Kinetic modeling of microscopic processes during electron cyclotron resonance microwave plasma-assisted molecular beam epitaxial growth of GaN/GaAs-based heterostructures

Microscopic growth processes associated with GaN/GaAs molecular beam epitaxy (MBE) are examined through the introduction of a first-order kinetic model. The model is applied to the electron cyclotron resonance microwave plasma-assisted MBE (ECR-MBE) growth of a set of delta-GaNyAs1–y/GaAs strained-layer superlattices that consist of nitrided GaAs monolayers separated by GaAs spacers, and that exhibit a strong decrease of y with increasing T over the range 540–580 °C. This y(T) dependence is quantitatively explained in terms of microscopic anion exchange, and thermally activated N surface-desorption and surface-segregation processes. N surface segregation is found to be significant during GaAs overgrowth of GaNyAs1–y layers at typical GaN ECR-MBE growth temperatures, with an estimated activation energy Es ~ 0.9 eV. The observed y(T) dependence is shown to result from a combination of N surface segregation/desorption processes

Certifying reality of projections

Computational tools in numerical algebraic geometry can be used to numerically approximate solutions to a system of polynomial equations. If the system is well-constrained (i.e., square), Newton's method is locally quadratically convergent near each nonsingular solution. In such cases, Smale's alpha theory can be used to certify that a given point is in the quadratic convergence basin of some solution. This was extended to certifiably determine the reality of the corresponding solution when the polynomial system is real. Using the theory of Newton-invariant sets, we certifiably decide the reality of projections of solutions. We apply this method to certifiably count the number of real and totally real tritangent planes for instances of curves of genus 4.Comment: 9 page

Microscopic processes during electron cyclotron resonance microwave nitrogen plasma-assisted molecular beam epitaxial growth of GaN/GaAs heterostructures: Experiments and kinetic modeling

A set of delta-GaNyAs1–y/GaAs strained-layer superlattices grown on GaAs (001) substrates by electron cyclotron resonance (ECR) microwave plasma-assisted molecular beam epitaxy (MBE) was characterized by ex situ high resolution X-ray diffraction (HRXRD) to determine nitrogen content y in the nitrided GaAs monolayers as a function of growth temperature T. A first order kinetic model is introduced to quantitatively explain this y(T) dependence in terms of an energetically favorable N for As anion exchange and thermally activated N-surface desorption and surface segregation processes. The nitrogen surface segregation process, with an estimated activation energy Es ~ 0.9 eV appears to be significant during the GaAs overgrowth of GaNyAs1–y layers, and is shown to be responsible for strong y(T) dependence

Extracting the depolarization coefficient D_NN from data measured with a full acceptance detector

The spin transfer from vertically polarized beam protons to Lambda or Sigma hyperons of the associated strangeness production pp -> pK Lambda (Sigma) is described with the depolarization coefficient D_NN. As the polarization of the hyperons is determined by their weak decays, detectors, which have a large acceptance for the decay particles, are needed. In this paper a formula is derived, which describes the depolarization coefficient D_NN by count rates of a 4 pi detector. It is shown, that formulas, which are given in publications for detectors with restricted acceptance, are specific cases of this formula for a 4 pi detector.Comment: Accepted for publication by Nuclear Instruments and Methods in Physics Research Section

Accommodation of lattice mismatch in Ge_(x)Si_(1−x)/Si superlattices

We present evidence that the critical thickness for the appearance of misfit defects in a given material and heteroepitaxial structure is not simply a function of lattice mismatch. We report substantial differences in the relaxation of mismatch stress in Ge_(0.5)Si_(0.5)/Si superlattices grown at different temperatures on (100) Si substrates. Samples have been analyzed by x‐ray diffraction, channeled Rutherford backscattering, and transmission electron microscopy. While a superlattice grown at 365 °C demonstrates a high degree of elastic strain, with a dislocation density <10^5 cm^(−2) , structures grown at higher temperatures show increasing numbers of structural defects, with densities reaching 2×10^(10) cm^(−2) at a growth temperature of 530 °C. Our results suggest that it is possible to freeze a lattice‐mismatched structure in a highly strained metastable state. Thus it is not surprising that experimentally observed critical thicknesses are rarely in agreement with those predicted by equilibrium theories