Using the signals of four backscattered electron (BSE) detectors with different detection angles in the scanning electron microscope (SEM) the three‐dimensional surface topography of various samples, i.e. catalysts, fractured surfaces and micro‐devices can be derived and analyzed [1], [2]. An efficient shape from shading reconstruction algorithm is applied to these signals to extract high resolution height and texture information. The surface reconstruction is very fast and needs no sample tilting since the surface topography is calculated from the four simultaneous recorded backscattered electron images.
While the 3D reconstruction of the surface topography works very well, the calculation of quantitative height differences depends on different imaging and geometric parameters and requires a calibration of the used BSE detectors. This includes the adjustment of gain and offset of the signals as well as the checking of the geometrical properties of the detector, i.e. detector radius, height, detection area and the horizontal angle to the scan rotation. Especially the height determination, which also depends on the adjustment of the working distance, is hard to determine. Therefore, a spatial calibration is applied with the help of 3D calibration standards [3]. As a result, not only lateral scaling factors, but also z‐scale and shearing effects are estimated. Furthermore, nonlinear deviations are calculated and allow an evaluation of the local and overall accuracy of topographic data, which is achieved applying 3D reconstruction using a calibrated 4Q‐BSE detector.
For better accuracy, the reconstruction algorithm was improved by applying refined geometry for the primary and the backscattered electron beam. At low magnifications, the electron beam is not perpendicular to a horizontal specimen surface and the distribution of the backscattered electrons is not isotropic. In addition, the distance between the specimen and the detector is not constant for all image points. Without consideration and correction, this yields to spherical distorted surfaces. The advanced 3D reconstruction algorithm includes geometrical improvements, allowing a distortion‐free mapping of the surface topography over a large magnification range.
As an example for application of 3D reconstruction in material sciences, fracture surfaces of a copper base alloy were analyzed. The applied SEM (Hitachi S‐520) is equipped with a complete digital imaging system and in particular with a 4‐quadrant BSE detector (point electronic GmbH) and was geometrically calibrated using a 3D calibration standard. Thus, the spatial scale factors were determined for a magnification of 1000x to cx = 1.013, cy = 1.024, cz = 1.198. While the remaining maximum geometrical deviations after application of these calibration parameters were evaluated with dx = 60 nm, dy = 41 nm and dz = 57 nm the spatial mean deviations for the whole measurement volume is 16 nm.
The figures present some results of the investigation. The upper row of pictures shows the dimpled surface microstructure of a forced fracture where the material mostly cracks in a ductile trans‐crystalline manner. The pictures of the bottom row show some crystallographically oriented facets of a fatigue fracture of the same material. On the left for both cases the secondary electron (SE) images are shown, on the right side pictures of the 3D reconstructions of the BSE images are presented. Height differences can be visualised immediately whereas more complex data will be derived from the 3D datasets.
The improved 3D reconstruction algorithm is available as standalone software version as well as integrated solution for SEM. Integration into a SEM system allows not only on‐line 3D visualisation, but also easier calibration and especially more reliable application, because full control over all relevant physical and imaging parameters is guaranteed. The integrated topographic 3D reconstruction was developed in cooperation with point electronic GmbH and is now available within their SEM control hard‐ and software DISS. Therefore we like to thank point electronic GmbH for the fruitful cooperation.
