The optical and electronic characteristics of devices based on GaAs (LEDS, laser diodes, etc.) are adversely affected by the dislocations originating in the substrates. We demonstrate by means of thermoelastic analysis that the primary cause for the observed dislocation density patterns in Czochralski‐pulled GaAs single crystals, which serve as a source for substrates, is crystallographic glide, induced by the excessive thermal stresses arising during the growth process. First, we formulate a tractable model for crystal growth. We obtain the temperature distribution in the crystal by solving the quasi‐steady‐state partial differential equation for heat conduction subject to appropriate boundary conditions. The closed‐form solution includes time, pull rate, axial location, radius, convective and radiative heat transfer coefficients (hr + hc), and a fixed ambient temperature (Tα) among the variables. Next, from the temperature profiles we determine the radial, tangential, and axial stress components acting on the GaAs boule. These stresses permit the evaluation of the 12 resolved shear stress components for the {111}, <110> slip system. We postulate the sum of the absolute values of the 12 components (σtot) to be proportional to the dislocation density within an additive constant. Employing σtot as a parameter, we have constructed dislocation distribution contour maps for {100} GaAs wafers which are in good accord with the dislocation patterns observed on KOH‐etched wafers cut from near the top end of Cr and Te‐doped GaAs boules. A detailed examination of the effect of the numerous parameters on the dislocation density of Czochralski‐pulled GaAs is also given. Only by a drastic increase of Tα and a substantial decrease of hr + hc would one be able to overcome the natural limitations imposed by the thermal and mechanical properties on dislocation density. Finally, we pay attention to the effects of elastic anisotropy and interfacial heat flux, discuss the philosophical and mathematical difficulties associated with finding a true transient solution, and provide some practical suggestions.
Articles you may be interested inComparison of intrinsic and extrinsic carbon doping sources for GaAs and AlGaAs grown by metalorganic molecular beam epitaxy J. Vac. Sci. Technol. A 12, 1186 (1994); 10.1116/1.579293 Study on thermal stability of carbondoped GaAs using novel metalorganic molecular beam epitaxial structures Characterization of heavily carbondoped GaAs grown by metalorganic chemical vapor deposition and metalorganic molecular beam epitaxy J. Appl. Phys. 72, 981 (1992); 10.1063/1.351776Hydrogen in carbondoped GaAs grown by metalorganic molecular beam epitaxy Lattice contraction due to carbon doping of GaAs grown by metalorganic molecular beam epitaxy
Powders and coatings of zirconia doped with 2.5 mole% yttria have been produced via the sol-gel route. The phase structure and subsequent thermal evolution in heating and cooling cycles have been investigated using mainly perturbed angular correlations spectroscopy. Thermal analyses and XRD as a function of temperature have also been performed to obtain complementary information. Upon heating, the amorphous gels crystallized into the tetragonal structure and showed the same hyperfine pattern and thermal behavior as observed in tetragonal zirconia obtained by the ceramic route: the two configurations of vacancies around zirconium ions denoted as t1 and t2 forms and their mutual t1 → t2 transformation. While the powder sample exhibited an incipient thermal instability above 1000 °C and underwent completely the t2 form to m–ZrO2 transition during subsequent, gradual cooling below 500 °C, the coating retained the tetragonal phase within the whole temperature range investigated. Hyperfine results suggest that the tetragonal phase stabilization is favored by the highly defective nature of the t1 form and consequently hardened by the availability of oxygen. The PAC derived activation energy for the fast diffusion of the oxygen vacancies inherent to the t2 form was determined as 0.54 ± 0.14 eV.
The Ga concentration in normalGaP crystals prepared by a variety of techniques (pulled by the liquid encapsulation Czochralski technique from stoichiometric or nonstoichiometric melts, solution grown, and annealed) has been determined by precision coulometric titration, yielding the experimental solidus boundary which exhibits an excess of Ga along the Ga‐rich liquidus. Based on a thermodynamic model, assuming that neutral Ga and P vacancies are the predominant native defects, the analysis of the solidus data permitted the evaluation of the vacancy concentrations over a wide temperature range. At the melting point of normalGaP (1465°C) there are 8 × 1018 and 1.3 × 1019 cm−3 Ga and P vacancies, respectively, in the crystal. The calculated solidus curve well represents the totality of experimental data and shows retrograde temperatures at 1375° and 1400°C on the Ga‐ and P‐rich sides, respectively. The enthalpies and entropies associated with vacancy formation are given and discussed. It is shown that the data provide strong additional support to the previous identification of Ga vacancies with killer centers in normalGaP .
Sol-gel-derived powder samples of zirconia (ZrO 2 ) prepared via the dissolution of zirconium n-propoxide in methanol, ethanol, and 2-propanol have been characterized mainly using perturbed angular correlations spectroscopy, as a function of temperature. Results indicate that the nanostructures and subsequent thermal evolution are alcohol dependent: the shorter the alcohol chain, the more hydrolyzed the product. ZrO 2 powder that has been obtained using ethanol as the solvent is the product that exhibits the better stabilization of the metastable tetragonal phase (t-phase). It undergoes a clear and detailed t 1 -form 3 t 2 -form 3 monoclinic ZrO 2 thermal transformation and shows the highest activation energy against the transformation to the monoclinic phase.
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