The Materials Science of Thin Films 2011 Part 11 pot

470 Electrical and Magnetic Properties of Thin Films reason that technological interest has centered on insulating films employed in microelectronics, notably the gate oxide, where dielectric breakdown is a serious reliability concern. The remainder of this section will therefore be devoted to SiO, films (Ref. 19). It is generally agreed that electron impact ionization is responsible for intrinsic breakdown in SiO, films. In this process, electrons colliding with lattice atoms break valence bonds, creating electron-hole pairs. These new electrons accelerate in the field and through repeated impacts generate more electrons. Ultimately a current avalanche develops that rapidly and uncontrol- lably leads to excessive local heating and dielectric failure. Typical of theoreti- cal modeling (Refs. 19, 20) of breakdown is the consideration of three interdependent issues; Electrode charge injection into the insulator, e.g., by tunneling (Eq. 10-22). This formula connects current and applied field. The local electric field that is controlled by the relatively immobile hole density through the Poisson equation. A time-dependent change in hole density that increases with extent of impact ionization, but decreases with amount of hole recombination or drift away. The resulting rate equation depends on both current and field. Simultaneous satisfaction of these coupled relationships leads to the predic- tion that the current-voltage characteristics display negative resistance. This appears as a knee in the response above a critical applied voltage and reflects a current runaway instability. Another prediction is that the average break- down field rises sharply as the film thickncss decreases. Reliability concerns for thin SiO, films in MOS transistors have fostered much statistical analysis of life-testing results and some typical experimental findings include: 1. 2. 3. The histogram of the number of breakdown failures due to intrinsic causes peaks sharply at about 1.1 x lo7 V/cm (Fig. 10-14a). The failure probabil- ity is nil below 7 x IO6 V/cm. Time to failure (TTF) accelerated testing has revealed that 0.33 eV kT TTF a exp- exp - 2.47 V, (10-32) where the exponentials represent individual temperature and voltage accel- eration factors (Ref. 21). Contrary to theory, thinner oxides present a greater failure risk. The lifetime dependence on oxide film thickness is shown in Fig. 10-14b. Note 10.4. Semiconductor Contacts and MOS Structures 479 300 270 240 5 210 5 180 8 150 pj 120 g90 3 260 30 n L 0 24 6 8 10 12 14 E (MV/cm) (a) 104 STRESS FIELD : 8 MV Icm CUMULATIVE PERCENT (b) Figure 10-14. (a) Histogram of number of failures versus applied electric field in thin SO, films. (From D. R. Wolters and J. J. van der Schoot, Philips J. Res. 40, 115, 1985). (b) Time-dependent dielectric breakdown in SO,. (Courtesy of A. M-R Lin, AT&T Bell Laboratories.) 480 Electrical and Magnetic Properties of Thin Films that a 100-i difference in film thickness signifies a four-order-of-magnitude change in failure time. 4. Film defects cause breakdown to occur at smaller than intrinsic fields and in correspondingly shorter times. As an example illustrating the use of Eq. 10-32 assume that the lifetime of SiO, films is 100 h during accelerated testing at 125 “C and 9 V. What lifetime can be expected at 25 “C and 8 V? Clearly, TTF = l0Oexp0.33/k(l/T2 - l/T,)exp - 2.47(V2 - V,), where T2 = 298, T, = 398, V, = 8, V, = 9, and k = 8.63 x eV/K. Substitution yields a value for TTF = 29,700 h. 10.5. SUPERCONDUCTIVITY IN THIN FILMS 10.5.1. Overview The discovery in 1986- 1987 that superconductivity is exhibited by oxide materials at temperatures above the boiling point of liquid nitrogcn ignited intense worldwide research devoted to understanding and exploiting the phe- nomenon. For a perspective of superconducting effects in these new materials and prospects for thin-film uses, it is worthwhile to view the subject against the 75-year backdrop of prior activity. This pre-1988 “classical” experience with superconductivity will therefore be surveyed first in this chapter (Ref. 22); in Chapter 14 high-temperature superconductivity will be discussed. Superconductivity was discovered by Kamerlingh Onnes, who, in 191 1, found that the electrical resistance of Hg vanished below 4.15 K. Actually it was estimated from the time decay of (nearly) persistent supercurrents in a toroid that the resistivity of the superconducting state does not exceed - lo-’’ Q-cm, some 14 orders of magnitude below that for Cu. Some basic attributes possessed by superconductors have been experimentally verified and theoreti- cally addressed over the years. These are briefly enumerated here. 1. Occurrence of Superconductivity. The phenomenon of superconductiv- ity has been observed to occur in at least 26 elements and in hundreds and perhaps thousands of metallic alloys and compounds. It is favored by a large atomic volume or lattice parameter, and when there are between two and eight valence electrons per atom. 2. Critical Temperature and Magnetic Field. The superconducting state only exists in a specific range of temperature (T) and magnetic field strength 10.5. Superconducitivity In Thin Films 481 Table 10-3. Values of T, and H, for Superconducting Materials Alloy Element T, (K) H, (a) or Compound T', (K) Hs (a)** ~~ AI 1.19 In 3.41 UP) 5.9 N-b 9.2 Pb 7.18 Re 1.70 Sn 3.72 Ta 4.48 Tc 8.22 Th 1.37 TI 2.39 V 5.13 98.8 285 lo00 800 200 308 825 2,o00*, 3,o00** 161 170 1290*, 7000** v3Ga V3Si Nb,Sn Nb3a M3Ge PbMO,S, NbN YBa,Cu ,O, BiSrCaCuO TlBaCaCuO 14.8 25 X lo4 16.9 24 X lo4 18.3 28 X lo4 20.2 34 x io4 22.5 38 x lo4 14.4 60 x io4 15.7 15 x lo4 93 - 107 - 120 - (HI. Critical values of these quantities are experimentally found to be closely described by (10-33) where H, is the critical field, No is the maximum field at T = 0 K, and T, is the highest temperature at which superconductivity is observed. On an H vs. T plot the division between superconducting and normal conduction regimes is defined by Eq. 10-33. A temperature spread of only - K K in pure metals, lo-' K in alloys) about the value of T, characterizes the sharpness of the transition between the two states. Superconductivity can be extinguished by exposure to a field greater than H, or by passing a supercur- rent that induces a magnetic field in excess of H,. Values of T, and H, are listed in Table 10-3 for a number of superconducting materials. 3. Meissner Effect. One of the remarkable features of the superconducting state is the Meissner effect. It is characterized by the exclusion of magnetic flux and, hence, electrical currents from the bulk of the superconductor. The exclusion is not total, however, and both flux and current are confined to a surface layer known as the penetration depth A,. The London theory of superconductivity indicates that ( 10-34) 482 Electrical and Magnetic Properties of Thin Films where A,y(0) is the penetration depth at 0 K. Typically, A, is 500-1000 A. The Meissner effect means that if a superconductor is approached by an H field, screening currents are set up on its surface. This screening current establishes an equal and opposite H field so that the net field vanishes in the supercon- ductor interior. The now common displays of permanent magnets levitated over chilled high-T, superconductors is visual evidence of the Meissner effect. 4. Type Z and Type ZZ Superconductors. There are two types of supercon- ductors: type I (or soft) and type I1 (or hard). With the exception of Nb and V the elements are type I superconductors. In such materials the superconducting transition is abrupt, and flux penetrates only for fields larger than H, . In type I1 superconductors (exemplified by Nb, V, alloys (e.g., Mo-Re, Nb-Ti), and A-15 compounds (e.g., Nb,Sn, Nb,Ge)), there are two critical fields H,(I) and HJu), the lower and upper values. If the applied field is below Hs(/), type I1 behavior is the same as that displayed by type I superconductors. For fields above HJI) but below HJu), there is a mixed superconducting state, whereas for H > H,(u), normal conductivity is observed. Importantly, type I1 superconductors can survive in the mixed state up to extremely high H values (e.g., in excess of lo5 gauss). This property has earmarked their use in commercial superconducting magnets. In the mixed state, just above Hs([), flux starts to penetrate the material in microscopic tubular filaments (- loo0 in diameter), known as fluxoids or vortices, that lie parallel to the field direction. The core of the fluxoid is normal while the sheath is superconduct- ing; the circulating supercurrent of the latter establishes the field that keeps the core normal. Fluxoids, which are usually arranged in a lattice array, grow in size as the field is increased with progressively more flux penetration. Above H,( u), flux penetrates everywhere. The current flow is not entirely lossless in the mixed state, however, because a small amount of power is dissipated by viscous fluxoid motion. Fluxoid pinning due to introduction of alloying ele- ments or defects is a practical way to minimize this energy loss. 5. The BCS Theory. The theory by Bardeen, Cooper, and Schrieffer (BCS) (Ref. 24) in 1957 provided the basis for understanding superconductivity at a microscopic level, superceding previous phenomenological approaches. Cen- tral to the BCS theory is the complex coupling between a pair of electrons of opposite spin and momentum through an interaction with lattice phonons. The electrons that normally repel each other develop a mutual attraction, forming Cooper pairs. A measure of the average maximum length at which the phonon coupled attraction can occur is known as the coherence length 5. Schrieffer described the theoretical issue as “how to choreograph a dance for more than a million, million, million couples” so that they condense into a single state that 10.5. Supelconducitivlty in Thin Films 483 moves in step or flows like a frictionless fluid (Ref. 24). Since the electron coupling is weak, the energy difference between normal and superconducting states is small with the latter lying a distance 2A below the former. Thus, a forbidden energy gap of width 2A = 3.5kT, (10-35) appears in the density of states centered about the Fermi energy at 0 K. This predicted relationship has been verified in many superconductors by tunneling measurements, which are described in the next section. When the temperature is raised, the amplitude and frequency of lattice atomic motion increase, interfering with the propagation of phonons between correlated Cooper pairs. The attraction between electrons is diminished and 2A decreases. At T = T,, A = 0. Any perturbation in structure or composition extending over the coherence length can alter T, or 2A, placing a practical limit on useful superconducting behavior. 10.5.2. Superconductivity in Thin Films; Tunneling Thin films have traditionally played a critical role in testing theories of superconductivity and in establishing new effects. Superconductivity appar- ently persists to film thicknesses of - 10 A. Lower limits are difficult to establish because films of such thickness are generally discontinuous. The dependence of T, on deposition conditions and film thickness has been studied for a long time, and interesting, though not easily predictable or explainable, effects have been reported. When either A, or t becomes comparable to the thin film thickness, deviation from bulk superconducting properties may be expected. For example, enhanced superconductivity has been reported in vapor-quenched, amorphous Bi and Be films where T, values of 6 and 8 K were obtained, even though these metals are not superconducting in bulk. Higher T, values with decreasing film thickness have been observed by several investigators. The size of these effects ranges from fractions to several degrees K and depends on the magnitude and sign of the film stress, impuri- ties, lattice imperfections, and grain size in generally inexplicable ways. A link between T, and the fundamental nature of the material is suggested by the BCS formula 1.14hv 1 T, = ~ exp - k N(EFP (10-36) (for N( EF)U -4 1). The quantity N(EF) is the density of states at the Fermi level, U is the magnitude of the attractive electron-lattice interaction, and v corresponds to the lattice (Debye) frequency. Normally N(EF)U is weakly 484 Electrical and Magnetic Properties of Thin Films sensitive to lattice dimensions and has a value between 0.1 to 0.5. Furthermore if N(E,), U, or v increase, so does T,. However, connections between these quantities, on the one hand, and film composition and structure, on the other, are uncertain at best. The most extensive experimentation in thin films has involved tunneling phenomena. Unlike the tunneling between normal metals considered earlier (Section 10.3.1), a superconducting tunnel junction consists of two metal films, one or both being a superconductor, separated by an ultrathin oxide or insulator film. Tunneling currents generally flow when electrons emerge from one metal to occupy allowable empty electron states of the same energy in the opposite metal. Through application of voltage bias, relative shifts of the entire electron distribution of both metals occur, either permitting or disallowing tunneling transitions. Thus, if electrons at the Fermi level of a normal metal lie opposite the forbidden energy gap at the Fermi level of the superconductor, no tunnel current flows. Translation of band states by a voltage A /q, or half the energy gap, causes occupied energy levels of the former to line up with unoccupied levels of the latter resulting in current flow. If both electrodes are the same superconductor, a voltage corresponding to the whole energy gap must be applied before tunnel current flows. Current-voltage characteristics corresponding to these two cases are shown in Fig. 10-15. A more complicated behavior is exhibited when two different superconductors with energy gaps Figure 1 0-1 5. Current-voltage characteristics of tunnel junctions: tunnel junctions (a) one metal normal-one metal superconducting. @) both metals identical supercon- ductors. (c) both metals superconducting but with different energy gaps. (d) Josephson tunneling branch (1) and normal superconducting tunneling branch (2). J, is the critical junction current density. 10.6. Introduction to Ferromagnetism 485 2A, and 26, are paired. By yielding precise values of 2A, such measurements have provided direct experimental verification of the BCS theory. One of the very important advances in superconductivity was the remarkable discovery by Josephson (Ref. 25) that supercurrents can tunnel through a junction. Thus tunneling of Cooper pairs and not only electrons is possible. Two superconducting electrodes sandwiching an ultrathin insulator - 50 thick are required. The current-voltage characteristic has two branches (Fig. 10-15d). The normal tunneling branch is similar to Fig. 10-15 but with a reduced negative resistance feature. The Josephson tunneling current branch consists of a current spike; no voltage develops across the superconducting junction in this case. Because the Josephson current is extremely sensitive to H fields, the junction can be easily switched from one branch to the other. Josephson devices known as SQUIDS (superconducting quantum interfer- ence devices) capitalize on these effects to detect very small H fields or to switch currents at ultrahigh speed in computer logic circuits. These applica- tions will be described in more detail in Section 14.8.3. 1 0.6. INTRODUCTION TO FERROMAGNETISM The remainder of this chapter is devoted to some of the ferromagnetic properties of thin films (Refs. 26, 27). We start with the idea that magnetic phenomena have quantum mechanical origins stemming from the quantized angular momentum of orbiting and spinning atomic electrons. These circulat- ing charges effectively establish the equivalent of microscopic bar magnets or magnetic moments. When neighboring moments due to spin spontaneously and cooperatively order in parallel alignment over macroscopic dimensions in a material to yield a large moment of magnetization (M), then we speak of ferromagnetism. The quantity M is clearly a vector with a magnitude equal to the vector sum of magnetic moments per unit volume. In an external magnetic field (H) the interaction with M yields a field energy density (EH) given by E,= -H*M. (10-37) However, no external field need be applied to induce the ferromagnetic state. The phenomenon of ferromagnetism has a number of characteristics and properties worth noting at the outset. 1. Elements (e.g., Fe, Ni, Co), alloys (e.g., Fe-Ni, Co-Ni), oxide insula- tors (e.g., nickel-zinc ferrite, strontium ferrite) and ionic compounds (e.g., CrBr,, EuS, Ed,) all exhibit ferromagnetism. Not only are all crystal 486 Electrical and Magnetic Properlies of Thin Films structures and bonding mechanisms represented, but amorphous ferromagnets have also been synthesized (e.g., melt-quenched Fe,,B,, ribbons and vapor- deposited Co-Gd films). 2. Quantum mechanical exchange interactions cause the parallel spin align- ments that result in ferromagnetism. It requires an increase in system energy to disorient spin pairings and cause deviations from the parallel alignment direc- tion. This energy, known as the exchange energy (Eex), is given by E,, = A,(VdJ)* (10-38) and is a measure of the “stiffness” of M or how strongly neighboring spins are coupled. The exchange constant Ax is a property of the material and equal to - ergs/cm in Ni-Fe. Avoidance of sharp gradients in 4, the angle between M and the easy axis of magnetization, leads to small values of E,, . 3. Absorbed thermal energy serves to randomize the orientation of the spin moments ps . At the Curie temperature (T,) the collective alignment collapses, and the ferromagnetism is destroyed. By equating the thermal energy absorbed to the internal field energy (pJH,), i.e., kT, = p,N,, values of H, can be estimated. The internal field U, permeating the matrix is established by exchange interactions. Typically, H, is predicted to be in excess of lo6 Oe, an extremely high field. 4. Magnetic anisotropy phenomena play a dominant role in determining the magnetic properties of ferromagnetic films. By anisotropy we mean the tendency of M to lie along certain directions in a material rather than be isotropically distributed. In single crystals, M prefers to lie in the so-called easy direction, say [loo] in Fe and [lll] in Ni. To turn A4 into other orientations, or harder directions, requires energy (i.e., magnetocrystalline anisotropy energy ( EK)). Consider now a fine-grained polycrystalline ferro- magnetic film of Permalloy (- 80 Ni-20 Fe). Surprisingly, it also exhibits anisotropy with M lying in the film plane. In such a case EK is a function of the orientation of M with respect to film coordinates. For uniaxial anisotropy EK = K,sin20, (10-39) where K, is a constant with units of energy/volume, and 8 is the angle between the in-plane saturation magnetization and the easy axis. The source of the anisotropy is not due to crystallographic geometry but rather to the anisotropy arising from shape effects (Le., shape anisotropy). When ferromagnetic bodies are magnetized, magnetic poles are created on the surface. These poles establish a demagnetizing field ( H,,) proportional and antiparallel to M, i.e., H,, = - NM, where N is known as the demagnetizing 10.6. lntroductlon to Ferromagnetism 487 factor and depends on the shape of the body. For a thin film, N = 47r in the direction normal to the film plane. Therefore, Hd = -4rM. In evaporated Permalloy films H,, can be as large as - lo4 Oe. However, in the film plane H,, is much smaller so that M prefers to lie in this plane. There are other magnetic films of great technological importance-garnets for magnetic bubble devices (Section 10.8.4) and Co-Cr for perpendicular magnetic recording applications (Section 14.4.3)-where M is perpendicular to the film plane. Associated with Hd is magnetostatic energy (E,) of amount per unit volume. The 1/2 arises because self-energy is involved, i.e., Hd is created from the distribution of M in the film. In the hard direction the energy density is therefore EM = 2uM2. (1041) The origins of anisotropy are complex and apparently involve directional ordering of magnetic atom pairs, e.g., Fe-Fe. Film anisotropy is affected by film deposition method and variables, impingement angle of the incident vapor flux, applied magnetic fields during deposition, composition, internal stress, EM= (1/2)HdM ( 10-40) M t HARD /H," Figure 10-16. Schematic hysteresis loops for soft and hard magnetic materials. For soft magnets H, 5 0.05 Oe. For hard magnets H, 2 300 Oe. (From Ref. 28). [...]... applications of metal and dielectric thin films 11. 2 PROPERTIES OPTICAL OF FILM MATERIALS 11. 2.1 General Considerations In order to understand the optical behavior of films and film systems, one must become familiar with the optical constants of materials, their origins, magni- 11. 2 509 Proporties ot Optlcal Fllm Materials tudes, and how they depend on the way film are processed The purpose of Section 11. 2... Properties of Thin Films 11. l.INTRODUCTION Thin films were first exploited practically for their optical properties In the latter part of the nineteenth and first half of the twentieth centuries, the reflecting properties of metal films were utilized in assorted components of precision optical equipment A noteworthy example was the Fabry-Perot interferometer developed in 1899, which required mirrors of very... beyond the scope intended here Discussions will stress meanings and implications rather than mathematical rigor Electromagnetic radiation propagates differently in materials than in free space because of the presence of charge As a result, there is a change in the wave velocity and intensity of the radiation described by the complex index of refraction N = n - ik (11- 11 The quantity n is the real index of. .. the wavelength In free space the index of refraction is unity and the wave velocity is c, the speed of light; in the medium these respective quantities are n and c / n The real function exp 2 T kx /A represents an exponential damping or attenuation of the wave due to some absorption process within the material On the other hand, the imaginary exponential portion of Eq 11- 2 contains n and reflects... 10-18 The detection of y-ray-induced conversion electrons plus the use of enriched 57Felayers provide the necessary sensitivity - 10.8 493 Magnetic Thin Flims for Memory Applications -6 -4 -2 0 2 4 V [ mmls J I 1 6 Figure 10-18 Mossbauer spectra of ultrathin epitaxial (110 ) Fe films on (111 ) Ag at room temperature (From Ref 32 with permission from Elsevier Science Publishers) to probe ultrathin films. .. direct or indirect evidence of ferromagnetic order in thin films They broadly fall into three categories, depending on whether the 1 spin polarization of electrons, 2 net magnetic moment of the sample, or 3 internal magnetic (hyperfine) field 492 Electrical and Magnetic Properties of Thin Films is measured The first relies on extracting electrons from the conduction bands of ferromagnetic solids by... exhibited by the many thin- film coating applications irrespective of operating wavelength range Specific metal, dielectric, and semiconductor films have been deposited, frequently in layered combinations, to produce the necessary optical characteristics For these reasons the broad topical outline of the chapter includes: 11. 2 Properties of Optical Film Materials 11. 3 Thin- Film Optics 11. 4 Multilayer... number of dB = 10log,oIo/Z By comparison with Eq 11- 3, 1 dB/cm is 510 Optical Properties of Thin Films - equal to 4.34~~ Extremely low absorption losses of 1 dB/km are common in silica-based optical fibers In contrast, a 1-dB loss occurs within a few angstroms of penetration beneath the surface of a metal This corresponds to a difference of some 12 orders of magnitude in absorption behavior on the part of. .. metals in the visible and infrared region The characteristic color of some metals is due to the preferential absorption of some portion of the visible spectrum In gold, for example, the green portion is absorbed, and the metal assumes the coloration 511 11.2 Properties of Optical Film Materials Table 11- 1 Optical Constantsof Metal Films Employed for Mirrors Gold Silver copper n Wavelengths, p n k n... free poles exist In very thin films there is another type of wall with a much lower value of E It is shown in Fig , 10-19b, and is known as the NCel wall In NCel walls the direction of magnetization turns about an axis perpendicular to the film plane; there are no free poles in this case In both types of domain walls EK is smallest when the change in A4 is abrupt-Le., when the wall is as MITOW as possible; . parallel to the field direction. The core of the fluxoid is normal while the sheath is superconduct- ing; the circulating supercurrent of the latter establishes the field that keeps the core. on the surface than in the interior is the reason. Therefore, the question has been raised of how thin films can be and still retain ferromagnetic properties. At least four decades of both theoretical. exist. In very thin films there is another type of wall with a much lower value of E,. It is shown in Fig. 10-19b, and is known as the NCel wall. In NCel walls the direction of magnetization