Rough surface scattering in many-mode conducting channels: Gradient versus amplitude scattering

We study the effect of surface scattering on transport properties in many-mode conducting channels (electron waveguides). Assuming a strong roughness of the surface profiles, we show that there are two independent control parameters that determine statistical properties of the scattering. The first parameter is the ratio of the amplitude of the roughness to the transverse width of the waveguide. The second one, which is typically omitted, is determined by the mean value of the derivative of the profile. This parameter may be large, thus leading to specific properties of scattering. Our results may be used in experimental realizations of the surface scattering of electron waves, as well as for other applications (e.g., for optical and microwave waveguides)