General Considerations
Electrical properties of thin films have long been of practical importance and theoretical interest. The solid-state revolution has created important new roles for thin film electrical conductors, insulators, and devices. What was once accomplished with large discrete electrical components and systems is now more efficiently and reliably achieved with microscopic thin-film-based inte-grated circuit chips. Regardless of the class of material involved, its physical state or whether it is in bulk or film form, an electric current of density J (amps/cm2) is said to flow when a concentration of carriers n (number/cm3) with charge q moves with velocity v (cm/sec) past a given reference plañe in response to an applied electric field S (V/cm). The magnitude of the current flow is expressed by the simple relation
J=nqv. (10-1)
For most materials, especially at small electric fields the carrier velocity is proportional to $ so that
v = n$. (10-2)
The proportionality constant or velocity per unit field is known as the mobility (x. Therefore,
J=nq(ii, (10-3)
and by Ohm's law (J = ai) the conductivity a or reciprocal of the resistivity p is given by
o= l/p = nqix. (10-4)
Quantitative theories of eléctrica! conductivity seek to define the nature, magnitude, and attributes of the material constants in these equations. Corol-lary questions revolve about how n and v oí |i vary as a function of temperature, composition, defect structure, and electric field. An alteraative complementary approach to understanding the response of materials to elec-trical fields involves electronic band structure considerations that, as noted in Chapter 1, have successfully modeled property differences. Comprehensive descriptions of conduction intégrate what might be termed the "charge carrier dynamics" approach with the band structure viewpoint. The former is more intuitive and will be adopted here for the most part, but resort will also be made to band diagrams and concepts.
This chapter focuses primarily on the electrical conduction properties of thin metal, insulating, and superconducting films. Almost half of the classic Handbook of Thin Film Technology, edited by Maissel and Glang, is devoted to a treatment of electrical and magnetic properties of thin films. Though dated, this handbook remains a useful general reference for this chapter. Much of what is already known about bulk conduction provides a good basis for understanding thin-film behavior. But there are important differences that give thin films unique characteristics and these are enumerated here:
1. Size effects or phenomena that arise because of the physically small dimensions involved— Examples include surface scattering and quantum mechanical tunneling of charge carriers.
2. Method of film preparation—ll cannot be sufficiently stressed that the electrical properties of metal and insulator films are a function of the way they are deposited or grown. Depending on conditions employed, varying degrees of crystal perfection, structural and electronic defect concentra-tions, dislocation densities, void or porosity content, density, grain mor-phology, chemical composition and stoichiometry, electrón trap densities, eventual contact reactions, etc., result with dramatic property implications. Insulators (e.g., oxides, nitrides) are particularly prone to these effects and metáis are less affected.
3. Electrode effects—Frequently the substrate and a subsequently deposited conducting film become the electrodes for the film in question that is sandwiched in between. In general, insulating films cannot be considered apart from the electrodes that contact their surfaces. The electrical response of structures containing insulator (I) or oxide (O) films between metáis (MIM), semiconductors (SOS), and mixed electrodes (MIS, MOS) is strongly influenced by the specific metal or semiconductor electrode mate-rials employed. Interfacial adhesión, stress, interdiffusion, incorporated or adsorbed impurities, are some of the factors that can alter the character of charge transpon at an interface.
4. Degree of film continuity—conduction mechanisms in discontinuous, island structure films differ from those in continuous films.
5. Existence of high electric field conduction phenomena—Modérate volt-ages applied across very small dimensions conspire to make high field effects readily accessible in films.
6. High chemical reactivity—fúms are susceptible to aging or time-depen-dent changes in electrical properties due to corrosión, absorption of water vapor, atmospheric oxidation and sulfidation, and low-temperature solid-state reactions.
3. In virtually all cases, thin metal films are more resistive, while insulating films are more conductive than their respective bulk counterparts. For metáis the differences between film and bulk electrical properties are relatively small; ¡n insulators the differences can be huge. Why this is so will unfold in the ensuing pages.
Measurement of Film Resistlvity
A number of techniques have been employed to measure electrical properties of thin films. Some are adaptations of well-known methods utilized in bulk materials. For insulating films, where current flows through the film thickness, electrodes are situated on opposite film surfaces. Small evaporated or sputtered circular electrodes frequently serve as a set of equivalent contacts; the substrate is usually the other contact. If charge leaks along the surface from contact to contact, circumventing through-film conduction, then a guard electrode is required.
For more conductive metal and semiconductor films, it is common to place all electrodes on the same film surface. Such measurements employ four terminals-two to pass current and two to sense voltage. Several contact configurations shown in Fig. 10-1 are suitable for this purpose. Through the use of lithographic patterning methods (Chapter 14), long stripes can be configured with outer current and inner voltage leads that are extensions of the film itself (Fig. 10-la). In this way contact resistance problems are eliminated. Independent measurements of voltage and current yield the film resistance through Ohm's law, and the resistivity if film dimensions are known.
A very common way to report valúes of thin-film resistivity is in terms of sheet resistance with units "ohms per square." To understand this property and the units involved, consider the film of length /, width w, and thickness d in Fig. 10-2. If the film resistivity is p, the film resistance is R = pl/wd. Furthermore, in the special case of a square film (/ = w),
R = Rs = p/d ohms/D, (10-5)
where Rs is independent of film dimensions other than thickness. Any square, irrespective of size, would have the same resistance. As an example, consider a film stripe measuring 3 /¿m X 30 fim with Rs = 15 Í2/D. The overall stripe resistance is 10 x 15 = 150 0 because there are 10 squares (3 ^m x 3 ftm) in series.
A very convenient way to measure the sheet resistance of a film is to lightly press a four-point metal-tip probé assembly into the surface as shown in Fig. 10-lb. The outer probes are connected to the current source, and the inner probes detect the voltage drop. Electrostatic analysis of the electric potential and field distributions within the film yields
Rs = KV/I, (10-6)
where K is a constant dependent on the configuration and spacing of the contacts. If the film is large in extent compared with the probé assembly and the probé spacing large compared with the film thickness, K = ir/ln2 = 4.53. Otherwise correction factors must be applied (Ref. 1). Four-point probé assemblies are available commercially with square as well as the more com-mon linear contact arrays.
Conduction in Metal Films
Matthiessen's Rule
Much can be learned about electrical conduction in metáis from Matthiessen's rule. Originally suggested for bulk metáis, it is also valid for thin metal films. It simply states that the various electrón scattering processes that contribute to the total resistivity (pr) of a metal do so independently and additively; i.e.,
Pt = PTh + Pi + Pd (10-8)
The individual thermal, impurity, and defect resistivities are pTh, p,, and pD, respectively. Electrón collisions with vibrating atoms (phonons) displaced from their equilibrium lattice positions are the source of the thermal or phonon (p^) contribution, which increases linearly with temperature. This causes the well-known positive temperature coefficient of resistivity, an unambiguous sign of metallic behavior. Impurity atoms, defeets such as vacancies, and grain boundaries locally disrupt the periodic electric potential of the lattice. Due to atomic valence and size differences at these singularities, electrons are effec-tively scattered. However, the contributions from p, and pD are temperature independent, as shown in Fig. 10-3 if the concentration of impurities and defeets is low.
As an application of Matthiessen's rule, consider the problem of assessing the purity and defect contení of "puré" metal films. A measure of these properties is the residual resistivity ratio or RRR. The latter is defined by RRR = pT(300 K)/pr(4.2 K) and is readily determined experimentally by measuring the resistivity at the two indicated temperatures. For relatively puré annealed metal films at 300 K, pTh> p, + pD- At 4.2 K, however, lattice vibrations are frozen out and thermal scattering is dramatically reduced compared to impurity and defect scattering; i.e., p, + pD > pTh. Therefore, to a good approximation,
RRR~pTh(300K)/p/ + pD(4.2K), (10-9)
and it is clear that the purer and more defect-free the film is, the higher the ratio is. Resistivity ratio determinations of sputtered films as well as sputtering target metáis have been a useful way to assess their quality. Measured valúes of RRR broadly range from below 10 to several thousand. For extremely puré metal films, chemical analysis methods fail because of limited sensitivity, and the valué of RRR is the only practical means available for determining purity. An alternative formulation of Matthiessen's rule in terms of the respective mean free-electron lengths (X) between collisions has the form
1/Xr=l/Xn,+ 1/X/+1/X2,. (10-10)
This result stems from the intuitive direct proportionality between a and X, so that p¡ oc 1/X,. Theory has suggested that X^ can be hundreds to thousands of angstroms—lengths difficult to reconcile with classical models of vibrating atoms. Clearly quantum effects are involved here. In films of thickness d that are sufficiently thin so that d < \T, the possibility arises that a new source of scattering—that due to the film surfaces—can increase the measured film resistivity. It is to this subject that we now turn our attention.
Electrón Scattering from Film Surfaces
The problem of electrón scattering from thin metal film surfaces has been of interest for almost a century; even today the subject is not free of controversy. Critical issues revolve about the nature of the film surface and what happens when an electrón fails to execute the full mean-free path because its motion is interrupted through colusión with the film surface. The electrons then undergo either specular or diffuse scattering. In specular or elastic scattering the electrón reflects in much the same way a photon does from a mirror. In this case one can imagine removing the surface and doubling the film thickness (or tripling it for two surface reflections, etc.). The electrón now continúes on an imaginary straight path to complete the path it would have in bulk, finally scattering at a point interior to the extended surface. If this happens, the film resistivity is the same as in the bulk, and there is no film thickness effect on resistivity. When scattering is totally nonspecular, or diffuse (inelastic), the electrón mean-free path is terminated by impinging on the film surface. After a surface colusión the electrón trajectory is independent of the impingement direction, and the subsequent scattering angle is random. The resistivity rises because fewer electrons flow through the reference plañe registering current flow.
Ronellys Flores---CRF---libro the materials science of thin films
No hay comentarios:
Publicar un comentario