Effective electron mean free path in TiN(001)

Abstract

The measured resistivity ρ of smooth stoichiometric epitaxial TiN(001) is 13 and 3.0 μΩ cm at 298 and 77 K for bulk layers but is 8 and 25 times higher when the layer thickness d is reduced to 2 nm. The increase in ρ with decreasing d is attributed to diffuse electron-surface scattering and is well described by the classical Fuchs-Sondheimer (F-S) model. This is unexpected because the F-S model is based on the nearly free electron model, while TiN exhibits a highly non-spherical Fermi surface and three bands crossing the Fermi-level. The measured room temperature effective electron mean free path λ for bulk scattering is 45 ± 4 nm, which is an order of magnitude larger than the free-electron prediction. This deviation is attributed to ∼93% of charge transport in TiN being due to two slightly filled bands which represent only 4% of conduction electrons. The F-S model is applicable to TiN because these two bands are nearly parabolic and nearly degenerate, yielding a single value for λ, which is estimated based on the published band structure to be 49 nm, in excellent agreement with the experimental 45 nm. These results demonstrate that the F-S model is applicable to metals with non-spherical Fermi-surfaces as long as the charge transport is dominated by a single (or multiple degenerate) band(s).

The electron-phonon relaxation time in thin superconducting titanium nitride films

“…In our case, the dirty limit in the sense of q T l ( 1 (where q T ¼ k b T=hu is the wave number of thermal phonons, u is the sound velocity, ' is the electron mean free path) is achieved already at T % 4.2 K with q T ' ¼ 0.1. The values of the mean free path are estimated with l ¼ 3D=v F with the Fermi velocity v F ¼ 7 Â 10 5 m/s for TiN films 24 and are listed in Table I. The fact that we find n ¼ 3 rather than n ¼ 4 may be due to the fact that the predicted temperature dependence is based on the Debye phonon spectrum.…”

Comparison of the ultrafast hot electron dynamics of titanium nitride and gold for plasmonic applications

“…This results in the heating of the thermal electron population and decay of the nonthermal component until the total electron distribution reaches an elevatedtemperature Fermi-Dirac distribution with a well-defined total temperature, 8 . The decay of the nonthermal electron distribution is described by Fermi liquid theory 3 using a thermalization time, .…”

“…Following the heating of the thermal population, there remains an electron temperature gradient, as a result, heat is conducted away from the laser spot with associated carrier thermal conductivity, 8 . The second loss channel is scattering with phonons, which has associated coupling parameter, .…”

“…These heat the thermal electrons via electron-electron interactions at a rate quantified by , the electron gas heating rate. The energy of the thermal electrons is described by the electron temperature 8 corresponding to the Fermi-Dirac distribution, whose temperature change is modulated by the electron heat capacity, 8 .…”

First-Principles Study of TiN/MgO Interfaces

“…MgO is a suitable substrate for the growth of a TiN film due to the small lattice mismatch between these two compounds (0.5% see Table I). Consequently, several studies have examined TiN/MgO interfaces in the light of both theory [10,12,13] and experiment [9,[14][15][16][17][18][19][20][21][22][23]. Fur- * This paper was presented at the 12th International Conference on Atomically Controlled Surfaces, Interfaces and Nanostructures (ACSIN-12) in conjunction with the 21st International Colloquium on Scanning Probe Microscopy (ICSPM21), Tsukuba International Congress Center, Tsukuba, Japan, November 4-8, 2013.…”