The mean free path of electrons in metals
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Citations
In situ measurement of thickness dependent electrical resistance of ultrathin Co films on SiO2/Si(111) substrate
Structural study of bismuth films and its consequences on their electrical properties
The variation of resistance of gold films with time and annealing procedure
Electrical resistivity of gold thin film as a function of film thickness
Parameter-dependent oxidation of physically sputtered Cu and the related fabrication of Cu-based semiconductor films with metallic resistivity
References
The conductivity of thin metallic films according to the electron theory of metals
The Theory of Metals
Related Papers (5)
Frequently Asked Questions (14)
Q2. What is the effect of the process of drawing wires of these metals?
The process of drawing wires of these metals produces an amorphous layer which is not easily removed by annealing, but which, in Chambers’ experiments, was removed by electrolytic polishing.
Q3. What is the case of a thin wire in a longitudinal magnetic ®eld?
When the electric and magnetic ®elds are parallel, the magnetic force on the electrons is always perpendicular to the electric force; the authors can then regard the electric ®eld alone as producing a drift current in the usual way, and the magnetic ®eld simply as modifying the electronic trajectories.
Q4. What is the eective conductivity of a conductor?
The e ective conductivity ¼ is obtained by integrating the current density over the cross-sectional area S of the conductor, and the ratio of ¼ to the bulk conductivity ¼0 may be written in the compact form¼
Q5. What is the simplest way to determine the distribution function of the electrons?
The problem is essentially a one-dimensional one, and the distribution function of the electrons may be written in the formf ˆ f0 ‡ f1…v; z†; …8†where the function f1 which has to be determined depends on the space variables only through z.
Q6. What was the main purpose of the modern electron theory of metals?
The foundations of the modern electron theory of metals were laid at the beginning of the present century, when the existence of a gas of free electrons was postulated by Drude in order to explain the conducting properties of metals; the behaviour of the electrons was subsequently analysed by Lorentz by means of the statistical methods of the dynamical theory of gases.
Q7. What is the conductivity of thin wires in a longitudinal magnetic ®eld?
The conductivity of thin wires in a longitudinal magnetic ®eld MacDonald, at the time of his discovery of the e ect, correctly interpreted its physical origin, and in particular he explained the simple decrease in resistance which occurs in a wire in a longitudinal ®eld as being due to the lessened infuence of scattering at the walls of the wire when the electrons are forced to pursue spiral paths around the lines of force of the magnetic ®eld.
Q8. What is the distribution function of the electrons leaving each surface?
The distribution function of the electrons leaving each surface must then be independent of direction; equation (10) shows that this can only be satis®ed if the authors choose F…v† so that f1…v; 0† ˆ 0 for all v such that vz > 0 (that is, for electrons moving away from the surface z ˆ 0), and f1…v; a† ˆ 0 for all v such that vz < 0:
Q9. What is the obvious method to determine the free path in a metal?
The most obvious method is to use a thin ®lm or wire and to arrange that the free path is comparable in magnitude with the thickness or diameter of the specimen; the arti®cial limitation of the free path by the boundaries of the specimen causes an increase in the resistivity above its value in the bulk metal, and this may be used to deduce the ratio of free path to thickness or diameter.
Q10. What is the definition of the term sizee ect?
This term takes into account the non-uniform distribution in space of the conduction electrons which is characteristic of the sizee ect phenomena.
Q11. What is the limit of zero magnetic ®eld?
In the limit of zero magnetic ®eld … ˆ 0†, equation (54) for the conductivity reduces to equation (16), and (55) gives a corresponding expression for the Hall coe cient of a thin ®lm in a vanishingly small magnetic ®eld.
Q12. What is the advantage of using a magnetic ®eld?
The advantage of using a magnetic ®eld is that all the required information can be obtained from one specimen only, and it is not necessary to assume, as in zero-®eld experiments, that the free path in a thin specimen is the same as in a bulk specimen.
Q13. What are the probable errors for copper, silver, gold, and aluminium?
The values for copper, silver, gold, and tin were obtained by Chambers,{ and are subject to probable errors of about 5%; the values for mercury and aluminium have been deduced from Pippard’s measurements and have larger probable errors.
Q14. Why does the departure from theory in high ®elds interfere with the comparison between theory and?
The departure from theory in high ®elds is, in fact, due to the onset of the bulk e ect, but this does not interfere seriously with the comparison between theory and experiment.