The study of temperature coefficient of resistivity of polycrystalline metal films

The temperature coefficient of resistivity (t.c.r.) has been studied for the polycrystalline metal tin and lead films of various thicknesses. The t.c.r. is found to increase with thickness and thus exhibits the size effect. This thickness dependence of t.c.r. is successfully explained with the help of a three-dimensional model. The grain boundary t.c.r. and specularity parameter are determined from the measurements.     

The thermoelectric power and the temperature coefficient of resistance of thin polycrystalline antimony films

Starting from the Mayadas-Shatzkes equations for the conductivity of a metal film, the temperature coefficient of resistivity and the thermoelectric power for polycrystalline semi-metal films were calculated.From the data obtained for various grain sizes D in the range 200–2000 Å, the concentrations n of electrons and p of holes, as well as the respective mobilities μ_n and μ_p, were determined without assuming n = p. Good agreement was found between experimental results and the theoretical equations we proposed.     

Absolute thermoelectric power and temperature coefficient of resistance of thin continuous metal films

General expressions are derived in terms of a function F(K), which is equal to the ratio of film to bulk conductivity, for the following: the ratio of film to bulk resistivity, the absolute thermoelectric power of the film material and the ratio of film to bulk temperature coefficient of resistance. The exact and approximate forms of the function F(K) for various theories of the scattering mechanism at the film surfaces are reported. Also plots of the derived expressions using some of these forms are given.     

Size and temperature dependence of thermoelectric power and electrical resistivity of vacuum-deposited antimony thin films

Thin antimony films of thicknesses in the range 30 to 200 nm have been vacuum deposited on glass substrates at room temperature. After annealing for about an hour at 500 K, the thermoelectric power and electrical resistivity were measured in vacuum as a function of temperature. The thermoelectric power and electrical conductivity data were combined and simultaneously analysed using the effective mean free path theory of size effect in thin films developed by Tellier and Pichard et al. In addition, their temperature dependence was also analysed. It was found that the thermoelectric power is positive and increases with increasing temperature and is inversely proportional to the thickness of the film. The electrical resistivity was found to be temperature dependent with the temperature coefficient of resistivity being positive, and inversely proportional to the thickness of the film. Analysis combining the data from the thermoelectric power and electrical conductivity measurements has led to the determination of mean free path, carrier concentration, effective mass, Fermi energy and the parameter The data were analysed for least squares fitting by local functions, such as the spline functions, which eliminates possible errors in conventional least squares fitting of data using non-local functions valid throughout the range.     

General expression for the temperature coefficient of resistivity of polycrystalline semi-metal films

After calculating the different contributions to the resistivity of a thin film, a general expression for the temperature coefficient of resistivity in a polycrystalline semi-metal film is derived by taking into consideration the influence of internal size effects on the film resistivity in terms of the Mayadas-Shatzkes function, thermal strains and the difference in the thermal expansion coefficients between the film and its substrate. A comparison with experimental data, in the temperature range 77 to 500 K, over grain size range 30 to 200 nm, for antimony films, 200 nm thick, is made. Good agreement has been found between experiments and the theoretical equations we proposed.     

The resistivity, temperature coefficient of resistivity and thermoelectric power of thin continuous metal films II: A methodology for computer processing of thin film data to extract parameters with associated error estimates

A straightforward computer-based general methodology is presented which will enable parameter values and associated error estimates to be extracted from experimental thin film data points. The methodology operates on exact thin film relationships and overcomes problems in interpreting results, such as having to resort to the use of approximate thin film relationships.

The methodology is presented within the framework of the well-known Fuchs-Sondheimer model for conduction in thin continuous metal films. However, its general nature means that it is equally applicable to other theoretical thin film models. An illustration of the methodology's use is given by applying it to a set of thin film resistive, temperature coefficient of resistivity and thermoelectric power data obtained from measurements on thin continuous copper films.     

Electrical resistivity and thermoelectric power of copper-germanium films

CuGe films over the whole composition range were prepared by the vapour quenching of the alloys onto glass substrates held at 300 K. The electrical resistivity, thermoelectric power and temperature dependence of the films were studied in the temperature range 100–500 K. The observed behaviour of the electrical resistivity and thermoelectric power is understandable on the basis of transmission electron microscopy and electron diffraction observations which indicate three structural regions. Up to 5 at.% Ge in copper the films are single phase with a structure similar to that of pure copper; in the range 5–80 at.% Ge in copper the films consist of a mixture of Cu₃Ge, copper and germanium; beyond 80 at.% the CuGe films are single-phase amorphous.     

Electrical resistivity and temperature coefficient of resistivity in gold-copper films

In situ measurements were carried out in order to study the electrical behaviour of gold-copper films (300–3000 Å) of various compositions in the temperature range 30–150°C. The experimental observations were correlated with the structural information obtained from an electron microscope study.     

The resistivity, temperature coefficient of resistivity and thermoelectric power of thin continuous metal films I: A survey and critical appraisal of the application of processing methods to experimental data

In this paper the results are reported of an investigation into the accuracy and applicability of the methods which have been used to extract parameter values from sets of experimental data points. Theoretical models describing resistivity, temperature coefficient of resistivity and thermoelectric power of thin continuous metal films and experimental processing methods are identified and categorized. A critical appraisal is given of experimental work reported in papers published between 1961 and 1984. This is followed by details of investigations into the methods commonly used for fitting data to exact and thick film relationships. These investigations are presented within the framework of the Fuchs-Sondheimer relationships. However, the major problem areas that are identified are of a general nature and do not appear to be limited to this model. The problems with the methods investigated, especially those associated with thick film approximations, are shown to be so great as to cast doubt on many published values.     

Electrical resistivity and thermoelectric power of polycrystalline and amorphous Se-Te-Cu system

The dark electrical resistivity and thermoelectric power have been measured for the bulk ternary alloy Se-Te-Cu. The samples were both polycrystalline and amorphous in structure. The measurements were carried out below room temperature. Depending on Cu addition, crystallographic structure, and amorphous or polycrystalline state, the samples manifested semiconducting or metallic behaviour. The maximum difference in electrical resistivity magnitude was of 14 orders. The activation energy ΔE of charge carriers determined for all semiconducting samples ranged from 0.07 to 0.25 eV. An increase in thermoelectric power resulting from the electron–phonon mass enhancement was estimated.     

Temperature variation in the thermoelectric power of polycrystalline CdS films

The variation with temperature in the thermoelectric power of vacuum- deposited CdS films grown under the influence of a longitudinal d.c. electric field was investigated. The electric field strength was ±70, ±140 or ±210 V cm⁻¹, and the films were deposited onto glass substrates. The temperature variation in the resistance of the film is also reported and the field variation in the activation energy is discussed.     

Exact and approximate expressions for the temperature coefficient of resistivity of polycrystalline films using the Mayadas-Shatzkes model

Starting from the Mayadas-Shatzkes equations for film conductivity, exact analytical expressions for the temperature coefficient of resistivity for monocrystalline and polycrystalline films were calculated. The temperature coefficient of resistivity for an infinitely thick polycrystalline film and a tabulated function were introduced into the linearized expression for the polycrystalline film; good agreement with previous experiments was obtained.     

Effect of thermal expansion of the grain boundary reflection coefficient on the temperature coefficient of resistivity of thin polycrystalline films

Numerical values for the exact temperature coefficient of resistivity (TCR) ratio β_Fp/β₀ of thin polycrystalline films were evaluated taking into account the influence of the thermal expansion coefficient of thickness a, the grain size a_g and the grain boundary reflection coefficient r. When the thermal expansion coefficient γ_r related to r is less than (1 ? r) × 10^?5K^?1 we may conclude that for polycrystalline metallic films the TCR dependence on thickness is described with a good agreement by the approximate expression previously derived.     

Graphical determination of the energy dependence of the thermoelectric power of thin monocrystalline metal films

Some theoretical results of the conductivity dependence of the thermoelectric power and of the difference in thermoelectric power are explained in the framework of the bidimensional model of conduction for monocrystalline metal films. Thermoelectric power data on thin metal films previously reported by different authors allow an accurate calculation of the energy dependence of the mean free-path,, and Fermi-surface area,v.     

Resistivity and temperature coefficient of resistivity of tin films

The electrical resistivity and the temperature coefficient of resistivity of tin films (490 to 5000 Å) deposited onto glass substrates at room temperature (30° C) were measured in situ in the temperature range 30 to 150° C. It is concluded that Mayadas-Shatzkes theory reproduces the experimental observations more faithfully than Fuchs-Sondheimer's theory.     

The influence of annealing on the resistivity and the thermoelectric power of evaporated palladium films

Palladium films in the thickness range from 5 to 60 nm were evaporated at 80 K and annealed at various temperatures up to 440 K. The resistivity and the thermoelectric power of the films were measured as functions of the thickness, the annealing temperature and the measuring temperature. It is necessary to use annealing temperatures as high as 400–440 K in order to obtain films in which the resistivity $\text{(?}{}_0\text{(280}\text{K}\text{) = 11.5 μΩ}\text{cm}\text{)}$ and the thermoelectric power (S₀(280 K) = ?9.3 μV K^?1) approach, when extrapolated to infinite thickness, the values of well-ordered bulk palladium (? = 10.03 μΩ cm, S = ?9.30 > μV K^?1 at 280 K).