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

A Revlew of Materials Science C BAND C BAND LV BANDVBAND METAL INSULATOR SEMI- CONDUCTOR q(4, V BAND V BAND N-TYPE P-TYPE Figure 1-9. Schematic band structure for(a)metal; (b) insulator, (c) semiconductor: (d)N-type semiconductor;(e) P-type semiconductor;(f) P-N semiconductor junction uppermost band shown is called the conduction band because once electrons access its levels, they are essentially free to conduct electricity Metals have high conductivity because the conduction band contains elec- trons from the outset. One has to imagine that there are a mind-boggling 1022 electrons per cubic centimeter ( one per atom) in the conduction band, all of which occupy different quantum states. Furthermore, there are enormous numbers of states all at the same energy level, a phenomenon known as degeneracy. Lastly, the energy levels are extremely closely spaced and com- pressed within a typical 5-eV conduction-band energy width. The available electrons occupy states within the band up to a certain level known as the Fermi energy Er. Above Er are densely spaced excited levels, but they are all vacant. If electrons are excited sufficiently (e.g, by photons or through heating), they can gain enough energy to populate these states or even leave the metal altogether (i. e, by photo- and thermionic emission) and enter the vacuum. As indicated in Fig. 1-9a, the energy difference between the vacuum level and E is equal to qom, where y is the work function in volts and q is the electronic charge. Even under very tiny electric fields, the electrons in states at E can easily move into the unoccupied levels above it, resulting in a net current flow. For this reason, metals have high conductivities t the other extreme are insulators, in which the conduction band normally has no electrons. The valence electrons used in bonding completely fill the valence band. A large energy gap E ranging from 5 to 10 eV separates the

20 a. METAL 'VACUI Egap . 1 eV V BAND N-TYPE V BAND P-TYPE a Review of Materials Science SEMI￾CONDUCTOR 1. JUNCTION Figure 1-9. Schematic band structure for (a) metal; (b) insulator, (c) semiconductor; (d) N-type semiconductor; (e) P-type semiconductor; (0 P-N semiconductor junction. uppermost band shown is called the conduction band because once electrons access its levels, they are essentially free to conduct electricity. Metals have high conductivity because the conduction band contains elec￾trons from the outset. One has to imagine that there are a mind-boggling electrons per cubic centimeter (- one per atom) in the conduction band, all of which occupy different quantum states. Furthermore, there are enormous numbers of states all at the same energy level, a phenomenon known as degeneracy. Lastly, the energy levels are extremely closely spaced and com￾pressed within a typical 5-eV conduction-band energy width. The available electrons occupy states within the band up to a certain level known as the Fermi energy Ef. Above Ef are densely spaced excited levels, but they are all vacant. If electrons are excited sufficiently (e.g., by photons or through heating), they can gain enough energy to populate these states or even leave the metal altogether @e., by photo- and thermionic emission) and enter the vacuum. As indicated in Fig. 1-9a, the energy difference between the vacuum level and Ef is equal to q4M, where q5M is the work function in volts and q is the electronic charge. Even under very tiny electric fields, the electrons in states at Ef can easily move into the unoccupied levels above it, resulting in a net current flow. For this reason, metals have high conductivities. At the other extreme are insulators, in which the conduction band normally has no electrons. The valence electrons used in bonding completely fill the valence band. A large energy gap Eg ranging from 5 to 10 eV separates the

filled valence band from the empty conduction band. There are normally no states and therefore no electrons within the energy gap. In order to conduct electricity, electrons must acquire sufficient energy to span the energy gap, but for all practical cases this energy barrier is all but insurmountable Pure (intrinsic) semiconductors at very low temperatures have a band structure like that of insulators, but E, is smaller; e.g., Eg= 1. I ev in Si and 0.68 eV in Ge. When a semiconductor is doped, new states are created within the energy gap. The electron (or hole) states associated with donors(or acceptors) are usually only a small fraction of an electron volt from the bottom of the conduction band (or top of the valence band). It now takes very little stimulation to excite electrons or holes to conduct electricity. The actual location of E with respect to the band diagram depends on the type and amount of doping atoms present In an intrinsic semiconductor, E, lies in the middle of the energy gap, because E, is strictly defined as that energy level for which the probability of occupation is 1/2. If the semiconductor is doped with donor atoms to make it N-type, E, lies above the midgap energy,as shown in Fig. 1-9d. If acceptor atoms are the predominant dopants, E lies below the midgap energy and a P-type semiconductor results(Fig. 1-9e) Band diagrams have important implications in thin-film systems where composite layers of different materials are involved. A simple example is the P-N junction, which is shown in Fig. 1-9f without any applied electric fields A condition ensuring thermodynamic equilibrium for the electrons is that Er must be constant throughout the system. This is accomplished through electron transfer from the N side with high E, (ow N) to the P side with low Er (high p). An internal built-in clectric field is established due to this charge transfer resulting in both valence- and conduction-band bending in the junction region. In the bulk of each semiconductor, the bands are unaffected as previously noted. Similar band bending occurs in thin-film metal-semiconduc- tor contacts, semiconductor superlattices, and in metal-oxide semiconductor (MOS) structures over dimensions comparable to the film thicknesses in- volved. Reference to some of these thin-film structures will be made in later 1.5. THERMODYNAMICS OF MATERIALS Thermodynamics is definite about events that are impossible. It will say, for example, that reactions or processes are thermodynamically impossible. Thus, gold films do not oxidize and atoms do not normally diffuse up a concentration gradient On the other hand, thermodynamics is none

1.5. Thermodynamics of Materials 21 filled valence band from the empty conduction band. There are normally no states and therefore no electrons within the energy gap. In order to conduct electricity, electrons must acquire sufficient energy to span the energy gap, but for all practical cases this energy barrier is all but insurmountable. Pure (intrinsic) semiconductors at very low temperatures have a band structure like that of insulators, but E, is smaller; e.g., E, = 1.1 eV in Si and 0.68 eV in Ge. When a semiconductor is doped, new states are created within the energy gap. The elettron (or hole) states associated with donors (or acceptors) are usually only a small fraction of an electron volt from the bottom of the conduction band (or top of the valence band). It now takes very little stimulation to excite electrons or holes to conduct electricity. The actual location of E, with respect to the band diagram depends on the type and amount of doping atoms present. In an intrinsic semiconductor, Ef lies in the middle of the energy gap, because Ef is strictly defined as that energy level for which the probability of occupation is 1/2. If the semiconductor is doped with donor atoms to make it N-type, Er lies above the midgap energy, as shown in Fig. 1-9d. If acceptor atoms are the predominant dopants, Ef lies below the midgap energy and a P-type semiconductor results (Fig. 1-9e). Band diagrams have important implications in thin-film systems where composite layers of different materials are involved. A simple example is the P-N junction, which is shown in Fig. 1-9f without any applied electric fields. A condition ensuring thermodynamic equilibrium for the electrons is that E, must be constant throughout the system. This is accomplished through electron transfer from the N side with high Ef (low +N) to the P side with low E, (high +p). An internal built-in electric field is established due to this charge transfer resulting in both valence- and conduction-band bending in the junction region. In the bulk of each semiconductor, the bands are unaffected as previously noted. Similar band bending occurs in thin-film metal- semiconduc￾tor contacts, semiconductor superlattices, and in metal-oxide semiconductor (MOS) structures over dimensions comparable to the film thicknesses in￾volved. Reference to some of these thin-film structures will be made in later chapters. 1.5. THERMODYNAMICS OF MATERIALS Thermodynamics is definite about events that are impossible. It will say, for example, that reactions or processes are thermodynamically impossible. Thus, gold films do not oxidize and atoms do not normally diffuse up a concentration gradient. On the other hand, thermodynamics is noncommittal about permissi-

A Review of Materials Science ble reactions and processes. Thus even though reactions are thermodynami cally favored. they may not occur in practice. Films of silica glass should revert to crystalline form at room temperature according to thermodynamics, amorphous SiO, is stable. A convenient measure of the extent of reaction feasibility is the free-energy function G defined as where H is the enthalpy, S the entropy, and T the absolute temperature Thus, if a system changes from some initial (i) to final (D state at constant temperature due to a chemical reaction or physical process, a free-energy change AG= Gr-G, occurs given by △G=△H-T△S where AH and As are the corresponding enthalpy and entropy changes, A consequence of the second law of thermodynamics is that spontaneous reac- tions occur at constant temperature and pressure when AG <0. This condition mplies that systems will naturally tend to minimize their free energy and successively proceed from a value G, to a still lower, more negative value G, until it is no longer possible to reduce G further. When this happens, AG=0 The system has achieved equilibrium, and there is no longer a driving force for change On the other hand, for a process that cannot occur, AG >0. Note that neither the sign of AH nor of AS taken individually determines reaction direction; rather it is the sign of the combined function AG that is crucial Thus, during condensation of a vapor to form a solid film, As<0 because fewer atomic configurations exist in the solid. The decrease in enthalpy however, more than offsets that in entropy, and the net change in AG is The concept of minimization of free energy as a criterion for both stability in a system and forward change in a reaction or process is a central theme materials science. The following discussion will develop concepts of thermody. namics used in the analysis of chemical reactions and phase diagrams. Subse- quent applications will be made to such topics as chemical vapor deposition interdiffusion, and reactions in thin films 1.5.1. Chemical Reactions The general chemical reaction involving substances A, B, and C in equilibrium (1-7)

22 A Review of Materials Science ble reactions and processes. Thus, even though reactions are thermodynami￾cally favored, they may not occur in practice. Films of silica glass should revert to crystalline form at room temperature according to thermodynamics, but the solid-state kinetics are so sluggish that for all practical purposes amorphous SiO, is stable. A convenient measure of the extent of reaction feasibility is the free-energy function G defined as G=H- TS, (1-5) where H is the enthalpy, S the entropy, and T the absolute temperature. Thus, if a system changes from some initial (i) to final (9 state at constant temperature due to a chemical reaction or physical process, a free-energy change AG = G, - C, occurs given by AG = AH - TAS, where AH and AS are the corresponding enthalpy and entropy changes. A consequence of the second law of thermodynamics is that spontaneous reac￾tions occur at constant temperature and pressure when AG < 0. This condition implies that systems will naturally tend to minimize their free energy and successively proceed from a value G, to a still lower, more negative value G, until it is no longer possible to reduce G further. When this happens, AG = 0. The system has achieved equilibrium, and there is no longer a driving force for change. On the other hand, for a process that cannot occur, AG > 0. Note that neither the sign of AH nor of AS taken individually determines reaction direction; rather it is the sign of the combined function AG that is crucial. Thus, during condensation of a vapor to form a solid film, AS < 0 because fewer atomic configurations exist in the solid. The decrease in enthalpy, however, more than offsets that in entropy, and the net change in AG is negative. The concept of minimization of free energy as a criterion for both stability in a system and forward change in a reaction or process is a central theme in materials science. The following discussion will develop concepts of thermody￾namics used in the analysis of chemical reactions and phase diagrams. Subse￾quent applications will be made to such topics as chemical vapor deposition, interdiffusion, and reactions in thin films. (1-6) 1 51. Chemical Reactions The general chemical reaction involving substances A, B, and C in equilibrium is aA + bB * cC. (1-7)

5. Thermodynamics of Materials The free-energy change of the reaction is given by where a, b, and c are the stoichiometric coefficients. It is customary to denote he free energy of individual reactant or product atomic or molecular species by G =Gi+RT In a Gi is the free energy of the species in its reference or standard state. For solids this is usually the stable pure material at 1 atm at a given temperature nd reflects the ay be viewed as an effective thermodynamic concentration standard state. Substitution of Eq. 1-9 into Eq. 1-8 yields △G=△G°+RTln (1-10) where△G°=cGC-aGA-bB. If the system is now AG =0 and a; is the equilibrium value ai(eg). Thus, 0=△G+RTln (1-11) △G°= RTIn K, where the equilibrium constant K is defined by the quantity in braces Equation 1-12 is one of the most frequently used equations in chemical thermodynamics and will be helpful in analyzing CVD reactions Combining Eqs. I-10 and 1-11 gives △G=RTIn (1-13) Each term a: /aieg represents a supersaturation of the species if it exceeds I and a subsaturation if it is less than 1. Thus, if there is a supersaturation reactants and a subsaturation of products, AG 0. The reaction proceeds spontaneously as written with a driving force proportional to the magnitude of AG. For many practical cases the ai differ little from the standard-st activities, which are taken to be unity. Therefore, in such a case Eq. 1-10 yields △G=△G° (1-14

1.5. Thermodynamics of Materials 23 AG = RT In< The free-energy change of the reaction is given by AG = cG~ - uGA - bG,, (1-8) where a, b, and c are the stoichiometric coefficients. It is customary to denote the free energy of individual reactant or product atomic or molecular species by Gi = G,o + RTIn ai. (1-9) G,o is the free energy of the species in its reference or standard state. For solids this is usually the stable pure material at 1 atm at a given temperature. The activity ai may be viewed as an effective thermodynamic concentration and reflects the change in free energy of the species when it is not in its standard state. Substitution of Eq. 1-9 into Eq. 1-8 yields I a; a:.; ' AG = AG" -k RT In- (1-10) where AG' = cGG - aGi - bGi. If the system is now in equilibrium, AG = 0 and ai is the equilibrium value ai(eg). Thus, or O=AGo+RTln( L1 4(e4l) } 'A(,) -AGO = RTln K, (1-1 1) (1-12) where the equilibrium constant K is defined by the quantity in braces. Equation 1-12 is one of the most frequently used equations in chemical thermodynamics and will be helpful in analyzing CVD reactions. Combining Eqs. 1-10 and 1-11 gives (1-13) Each term a, / ai(eg) represents a supersaturation of the species if it exceeds 1, and a subsaturation if it is less than 1. Thus, if there is a supersaturation of reactants and a subsaturation of products, AG < 0. The reaction proceeds spontaneously as written with a driving force proportional to the magnitude of AG. For many practical cases the ai differ little from the standard-state activities, which are taken to be unity. Therefore, in such a case Eq. 1-10 yields AG = AGO. (1-14)

A Review of Materials Science Quantitative information on the feasibility of chemical reactions is thus provided by values of AG, and these are tabulated in standard references on thermodynamic data. The reader should be aware that although much of the data are the result of measurement some values are inferred from various connecting thermodynamic laws and relationships. Thus, even though the vapor pressure of tungsten at room temperature cannot be directly measured its value is nevertheless"known. "In addition, the data deal with equilibriun conditions only, and many reactions are subject to overriding kinetic limita tions despite otherwise favorable free-energy considerations A particularly useful representation of AG data for formation of metal oxides as a function of temperature is shown in Fig. 1-10 and is known as an Ellingham diagram. As an example of its use, consider two oxides of impor- tance in thin-film technology, SiO, and Al2O3, with corresponding oxidation reactIons si+O2→S02:△Gso2 (4/3)A+O2→(2/3)Al2O3 (1-15b) Through elimination of O, the reaction (4/3)A+SO2→(2/3)A2O3+Si (1-16) results, where△G=△GA,-△ GSio,. Since the△ G-T curve for Al2O3 is more negative or lower than that for SiO,, the reaction is thermodynami- cally favored as written.At400°C, for example,△o° for Eq. I-l6is 233-(-180)=-53 kcal/mole. Therefore, Al films tend to reduce SiOz films, leaving free Si behind, a fact observed in early field effect transistor structures. This was one reason for the replacement of Al film gate electrodes by polycrystalline Si films. As a generalization then, the metal of an oxide that has a more negative AG than a second oxide will reduce the latter and be oxidized in the process. Further consideration of Eqs. 1-12 and 1-15b indicates The Al, O, and Al may be considered to exist in pure standard states with unity activities while the activity of O, is taken to be its partial pressure Pc Therefore, AG"=RT In Po, If Al were evaporated from a crucible to produce a film, then the value of Po. in equilibrium with both Al and Al2O, can be calculated at any temperature when AG is known. If the actual oxygen partial pressure exceeds the equilibrium pressure, then Al ought to oxidize. If the reverse is true, Al2O, would be reduced to Al. At 1000'C, AG=-202

24 A Review of Materials Science Quantitative information on the feasibility of chemical reactions is thus provided by values of AGO, and these are tabulated in standard references on thermodynamic data. The reader should be aware that although much of the data are the result of measurement, some values are inferred from various connecting thermodynamic laws and relationships. Thus, even though the vapor pressure of tungsten at room temperature cannot be directly measured, its value is nevertheless “known.” In addition, the data deal with equilibrium conditions only, and many reactions are subject to overriding kinetic limita￾tions despite otherwise favorable free-energy considerations. A particularly useful representation of AGO data for formation of metal oxides as a function of temperature is shown in Fig. 1-10 and is known as an Ellingham diagram. As an example of its use, consider two oxides of impor￾tance in thin-film technology, SiO, and A,O, , with corresponding oxidation reactions Si + 0, + SiO, ; AGiio2, (1-15a) (4/3)A + 0, + (2/3)A1,O3; AGi12~, . (1-15b) Through elimination of 0, the reaction (4/3)AI + S~O, + (2/3)~l,0, + Si (1-16) results, where AGO = AGAz0, - AGiio2. Since the AGO- T curve for Al,O, is more negative or lower than that for SiO,, the reaction is thermodynami￾cally favored as written. At 400 OC, for example, AG” for Eq. 1-16 is - 233 - (- 180) = - 53 kcal/mole. Therefore, Al films tend to reduce SiO, films, leaving free Si behind, a fact observed in early field effect transistor structures. This was one reason for the replacement of Al film gate electrodes by polycrystalline Si fdms. As a generalization then, the metal of an oxide that has a more negative AGO than a second oxide will reduce the latter and be oxidized in the process. Further consideration of Eqs. 1-12 and 1-15b indicates that )2/3 AG = exp - -. ( aAl,03 K= (aAl Y3pO2 RT (1-17) The A1,0, and A1 may be considered to exist in pure standard states with unity activities while the activity of 0, is taken to be its partial pressure Po,. Therefore, AGO = RT In Po,. If Al were evaporated from a crucible to produce a film, then the value of Po, in equilibrium with both Al and A1203 can be calculated at any temperature when AGO is known. If the actual oxygen partial pressure exceeds the equilibrium pressure, then A1 ought to oxidize. If the reverse is true, AZO, would be reduced to Al. At lo00 ‘C, AGO = -202