Optical and structural characterization of Si/SiGe heterostructures grown by RTCVD

Three-dimensional correlation of speckles in deep Fresnel region: extracting the roughness exponent of random surface

“…and D t is the integral region at t 1.  The above equation indicates that the scattered intensity profile S(k r ) in the high frequency range decreased with the parallel component of the wave vector k r according to the negative power law and the power value is l 2 2, a = + which is agreed with the result that mentioned in our previous research [22]. Substituting equation (8) into equation (4), we finally obtain the expression of the longitudinal correlation function in the paraxial region as following:…”

“…With the increase of the propagation distance, the spread area of scattered intensity profile will become much larger than the conventional aperture of beam illumination, and the cross correlation function will be determined by the conventional aperture. The [21][22][23] have demonstrated that the ground glass screens can describe self-affine fractal random surface every well and its height autocorrelation function is expressed as:…”

“…However, it is generally difficult to obtain the analytic expression of the equation (5). In most cases, the relationship between S(k || ) and the random surface parameters can be established by using some approximate conditions [22][23][24]. It is known that the fractal characteristic of the random surface is mainly reflected in the region r x  in the height-height correlation function, which represents the high frequency component in spatial frequency domain.…”