Composition quantification of thin samples by backscattered electron imaging in scanning electron microscopy
Authors: Müller Erich , Gerthsen Dagmar 
Published: December 2016

The contrast of backscattered electron (BSE) images in scanning electron microscopy can be exploited for atomic number or material density determination [1]. However, BSE images suffer from limited spatial resolution for bulk specimens due to the large interaction volume of the primary electrons. This limitation can be overcome by using electron transparent samples as is demonstrated in this work.
Comparison of experimental BSE intensities with calculations is required for the quantification of material contrast. We apply here the electron diffusion model of Werner et al. [2] which considers single electron scattering and electron diffusion. To verify and adapt the diffusion model, the calculated results are compared with Monte‐Carlo (MC) simulations [3]. The limited detection angle range of the used annular semiconductor detector from 2.3 rad to 2.77 rad must be taken into account in the calculations. It is also important to take into account the threshold energy of the semiconductor detector, because BSE below 2 keV are not detected by our BSE detector. Hence, the calculation of the energy loss of the BSE is necessary and was accomplished on the basis of an expression for the electron energy dissipation given in [4]. The validity of our procedure for composition analysis is verified by analyzing a sample with known composition and geometry.

The investigated sample contains four In
x
Ga
1‐x
As layers of 25 nm thickness with In‐concentrations of x = 0.1, 0.2, 0.3 and 0.4 which are embedded in GaAs‐barrier layers with 35 nm thickness. Details on the growth and verification of the composition of the analyzed sample by alternative techniques are outlined by Volkenandt et al. [5]. Cross‐section samples with wedge‐shaped thickness profiles are prepared perpendicular to the layer system by focused‐ion‐beam (FIB) techniques. A FEI Quanta ESEM equipped with an annular BSE semiconductor detector is used for the measurements.

Fig. 1a shows a BSE cross‐section image of a wedge sample with the brighter In
x
Ga
1‐x
As layers separated by GaAs with lower intensity. A Pt‐layer was deposited prior to FIB milling to protect the sample. The thickness of the wedge sample is determined in a region with known composition (here GaAs). For this purpose, an intensity line scan along the wedge with increasing thickness is performed in the GaAs substrate (green arrow in Fig. 1a) at different primary electron energies (Fig. 1b). The thickness‐dependent BSE intensity is normalized with respect to intensity in the thickest part of the wedge, which corresponds in a good approximation to the bulk BSE intensity. By comparison with calculations of the thickness‐dependent backscattering‐coefficient ratio η(t)/η(bulk) (black lines) the offset thickness at the thin edge of the wedge and the local thickness along the line scan can be determined.

Subsequently a line scan perpendicular to the layer system (red arrow in Fig. 1a) is performed at a constant thickness of 200 nm. BSE intensity ratios of the In
x
Ga
1‐x
As quantum wells with respect to the GaAs barrier layers are shown in Fig. 2a. Lines with different colors denote calculations for
η(t)

InGaAs

/η(t)

GaAs

for different
E

0

and thicknesses of (200 ± 20) nm. The calculated intensity ratios agree well with the measurements. The accuracy of the technique improves for higher
E

0

values because the gradient of the intensity ratios increases. This allows to distinguish In‐concentration differences of 10%.

Fig. 2b shows
η(t)

InGaAs

/η(t)

GaAs

for 20 keV as a function of the sample thickness. Only a weak dependence on the local specimen thickness is observed between 50 and 250 nm giving the optimal range for composition quantifications. At lower thicknesses the BSE intensity is low, while at higher thicknesses the contrast blurs due to the electron beam broadening.

It is shown that contrast quantification of BSE images is possible with a high lateral resolution. The sample thickness and the material composition were determined within one single image. Quantifications are successfully performed by comparison of the experimental with calculated data from an analytical model.