There has been an enormous infusion of new ideas in the field of solar cells over the last 15 years; discourse on energy transfer has gotten much richer, and nanostructures and nanomaterials have revolutionized the possibilities for new technological developments. However, solar energy cannot become ubiquitous in the world's power markets unless it can become economically competitive with legacy generation methods such as fossil fuels. The new edition of Dr. Stephen Fonash's definitive text points the way toward greater efficiency and cheaper production by adding coverage of cutting-edge topics in plasmonics, multi-exiton generation processes, nanostructures and nanomaterials such as quantum dots. This book's new structure improves readability by shifting many detailed equations to appendices, and balances the first edition's semiconductor coverage with an emphasis on thin-films. Further, it now demonstrates physical principles with simulations in the well-known AMPS computer code developed by the author. This classic text is now updated with new advances in nanomaterials and thin films that point the way to cheaper, more efficient solar energy production and, many of the detailed equations from the first edition have been shifted to appendices in order to improve readability. It carries important theoretical points are now accompanied by concrete demonstrations via included simulations created with the well-known AMPS computer code.

太阳电池器件物理 = Solar cell device physics

The aim of this paper is to provide a survey on the recent development in level set methods in inverse problems and optimal design. We give introductions on the general features of such problems involving geometries and on the general framework of the level set method. In subsequent parts we discuss shape sensitivity analysis and its relation to level set methods, various approaches on constructing optimization algorithms based on the level set approach, and special tools needed for the application of level set based optimization methods to ill-posed problems. Furthermore, we provide a review on numerical methods important in this context, and give an overview of applications treated with level set methods. Finally, we provide a discussion of the most challenging and interesting open problems in this field, that might be of interest for scientists who plan to start future research in this field.

A survey on level set methods for inverse problems and optimal design

Solving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method

We present a new phase-field model for strongly anisotropic crystal and epitaxial growth using regularized, anisotropic Cahn–Hilliard-type equations. Such problems arise during the growth and coarsening of thin films. When the anisotropic surface energy is sufficiently strong, sharp corners form and unregularized anisotropic Cahn–Hilliard equations become ill-posed. Our models contain a high-order Willmore regularization, where the square of the mean curvature is added to the energy, to remove the ill-posedness. The regularized equations are sixth order in space. A key feature of our approach is the development of a new formulation in which the interface thickness is independent of crystallographic orientation. Using the method of matched asymptotic expansions, we show the convergence of our phase-field model to the general sharp-interface model. We present two- and three-dimensional numerical results using an adaptive, nonlinear multigrid finite-difference method. We find excellent agreement between the dynamics of the new phase-field model and the sharp-interface model. The computed equilibrium shapes using the new model also match a recently developed analytical sharp-interface theory that describes the rounding of the sharp corners by the Willmore regularization.

A new phase-field model for strongly anisotropic systems

Surfaces and interfaces can significantly influence the overall response of a solid body. Their behavior is well described by continuum theories that endow the surface and interface with their own energetic structures. Such theories are becoming increasingly important when modeling the response of structures at the nanoscale. The objectives of this review are as follows. The first is to summarize the key contributions in the literature. The second is to unify a select subset of these contributions using a systematic and thermodynamically consistent procedure to derive the governing equations. Contributions from the bulk and the lower-dimensional surface, interface, and curve are accounted for. The governing equations describe the fully nonlinear response (geometric and material). Expressions for the energy and entropy flux vectors, and the admissible constraints on the temperature field, all subject to the restriction of non-negative dissipation, are explored. A particular emphasis is placed on the structure of these relations at the interface. A weak formulation of the governing equations is then presented that serves as the basis for their approximation using the finite element method. Various forms for a Helmholtz energy that describes the fully coupled thermomechanical response of the system are given. They include the contribution from surface tension. The vast majority of the literature on surface elasticity is framed in the infinitesimal deformation setting. The finite deformation stress measures are, thus, linearized and the structure of the resulting stresses discussed. The final objective is to elucidate the theory using a series of numerical example problems.

Thermomechanics of Solids With Lower-Dimensional Energetics: On the Importance of Surface, Interface, and Curve Structures at the Nanoscale. A Unifying Review

When the interfacial energy is a nonconvex function of orientation, the anisotropic-curvature-flow equation becomes backward parabolic. To overcome the instability thus generated, a regularization of the equation that governs the evolution of the interface is needed. In this paper we develop a regularized theory of curvature flow in three dimensions that incorporates surface diffusion and bulk-surface interactions. The theory is based on a superficial mass balance; configurational forces and couples consistent with superficial force and moment balances; a mechanical version of the second law that includes, via the configurational moments, work that accompanies changes in the curvature of the interface; a constitutive theory whose main ingredient is a positive-definite, isotropic, quadratic dependence of the interfacial energy on the curvature tensor. Two special cases are investigated: (i) the interface is a boundary between bulk phases or grains, and (ii) the interface separates an elastic thin film bonded to a rigid substrate from a vapor phase whose sole action is the deposition of atoms on the surface.

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Interface Evolution in Three Dimensions¶with Curvature-Dependent Energy¶and Surface Diffusion:¶Interface-Controlled Evolution, Phase Transitions, Epitaxial Growth of Elastic Films

We derive, in the form of coupled partial differential equations, the evolution equations for the epitaxial growth, via step flow, of a multispecies crystal on a stepped surface. Both adsorption–desorption on the terraces and attachment–detachment along the step edges are accompanied by chemical reactions and adatom diffusion. Moreover, we account for deposition from either a vacuum, e.g., in molecular beam epitaxy, or a gas, e.g., during vapour phase epitaxy (chemical or physical). Our theory (i) endows the steps with a thermodynamic structure whose main ingredients are a free-energy density and species edge chemical potentials, (ii) incorporates anisotropy into the terrace species diffusion as well as into the edge free energy, species mobilities, attachment–detachment and reaction-rate coefficients, (iii) allows for large departures from local equilibrium along the steps, and (iv) ensures the consistency of the constitutive relations for the terrace and edge chemical rates with the second law. In particular, a configurational force balance at each step yields a generalization of the classical Gibbs–Thomson relation. Finally, the special case of steady-state growth of a binary compound is discussed.

Multispecies epitaxial growth on vicinal surfaces with chemical reactions and diffusion

A thermodynamically consistent continuum theory for single-species, step-flow epitaxy that extends the classical Burton-Cabrera-Frank (BCF) framework is derived from basic considerations. In particular, an expression for the step chemical potential is obtained that contains two energetic contributions--one from the adjacent terraces in the form of the jump in the adatom grand canonical potential and the other from the monolayer of crystallized adatoms that underlies the upper terrace in the form of the nominal bulk chemical potential--thus generalizing the classical Gibbs-Thomson relation to the dynamic, dissipative setting of step-flow growth. The linear stability analysis of the resulting quasistatic free-boundary problem for an infinite train of equidistant rectilinear steps yields explicit--i.e., analytical--criteria for the onset of step bunching in terms of the basic physical and geometric parameters of the theory. It is found that, in contrast with the predictions of the classical BCF model, both in the absence as well as in the presence of desorption, a growth regime exists for which step bunching occurs, except possibly in the dilute limit where the train is always stable to step bunching. In the present framework, the onset of one-dimensional instabilities is directly attributed to the energetic influence on the migrating steps of themore » adjacent terraces. Hence the theory provides a ''minimalist'' alternative to existing theories of step bunching and should be relevant to, e.g., molecular beam epitaxy of GaAs where the equilibrium adatom density is shown by Tersoff, Johnson, and Orr [Phys. Rev. B 78, 282 (1997)] to be extremely high.« less

Possible mechanism for the onset of step-bunching instabilities during the epitaxy of single-species crystalline films

We revisit the step bunching instability without recourse to the quasistatic approximation and show that the stability diagrams are significantly altered, even in the low-deposition regime where it was thought sufficient. In particular, steps are unstable against bunching for attachment-detachment limited growth. By accounting for the dynamics and chemical effects, we can explain the onset of step bunching in $\mathrm{Si}(111)\text{\ensuremath{-}}(7\ifmmode\times\else\texttimes\fi{}7)$ and GaAs(001) without resort to the inverse Schwoebel barrier or step-edge diffusion. Further, the size-scaling analysis of step-bunch growth, as induced by these two combined effects, agrees with the bunching regime observed at $750\text{ }\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ in $\mathrm{Si}(111)\text{\ensuremath{-}}(7\ifmmode\times\else\texttimes\fi{}7)$.

Stability of Vicinal Surfaces: Beyond the Quasistatic Approximation.

It is well known that mechanical strains influence the electronic properties of semiconductor devices. Modeling the fully coupled mechanical, electrical, and electronic responses of semiconductors is therefore essential for predicting the effects of mechanical loading on their overall electronic response. In the first part of this paper, we develop a general continuum model that couples the mechanical, electrical, and electronic responses of a finitely deformable semiconductor. The proposed model accounts for the dependence of the band edge energies, densities of states, and electronic mobilities on strain. The governing equations are derived from the basic principles of the thermomechanics of electromagnetic continua undergoing electronic transport. In particular, we find that there exists electronically induced strains that can exceed their electromagnetic (Maxwell) counterparts by an order of magnitude. In the second part, motivated by applications that involve the bending of a photovoltaic cell, we use asymptotic methods to compute the current–voltage characteristic of a p − n junction under nonuniform strains. We find that, for a typical monocrystalline silicon solar cell, the changes in dark current are significant, i.e., of the order of 20% for strains of 0.2%.

Michel E. Jabbour

Papers

Interface Evolution in Three Dimensions¶with Curvature-Dependent Energy¶and Surface Diffusion:¶Interface-Controlled Evolution, Phase Transitions, Epitaxial Growth of Elastic Films

Multispecies epitaxial growth on vicinal surfaces with chemical reactions and diffusion

Possible mechanism for the onset of step-bunching instabilities during the epitaxy of single-species crystalline films

Stability of Vicinal Surfaces: Beyond the Quasistatic Approximation.

The p−n junction under nonuniform strains: general theory and application to photovoltaics