The Young's modulus (E) of a material is a key parameter for mechanical engineering design. Silicon, the most common single material used in microelectromechanical systems (MEMS), is an anisotropic crystalline material whose material properties depend on orientation relative to the crystal lattice. This fact means that the correct value of E for analyzing two different designs in silicon may differ by up to 45%. However, perhaps, because of the perceived complexity of the subject, many researchers oversimplify silicon elastic behavior and use inaccurate values for design and analysis. This paper presents the best known elasticity data for silicon, both in depth and in a summary form, so that it may be readily accessible to MEMS designers.

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What is the Young's Modulus of Silicon?

Publisher Summary This chapter discusses the progress in the field of plasticity of the diamond cubic structure (D.S.) from the standpoint of a micromechanical (dislocation dynamical) theory of macroscopic plastic properties. It is suggested that hat the high resistance to dislocation motion of D.S. crystals stems from a high Peierls potential. The problem is to understand the creation and movement of kinks as the elementary vehicles of dislocation motion. How do kinks interact with each other and with other lattice defects, including phonons? How does a distribution of kinks arise which shows up in the shape of dislocation lines frozen-in after deformation and observed in electron transmission? Semiconductor doping provides a unique possibility for manipulating the core structure of the dislocation in the D.S. and thus the Peierls potential. Its effect shows up microscopically in the dislocation dynamics as well as macroscopically in the deformation curves of D.S. crystals. The study of the charge on a dislocation in a doped semiconductor by measurement of its electrical properties discussed that may serve as a link in understanding the doping effects in dislocation dynamics.

Dislocations and Plastic Flow in the Diamond Structure

Light-matter interactions that lead to nonthermal changes in size of the sample constitute a photostrictive effect in many compounds The photostriction phenomenon was observed in four main groups of materials, ferroelectrics, polar, and non-polar semiconductors, as well as in organic-based materials that are reviewed here The key mechanisms of photostriction and its dependence on several parameters and perturbations are assessed The major literature of the photostriction is surveyed, and the review ends with a summary of the proposed technical applications

Photostrictive materials

Publisher Summary The electronic energy levels of a semiconductor depend on the state of strain of the semiconductor crystal. If some of the levels are occupied, the electronic contribution to the free energy of the crystal depends on the state of strain. The electronic contribution to the dependence of the energy on strain can be significant in moderately and heavily doped semiconductors and gives rise to easily observable dependences of elastic properties on doping. This chapter describes the electronic contribution to the elastic properties of certain types of semiconductors. Electronic energy is responsible for the binding and the elastic properties of many solids. Electronic models have frequently been used in calculations of the elastic constants of metal. The characteristic feature of this chapter is the use of semiconductor models that are useful in describing many other properties of semiconductors and whose parameters can be determined in a variety of ways. The study of electronic effects in the elastic properties of semiconductors has value for a number of reasons that are worth describing. Firstly, semiconductors are extremely important technologically. It is important to know their elastic properties in order that they may be properly used. Changes in moduli, thermal expansion, or magnetostriction with doping may have significant practical impact.

Electronic Effects in the Elastic Properties of Semiconductors

Publisher Summary This chapter attempts to give a systematic presentation of the theory of the acoustic phonon-conduction electron interaction as it stands today. It places particular emphasis on the effect of dc magnetic and electric fields on the electron-phonon interaction. It is restricted mainly to conduction electrons in spherical energy bands, thus ignoring the effects of complicated Fermi surfaces on the interaction. These effects have been covered in some detail in review articles by other authors and in articles on the Fermi surface. However, some discussion is given on the extension of the calculations to more general energy bands. This chapter concentrates mainly on presenting a clear physical picture of the interaction, with more emphasis on the theoretical aspects than on the experimental aspects. However, sufficient reference is made to experiments to illustrate the applicability of the theory. Reference is also made to the powerful tool this interaction represents in exploring the band structure of solids.

Interaction of Acoustic Waves and Conduction Electrons

Theories of several elastic effects resulting from the contribution of electrons to the strain energy function of germanium are presented. They show that the elastic properties are appreciably changed by doping with donor and acceptor impurities. The properties considered are: (1) volume, (2) elastic constants of degenerate n-type material, (3) third-order elastic constants of degenerate n-type material, (4) elastic constants of degenerate p-type material, (5) elastic constants of material containing electrons bound to donors, (6) elastic constants of material containing electrons bound to pairs of donor atoms. The most striking effect is found for the case of degenerate n-type germanium, in which the theory predicts that c44 can be lowered by 8% with attainable doping levels.

R. W. Keyes

Papers

The electronic contribution to the elastic properties of germanium