Conductivity Of Thin Metal Films Research Articles

Evaluating size effects on the thermal conductivity and electron-phonon scattering rates of copper thin films for experimental validation of Matthiessen’s rule

As metallic nanostructures shrink towards the size of the electronic mean free path, thermal conductivity decreases due to increased electronic scattering rates. Matthiessen’s rule is commonly applied to assess changes in electron scattering rates, although this rule has not been validated experimentally at typical operating temperatures for most of the electronic systems (e.g., near room temperature). In this study, we experimentally evaluate the validity of Matthiessen’s rule in determining the thermal conductivity of thin metal films by measuring the in-plane thermal conductivity and electronic scattering rates of copper (Cu) films with varying thicknesses (27 nm — 5 µm), microstructures, and grain boundary segregation. Comparing total electron scattering rates measured with infrared ellipsometry to infrared ultrafast pump-probe measurements, we find that the electron-phonon coupling factor is independent of film thickness, whereas the total electronic scattering rate increases with decreasing film thickness. Our findings provide experimental validation of Matthiessen’s rule for electron transport in thin metal films at room temperature and also introduce an approach to discern critical heat transfer processes in thin metal interconnects, which holds significance for the advancement of future CMOS technology.

AUTOMATED CONTROL OFTHE THIN FILMS ELECTRICALCONDUCTIVITY BY THE EDDY CURRENT METHOD

The article considers the possibility of using the eddy current method of non-destructive testing for the problems of measuring the electrical conductivity of thin metal films. As the object of measurement, we used copper films of various thicknesses obtained by vacuum vapor deposition. A review of current trends in the use of copper films in modern industry and science is presented, and an analysis is made of current methods of non-destructive testing suitable for studying thin copper films. A brief description of the deposition method and the hardware-software complex for measuring the electrical conductivity of the film is presented. A calibration curve is presented, which makes it possible to restore the values of the electrical conductivity of the film from the value of the signal of the eddy current transducer. GaAs samples were selected to construct a calibration curve. The decision is explained by the proximity of the values of the electrical conductivity of this chemical compound to the calculated indicators of the obtained thin films. The results of testing films with different characteristics are presented and the distribution of the electrical conductivity of the films depending on the batch is shown. A series of practical measurements of thin films demonstrated the existence of a relationship between the mass of the initial substance that was subjected to deposition and the characteristics of the resulting films. According to different values of electrical conductivity within the same batch, it was concluded that there is a difference in the quality of deposition of different films.

Measurements of Thermophysical Characteristics of Thin Film Metal Filters for Extreme Ultraviolet Radiation

Knowledge of the emissivity and thermal conductivity of thin metal films used in conjunction with multilayer mirrors for spectral selection of radiation in the extreme ultraviolet and soft X-ray wavelength ranges is necessary in order to correctly calculate the heating of film elements at high heat loads. Heating is associated with the absorption in the film of a significant fraction of the incident intensity, and the concept of a high heat load is somewhat arbitrary, since even at an absorbed intensity level of the order of 1 W/cm2 a freestanding film can be heated in vacuum by several hundred degrees. In the first approximation, to estimate the thermal conductivity coefficient, one could use tabular values for massive samples of the corresponding metals or use the well-known Wiedemann–Franz law which links the thermal conductivity and the electrical resistivity of the sample – the latter is easier to be measured. However, an analysis of the literature data indicates significant errors that are possible when using any of these approaches. Therefore, in this work, we have measured the thermal conductivity directly by processing the temperature distribution obtained by IR pyrometry over a film sample mounted on a heated frame or heated by a flowing electric current. Thermophysical characteristics (thermal conductivity and emissivity) were determined for samples of film absorption filters based on Mo, Al, and Be of submicron thickness (from 100 nm), as well as for films of copper – a metal whose bulk samples have high thermal and electrical conductivity. As expected, significant differences were found between the thermal and electrical properties of the film materials and the properties of the same metals in monolithic samples.

Effect of Rough Walls on Transport in Mesoscopic 3He Films

The interplay of bulk and boundary scattering is explored in a regime where quantum size effects modify mesoscopic transport in a degenerate Fermi liquid film of $^3$He on a rough surface. We discuss mass transport and the momentum relaxation time of the film in a torsional oscillator geometry within the framework of a quasiclassical theory that includes the experimentally determined power spectrum of the rough surface. The theory explains the anomalous temperature dependence of the relaxation rate observed experimentally. We model further studies on $^3$He confined in nanofluidic sample chambers with lithographically defined surface roughness. The improved understanding of surface roughness scattering can be extended to the analogous system of electrons in metals and suggests routes to improve the conductivity of thin metallic films.

Non‐contact evaluation of the electrical conductivity of thin metallic films by eddy current microscopy

An eddy current microscopy technique to evaluate the electrical conductivity of thin metallic films in a non‐contact manner is reported. A narrow track formed in an approximately 100 nm thick Au film was prepared, and a Co–Cr coated magnetic tip was driven to oscillate above the track both with and without current passing through the track. Despite the absence of current, the electromagnetic interaction between the tip and the stray magnetic field from the track gave rise to a phase delay in the probe. This was due to an eddy current being induced within part of the track. Moreover, measurements of the phase change in the probe oscillation for different metallic films with thicknesses of about 100 nm found this to be proportional to the electrical conductivity of the film. Finally, the electrical conductivity of an Al film was evaluated using the eddy current microscopy technique. Copyright © 2012 John Wiley & Sons, Ltd.

Broadband microwave spectroscopy in Corbino geometry at 3He temperatures

A broadband microwave spectrometer has been constructed to determine the complex conductivity of thin metal films at frequencies from 45 MHz to 20 GHz working in the temperature range from 0.45 K to 2 K (in a (3)He cryostat). The setup follows the Corbino approach: a vector network analyzer measures the complex reflection coefficient of a microwave signal hitting the sample as termination of a coaxial transmission line. As the calibration of the setup limits the achievable resolution, we discuss the sources of error hampering different types of calibration. Test measurements of the complex conductivity of a heavy-fermion material demonstrate the applicability of the calibration procedures.

409 渦電流誘導による金属薄膜の導電率評価(材料・設計(2))

409 渦電流誘導による金属薄膜の導電率評価(材料・設計(2))

Relaxation time effects on dynamic conductivity of alloyed metallic thin films in the infrared band

The behavior of nanoscale infrared antenna elements depends upon the dynamic conductivity of thin metallic films. Spectroscopic ellipsometer measurements of noble metal films show that when the product of the incident radiation frequency and the relaxation time is greater than unity, anomalous dynamic electron transport effects occur. In this regime electron scattering increases the conductivity of alloyed metallic films as demonstrated by ellipsometry measurements of films from the Au-Cu system. A binary alloy thin film was fabricated with equal parts of Au and Cu, and the dynamic conductivity was measured to be 300% larger than the high frequency conductivity of pure Au or pure Cu films at wavelengths in the 3–5 μm band. When electronic scattering is reduced, ellipsometer measurements of Au and Cu films taken near 4 K demonstrate that the IR conductivity decreases to 20% of the value measured at 300 K at wavelengths in the 3–5 μm band. Using measured dc relaxation times, a model to explain deviations from Drude behavior was developed using the theory of the anomalous skin effect and frequency dependent relaxation time. This model was in quantitative agreement with the measured data. The ability to design an alloyed metallic thin film using a calculated ideal dc relaxation time to produce the greatest possible dynamic conductivity for infrared antennas and metamaterials was demonstrated.

Terahertz conductivity of thin metal films

The conductivities of thin Al, Au, and Ag films were measured via their transmission at terahertz frequencies. The conductivities of all the films, particularly the thinner films and Al films, were much smaller than their bulk dc values. This reduced conductivity can be quantitatively understood in terms of an increased scattering rate from defects. The transmission is consistent with a frequency independent conductivity, implying a very fast electron scattering time.

Size Effect on the Thermal Conductivity of Thin Metallic Films Investigated by Scanning Joule Expansion Microscopy

A technique to extract in-plane thermal conductivity of thin metallic films whose thickness is comparable to electron mean free path is described. Microscale constrictions were fabricated into gold films of thicknesses 43nm and 131nm. A sinusoidal voltage excitation across the constriction results in a local temperature rise. An existing technique known as scanning joule expansion microscopy, measures the corresponding periodic thermomechanical expansion with a 10nm resolution and determines the local temperature gradient near the constriction. A three-dimensional finite-element simulation of the frequency-domain heat transfer fits the in-plane thermal conductivity to the measured data, finding thermal conductivities of 82±7.7W∕mK for the 43nm film and 162±16.7W∕mK for the 131nm film, at a heating frequencies of 100kHz and 90kHz, respectively. These values are significantly smaller than the bulk thermal conductivity value of 318W∕mK for gold, showing the electron size effect due to the metal-dielectric interface and grain boundary scattering. The obtained values are close to the thermal conductivity values, which are derived from electrical conductivity measurements after using the Wiedemann–Franz law. Because the technique does not require suspended metal bridges, it captures true metal-dielectric interface scattering characteristics. The technique can be extended to other films that can carry current and result in Joule heating, such as doped single crystal or polycrystalline semiconductors.

136 渦電流顕微鏡法による金属ナノ薄膜の導電率評価(材料力学III)

136 渦電流顕微鏡法による金属ナノ薄膜の導電率評価(材料力学III)

Effect of weak electric fields on the conduction in thin metal films

The variation of conduction in island metallic Ti, Co, W, and FeNi films in weak electric field is studied. The variation of the differential conductivity of island metallic films with an electric field at temperatures from T = 77 to 300 K is measured, as well as the temperature dependence of the differential conductivity in the same temperature range. It is shown that a thermally activated conduction mode is realized in such structures. The mechanism of variation of conductivity of island metallic films in a weak electric field is discussed.

Nanostructure and conductivity of thin metal films

Amorphous silver, copper, gold, and iron films of a thickness between 6 and 350 nm are grown on polymeric substrates by vacuum evaporation. The nanostructure of the films is investigated. The dependence of the conductivity on the film thickness is obtained, and a correlation between the surface morphology and the conductivity is established.

Femtosecond pump–probe nondestructive examination of materials (invited)

Ultrashort-pulsed lasers have been demonstrated as effective tools for the nondestructive examination (NDE) of energy transport properties in thin films. After the instantaneous heating of the surface of a 100 nm metal film, it will take ∼100 ps for the influence of the substrate to affect the surface temperature profile. Therefore, direct measurement of energy transport in a thin film sample requires a technique with picosecond temporal resolution. The pump–probe experimental technique is able to monitor the change in reflectance or transmittance of the sample surface as a function of time on a subpicosecond time scale. Changes in reflectance and transmittance can then be used to determine properties of the film. In the case of metals, the change in reflectance is related to changes in temperature and strain. The transient temperature profile at the surface is then used to determine the rate of coupling between the electron and phonon systems as well as the thermal conductivity of the material. In the case of semiconductors, the change in reflectance and transmittance is related to changes in the local electronic states and temperature. Transient thermotransmission experiments have been used extensively to observe electron-hole recombination phenomena and thermalization of hot electrons. Application of the transient thermoreflectance (TTR) and transient thermotransmittance (TTT) technique to the study of picosecond phenomena in metals and semiconductors will be discussed. The pump–probe experimental setup will be described, along with the details of the experimental apparatus in use at the University of Virginia. The thermal model applicable to ultrashort-pulsed laser heating of metals will be presented along with a discussion of the limitations of this model. Details of the data acquisition and interpretation of the experimental results will be given, including a discussion of the reflectance models used to relate the measured changes in reflectance to calculated changes in temperature. Finally, experimental results will be presented that demonstrate the use of the TTR technique for measuring the electron–phonon coupling factor and the thermal conductivity of thin metallic films. The use of the TTT technique to distinguish between different levels of doping and alloying in thin film samples of hydrogenated amorphous silicon will also be discussed briefly.

Thermal conductivity of thin metallic films measured by photothermal profile analysis

Thermal conductivity of nickel and gold films on quartz (thickness 0.4–8 μm) was measured by a modulated thermoreflectance technique recording the surface temperature profile. Model calculations predict an optimum frequency for measuring thermal transport within the film. Measurements on films with various thicknesses reveal a thermal conductivity close to the bulk value for nickel while gold films exhibit a reduced conductivity with decreasing film thickness.

Quantum Monte Carlo Simulations of Disordered Magnetic and Superconducting Materials

ABSTRACTOver the last decade, Quantum Monte Carlo (QMC) calculations for tight binding Hamiltonians like the Hubbard and Anderson lattice models have made the transition from addressing abstract issues concerning the effects of electron-electron correlations on magnetic and metal-insulator transitions, to concrete contact with experiment. This paper presents results of applications of “determinant” QMC to systems with disorder such as the conductivity of thin metallic films, the behavior of the magnetic susceptibility in doped semiconductors, and Zn doped cuprate superconductors. Finally, preliminary attempts to model the Kondo volume collapse in rare earth materials are discussed.

Thermal Conductivity of Thin Metallic Films

This study examines the effect of transverse thickness on the in-plane thermal conductivity of single crystal, defect-free, thin metallic films. The imposed temperature gradient is along the film and the transport of thermal energy is predominantly due to free electron motion. The small size necessitates an evaluation of the Boltzmann equation of electron transport along with appropriate electron scattering boundary conditions. Simple expressions for the reduction of conductivity due to increased dominance of boundary scattering are presented and the results are compared with other simplified approaches and experimental data from the literature. Grain boundary scattering is also considered via simple arguments.

Evidence of interference between electron-phonon and electron-impurity scattering on the conductivity of thin metal films.

The temperature dependence of the resistivity p of thin gold films (thickness d=100-400 A) has been measured at T=30 mK-300 K. In a wide temperature range below θ D /15 (θ D is the Debye temperature) Δρ(T)/p is proportional to T 2 and does not depend on the mean free path of electrons. Experimental determinations of the dependences Δρ(T)/ρ in this temperature range are in good agreement with the correction to the impurity resistivity of a normal metal due to the quantum interference between the electron-phonon and electron-impurity interactions

Conductivity of Thin Metallic Films

physica status solidi (a)Volume 119, Issue 2 p. K117-K120 Original Paper Conductivity of Thin Metallic Films J. Kierul, J. Kierul Solid State Physics Department, University of łódź Search for more papers by this authorJ. Ledzion, J. Ledzion Solid State Physics Department, University of łódź Search for more papers by this author J. Kierul, J. Kierul Solid State Physics Department, University of łódź Search for more papers by this authorJ. Ledzion, J. Ledzion Solid State Physics Department, University of łódź Search for more papers by this author First published: 16 June 1990 https://doi.org/10.1002/pssa.2211190241Citations: 2 PL-90-−238 łódź, Nowotki 149/153, Poland. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume119, Issue216 June 1990Pages K117-K120 RelatedInformation

Some transport coefficients of multilayer metallic film

This paper deals with a derivation of some transport coefficients of multilayer metallic film. The derivation is performed on the basis of Fuchs–Sondheimer theory in which the electrical conductivity of thin metallic films is strongly affected by a surface scattering process. The multilayer metallic film consists of alternating layers of two different metals. The scattering of conduction electrons at the interfaces between the layers are described by the Fuchs specularity reflection parameter P and the refractive parameter Q. The latter parameter corresponds to the fraction of conduction electrons refracted at the interfaces. However, the background mechanism of the scattering of conduction electrons in the layers are described by two different relaxation times, which are assumed to be functions of energy. Numerical results are obtained for parameters characteristic of alternating layers of silver and gold.