11.3.Superconductivity 195 TABLE 11.1 Critical temperatures of some superconducting materials Materials Te [K] Remarks Tungsten 0.01 Mercury 4.15 H.K.Onnes (1911) Sulfur-based organic 8 S.S.P.Parkin et al.(1983) superconductor Nb3Sn and Nb-Ti 9 Bell Labs (1961),Type II V3Si 17.1 J.K.Hulm (1953) Nb3Ge 23.2 (1973) La-Ba-Cu-O 40 Bednorz and Muller (1986) YBa2Cu307-x 92 Wu,Chu,and others (1987) RBa2Cu307-x 92 R=Gd,Dy,Ho,Er,Tm,Yb,Lu Bi2Sr2Ca2Cu3010+8 113 Maeda et al.(1988) Tl2CaBa2Cu2010+8 125 Hermann et al.(1988) HgBa2Ca2Cu30s+8 134 R.Ott et al.(1995) high-Te superconductors are the 1-2-3 compounds such as YBa2Cu3O7x whose molar ratios of rare earth to alkaline earth to copper relate as 1:2:3.Their transition temperatures range from 40 to 134 K.Ceramic superconductors have an orthorhombic,lay- ered,perovskite crystal structure (similar to BaTiO3;see Figure 11.30)which contains two-dimensional sheets and periodic oxy- gen vacancies.(The superconductivity exists only parallel to these layers,that is,it is anisotropic.)The first superconducting mate- rial was found by H.K.Onnes in 1911 in mercury which has a Te of4.15K. A high magnetic field or a high current density may eliminate superconductivity.In Type I superconductors,the annihilation of the superconducting state by a magnetic field,that is,the transi- Pure metal Impure metals and FIGURE 11.9.Schematic represen- ceramic sup.cond. tation of the resistivity of pure and compound superconducting materials.Te is the critical or transition temperature,below which superconductivity com- 0.1K+ mences
11.3 • Superconductivity 195 high-Tc superconductors are the 1-2-3 compounds such as YBa2Cu3O7x whose molar ratios of rare earth to alkaline earth to copper relate as 1:2:3. Their transition temperatures range from 40 to 134 K. Ceramic superconductors have an orthorhombic, layered, perovskite crystal structure (similar to BaTiO3; see Figure 11.30) which contains two-dimensional sheets and periodic oxygen vacancies. (The superconductivity exists only parallel to these layers, that is, it is anisotropic.) The first superconducting material was found by H.K. Onnes in 1911 in mercury which has a Tc of 4.15 K. A high magnetic field or a high current density may eliminate superconductivity. In Type I superconductors, the annihilation of the superconducting state by a magnetic field, that is, the transi- 0 Tc T 0.1K Pure metal Impure metals and ceramic sup. cond. FIGURE 11.9. Schematic representation of the resistivity of pure and compound superconducting materials. Tc is the critical or transition temperature, below which superconductivity commences. TABLE 11.1 Critical temperatures of some superconducting materials Materials Tc [K] Remarks Tungsten 0.01 — Mercury 4.15 H.K. Onnes (1911) Sulfur-based organic 8 S.S.P. Parkin et al. (1983) superconductor Nb3Sn and Nb–Ti 9 Bell Labs (1961), Type II V3Si 17.1 J.K. Hulm (1953) Nb3Ge 23.2 (1973) La–Ba–Cu–O 40 Bednorz and Müller (1986) YBa2Cu3O7–x 92 Wu, Chu, and others (1987) RBa2Cu3O7–x 92 R Gd, Dy, Ho, Er, Tm, Yb, Lu Bi2Sr2Ca2Cu3O10 113 Maeda et al. (1988) Tl2CaBa2Cu2O10 125 Hermann et al. (1988) HgBa2Ca2Cu3O8 134 R. Ott et al. (1995)
196 11.Electrical Properties of Materials P Supercon- Normal ducting state FIGURE 11.10.Schematic state representation of the re- sistivity of (a)Type I (or soft)and(b)TypeⅡ(or hard)superconductors in an external magnetic field.The solids behave like normal conductors He H Hcr He2 H above He and He2 respec- tively. (a) (b) tion between superconducting and normal states,occurs sharply; Figure 11.10(a).The critical field strength Hc,above which super- conductivity ceases,is relatively low.The destruction of the su- perconducting state in Type II superconductors occurs instead, more gradually,i.e.,in a range between Hcl and He2,where He2 is often 100 times larger than Hc [Figure 11.10(b)].In the interval between Hei and He2,normal conducting areas,called vortices,and superconducting regions are interspersed.The terms "Type I"and "Type II"superconductors are occasionally also used when a dis- tinction between abrupt and gradual transition with respect to temperature is described;see Figure 11.9.In alloys and ceramic superconductors,a temperature spread of about 0.1 K has been found whereas pure gallium drops its resistance within 10-5 K. Type II superconductors are utilized for strong electromagnets employed,for example,in magnetic resonance imaging devices (used in medicine),high-energy particle accelerators,and elec- tric power storage devices.(An electric current induced into a loop consisting of a superconducting wire continues to flow for an extended period of time without significant decay.)Further potential applications are lossless power transmission lines;high- speed levitation trains;faster,more compact computers;and switching devices,called cryotrons,which are based on the de- struction of the superconducting state in a strong magnetic field. Despite their considerably higher transition temperatures,ce- ramic superconductors have not yet revolutionized current tech- nologies,mainly because of their still relatively low T,their brit- tleness,their relatively small capability to carry high current densities,and their environmental instability.These obstacles may be overcome eventually,however,by using other materials, for example,compounds based on bismuth,etc.,or by produc- ing thin-film superconductors.At present,most superconducting electromagnets are manufactured by using niobium-titanium al- loys which are ductile and thus can be drawn into wires
196 11 • Electrical Properties of Materials tion between superconducting and normal states, occurs sharply; Figure 11.10(a). The critical field strength Hc, above which superconductivity ceases, is relatively low. The destruction of the superconducting state in Type II superconductors occurs instead, more gradually, i.e., in a range between Hc1 and Hc2, where Hc2 is often 100 times larger than Hc1 [Figure 11.10(b)]. In the interval between Hc1 and Hc2, normal conducting areas, called vortices, and superconducting regions are interspersed. The terms “Type I” and “Type II” superconductors are occasionally also used when a distinction between abrupt and gradual transition with respect to temperature is described; see Figure 11.9. In alloys and ceramic superconductors, a temperature spread of about 0.1 K has been found whereas pure gallium drops its resistance within 105 K. Type II superconductors are utilized for strong electromagnets employed, for example, in magnetic resonance imaging devices (used in medicine), high-energy particle accelerators, and electric power storage devices. (An electric current induced into a loop consisting of a superconducting wire continues to flow for an extended period of time without significant decay.) Further potential applications are lossless power transmission lines; highspeed levitation trains; faster, more compact computers; and switching devices, called cryotrons, which are based on the destruction of the superconducting state in a strong magnetic field. Despite their considerably higher transition temperatures, ceramic superconductors have not yet revolutionized current technologies, mainly because of their still relatively low Tc, their brittleness, their relatively small capability to carry high current densities, and their environmental instability. These obstacles may be overcome eventually, however, by using other materials, for example, compounds based on bismuth, etc., or by producing thin-film superconductors. At present, most superconducting electromagnets are manufactured by using niobium–titanium alloys which are ductile and thus can be drawn into wires. (a) (b) Superconducting state Normal state HC H HC1 HC2 H FIGURE 11.10. Schematic representation of the resistivity of (a) Type I (or soft) and (b) Type II (or hard) superconductors in an external magnetic field. The solids behave like normal conductors above Hc and Hc2 respectively
11.4·Semiconductors 197 The quantum-mechanical theory,which explains supercon- ductivity and which was developed in 1957 by Bardeen,Cooper, and Schrieffer,is quite involved and is therefore beyond the scope of this book. 11.4。Semiconductors Semiconductors such as silicon or germanium are neither good conductors nor good insulators as seen in Figure 11.1.This may seem to make semiconductors to be of little interest.Their use- fulness results,however,from a completely different property, namely,that extremely small amounts of certain impurity ele- ments,which are called dopants,remarkably change the electri- cal behavior of semiconductors.Indeed,semiconductors have been proven in recent years to be the lifeblood of a multibillion dollar industry which prospers essentially from this very feature. Silicon,the major species of semiconducting materials,is today the single most researched element.Silicon is abundant(28%of the earth's crust consists of it);the raw material (SiO2 or sand) is inexpensive;Si forms a natural,insulating oxide;its heat con- duction is reasonable;it is nontoxic;and it is stable against en- vironmental influences. Intrinsic The properties of semiconductors are commonly explained by Semi- making use of the already introduced electron band structure which is the result of quantum-mechanical considerations.In conductors simple terms,the electrons are depicted to reside in certain al- lowed energy regions as explained in Section 11.1.Specifically, Figures 11.6(c)and 11.11 depict two electron bands,the lower of which,at 0 K,is completely filled with valence electrons.This band is appropriately called the valence band.It is separated by a small gap (about 1.1 eV for Si)from the conduction band, which,at 0 K,contains no electrons.Further,quantum me- chanics stipulates that electrons essentially are not allowed to re- side in the gap between these bands (called the forbidden band). Since the filled valence band possesses no allowed empty energy states in which the electrons can be thermally excited (and then accelerated in an electric field),and since the conduction band contains no electrons at all,silicon,at 0 K,is an insulator. The situation changes decisively once the temperature is raised. In this case,some electrons may be thermally excited across the band gap and thus populate the conduction band (Figure 11.11). The number of these electrons is extremely small for statistical reasons.Specifically,about one out of every 1013 atoms con- tributes an electron at room temperature.Nevertheless,this num-
11.4 • Semiconductors 197 The quantum-mechanical theory, which explains superconductivity and which was developed in 1957 by Bardeen, Cooper, and Schrieffer, is quite involved and is therefore beyond the scope of this book. Semiconductors such as silicon or germanium are neither good conductors nor good insulators as seen in Figure 11.1. This may seem to make semiconductors to be of little interest. Their usefulness results, however, from a completely different property, namely, that extremely small amounts of certain impurity elements, which are called dopants, remarkably change the electrical behavior of semiconductors. Indeed, semiconductors have been proven in recent years to be the lifeblood of a multibillion dollar industry which prospers essentially from this very feature. Silicon, the major species of semiconducting materials, is today the single most researched element. Silicon is abundant (28% of the earth’s crust consists of it); the raw material (SiO2 or sand) is inexpensive; Si forms a natural, insulating oxide; its heat conduction is reasonable; it is nontoxic; and it is stable against environmental influences. The properties of semiconductors are commonly explained by making use of the already introduced electron band structure which is the result of quantum-mechanical considerations. In simple terms, the electrons are depicted to reside in certain allowed energy regions as explained in Section 11.1. Specifically, Figures 11.6(c) and 11.11 depict two electron bands, the lower of which, at 0 K, is completely filled with valence electrons. This band is appropriately called the valence band. It is separated by a small gap (about 1.1 eV for Si) from the conduction band, which, at 0 K, contains no electrons. Further, quantum mechanics stipulates that electrons essentially are not allowed to reside in the gap between these bands (called the forbidden band). Since the filled valence band possesses no allowed empty energy states in which the electrons can be thermally excited (and then accelerated in an electric field), and since the conduction band contains no electrons at all, silicon, at 0 K, is an insulator. The situation changes decisively once the temperature is raised. In this case, some electrons may be thermally excited across the band gap and thus populate the conduction band (Figure 11.11). The number of these electrons is extremely small for statistical reasons. Specifically, about one out of every 1013 atoms contributes an electron at room temperature. Nevertheless, this numIntrinsic Semiconductors 11.4 • Semiconductors