Influence of anomalous roughness growth on the electrical conductivity of thin films

In this work it is explored how anomalies in the dynamic evolution of self-affine interface roughness influence electrical conduction in thin films. For metallic films if the roughness amplitude $w$ increases faster than the correlation length $\xi$ with increasing film thickness that leads to higher scattering and thus lower conductivity. The latter still increases with increasing roughness exponent $H$ due to interminiband scattering. The opposite behavior was observed for semiconducting films where only one miniband was occupied, therefore excluding interminiband scattering effects. Therefore, dynamic roughness evolution and interminiband scattering can interact and influence the thickness dependent conductivity of thin films. Indeed for semiconducting films the evolution of the long wavelength roughness parameters $w$ and $\xi$ can obscure the smoothing effect due to increment of the roughness exponent $H$ and decrease the conductivity in the case of rapid surface/interface roughening.

Figure 1

Metallic films: Conductivity $\sigma$ vs thickness $d$ for specified roughness exponents (a) $H=0.3$ and (b) $H=0.9$ and values of $c=0.5$, 1, 2, 3, 4, 5 leading to consecutive conductivity decrement as can be seen clearly for large thickness $d$.

Figure 2

Metallic films: Conductivity $\sigma$ vs thickness $d$ for two distinct values of the factor $c=2$, 10 and various roughness exponents $H$: (a) $H=0.1$ solid line, $H=0.2$ dashes, $H=0.3$ dots, $H=0.6$ line-square, and $H=0.9$ line-cross and (b) $H=0.1$ solid line, $H=0.3$ dashes, $H=0.6$ dots, and $H=0.9$ line-cross.

Figure 3

Semiconducting films: Conductivity $\sigma$ vs thickness $d$ for (a) roughness exponent $H=0.3$ and values of $c=0.5$, 1, 3, 5. (b) $c=2$ and various roughness exponents $H$ as indicated.