The effect of clustering on the precision of estimation : a thesis presented in partial fulfilment of the requirements for the degree of Master of Business Studies in Marketing at Massey University

The effect of clustering interval on design effect may be important in selection of alternative sampling designs by evaluating the cost-efficiency in the context of face-to-face interview surveys. There has been little work in investigating this effect in New Zealand. This study attempts to investigate this effect by using data from a two-stage sampling face-to-face interview survey. Seventeen stimulated samples are generated. A simple method, design effect =msb /ms, is developed to estimate design effects for 81 variables for both the simulated samples and the original sample. These estimated design effects are used to investigate the effect of clustering interval. This study also investigates the effect of cluster size. The results indicate that clustering interval has little influence on design effect but cluster size substantial influence. The evaluation of the cost-efficiency in alternative clustering intervals is discussed. As an improvement in the efficiency of a sample design by an increase in clustering interval can not be justified by the increase in cost, it seems that the sample design with the smallest clustering interval is the best. An alternative method design effect ≈ mr2 is also discussed and tested in estimating design effects. The result indicates that the applicability of design effect ≈ mr2 is the same as that of design effect = msb /ms

Effects of Interface Disorder on Valley Splitting in SiGe/Si/SiGe Quantum Wells

A sharp potential barrier at the Si/SiGe interface introduces valley splitting (VS), which lifts the 2-fold valley degeneracy in strained SiGe/Si/SiGe quantum wells (QWs). This work examines in detail the effects of Si/SiGe interface disorder on the VS in an atomistic tight binding approach based on statistical sampling. VS is analyzed as a function of electric field, QW thickness, and simulation domain size. Strong electric fields push the electron wavefunctions into the SiGe buffer and introduce significant VS fluctuations from device to device. A Gedankenexperiment with ordered alloys sheds light on the importance of different bonding configurations on VS. We conclude that a single SiGe band offset and effective mass cannot comprehend the complex Si/SiGe interface interactions that dominate VS.Comment: 5 figure

Million Atom Electronic Structure and Device Calculations on Peta-Scale Computers

Semiconductor devices are scaled down to the level which constituent materials are no longer considered continuous. To account for atomistic randomness, surface effects and quantum mechanical effects, an atomistic modeling approach needs to be pursued. The Nanoelectronic Modeling Tool (NEMO 3-D) has satisfied the requirement by including emprical $sp^{3}s^{*}$ and $sp^{3}d^{5}s^{*}$ tight binding models and considering strain to successfully simulate various semiconductor material systems. Computationally, however, NEMO 3-D needs significant improvements to utilize increasing supply of processors. This paper introduces the new modeling tool, OMEN 3-D, and discusses the major computational improvements, the 3-D domain decomposition and the multi-level parallelism. As a featured application, a full 3-D parallelized Schr\"odinger-Poisson solver and its application to calculate the bandstructure of $\delta$ doped phosphorus(P) layer in silicon is demonstrated. Impurity bands due to the donor ion potentials are computed.Comment: 4 pages, 6 figures, IEEE proceedings of the 13th International Workshop on Computational Electronics, Tsinghua University, Beijing, May 27-29 200

Trace Map on Chiral Weyl Algebras

We construct a trace map on the chiral homology of chiral Weyl algebra for any smooth Riemann surface. Our trace map can be viewed as a chiral version of the deformed HKR quasi-isomorphism. This also provides a mathematical rigorous construction of correlation function for symplectic bosons in physics. We calculate some examples of trace maps with one insertion and find they are closely related to the variation of analytic torsion for holomorphic bundles on Riemann surfaces.Comment: 40 pages. Comments are welcom