somewhere in between deposition temperature and destination room temperature. If it will have happened confirmed that special risky for cracks like defects temperature interval is exist the design of sophisticated temperature profile with long annealing of film just above of such risky temperature could to reduce stress a concentration of such defects.. In the proposed work the model of temperature stresses and crack of layers with different materials during cooling down supposed to be developed and elaborated. One of the challenging part of this approach will be the fact that GaN has higher temperature expansion coefficient then substrates and will be suffered with pressing stress during cooling and so not supposed to be broken because of it. To resolve this paradox the model based on finite elements method to obtain vector stress map profile in the film in depths - length coordinates has to be employed to find point with the most expansion stress that will be the weak link of the structure. The vector map of the stresses during cooling produced with the model will be developed and verified for the films of different thickness on different substrates with variation of deposition temperature. Upon the method verification the composed structure with buffer layers or their combination like AlN, CeN, HfN on the sapphire and silicon substrates will be examined. Special attention will be paid to the optimization of the thickness of buffer and semiconductor layers for maximum reducing of the stresses. Experimental verification of models results. For the comparison of an output of proposed software models with experimental data of grain and crystalline structure of deposited films X-ray diffraction and atomic force and electron microscopy are supposed to be used as primary tools. Other methods such as DTA, SEM, EDS could be practical as well. Resolution of the modern atomic force microscopy devises [8] permits a direct measure of roughness of the surface that is one of the outputs of a Monte Carlo crystal growth simulation. It also can supply quality information about ratio screw and edge type dislocations together with the grains size and orientation. The profile of X-ray diffraction reflections, so named rock curve, is adequate characteristic of the average tilt and twist of grains [9] and can be directly calculated from the end result of simulated models and compared with the intensity- scanning angle figures produced by the four circle high resolution diffractometer. Literature: [1]. S. Nakamura, "InGaN-based violet laser diodes," Semiconductor Science and Technology 14, pp. R27-40, 1999.
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