A Revlew of Materials Science 1. 3. DEFECTS IN SOLIDS The picture of a perfect crystal structure repeating a particular geometric pattern of atoms without interruption or mistake is somewhat exaggerated Although there are materials-carefully grown silicon single crystals, for example-that have virtually perfect crystallographic structures extending over macroscopic dimensions, this is not generally true in bulk materials. In thin crystalline films the presence of defects not only serves to disrupt the geomet ric regularity of the lattice on a microscopic level, it also significantl nfluences many film properties, such as chemical reactivity, electrical conduc tion, and mechanical behavior. The structural defects briefly considered in this section are grain boundaries, dislocations, and vacancies 1.3.1. Grain Boundaries Grain boundaries are surface or area defects that constitute the interface between two single-crystal grains of different crystallographic orientation. The atomic bonding, in particular grains, terminates at the grain boundary where more loosely bound atoms prevail. Like atoms on surfaces, they are necessar ly more energetic than those within the grain interior. This causes the grain boundary to be a heterogeneous region where various atomic reactions and processes, such as solid-state diffusion and phase transformation, precipitation corrosion, impurity segregation, and mechanical relaxation, are favored or accelerated. In addition, electronic transport in metals is impeded through increased scattering at grain boundaries, which also serve as charge recombina- tion centers in semiconductors. Grain sizes in films are typically from 0.01 to 1.0 um in dimension and are smaller, by a factor of more than 100, than common grain sizes in bulk materials. For this reason, thin films tend to be more reactive than their bulk counterparts. The fraction of atoms associate with grain boundaries is approximately 3a/l, where a is the atomic dimension ind I is the grain size. For 1=1000 A, this corresponds to about 5 in 1000 Grain morphology and orientation in addition to size control are not only important objectives in bulk materials but are quite important in thin-film technology. Indeed a major goal in microelectronic applications is to eliminate grain boundaries altogether through epitaxial growth of single-crystal semicon- ductor films onto oriented single-crystal substrates. Many special techniques involving physical and chemical vapor deposition methods are employed in this in semicond
10 A Review of Materials Science 1.3. DEFECTS IN SOLIDS The picture of a perfect crystal structure repeating a particular geometric pattern of atoms without interruption or mistake is somewhat exaggerated. Although there are materials-carefully grown silicon single crystals, for example-that have virtually perfect crystallographic structures extending over macroscopic dimensions, this is not generally true in bulk materials. In thin crystalline films the presence of defects not only serves to disrupt the geometric regularity of the lattice on a microscopic level, it also significantly influences many film properties, such as chemical reactivity, electrical conduction, and mechanical behavior. The structural defects briefly considered in this section are grain boundaries, dislocations, and vacancies. 1.3.1. Grain Boundaries Grain boundaries are surface or area defects that constitute the interface between two single-crystal grains of different crystallographic orientation. The atomic bonding, in particular grains, terminates at the grain boundary where more loosely bound atoms prevail. Like atoms on surfaces, they are necessarily more energetic than those within the grain interior. This causes the grain boundary to be a heterogeneous region where various atomic reactions and processes, such as solid-state diffusion and phase transformation, precipitation, corrosion, impurity segregation, and mechanical relaxation, are favored or accelerated. In addition, electronic transport in metals is impeded through increased scattering at grain boundaries, which also serve as charge recombination centers in semiconductors. Grain sizes in films are typically from 0.01 to 1.0 pm in dimension and are smaller, by a factor of more than 100, than common grain sizes in bulk materials. For this reason, thin films tend to be more reactive than their bulk counterparts. The fraction of atoms associated with grain boundaries is approximately 2 a /I, where a is the atomic dimension and 1 is the grain size. For 1 = loo0 A, this corresponds to about 5 in 1OOO. Grain morphology and orientation in addition to size control are not only important objectives in bulk materials but are quite important in thin-film technology. Indeed a major goal in microelectronic applications is to eliminate grain boundaries altogether through epitaxial growth of single-crystal semiconductor films onto oriented single-crystal substrates. Many special techniques involving physical and chemical vapor deposition methods are employed in this effort, which continues to be a major focus of activity in semiconductor technology
1. 3. Defects In Solids 1. 3.2. DIslocations Dislocations are line defects that bear a definite crystallographic relationship to the lattice. The two fundamental types of dislocations-the edge and the screw -are shown in Fig. 1-6 and are represented by the symbol 1. The edge dislocation results from wedging in an extra row of atoms; the screw disloc tion requires cutting followed by shearing of the perfect crystal lattice. The geometry of a crystal containing a dislocation is such that when a simple closed traverse is attempted about the crystal axis in the surrounding lattice, there is a closure failure; i.e., one finally arrives at a lattice site displaced from the starting position by a lattice vector, the so-called Burgers vector b. The ndividual cubic cells representing the original undeformed crystal lattice are now distorted somewhat in the presence of dislocations. Therefore, even without application of external forces on the crystal, a state of internal stress exists around each dislocation. Furthermore, the stresses differ around edge and screw dislocations because the lattice distortions differ. Close to the dislocation axis the stresses are high, but they fall off with distance(r) according to a 1/r dependence Dislocations are important because they have provided a model to help explain a great variety of mechanical phenomena and properties in all classes of crystalline solids. An early application was the important process of plastic deformation, which occurs after a material is loaded beyond its limit of elastic response. In the plastic range, specific planes shear in specific directions relative to each other much as a deck of cards shear from a rectangular prism EDGE DISLOCATION SCREW DISLOCATION FIgure 1-6.(left)Edge dislocation; (right) screw dislocation.( Reprinted with per- mission from John Wiley and Sons, H. w. Hayden, w.G. Moffatt, and J, Wulff, The Structure and Properties of Materials, Vol. Ill, Copyright 1965, John Wiley and
1.3. Defects in Solids 11 1.3.2. Dislocations Dislocations are line defects that bear a definite crystallographic relationship to the lattice. The two fundamental types of dislocations-the edge and the screw -are shown in Fig. 1-6 and are represented by the symbol I . The edge dislocation results from wedging in an extra row of atoms; the screw dislocation requires cutting followed by shearing of the perfect crystal lattice. The geometry of a crystal containing a dislocation is such that when a simple closed traverse is attempted about the crystal axis in the surrounding lattice, there is a closure failure; i.e., one finally amves at a lattice site displaced from the starting position by a lattice vector, the so-called Burgers vector b. The individual cubic cells representing the original undeformed crystal lattice are now distorted somewhat in the presence of dislocations. Therefore, even without application of external forces on the crystal, a state of internal stress exists around each dislocation. Furthermore, the stresses differ around edge and screw dislocations because the lattice distortions differ. Close to the dislocation axis the stresses are high, but they fall off with distance (r) according to a 1 / r dependence. Dislocations are important because they have provided a model to help explain a great variety of mechanical phenomena and properties in all classes of crystalline solids. An early application was the important process of plastic deformation, which occurs after a material is loaded beyond its limit of elastic response. In the plastic range, specific planes shear in specific directions relative to each other much as a deck of cards shear from a rectangular prism EDGE DISLOCATION SCREW DISLOCATION Figure 1-6. (left) Edge dislocation; (right) screw dislocation. (Reprinted with permission from John Wiley and Sons, H. W. Hayden, W. G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. 111, Copyright 0 1965, John Wiley and Sons)
- FORCE FORCE Figure 1-7.(a)Edge dislocation motion through lattice under applied shear stress printed with permission from J. R. Shackelford, Introduction to Materials Science for Engineers, Macmillan, 1985).(b)Dislocation model of a grain boundary. The crystallographic misorientation angle 8 between grains is b/de to a parallelepiped. Rather than have rows of atoms undergo a rigid group displacement to produce the slip offset step at the surface, the same amount of plastic deformation can be achieved with less energy expenditure. This alterna tive mechanism requires that dislocations undulate through the crystal, making and breaking bonds on the slip plane until a slip step is produced, as shown in Fig. 1-7a. Dislocations thus help explain why metals are weak and can be deformed at low stress levels. Paradoxically, dislocations can also explain why metals work-harden or get stronger when they are deformed. These explana tions require the presence of dislocations in great profusion. In fact, a density of as many 10 2 dislocation lines threading I cm2 of surface area has been observed in highly deformed metals. Many deposited polycrystalline metal thin s also have high dislocation densities. Some dislocations are stacked vertically, giving rise to so-called small-angle grain boundaries(Fig. 1-7b) The superposition of extermally applied forces and internal stress fields of individual or groups of dislocations, arrayed in a complex three-dimensional network, sometimes makes it more difficult for them to move and for the lattice to deform easily The role dislocations play in thin films is varied. As an example, consider he deposition of atoms onto a single-crystal substrate in order to gro epitaxial single-crystal film. If the lattice parameter in the film and substrate
12 A Review of Materials Science a b - - -----) FORCE FORCE - a. - b. cC. c- t. "b d. e. f. Figure 1-7. (a) Edge dislocation motion through lattice under applied shear stress. (Reprinted with permission from J. R. Shackelford, Introduction to Materials Science for Engineers, Macmillan, 1985). (b) Dislocation model of a grain boundary. The crystallographic misorientation angle 0 between grains is b / d, . to a parallelepiped. Rather than have rows of atoms undergo a rigid group displacement to produce the slip offset step at the surface, the same amount of plastic deformation can be achieved with less energy expenditure. This alternative mechanism requires that dislocations undulate through the crystal, making and breaking bonds on the slip plane until a slip step is produced, as shown in Fig. 1-7a. Dislocations thus help explain why metals are weak and can be deformed at low stress levels. Paradoxically, dislocations can also explain why metals work-harden or get stronger when they are deformed. These explanations require the presence of dislocations in great profusion. In fact, a density of as many 10l2 dislocation lines threading 1 cm2 of surface area has been observed in highly deformed metals. Many deposited polycrystalline metal thin films also have high dislocation densities. Some dislocations are stacked vertically, giving rise to so-called small-angle grain boundaries (Fig. 1-7b). The superposition of externally applied forces and internal stress fields of individual or groups of dislocations, arrayed in a complex three-dimensional network, sometimes makes it more difficult for them to move and for the lattice to deform easily. The role dislocations play in thin films is varied. As an example, consider the deposition of atoms onto a single-crystal substrate in order to grow an epitaxial single-crystal film. If the lattice parameter in the film and substrate
1.3. Defects In Solids differ, then some geometric accommodation in bonding may be required at the interface, resulting in the formation of interfacial dislocations. The latter are unwelcome defects particularly if films of high crystalline perfection are required. For this reason, a good match of lattice parameters is sought epitaxial growth. Substrate steps and dislocations should also be elimi where possible prior to growth. If the substrate has screw dislocations emerg ng normal to the surface, depositing atoms may perpetuate the extension of the dislocation spiral into the growing film. Like grain boundaries in semiconduc- tors, dislocations can be sites of charge recombination or generation as a result of uncompensated"dangling bonds. "" Film stress, thermally induced mechani cal relaxation processes, and diffusion in films are all influenced by disloc 1. 3.3. Vacancies The last type of defect considered is the vacancy. Vacancies are point defects that simply arise when lattice sites are unoccupied by atoms. Vacancies form because the energy a required to remove atoms from interior sites and place them on the surface is not particularly high. This low energy, coupled with the increase in the statistical entropy of mixing vacancies among lattice sites, gives rise to a thermodynamic probability that an appreciable number of vacancies will exist, at least at elevated temperature. The fraction f of total sites that will be unoccupied as a function of temperature T is predicted to be approximately /kT reflecting the statistical thermodynamic nature of vacancy formation. Noting that k is the gas constant and E, is typically 1 ev/atom gives f=10-3at 1000K Vacancies are to be contrasted with dislocations, which are not thermody- namic defects, Because dislocation lines are oriented along specific crystallo- graphic directions, their statistical entropy is low. Coupled with a high formation energy due to the many atoms involved, thermodynamics would predict a dislocation content of less than one per crystal. Thus, although it is possible to create a solid devoid of dislocations, it is impossible to eliminate vacant Vacancies play an important role in all processes related to solid-state diffusion, including recrystallization, grain growth, sintering, and phase trans formations. In semiconductors, vacancies are electrically neutral as well charged and can be associated with dopant atoms. This leads to a variety of normal and anomalous diffusional doping effects
1.3. Defects in Sollds 13 differ, then some geometric accommodation in bonding may be required at the interface, resulting in the formation of interfacial dislocations. The latter are unwelcome defects particularly if films of high crystalline perfection are required. For this reason, a good match of lattice parameters is sought for epitaxial growth. Substrate steps and dislocations should also be eliminated where possible prior to growth. If the substrate has screw dislocations emerging normal to the surface, depositing atoms may perpetuate the extension of the dislocation spiral into the growing film. Like grain boundaries in semiconductors, dislocations can be sites of charge recombination or generation as a result of uncompensated “dangling bonds. ” Film stress, thermally induced mechanical relaxation processes, and diffusion in films are all influenced by dislocations. 1.3.3. Vacancies The last type of defect considered is the vacancy. Vacancies are point defects that simply arise when lattice sites are unoccupied by atoms. Vacancies form because the energy required to remove atoms from interior sites and place them on the surface is not particularly high. This low energy, coupled with the increase in the statistical entropy of mixing vacancies among lattice sites, gives rise to a thermodynamic probability that an appreciable number of vacancies will exist, at least at elevated temperature. The fraction f of total sites that will be unoccupied as a function of temperature T is predicted to be approximately reflecting the statistical thermodynamic nature of vacancy formation. Noting that k is the gas constant and is typically 1 eV/atom gives f = lop5 at loo0 K. Vacancies are to be contrasted with dislocations, which are not thermodynamic defects. Because dislocation lines are oriented along specific crystallographic directions, their statistical entropy is low. Coupled with a high formation energy due to the many atoms involved, thermodynamics would predict a dislocation content of less than one per crystal. Thus, although it is possible to create a solid devoid of dislocations, it is impossible to eliminate vacancies. Vacancies play an important role in all processes related to solid-state diffusion, including recrystallization, grain growth, sintering, and phase transformations. In semiconductors, vacancies are electrically neutral as well as charged and can be associated with dopant atoms. This leads to a variety of normal and anomalous diffusional doping effects
A Revlew of Materials Sclence 1.4. BONDING OF MATERIALS Widely spaced isolated atoms condense to form solids due to the energy reduction accompanying bond formation. Thus, if N atoms of type a in the gas phase (g) combine to form a solid(s), the binding energy E, is released according to the equation NA。→NA+E Energy Eb must be supplied to reverse the equation and decompose the solid The more stable the solid, the higher is its binding energy. It has become the custom to picture the process of bonding by considering the energetics within and between atoms as the interatomic distance progressively shrinks. In each isolated atom, the electron energy levels are discrete, as shown on the right-hand side of Fig. 1-8a. As the atoms approach one another, the individual levels split, as a consequence of an extension of the Pauli exclusion principle to a collective solid; namely, no two electrons can exist in the same quantum state. Level splitting and broadening occur first for the valence or outer electrons, since their electron clouds are the first to overlap. During atomic attraction, electrons populate these lower energy levels, reducing the overall energy of the solid. with further dimensional shrinkage, the overlap increases and the inner charge clouds begin to interact. Ion-core overlap now results in strong repulsive forces between atoms, raising the system energy. A compro- mise is reached at the equilibrium interatomic distance in the solid where the ystem energy is minimized. At equilibrium, some of the levels have broad ened into bands of energy levels. The bands span different ranges of energy depending on the atoms and specific electron levels involved, Sometimes as in metals, bands of high energy overlap. Insulators and semiconductors have energy gaps of varying width between bands where electron states are not allowed. The whys and hows of energy-level splitting, band structure evolu tion, and implications with regard to property behavior are perhaps the most fundamental and difficult questions in solid-state physics. We briefly return he subject of electron-band structure after introducing the classes of solids An extension of the ideas expressed in Fig. 1-8a is commonly made by simplifying the behavior to atoms as a whole, in which case the potential energy of interaction V(r)is plotted as a function of interatomic distance r in Fig. 1-8b. The generalized behavior shown is common for all classes of sol materials, regardless of the type of bonding or crystal structure. Although the mathematical forms of the attractive or repulsive portions are complex,a er of qualitative features of these curves are not difficult to understand
14 A Review of Materials Science 1.4. BONDING OF MATERIALS Widely spaced isolated atoms condense to form solids due to the energy reduction accompanying bond formation. Thus, if N atoms of type A in the gas phase (8) combine to form a solid (s), the binding energy Eb is released according to the equation NA, + NA, -k Eb. Energy Eb must be supplied to reverse the equation and decompose the solid. The more stable the solid, the higher is its binding energy. It has become the custom to picture the process of bonding by considering the energetics within and between atoms as the interatomic distance progressively shrinks. In each isolated atom, the electron energy levels are discrete, as shown on the right-hand side of Fig. 1-8a. As the atoms approach one another, the individual levels split, as a consequence of an extension of the Pauli exclusion principle, to a collective solid; namely, no two electrons can exist in the same quantum state. Level splitting and broadening occur first for the valence or outer electrons, since their electron clouds are the first to overlap. During atomic attraction, electrons populate these lower energy levels, reducing the overall energy of the solid. With further dimensional shrinkage, the overlap increases and the inner charge clouds begin to interact. Ion-core overlap now results in strong repulsive forces between atoms, raising the system energy. A compromise is reached at the equilibrium interatomic distance in the solid where the system energy is minimized. At equilibrium, some of the levels have broadened into bands of energy levels. The bands span different ranges of energy, depending on the atoms and specific electron levels involved. Sometimes as in metals, bands of high energy overlap. Insulators and semiconductors have energy gaps of varying width between bands where electron states are not allowed. The whys and hows of energy-level splitting, band structure evolution, and implications with regard to property behavior are perhaps the most fundamental and difficult questions in solid-state physics. We briefly return to the subject of electron-band structure after introducing the classes of solids. An extension of the ideas expressed in Fig. 1-8a is commonly made by simplifying the behavior to atoms as a whole, in which case the potential energy of interaction V(r) is plotted as a function of interatomic distance r in Fig. 1-8b. The generalized behavior shown is common for all classes of solid materials, regardless of the type of bonding or crystal structure. Although the mathematical forms of the attractive or repulsive portions are complex, a number of qualitative features of these curves are not difficult to understand