Elastic strain engineering of charge and thermal transport in semiconductor nanostructures: the role of heterogeneity

A variety of emergent phenomena in mechanical behavior, heat conduction, and electronic charge transport arise in materials when length scales associated with the physical dimensions or intrinsic structure approach the nanoscale. For instance, defect ensemble interactions and poor mechanical strength give way to discrete plasticity and ultra high strength in elemental nanostructures; facile thermal transport gives way to abundant phonon scattering in nanomaterials; and electronic band structure becomes altered in quantum-confined systems. Despite novel structural and transport physics discovered in many inorganic nanostructures, the interconnections between these various fields to exploit further property enhancements have received only recent attention. In this discussion, we describe the combination of a large dynamic range of elastic strain available in nanostructures with unique transport physics to enable tunable functional response via elastic strain engineering. In particular, the effect of strain heterogeneity on thermal and charge transport will be addressed by way of two examples on Si nanostructures. First, we report experimental measurements of the effect of tensile stress on thermal conductivity of an individual suspended Si nanowire using in situ Raman piezothermography. Our results show that, whereas phononic transport in undoped Si nanowires is only marginally affected by uniform elastic tensile strain, point defects introduced via ion bombardment that disrupt the pristine lattice reduces the thermal conductivity by over 70%. The second example furthers the study of inhomogeneous strains by showing tunable electrical conductivity and Seebeck coefficients in strained silicon nanomeshes with architected porosity. Using batch fabrication of freestanding nanomesh films from silicon-on-insulator wafers, we present a unique platform for exploring the effects of both changes in nanomesh geometry and strain state on charge transport. Experimental results are analyzed by combining analytical models for electron mobility in uniformly stressed silicon with finite element analysis of strained silicon nanomeshes. Our results show that the nonuniform and multiaxial strain fields defined by the nanomesh geometry give rise to spatially varying band shifts and warping, which in aggregate accelerate electron transport along directions of high stress. This allows for global electrical conductivity and Seebeck enhancements beyond those of homogenous samples under equivalent far-field stresses, ultimately increasing thermoelectric power factor over unstrained samples

Mixed effects linear models with t-distributions for quantitative genetic analysis: a Bayesian approach

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Attenuating effects of preferential treatment with Student-t mixed linear models: a simulation study

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Longitudinal random effects models for genetic analysis of binary data with application to mastitis in dairy cattle

A Bayesian analysis of longitudinal mastitis records obtained in the course of lactation was undertaken. Data were 3341 test-day binary records from 329 first lactation Holstein cows scored for mastitis at 14 and 30 days of lactation and every 30 days thereafter. First, the conditional probability of a sequence for a given cow was the product of the probabilities at each test-day. The probability of infection at time t for a cow was a normal integral, with its argument being a function of "fixed" and "random" effects and of time. Models for the latent normal variable included effects of: (1) year-month of test + a five-parameter linear regression function ("fixed", within age-season of calving) + genetic value of the cow + environmental effect peculiar to all records of the same cow + residual. (2) As in (1), but with five parameter random genetic regressions for each cow. (3) A hierarchical structure, where each of three parameters of the regression function for each cow followed a mixed effects linear model. Model 1 posterior mean of heritability was 0.05. Model 2 heritabilities were: 0.27, 0.05, 0.03 and 0.07 at days 14, 60, 120 and 305, respectively. Model 3 heritabilities were 0.57, 0.16, 0.06 and 0.18 at days 14, 60, 120 and 305, respectively. Bayes factors were: 0.011 (Model 1/Model 2), 0.017 (Model 1/Model 3) and 1.535 (Model 2/Model 3). The probability of mastitis for an "average" cow, using Model 2, was: 0.06, 0.05, 0.06 and 0.07 at days 14, 60, 120 and 305, respectively. Relaxing the conditional independence assumption via an autoregressive process (Model 2) improved the results slightly

Genetic analysis of somatic cell scores in US Holsteins with a Bayesian mixture model.

The objective of this study was to apply finite mixture models to field data for somatic cell scores (SCS) for estimation of genetic parameters. Data were approximately 170,000 test-day records for SCS from first-parity Holstein cows in Wisconsin. Five different models of increasing level of complexity were fitted. Model 1 was the standard single-component model, and the others were 2-component Gaussian mixtures consisting of similar but distinct linear models. All mixture models (i.e., 2 to 5) included separate means for the 2 components. Model 2 assumed entirely homogeneous variances for both components. Models 3 and 4 assumed heterogeneous variances for either residual (model 3) or genetic and permanent environmental variances (model 4). Model 5 was the most complex, in which variances of all random effects were allowed to vary across components. A Bayesian approach was applied and Gibbs sampling was used to obtain posterior estimates. Five chains of 205,000 cycles were generated for each model. Estimates of variance components were based on posterior means. Models were compared by use of the deviance information criterion. Based on the deviance information criterion, all mixture models were superior to the linear model for analysis of SCS. The best model was one in which genetic and PE variances were heterogeneous, but residual variances were homogeneous. The genetic analysis suggested that SCS in healthy and infected cattle are different traits, because the genetic correlation between SCS in the 2 components of 0.13 was significantly different from unity

A Semi-parametric Analysis of Technology, with an Application to U.S. Dairy Farms

This article proposes a semi-parametric stochastic frontier model (SPSF) in which components of the technology and of technical efficiency are represented using semi-parametric methods and estimated in a Bayesian framework. The approach is illustrated in an application to US farm data. The analysis shows important scale economies for small and medium herds and constant return to scale for larger herds. With the exception of labor, estimates of marginal products were close to the value expected under profit maximization. Finally, the results suggest important opportunities to increase productivity through reductions in technical inefficiencies.