18 Scanning Electron Microscopy

Dr. Ajit K. Mahapatro

epgp books

Learning Objectives

From this module students may get to know about the following

i. Surface morphology and topography

ii. Secondary and backscattered electrons

iii. Electron-beam interactions

 

1. Introduction to surface morphology and topography

Morphology is a qualitative evaluation of the three dimensional shape of a surface and topography provides the quantitative dimensions of the feature. Morphology captures the shape, texture, and distribution of materials at a surface and is best-evaluated using imaging techniques, such as optical microscopy or electron microscopy (EM). These methods can also provide layer thickness using optical profilometer or taking image in the transverse section of the specimen. However, estimation for the roughness, step heights, and feature size can be addressed using atomic force microscopy (AFM), stylus profilometry or optical profilometry. Few analytical imaging techniques are,

• High resolution optical microscopy

• Scanning electron microscope (SEM)

• Fie ld emission scanning electron microscopy (FE-SEM)

• Ultra high resolution-SEM (UHR-SEM)

• Focused ion beam – scanning electron microscopy (FIB-SEM)

• Scanning transmission e lectron microscopy (STEM)

• Transmission electron microscopy (TEM)

1.1 Electron Microscopy

Waves in electron beam can be coherent (waves of same wavelengths) or incoherent (waves of different wavelengths). The electron source in the microscope generates a beam of coherent electron waves, which when fall on the surface of the specimen, it interacts with the atoms of the specimen and can form beams consisting of either coherent or incoherent scattered electrons. Here, the electron beam generated from the thermionic electron gun passes through the electromagnetic lenses and directed towards the column of the microscope   and  falls   onto the sample surface. Any changes in the electromagnetic wave after interacting with the sample surface could affect the movement of the electrons. The positive charges of the atom are strongly concentrated at the nucleus, whereas the negatively charged electrons in the atoms are much more dispersed in the shell structure. Electrons entering a material interact as a negatively  charged  particle with  the  electric  field  near  the nucleus of the atoms in the specimen. These interactions can be classified into e lastic or inelastic interactions and are discussed briefly in the following sections.

Figure 1. Schematic diagram of the optical microscope, TEM, and SEM.

 

1.2 Optical and Electron Microscope

The schematic diagram with details of components for the optical and electron microscopies is shown in in Figure 1.

The salient features of the optical and electron microscopes are tabulated below

Generally, the objects with dimensions less than half the wavelength of the microscope’s illumination source can not be visible under the microscope. The optical microscopes use visible light (which has a minimum wavelength of 400 nm) and can not image the objects smaller than 200 nm (about the width of an average-sized bacterium). The wavelength of electron is thousands of times shorter than the visible light, enabling the electron microscopes to be able to resolve this issue and provide better magnification to image the objects at low dimensions. Hence, the electron microscopes can be used to visualize the inorganic, metallic , organic, and bio-molecular entities at atomic scale resolution.

 

2. Origin of Scattering Events

2.1 Introduction

Electron microscopy is a technique that offers unique possibilities to capture images at nanometer resolution for understanding the structure, topology, morphology, and composition of a materia l. The primary electrons after collision with atoms within the specimen impart energy to the specimen, resulting loss of energy (or change in momentum) of the primary beam electrons that generates equivalent amount of energy in other form. These various forms of energy phenomena produced during electron – specimen interaction have the potential to provide important information about the nature of the specimen. When an electron hits a material, different interactions can occur, as summarized in Figure 2.


Figure 2. Schematics for the electron-matter interactions arising from the impact of an electron beam onto a specimen surface.

 

The electron-specimen interactions can provide information on:

• Specimen composition

• Topography

• Crystallography

• Electrical Potential

• Local Magnetic Field

As an electron travels through the specimen interaction volume , it scatters, loses energy, and changes the direction with each atomic interaction. Scattering events can be divided into two general classes: Elastic scattering and Inelastic scattering.

 

2.2 Elastic scattering

When an electron beam approaches towards specimen, the electrons (of the beam) with various energies interact with the loca lized atoms (of the specimen), and during this process the electron trajectory changes and scatters. The process, in which the kinetic energy and velocity remain constant, is known as elastic scattering or electron backscattering (as shown in Figure 3). Here, there is no energy transfer takes place from the electron to the sample and the electron leaving the sample (with energy El) is having identica l initial energy E0, i.e., El  = E0.

Figure 3. Illustration for the elastic scattering.

A strong elastic scatterer very near to the nucleus may result the electrons leaving the specimen through backscattering and referred as the backscattered electrons (BSE). These electrons provide important information that is useful for the SEM imaging.

The probability of elastic scattering increases strongly with the square of the atomic number (Z2), since heavier atoms have much stronger positive charge at nucleus and decreases as square of the energy of the electron (1/E2).

If the electron passes through the sample without any interaction, no energy is transferred and travels in the same direction as the incident beam without deviation (Figure 4).

Figure 4. Scattering of an electron within the electron cloud in an atom.

 

2.3 Inelastic scattering

Inelastic scattering  is a process in which the energy  is transferred from incident electrons to sample, resulting a reduction in the electron energy after interaction,

EI  < E0

In inelastic scattering, the trajectory of the incident electron is only slightly perturbed, but energy is lost through interactions with the orbital electrons of the atoms in the specimen. The process is sketched in Figure 5).


Figure 5. Illustration for the inelastic scattering.

 

The inelastic interactions (Figure 5) produce diverse effects including:

• Secondary electrons

• Phonon excitation (heating)

• Cathodoluminescence (visible  light fluorescence)

• Continuum radiation (bremsstrahlung or “braking” radiation)

• Characteristic x-ray radiation

• Plasmon production (secondary electrons)

• Auger electron production (ejection of outer shell electrons)

The signals caused by inelastic electron-matter interactions are predominantly utilized in the methods of analytical electron microscopy.

 

2.4. Secondary Electrons

Several  mechanisms  of   inelastic  electron-matter  can  lead  to  the  ejection  of  secondary  electrons, abbreviated as SE:

  • Electrons located in the valence or conduction band (loosely bound outer electrons) need only the transfer of a small amount of energy to overcome the work function and to be ejected int o the vacuum. Typically they carry energies below 50 eV and are designated as slow SEs. These SEs are utilized     in    scanning    electron    microscopy    for     morphology    and    surface topography.
  • Electrons that are located in the inner shell are strongly bound and less readily ejected. This process leads to an ionization of the atom and subsequently to the generation of characteristic X-rays or Auger electrons, another kind of SE. These electrons from the inner shells can carry a relative ly large energy and are fast SEs.

Topographic information is obtained only from the SEs generated close to surface. Number of SEs is always larger than the number of incoming electrons. They are used to reveal the surface structure of a material and current technology could reach a resolution of ~1 nm or less.

Secondary Electron Coefficient: It is the ratio of the number of secondary electrons in the specimen (NSE) and number of beam electrons incident on the specimen (NB),

δ = NSE  / NB

When the escape depth of SE is small (a few nanometers), all the SEs created by the beam electrons at greater depths are lost.

For SEs, the intensity is not sensitive to atomic number, decreases as beam energy increases, increases with tilt, and decreases with angle. SEs are generated by using 3 different mechanisms (Figure 6).

SE(I): Produced by the interactions of electrons from the incident beam with specimen atoms. These SEs are produced in c lose proximity to the incident beam and thus represent a signal with high lateral resolution.

SE(II): Produced by interactions of the high energy BSE with specimen atoms. Both lateral and depth distribution characteristics of BSEs are found in the SE(II) sign a l and provides a comparatively low resolution signal.

SE(III): Produced by high energy BSE, which strike the pole pieces and other solid objects within the specimen chamber

 

Figure 6. Different mechanisms for generation of SE

 

2.4.1. Factors effecting SE emission

  • Work function of the surface.
  • Beam energy and beam current: The SE coefficient increases as the beam energy is lowered. The escape depth of SE is small (a few nanometers), so a ll of the SE created by the beam electrons at greater depths are lost.

Electron yield goes through a maximum at low accelerating voltage  and decreases with increasing accelerating voltage shown in Figure 7 below.

Figure 7. Electron yield with accelerating voltage

 

(c) Atomic number (Z)

• More SE(II) are created with increasing Z

• The Z-dependence is more pronounced at lower beam energies

(d) The effect of surface tilt for SE

In areas where the surface is tilted relative to the incident beam, the electrons, travel greater distances in the region close to the surface of the specimen. This indicates that as the angle (specimen tilt) increases, the secondary electron coefficient increases (escape depth).

 

Figure 8. Effect of tilt on SE

SE can escape from both the sides of ridges and edges. These effects cause tilted surfaces to appear brighter than flat surface.

 

2.5. Backscattered  Electrons

 

 

Figure 9. Backscattered electrons

Elastic scattering  of the electron beam produce backscattered and transmitted electrons as the strong electrical field of the specimen’s atomic nuclei deflects them, and no additional electrons are produced from the sample, where transmitted electrons completely passes through the material after interacting with it, backscattered electrons are ejected from the top surface of the specimen at high angles. Transmitted and backscattered electrons can have energies from  ~50  eV up to the accelerating  voltage (Eo). The number  of  backscattered electrons  produced  from a material may  be  quantified  by  its  backscattering coefficient, ηb.

ηb = NBSE / NB

NSE  = number of secondary electrons specimen

NB  = number of beam electrons incident on the specimen.

This coefficient depends strongly on a sample’s average atomic number, Z. BSE respond to composition allowing for atomic number or compositiona l contrast.

2.5.1. Factors effecting BSE emission

(a) BSE atomic number: The BSE coefficient increases with increasing atomic number.

(b) BSE beam energy: The BSE coefficient does not depend strongly on beam energy.

(c) BSE tilt: The BSE coefficient increases with tilt as the electrons can escape the surface with less total angular deviation (at very high angles, which correspond to grazing incidence, the value of NB  tends toward unity)


Figure 10. Effect of tilt on BSE

When the surface is normal (Figure 10a) to the inc ident beam, the BSE are distributed symmetrically around the inc ident beam in a manner described approximately by the cosine function.

N(ψ) ≈ Nn cos(ψ)

For small tilt angles (Figure 10b) the distribution of BSE remains roughly symmetrical l around the surface normal.

For large angles (Figure 10c) of surface tilt the distribution of BSE becomes asymmetrical with respect to the surface normal, developing a distinct lobe caused by a  predominance  of  forward scattering. These effects the contrast in images formed with BSE to show a strong dependence on surface topography, and on the location and characteristics of the BSE detector used.

(d) BSE angular distribution (as in Figure 11): is defined relative to the normal to the surface. It refers to the number of BSE escaping the surface at different angles (φ) relative to the norma l to the surface.

Figure 11. Effect of angular distribution on BSE

 

 

3. Electron Beam – Specimen Interaction

3.1. Interaction cross-section and mean free path

The probability of a scattering event could be determined by estimating the interaction cross-section (σ), or by the average distance of an electron trave ls between two interactions i.e. the mean free path λ . Each scattering event might be elastic or inelastic interaction. Hence, the total interaction cross section σT is the sum of all elastic and inelastic terms which can be estimated by,

σT = σ elast +  σ inelast

Each interaction of electrons with a material has certain cross section depends on the number of electron- atom scattering events. Considering a sample contains N number of atoms in a unit volume , a total scattering interaction cross section (QT) is given as,

QT = Nσ= N0σT þ/A

where, N0  is the Avogadro’s number; A is the atomic mass of the atom of density ρ.

The interaction cross-section with the sample thickness (t) is expressed as, QTt = N0σTρt / A, and gives the likelihood of a scattering event. The term ‘ρt’ is designated as mass-thickness. Doubling the va lue of ‘ρ’ leads to the same QT value, as observed after doubling the ‘t’ value. The mean free path is related to the scattering cross section by:

λmfp  = 1 / QT

For the probability P of scattering in a specimen of thickness t follows then:

P = t / λ= QTt

 

 

3.2. Differential cross section

Figure 12. Annular distribution of the electrons scattered after passing through a thin sample. The scattering semi-angle Θ with incremental changes of dΘ, and the solid angle Ω for their collection (and incremental changes dΩ) are used to describe this process quantitatively.

The angular distribution of electrons scattered by an atom during the electron-specimen interaction is described by the differential cross section, dσ/dΩ. Electrons are scattered by an angle (σ) and collected within a solid angle Ω (Figure 12). The cross-section (σ) decreases with increasing Θ.  Here,  the scattering into high angles is rather unlikely.

 

3.3. Interaction Volume

 

The combined effect of the elastic and inelastic interactions is to limit the penetration of the  beam into the solid. The  region of interaction between the solid and the beam is known  as  the interaction volume. Scattering in high angles or  even  backwards is unlikely in all materials but the likelihood for them increases with increasing Z.

Figure 13: Interaction of an electron beam with (a) low Z and (b) high Z materials. Most electrons are scattered  forward in the same direction undeviatedly. Beam broadening and the likelihood of large angle scattering events or backward scattering increases for higher Z.

Also, the beam broadening increases with Z (Figure 13). The intensity of the direct beam is weakened by the deflection of electrons out of the forward direction. Since the amount of deflected electrons and the weakening of the beam intensity depend strongly on Z. Different materials produces difference in the color contrast during imaging.If compact samples are considered (Figure 14), most electrons of the incoming electron beam are finally absorbed in the specimen resulting an interaction volume that has a pear-like shape. Few electrons interact in elastically and losing a part of their energy, on their traveling path through the sample. Although the probability of such events is quite small, the thicker samples produce moderate probable events, i.e. if the path of the electron through the sample is long. The smaller the energy of the electron, higher the likelihood of  its absorption in the sample  becomes. However, some of the incoming electrons are even back-scattered. The dependence of the shape of the interaction volume on the material and the voltage is schematically demonstrated in Figure 14. The size of the interaction volume and the penetration depth of  the  electrons  increase  with  increasing  electron energy  (voltage),  and  decrease  with  increasing  the  atomic  number  of  the  material  (high  scattering potential).

Figure 14: Interaction volumes for the incident electron beam (blue) in compact samples (grey) depending on the electron energy and atomic number, Z. The trajectories of few electrons are mark ed with yellow-lines and the directions are indicated as arrows.

For example, although secondary and Auger electrons are produced throughout the  interaction volume, they have very low energies and can only escape from a thin layer near the sample’s surface.

 

3.3.1. Volume of Excitation

The size and shape of the interaction volume is limited by two factors:

(1) energy loss through inelastic interactions

(2) electron loss or backscattering through elastic interactions.

The depth of penetration (x) for electron beam and the interaction volume of sample with which it interacts are function of the angle of incidence,  magnitude of current, the accelerating voltage, and average atomic number (Z) of the sample.

Generally, the values of ‘x’ ranges from 1-5 µm with the beam incidenting perpendicular to the sample. The depth of electron penetration (x) is approximately,

x (µm) = 0.1 Eo1.5 / ρ

where, Eo is the accelerating voltage (in keV) and ρ is the density (in g/cm3). The width of the excited volume (y) can be approximated by,

y (µm) = 0.077 Eo1.5 / ρ

 

 

3.3.2. Factors influencing the interaction volume

 

(a) Influence of beam energy on the interaction volume:

(i) As the beam energy is increased, the electron beam can penetrate to greater depths.

(ii) There is no significant change in the shape of the interaction volume with beam energy

 

(b) Influence of atomic number of the solid in the interaction volume:

(i) In specimens of high atomic number the electrons undergo more elastic scattering per unit distance and the average scattering angle is greater.

(ii) In the high atomic number materials, the electron trajectory tends to deviate from the initial direction of travel more quickly.

(iii) The shape of the interaction volume is greatly affected by the atomic number of the specimen.

(c) Influence of the tilt on the interaction volume:

As the angle of tilt of the specimen surface increases, the interaction volume becomes smaller and asymmetric.

 

SUMMARY

  • Electrons from a source interact with atoms in the specimen yielding variety of photons and electrons via elastic and inelastic scattering processes. These are the signals used for imaging and characterizing the composition of materials.
  • The primary electron after hitting an electron or a nucleus of the specimen continues in a new trajectory, and the process is known as scattering.
  • Electron beam and specimen interaction imparts various forms of energy phenomena, which can provide some interesting information about the specimen including topography and composition and many more.
  • Secondary electrons (low energy electrons, ~ 10 – 50 eV) are generated from the collision between the incoming electrons and the loosely bonded outer electrons (inelastic scattering), and can provide topographic information of the specimen. Factors like work function, atomic number, beam energy, beam current, and surface tilt can affect the SE emission.
  • BSE are high energy electrons produced during elastic scattering and can be affected by the factors like, beam energy, tilt and atomic number of the specimen.
  • Interaction volume increases with increasing acceleration voltage and decreases with increasing the atomic number.
you can view video on Scanning Electron Microscopy

 

References

  • Properties of Electrons, their Interactions with Matter and Applications in Electron Microscopy, Frank Krumeich Laboratory of Inorganic Chemistry, ETH Zurich, Vladimir-Prelog-Weg1, 8093 Zurich, Switzerland.
  • Practical Scanning Electron Microscopy,J.I.Goldstein, pp 49-94,Springer US.
  • Goodhew and Humphreys., Electron Microscopy and Analysis, 2nd edition., Taylor & Francis, 1998.
  • Fundamentals of Scanning Electron Microscopy (SEM), pp 1-40, Weilie Zhou, Robert Apkarian, Zhong Lin Wang, David Joy, Springer New York.