Backscattered electrons (BSEs) are generated by elastic scattering events. When the electrons in the primary beam travel close to the atom’s nuclei in the specimen, their trajectory is deviated due to the force they feel with the positive charges in the nuclei. Depending on the size of the atom nuclei, the number of backscattered electrons differs. This is the basic principle of BSE image contrast. In this blog we introduce the backscattering coefficient and explain how it is influenced by the inclination of the sample and the primary beam energy.

### The backscattering coefficient

Backscattered electrons are generated by elastic scattering events of the incident electrons in the primary beam and have energy higher than 50eV. The number of backscattered electrons generated depends on many factors, including the atomic number of the material in the specimen and the acceleration voltage of the primary beam.

The number of backscattered electrons generated from the beam-to-sample interaction is described by a coefficient called backscattering coefficient η and is defined as the ratio between the backscattered current IBSE and the probe current IP.

Where EB is the exit energy of the backscattered electrons. The backscattering coefficient is influenced by the beam acceleration voltage and the atomic number Z, as well as the angle between the sample surface and the incident beam.

### The effect of the tilting angle of the sample

The backscattering coefficient depends on the angle between the incident beam and the sample surface according to the following equation:

Polar diagram of the angular distribution of the backscattering coefficient, at normal incidence and at 60° and 80° for different elements (Au, Ag, Cu, Al and Be). Reference: Scanning Electron Microscopy, Physics of Image Formation and Microanalysis, L. Reimer, Springer edition, 1998.

In the schematics, the backscattering coefficient in polar coordinates is shown for different elements (in other words, the amount of emitted backscattered electrons for different atomic numbers) together with the SEM geometry, consisting of the pole piece, the BSE detector and the sample.

When the sample surface is perpendicular to the beam, the BSE emission is rotationally symmetric, as shown below on the left. When the sample is tilted, the BSE emission is not symmetric anymore, meaning that, in this case, the signal picked up by the right side of the BSD is less than the signal picked up by the left quadrant.

Schematics of the SEM, consisting of a sample, the BSE detector and the pole piece, together with the angular distribution of the backscattering coefficients of Au, Ag, Cu and Be in polar coordinates for a zero-tilted sample and a tilted sample.

When the sample is inclined, the backscattering coefficient increases, as shown here. In this graph, the backscattering coefficient is measured with Monte Carlo simulations for different elements (C, Al, Cu, Ag and Au), at different tilt angles. The coefficient for different elements not only increases with increasing inclination, but also converges.

To demonstrate this effect, we imaged with the BSE detector the EDX calibration sample, where three areas made of different materials can be seen: cupper, carbon and aluminum. The images below show the SEM micrographs of this sample taken at 0° tilting angle and at 45° tilting angle. The histogram of the two images is then extrapolated and shown below. The histogram has three peaks related to the composition of the sample. The peaks on the left of the graph are that of the carbon, the darker area in the SEM images, while the peaks on the right are that of cupper, that appears brighter in the BSE image. Most importantly, the three peaks become closer when the tilting angle increases, as predicted.

SEM images of the EDX calibration sample at 0° tilting angle (a) and at 45° tilting angle (b) and histogram of the two images (c), where the three peaks (carbon, aluminum and cupper) are visible.
The backscattering coefficient measured with Monte Carlo simulations for different elements (C, Al, Cu, Ag and Au) for different surface inclination, or tilting angles. Reference: Scanning Electron Microscopy and X-Ray Microanalysis, J.I. Goldstein, D.E. Newbury, J.R. Michael, N.W.M. Ritchie, J.H.J. Scott, D.C. Joy.

### The effect of the primary beam energy

The backscattering coefficient is also influenced by the acceleration voltage, as shown in Figure 5. The backscattered coefficient depends on the primary beam energy. This means that the amount of BSE emitted for the same beam current at different primary beam energy will vary.

For lower acceleration voltages, the backscatter coefficient of light elements increases, while the backscatter coefficient of heavy elements decreases. For beam energies higher than 10kV the backscatter coefficient is approximately constant for all elements.

However, in real life, the BSE detector also partly collects SE signals as well. So, if the beam energy increases, the edge effects and the topography information given by the SEs also increases.

Backscattering coefficient as a function of the electron energy from 1kV to 30kV for different elements. Reference: Scanning Electron Microscopy, Physics of Image Formation and Microanalysis, L. Reimer, Springer edition, 1998.

When the energy of the primary beam increases, the penetration depth also increases. So thin film layers on the sample surface will appear in BSE images only when using a primary beam with low acceleration voltage.

The images below show BSE images acquired of a tin ball sample and a flat surface with dirt on it using beam acceleration voltages of 5kV and 15kV. The dirt flakes, on both samples, are mainly made of carbon and appear dark in the low acceleration voltage images.

Since the flakes are very shallow, the beam fully penetrates them when a high acceleration voltage is used, reaching the underlying sample that is then revealed in the images. Hence, at 15kV, the shallow, dirty flakes become more transparent.

BSE images of the tin ball sample taken with 5kV and 15kV beam acceleration voltages.
BSE images of a dirty surface sample taken with 5kV and 15kV beam acceleration voltages.

### More on SEM

In this detailed description, we described how to improve the quality of BSE images when using an SEM. Has this made you curious about the technology behind scanning electron microscopy? And do you want to find out how you can select the right microscope for your research? Then it’s good to know that we have a comprehensive e-guide on How to Choose an SEM available for you.

The e-guide details the working principle of an SEM and enables you to gain a deeper understanding of the microscopy technique that produces high-quality images faster and easier. It helps you to choose the SEM that is most suitable for your research.