《材料科学导论 Introduction to Materials Science》参考书籍：The Materials Science of Thin Film

1. 4. Bonding of Materials VALENCE LEVE ENERGY CORE EVELS INTERATOMIC SPACING REPULSIVE ENERGY TOTAL ENERGY (BULK ATOMS) >uz TOTAL ENERGY (SURFACE ATOMS) INTERATOMIC SPACING() ATTRACTIVE ENERGY Figure 1-8. Splitting of electron levels (a) and energy of interaction between atoms (b)as a function of interatomic spacing. v(r) vs. r shown schematically for bulk and surface atoms

1.4. Bonding of Materials 15 I I I I 5-i I A I CORE LEVELS a, INTERATOMIC SPACING REPULSIVE ENERGY v - L > TOTAL ENERGY (BULK ATOMS) \ \ TOTAL ENERGY (SURFACE ATOMS) \'. \ INTERATOMIC I ~ATTRACTIVE ENERGY Figure 1-8. Splitting of electron levels (a) and energy of interaction between atoms (b) as a function of interatomic spacing. V(r) vs. r shown schematically for bulk and surface atoms

eview of Materlals Sclence For example, the energy at the equilibrium spacing r= ao is the binding nergy. Solids with high melting points tend to have high values of E,. The curvature of the potential energy is a measure of the elastic stiffness of the solid. To see this, we note that around ao the potential energy is approximately harmonic or parabolic. Therefore, V(r)=(1/2)K, r, where K, is related to the spring constant (or elastic modulus). Narrow wells of high curvature are associated with large values of K, broad wells of low curvature with small values of K,, Since the force F between atoms is given by F=-dv/dr, F=-K,, which has its counterpart in Hooke's law-i e, that stress is linearly proportional to strain. Thus, in solids with high K, values, corre- spondingly larger stresses develop under loading. Interestingly, a purely parabolic behavior for V implies a material with a coefficient of thermal expansion equal to zero. In real materials, therefore, some asymmetry or anharmonicity in v(r)exists For the most part, atomic behavior within a thin solid film can also be described by a v(r)-r curve similar to that for the bulk solid. The surface atoms are less tightly bound, however, which is reflected by the dotted line behavior in Fig. 1-8b. The difference between the energy minima for surface and bulk atoms is a measure of the surface energy of the solid. From the previous discussion, surface layers would tend to be less stiff and melt at lower temperatures than the bulk changes in equilibrium atomic spacing or lattice parameter at surfaces may also be expected Despite apparent similarities, there are many distinctions between the four important types of solid-state bonding and the properties they induce. A discussion of these individual bonding categories follows 1.4.1. Metallic The so-called metallic bond occurs in metals and alloys. In metals the outer valence electrons of each atom form part of a collective free-electron cloud or gas that permeates the entire lattice. Even though individual electron-electron interactions are repulsive, there is sufficient electrostatic attraction between the free-electron gas and the positive ion cores to cause bonding What distinguishes metals from all other solids is the ability of the electrons respond readily to applied electric fields, thermal gradients, and incident light. This gives rise to high electrical and thermal conductivities as well as high reflectivities. Interestingly, comparable properties are observed in liquid metals, indicating that aspects of metallic bonding and the free-electron model are largely preserved even in the absence of a crystal structure. Metallic electrical resistivities typically ranging from 10 to 10 ohm-cm should be

16 A Review of Materials Science For example, the energy at the equilibrium spacing r = a, is the binding energy. Solids with high melting points tend to have high values of Eb. The curvature of the potential energy is a measure of the elastic stiffness of the solid. To see this, we note that around a, the potential energy is approximately harmonic or parabolic. Therefore, V(r) = (1/2)K,r2, where K, is related to the spring constant (or elastic modulus). Narrow wells of high curvature are associated with large values of K,, broad wells of low curvature with small values of K, . Since the force F between atoms is given by F = - dV/dr, F = - Ksrr which has its counterpart in Hooke’s law-i.e., that stress is linearly proportional to strain. Thus, in solids with high K, values, corre￾spondingly larger stresses develop under loading. Interestingly, a purely parabolic behavior for I/ implies a material with a coefficient of thermal expansion equal to zero. In real materials, therefore, some asymmetry or anharmonicity in V(r) exists. For the most part, atomic behavior within a thin solid film can also be described by a V(r)-r curve similar to that for the bulk solid. The surface atoms are less tightly bound, however, which is reflected by the dotted line behavior in Fig. 1-8b. The difference between the energy minima for surface and bulk atoms is a measure of the surface energy of the solid. From the previous discussion, surface layers would tend to be less stiff and melt at lower temperatures than the bulk. Slight changes in equilibrium atomic spacing or lattice parameter at surfaces may also be expected. Despite apparent similarities, there are many distinctions between the four important types of solid-state bonding and the properties they induce. A discussion of these individual bonding categories follows. 1.4.1. Metallic The so-called metallic bond occurs in metals and alloys. In metals the outer valence electrons of each atom form part of a collective free-electron cloud or gas that permeates the entire lattice. Even though individual electron-electron interactions are repulsive, there is sufficient electrostatic attraction between the free-electron gas and the positive ion cores to cause bonding. What distinguishes metals from all other solids is the ability of the electrons to respond readily to applied electric fields, thermal gradients, and incident light. This gives rise to high electrical and thermal conductivities as well as high reflectivities. Interestingly, comparable properties are observed in liquid metals, indicating that aspects of metallic bonding and the free-electron model are largely preserved even in the absence of a crystal structure. Metallic electrical resistivities typically ranging from lop5 to ohm-cm should be

4. Bonding of Materials contrasted with the much, much larger values possessed by other classes of solids Furthermore, the temperature coefficient of resistivity is positive. Metal thus become poorer electrical conductors as the temperature is raised. The reverse is true for all other classes of solids. The conductivity of pure metals is always reduced with low levels of impurity alloying, which is also contrary to the usual behavior in other solids. The effect of both temperature and alloying element additions on metallic conductivity is to increase electron scattering which in effect reduces the net component of electron motion in the direction of the applied electric field. On the other hand, in ionic and semiconductor solids production of more charge carriers is the result of higher temperatures and solute additions The bonding electrons are not localized between atoms; thus, metals are said to have nondirectional bonds. This causes atoms to slide by each other and plastically deform more readily than is the case, for example, in covalent solids, which have directed atomic bonds Examples of thin-metal-film applications include Al contacts and intercon- nections in integrated circuits, and ferromagnetic alloys for data storage decorative coatings of various components and packaging materials s, and as applications. Metal films are also used in mirrors, in optical systems, and as 1.4.2. lonic lonic bonding occurs in compounds composed of strongly electropositive elements (metals)and strongly electronegative elements (nonmetals). The alkali halides(NaCl, LiF, etc. )are the most unambiguous examples of ionically bonded solids. In other compounds, such as oxides, sulfides, and many of the more complex salts of inorganic chemistry(e. g, nitrates, sulfates etc.), the predominant, but not necessarily exclusive, mode of bonding is ionic in character. In the rock-salt structure of NaCl, for example, there is an alternating three-dimensional checkerboard array of positively charged cations and negatively charged anions. Charge transfer from the 3s electron level of Na to the 3p level of Cl creates a single isolated NaCl molecule. In the solid however, the transferred charge is distributed uniformly among nearest neigh- bors. Thus, there is no preferred directional character in the ionic bond since the electrostatic forces between spherically symmetric inert gaslike ions is dependent of orientation Much success has been attained in determining the bond energies in alkali halides without resorting to quantum mechanical calculation. The alternating positive and negative ionic charge array suggests that Coulombic pair interac-

1.4. Bonding of Materials 17 contrasted with the much, much larger values possessed by other classes of solids. Furthermore, the temperature coefficient of resistivity is positive. Metals thus become poorer electrical conductors as the temperature is raised. The reverse is true for all other classes of solids. The conductivity of pure metals is always reduced with low levels of impurity alloying, which is also contrary to the usual behavior in other solids. The effect of both temperature and alloying element additions on metallic conductivity is to increase electron scattering, which in effect reduces the net component of electron motion in the direction of the applied electric field. On the other hand, in ionic and semiconductor solids production of more charge carriers is the result of higher temperatures and solute additions. The bonding electrons are not localized between atoms; thus, metals are said to have nondirectional bonds. This causes atoms to slide by each other and plastically deform more readily than is the case, for example, in covalent solids, which have directed atomic bonds. Examples of thin-metal-film applications include A1 contacts and intercon￾nections in integrated circuits, and ferromagnetic alloys for data storage applications. Metal films are also used in mirrors, in optical systems, and as decorative coatings of various components and packaging materials. 1.4.2. tonic Ionic bonding occurs in compounds composed of strongly electropositive elements (metals) and strongly electronegative elements (nonmetals). The alkali halides (NaCl, LiF, etc.) are the most unambiguous examples of ionically bonded solids. In other compounds, such as oxides, sulfides, and many of the more complex salts of inorganic chemistry (e.g., nitrates, sulfates, etc.), the predominant, but not necessarily exclusive, mode of bonding is ionic in character. In the rock-salt structure of NaC1, for example, there is an alternating three-dimensional checkerboard array of positively charged cations and negatively charged anions. Charge transfer from the 3s electron level of Na to the 3p level of C1 creates a single isolated NaCl molecule. In the solid, however, the transferred charge is distributed uniformly among nearest neigh￾bors. Thus, there is no preferred directional character in the ionic bond since the electrostatic forces between spherically symmetric inert gaslike ions is independent of orientation. Much success has been attained in determining the bond energies in alkali halides without resorting to quantum mechanical calculation. The alternating positive and negative ionic charge array suggests that Coulombic pair interac-

tions are the cause of the attractive part of the interatomic potential, which varies simply as-1/r. lonic solids are characterized by strong electrostatic bonding forces and, thus, relatively high binding energies and melting points They are poor conductors of electricity because the energy required to transfer electrons from anions to cations is prohibitively large. At high temperatures however, the charged ions themselves can migrate in an electric field, resulting in limited electrical conduction. Typical resistivities for such materials ca range from 10 to 10ohm-cm e Among the ionic compounds employed in thin-film technology are MgFz nS, and CeF3, which are used in antireflection coatings on optical compo- nents. Assorted thin-film oxides and oxide mixtures such as Y, Fes,2 Y3AlsO12, and LiNbO, are employed in components for integrated optics Transparent electrical conductors such as In, O3-SnOz glasses, which serve as heating elements in window defrosters on cars as well as electrical contacts over the light exposed surfaces of solar cells, have partial ionic character. 1. 4.3. Covalent Covalent bonding occurs in elemental as well as compound solids. The outstanding examples are the elemental semiconductors Si, Ge, and diamond and the Ill-V compound semiconductors such as GaAs and InP. Whereas elements at the extreme ends of the periodic table are involved in ionic bonding, covalent bonds are frequently formed between elements in neighbor- ing columns. The strong directional bonds characteristic of the group IV elements are due to the hybridization or mixing of the s and p electron wave functions into a set of orbitals which have high electron densities emanating from the atom in a tetrahedral fashion. a pair of electrons contributed by neighboring atoms makes a covalent bond, and four such shared electron pairs complete the bonding requirements Covalent solids are strongly bonded hard materials with relatively high melting points, Despite the great structural stability of semiconductors, rela- ively modest thermal stimulation is sufficient to release electrons from filled valence bonding states into unfilled electron states. We speak of electrons being promoted from the valence band to the conduction band, a process that increases the conductivity of the solid. Small dopant additions of group Ill elements like B and In as well as group V elements like P and As take up regular or substitutional lattice positions within Si and Ge. The bonding requirements are then not quite met for group Ill elements, which are one electron short of a complete octet. An electron deficiency or hole is thus created in the valence band

18 A Review of Materials Science tions are the cause of the attractive part of the interatomic potential, which varies simply as - 1 / r. Ionic solids are characterized by strong electrostatic bonding forces and, thus, relatively high binding energies and melting points. They are poor conductors of electricity because the energy required to transfer electrons from anions to cations is prohibitively large. At high temperatures, however, the charged ions themselves can migrate in an electric field, resulting in limited electrical conduction. Typical resistivities for such materials can range from lo6 to 1015 ohm-cm. Among the ionic compounds employed in thin-film technology are MgF,, ZnS, and CeF,, which are used in antireflection coatings on optical compo￾nents. Assorted thin-film oxides and oxide mixtures such as Y,Fe,O,, , Y3Al,01,, and LiNbO, are employed in components for integrated optics. Transparent electrical conductors such as In,O,-SnO, glasses, which serve as heating elements in window defrosters on cars as well as electrical contacts over the light exposed surfaces of solar cells, have partial ionic character. 1.4.3. Covalent Covalent bonding occurs in elemental as well as compound solids. The outstanding examples are the elemental semiconductors Si, Ge, and diamond, and the 111-V compound semiconductors such as GaAs and InP. Whereas elements at the extreme ends of the periodic table are involved in ionic bonding, covalent bonds are frequently formed between elements in neighbor￾ing columns. The strong directional bonds characteristic of the group IV elements are due to the hybridization or mixing of the s and p electron wave functions into a set of orbitals which have high electron densities emanating from the atom in a tetrahedral fashion. A pair of electrons contributed by neighboring atoms makes a covalent bond, and four such shared electron pairs complete the bonding requirements. Covalent solids are strongly bonded hard materials with relatively high melting points. Despite the great structural stability of semiconductors, rela￾tively modest thermal stimulation is sufficient to release electrons from filled valence bonding states into unfilled electron states. We speak of electrons being promoted from the valence band to the conduction band, a process that increases the conductivity of the solid. Small dopant additions of group 111 elements like B and In as well as group V elements like P and As take up regular or substitutional lattice positions within Si and Ge. The bonding requirements are then not quite met for group III elements, which are one electron short of a complete octet. An electron deficiency or hole is thus created in the valence band

1, 4. Bonding of Materials For each group V dopant an excess of one electron beyond the bonding octet can be promoted into the conduction band. As the name implies, semiconduc tors lie between metals and insulators insofar as their ability to conduct electricity is concerned. Typical semiconductor resistivities range from 10-3 to 105 ohm-cm. Both temperature and level of doping are very influential in altering the conductivity of semiconductors. lonic solids are similar in this The controllable spatial doping of semiconductors over very small lateral and transverse dimensions is a critical requirement in processing integrated circuits. Thin-film technology is thus simultaneously practiced in three dimen sions in these materials. Similarly, there is a great necessity to deposit compound semiconductor thin films in a variety of optical device applications Other largely covalent materials such as SiC, TiC, and BN have found coating applications where hard, wear-resistant surfaces are required. They are usually deposited by chemical vapor deposition methods and will be discussed at length 1. 4. 4. van der Waals Forces A large group of solid materials are held together by weak molecular forces This so-called van der Waals bonding is due to dipole-dipole charge interac tions between molecules that, though electrically neutral, have regions possess ing a net positive or negative charge distribution. Organic molecules such as methane and inert gas atoms are weakly bound together in the solid by these charges. Such solids have low melting points and are mechanically weak. Thin polymer films used as photoresists or for sealing and encapsulation purposes molecules that are typically bonded by van der Waals' force 1.4.5. Energy-Band Diagrams A common graphic means of distinguishing between different classes of solids involves the use of energy-band diagrams. Reference to Fig. 1-8a shows how individual energy levels broaden into bands when atoms are brought togethe to form solids. What is of interest here are the energies of electrons at the equilibrium atomic spacing in the crystal. For metals, insulators, and semicon ductors the energy-band structures at the equilibrium spacing are schematically dicated in Fig. 1-9a, b, c. In each case the horizontal axis can be loosely interpreted as some macroscopic distance within the solid with much larger than atomic dimensions. This distance spans a region within the homogeneous bulk interior where the band energies are uniform from point to point. The

1.4. Bonding of Materials 19 For each group V dopant an excess of one electron beyond the bonding octet can be promoted into the conduction band. As the name implies, semiconduc￾tors lie between metals and insulators insofar as their ability to conduct electricity is concerned. Typical semiconductor resistivities range from 10- to lo5 ohm-cm. Both temperature and level of doping are very influential in altering the conductivity of semiconductors. Ionic solids are similar in this regard. The controllable spatial doping of semiconductors over very small lateral and transverse dimensions is a critical requirement in processing integrated circuits. Thin-film technology is thus simultaneously practiced in three dimen￾sions in these materials. Similarly, there is a great necessity to deposit compound semiconductor thin films in a variety of optical device applications. Other largely covalent materials such as Sic, Tic, and BN have found coating applications where hard, wear-resistant surfaces are required. They are usually deposited by chemical vapor deposition methods and will be discussed at length in Chapter 12. 1.4.4. van der Waals Forces A large group of solid materials are held together by weak molecular forces. This so-called van der Waals bonding is due to dipole-dipole charge interac￾tions between molecules that, though electrically neutral, have regions possess￾ing a net positive or negative charge distribution. Organic molecules such as methane and inert gas atoms are weakly bound together in the solid by these charges. Such solids have low melting points and are mechanically weak. Thin polymer films used as photoresists or for sealing and encapsulation purposes contain molecules that are typically bonded by van der Waals’ forces. 1.4.5. Energy-Band Diagrams A common graphic means of distinguishing between different classes of solids involves the use of energy-band diagrams. Reference to Fig. 1-8a shows how individual energy levels broaden into bands when atoms are brought together to form solids. What is of interest here are the energies of electrons at the equilibrium atomic spacing in the crystal. For metals, insulators, and semicon￾ductors the energy-band structures at the equilibrium spacing are schematically indicated in Fig. 1-9a, b, c. In each case the horizontal axis can be loosely interpreted as some macroscopic distance within the solid with much larger than atomic dimensions. This distance spans a region within the homogeneous bulk interior where the band energies are uniform from point to point. The