Crystal Defects 1v293p

Chapter 2 Crystal Defects 1.0 Learning Objectives ?? ?? ?? ?? ?? ?? ?? ??

Define point defects. Define line defects. Define planar defects. Define edge, screw, and mixed dislocations. Determine the direction of motion for edge and screw dislocations. Calculate atomic density in a solid. Distinguish between defects of different dimensions. Calculate the concentration of vacancies as a function of temperature in a solid. ?? Distinguish between substitutional and interstitial impurities.

2.0 Resources [5]. Links for Defects & Imperfections in Materials: http://www.geocities.com/materialsworldweb/Imperfections.html [6]. Presentation on Defects (includes animation of edge & screw dislocations moving): http://www-classes.usc.edu/engr/ms/125/MDA125/defects/ [7]. Another Tutorial & Animation: http://www.uet.edu.pk/dmems/online_study_aid.htm [8]. Another Defect Tutorial & Animation: http://www.techfak.uni-kiel.de/matwis/amat/def_en/makeindex.html

3.0 Theory of Crystalline Defects Even though crystals are defined as ordered arrangements of atoms or ions, they are not perfect. There always exist crystalline defects, which can be point defects occurring at a single lattice point; line defects occurring along a row of atoms; or planar defects occurring over a two -dimensional surface in the crystal. There can also be three-dimensional defects such as voids. Defects influence the electrical and mechanical properties of solids; in fact it is the defects that are usually responsible for the existence of useful properties. Almost, or perhaps all, technology involving materials depends on the existence of some kind of defects.

3.1

Point Defects

A point defect is a defect that occurs at a specific lattice point. There are many types of point defects. The existence of point defects is thermodynamically predictable, and they influence the electronic properties of the crystal. There is

strain in the crystal in the immediate vicinity of the point defect. This particularly can affect the electrical properties of the crystal. A vacancy is a "missing" atom in a crystal. The concentration of vacancies (Nv ) in a crystal has an Arrhenius dependence on temperature, as:

?? E ?? Nv ? Nexp ??? v ?? ?? RT ?? (2) where N is the concentration of lattice sites, Ev is the formation energy of the vacancy in Joules/mol, R is the gas constant and T is the absolute temperature in Kelvin. Increasing the temperature of a solid causes the vacancy concentration to increase exponentially. This increase in vacancy concentration allows high temperature diffusion to take place, which is used to carefully control the impurity concentration in semiconductors during manufacturing. An interstitial is an atom occupying the space between regular lattice sites. A self-interstitial is an atom of the host crystal in an interstitial position, while an impurity interstitial is a different kind of atom in an interstitial position. A substitutional impurity occupies a regular lattice site, taking the place of the host atom. When there are a large number of impurities (on the order of a percent to 50 percent), the material is called a solid solution. Point defects may also combine to form, for example, divacancies. Interstitials and vacancies may be attracted to each other and form loops or clusters. A Frenkel defect is a vacancy and an interstitial bound together. In ionic materials, such as ceramics and semiconductors, point defects are usually charged. For example, in sodium chloride, a missing Na + ion is negatively charged, because of the “extra” electron associated with the anion. Since charge neutrality must be maintained overall, if there is a missing cation, there must also be a missing anion. A Schottky defect is an anion vacancy and a cation vacancy bound together. The latter defects can only occur in ionic materials. In fact, single vacancies cannot exist in ionic materials due to the necessity of maintaining charge neutrality in the crystal. Silicon is thought to contain both negatively and positively charged vacancies, and both singly and doubly charged vacancies and interstitials. The concentration of these point defects influences the rate of diffusion of impurities through the crystal and also influences the optical properties. Point defects cannot be observed directly, but their presence can be inferred through diffusion experiments or optical spectroscopy. Different kinds of point defects are shown in Callister Figures 4.1 and 4.2.

3.2

Line Defects

Line defects are defects that extend through the crystal along a one-dimensional boundary, such as a line or a curve. These defects, called dislocations , are created when planes of atoms are out of place. The crystal is divided in two by line defects, such that on each side of the defect the lattice planes are lined up perfectly, but the two sides are offset from each other. Thus it appears that there is an extra plane of atoms on one side. There are two types of dislocations: edge dislocations and screw dislocations. Edge dislocations can be thought of as an extra plane of atoms above or below the dislocation line. A screw dislocation winds through the dislocation like a screw. Dislocations are shown in Callister Figures 4.3 -4.5. Without dislocations, movement of atoms relative to each other would be very difficult, and no plastic deformation would be possible. The manufacture of most metal parts is possible because of dislocations. Likewise, the reason metallic parts bend under loads, rather than shatter, is because they contain enormous numbers of dislocations, and it is easy for dislocations to move. Semiconductors and ceramic materials, on the other hand, do not contain as many dislocations, and they do not move easily. These materials are hard, but brittle as a result.

3.3

Planar (Interfacial) Defects

Planar (interfacial) defects occur wherever the crystalline structure of the material is not continuous across a plane. Some examples are surfaces, grain boundaries, and interfaces between different layers of materials . For example, the boundary between a thin film of silicon dioxide and a silicon wafer is an important interface in microelectronics. Some examples are shown in Callister Figures 4.7-4.9. Most materials are polycrystalline. Although the material has the same composition and structure on either side of a boundary, the crystalline structure does not match up perfectly with the crystalline structure in a neighboring area. Each separate crystalline area is called a grain, and the boundaries between the grains are called grain boundaries. Polycrystalline silicon, or polysilicon as it is called, is an important material in microelectronics. It does not have the perfectly crystalline structure of the underlying silicon wafer, but it is useful as a conductor line in integrated circuits. Because of its grain boundaries, the polysilicon acts more like a metal.

Lab Worksheet 2.1 Atomic Density Calculate the density of body-centered cubic iron and compare it to the density of face-centered cubic iron. BCC Fe exists at temperatures below 1183 K and has a lattice parameter of 0.287 nm. FCC Fe exists between 1183 K and 1673 K and has a lattice parameter of 0.354 nm. Compare your results for the BCC iron to the actual measured value given in Callister: ?Fe = 7.87 g/cm3 How can you explain the discrepancy in of lattice defects?

Lab Bluesheet: 2.2 Building Defect Models Exercise I Using the styrofoam kits, build some model unit cells which contain vacancies, interstitials (both types) and substitutional impurities. Can you determine whether an impurity will be interstitial or substitutional from its size? Notice how the atomic bond lengths are affected by the presence of a vacancy or an impurity. Exercise 2 Make an array of unit cells which contains an edge dislocation, and notice where the dislocation line is. Which way will the dislocation move under various types of stress? Where is the strain in the lattice caused by the dislocation? Calculate the planar density of dislocations in your model. (The number of dislocations per unit area. You can determine this by counting the number of dislocations which intersect the "surface" of your crystal divided by the area of your crystal surface.) Exercise 3 Make a two dimensional array of unit cells and combine it with that of other students to demonstrate grain boundaries. Be sure everyone uses the same size atoms (spheres) and same lattice parameter (toothpick length). The "crystals" should be at least two unit cells thick. Determine the tilt angle between your two grains. Are the relative orientations of your two grains close to each other (low tilt angle) or very different (high tilt angle)? Exercise 4 Make an interface between two different crystal structures or materials with different lattice parameters. 1. Make two separate sets of simple cubic unit cells, using two different toothpick lengths to make two different lattice parameters (a1 and a 2) and different atomic sizes (spheres). 2. Fit the two "crystals" together with a set of atomic bonds (toothpicks) such that there are no "extra" or "missing" atoms at the interface. 3. Notice that the rows of atomic bonds on either side of the interface are strained due to the mismatch in lattice parameters. This is called a strained interface, because the difference in structure will cause strain in the bonds. This type of interface can be very harmful to electronic properties in semiconductors.