The effect of surfaces on the electron transport at reduced scales is attracting continuous interest due to its broad impact on both the understanding of materials properties and their application for nanoelectronics. The size dependence of for conductor’s electrical resistivity ρ due to electron surface scattering is most commonly described within the framework of Fuchs and Sondheimer (FS) and their various extensions, which uses a phenomenological scattering parameter p to define the probability of electrons being elastically (i.e. specularly) scattered by the surface without causing an increase of ρ at reduced size. However, a basic understanding of what surface chemistry and structure parameters determine the specularity p is still lacking. In addition, the assumption of a spherical Fermi surface in the FS model is too simple for transition metals to give accurate account of the actual surface scattering effect. The goal of this study is to develop an understanding of the physics governing electron surface/interface scattering in transition metals and to study the significance of their Fermi surface shape on surface scattering. The advancement of the scientific knowledge in electron surface and interface scattering of transition metals can provide insights into how to design high-conductivity nanowires that will facilitate the viable development of advanced integrated circuits, thermoelectric power generation and spintronics.
Sequential in situ and ex situ transport measurements as a function of surface chemistry demonstrate that electron surface/interface scattering can be engineered by surface doping, causing a decrease in the ρ. For instance, the ρ of 9.3-nm-thick epitaxial and polycrystalline Cu is reduced by 11–13% when coated with 0.75 nm Ni. This is due to electron surface scattering which exhibits a specularity p = 0.7 for the Cu-vacuum interface that transitions to completely diffuse (p = 0) when exposed to air. In contrast, Ni-coated surfaces exhibit partial specularity with p = 0.3 in vacuum and p = 0.15 in air, as Cu2O formation is suppressed, leading to a smaller surface potential perturbation and a lower density of localized surface states, yielding less diffuse electron scattering.
The localized surface density of states (LDOS) at the Fermi level N(Ef) as a primary parameter determining the surface scattering specularity is further confirmed by a different surface dopant. In particular, the measured sheet resistance of 9-25-nm-thick epitaxial Cu(001) layers increases when coated with dTi = 0.1-4.0 monolayers (ML) of Ti, but decreases again during exposure to 37 Pa of O 2. The corresponding changes in ρ are a function of d Cu and dTi and are due to a transition from partially specular electron scattering at the Cu surface to completely diffuse scattering at the Cu-Ti interface, and the recovery of surface specularity as the Ti is oxidized. X-ray reflectivity and photoelectron spectroscopy indicate the formation of a 0.47±0.03 nm thick Cu2O surface layer on top of the TiO2-Cu2O during air exposure, while density functional calculations of TiOx cap layers as a function of x = 0-2 and dTi = 0.25-1.0 ML show a reduction of N(Ef) by up to a factor of four. This reduction is proposed to be the key cause for the recovery of surface specularity and results in electron confinement and channeling in the Cu layer upon Ti oxidation. Transport measurements at 293 and 77 K confirm the electron channeling and demonstrate the potential for high-conductivity metal nanowires by quantifying the surface specularity parameter p = 0.67±0.05, 0.00±0.05, and 0.35±0.05 at the Cu-vacuum, Cu-Ti, and Cu-TiO 2 interfaces.
In order to determine the effect of the Fermi surface shape on the size effect, experimental and simulation results are combined to study how the resistivity changes with film thickness dw on monocrystalline W layers with different surface orientation, W(001) and W(110). As the first step of the experiments, the growth of epitaxial W(001) layers on MgO(001) substrates by ultra-high vacuum magnetron sputtering is studied, in order to obtain an alternative W layer orientation in addition to the well-known growth of epitaxial W(011) on Al2O3 substrates. X-ray diffraction ω-2&thetas; scans, ω-rocking curves, and pole figures show that 5-400 nm thick W(001) layers grown at Ts = 900 °C are monocrystalline with a relaxed lattice constant of 3.167±0.001 nm, as determined from high resolution reciprocal space mapping. The magnitude of the residual in-plane compressive strain decreases from -1.2±0.1% to 0.1±0.1% with increasing dw. This is attributed to the glide of threading dislocations which increases the average misfit dislocation length, causing relaxation of the stress associated with differential thermal contraction. X-ray reflectivity measurements indicate smooth surfaces with a root-mean-square surface roughness ≤1.0 nm and a roughness exponent of 0.38 for dw below 20 nm.
Secondly, the effect of surface roughness on surface scattering is investigated to ensure its contribution to the resistivity size effect is properly included when comparing W films grown on different substrates. In fact it is found the ρ of in situ annealed 4-20 nm thick epitaxial W(001) layers grown on MgO(001) samples show weaker dw dependence than that of unannealed samples in vacuum and air at both 295 and 77 K although completely diffuse surface scattering are present on both sets of films. No significant change in the structural quality of the samples after annealing is observed for d ≤ 20 nm. While a combination of X-ray reflectivity and Atomic Force Microscope study on surface morphology shows flatter surface mounds after annealing. Consequently, in situ annealing treatment is carried out on both epitaxial W(110) and W(001) from dw =4-320 nm to obtain surface with comparable rms roughness and lateral correlation length. Thus the ρ increase due to the surface roughness is estimated in similar degree for the two types of films.
Finally, a transport model for thin films with anisotropic Fermi surfaces is presented, which includes the effect of electron surface scattering. Simulations done using the calculated W Fermi surface show the resistivity ρ to be 1.15-2.23 and 1.21-3.14 times larger than that of bulk W for (011) and (001) oriented thin films, respectively at a layer thickness d = 37.5- 3.75 nm, indicating an orientation dependent surface scattering effect on ρ. The resistivity of epitaxial W(110) increases from 5.77±0.03 to 13.24±0.24 µΩ-cm as d decreases from 320 to 5.7 nm, but increases stronger for epitaxial W(001) from ρ = 5.77±0.03 to 24.42±0.58 µΩ-cm for d = 320 and 4.5 nm. This orientation dependence is quantified with a different effective mean free path lambda(110) = 18.5±0.3 nm vs lambda(001) = 33±0.4 nm at 295 K by fitting using ρ vs t with the Fuchs-Sondheimer (FS) model for spherical Fermi surfaces since their surface scattering is found completely diffuse by sequential in situ and ex situ electron transport measurements. Similarly, the ρ from simulation can be fitted to obtain another set of lambda(110) and lambda(001). The ratio lambda (110)/lambda(001) = 0.57±0.01 from simulations, in good agreement with 0.56±0.01 from experiment. The orientation dependent size effect is the result of (1) the projected Fermi surface area along the surface normal and (2) the rate of electrons approaching the surfaces due to the anisotropic electron Fermi velocity distribution along different directions.
|Commitee:||Duquette, David J., Lu, Toh-Ming, Ullal, Chaitanya K.|
|School:||Rensselaer Polytechnic Institute|
|School Location:||United States -- New York|
|Source:||DAI-B 77/07(E), Dissertation Abstracts International|
|Subjects:||Engineering, Materials science|
|Keywords:||Anisotropic size effect of electrical resistivity, Copper interconnect, Electrical resistivity size effect, Electron channeling, Electron surface scattering, Surface roughness effect on electrical resistivity|
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