Resistivity dominated by surface scattering in sub-50 nm Cu wires

Abstract

Electron scattering mechanisms in copper lines were investigated to understand the extendibility of copper interconnects when linewidth or thickness is less than the mean free path. Electron-beam lithography and a dual hard mask were used to produce interconnects with linewidths between 25 and 45 nm. Electron backscatter diffraction characterized grain structure. Temperature dependence of the line resistance determined resistivity, which was consistent with existing models for completely diffused surface scattering and line-edge roughness, with little contribution from grain boundary scattering. A simple analytical model was developed that describes resistivity from diffuse surface scattering and line-edge roughness.

Surface and grain boundary scattering in nanometric Cu thin films: A quantitative analysis including twin boundaries

“…Barmak et al 15 and Sun et al 13 used the same measures of goodness-of-fit in their respective studies, namely, the sum squared error (SSE) and the Bayesian information criterion (BIC) (described in later section), and in several cases, it was found that the fits to the reported data using the values of p and R of Sun et al provided a better fit to the data than the values of p and R given in the original reports, even when the authors concluded that surface scattering was dominant. 14 One question that was not answered in the Sun et al [11][12][13] analysis, however, was whether twin boundaries in Cu contribute significantly to the measured resistivity. Due to the difficulty of characterizing twin boundaries in Cu at the nanoscale, this contribution was ignored in these earlier studies.…”

“…1 Determining the relative contributions of surface and grain-boundary scattering toward this resistivity increase is an important step toward a quantitative understanding of the classical size effect. [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] A commonly used description for the surface scattering contribution to the resistivity increase is the Fuchs-Sondheimer (FS) model. 18 In this model, the resistivity increase is a result of diffuse scattering of conduction electrons at the conductor's exterior surfaces with a probability of 1 À p, where p (0 p 1) is a specular scattering coefficient that is typically inferred from experimental data.…”

Experimental study of electron-phonon coupling and electron internal thermalization in epitaxially grown ultrathin copper films

“…The effects of electron scattering in a confined geometry have been studied extensively in thin copper films [5][6][7][8][9][10] and nanoscale copper wires [2,[11][12][13][14][15]. When the sample size is reduced to the nanoscale level, the increase of electrical resistivity has been mostly explained by the increase in surface and grain boundary scattering [14,16]. It is less clear if the electron-phonon coupling strength changes when the sample size is reduced.…”

Electron scattering at surfaces and grain boundaries in Cu thin films and wires

“…The constants p and R are free and independent fitting parameters, 8,[21][22][23][24] and determine the relative contribution of surface and grain boundary scattering, respectively. Most studies find p ≈ 0 at all Cu interfaces, 8,21,25 corresponding to completely diffuse surface scattering, and 0.2 < R < 0.5. 3,26,27 However, the interdependence and the uncertainty in the quantification of grain size, thickness, and roughness of the Cu layers complicates the determination of p and R from any set of polycrystalline samples.…”