Influence of the surface morphology of the microwave microstrip line on its transmission performance

The main morphological parameters of 50-ohm Au/$i$-GaAs$\{100\}$ thin-film microwave microstrip gold coplanar transmission lines of the length lW affecting the active resistance of their skin layer $R$ and inductance $L$ are determined. It is found that the lateral character of the grain distribution and developed relief of their surfaces causes the appearance of additional electron scattering both at grain boundaries and at relief inhomogeneities. The small grain size $d_x<$ 133 nm at frequencies of $f>$ 10 GHz transforms an abnormal skin-effect into the normal one. Herewith, the linear dependence of $R$ on $l_W$ in the local approximation is provided by the fractal geometry of the surface relief and near-surface region of coplanar transmission lines, while the nonlinear dependence of the inductance $L$ on $l_W$ is provided not only by the fractal relief features of the two-dimensional surface of coplanar transmission lines but also by the fractal features of the three-dimensional distribution of its grains.