{"id":350,"date":"2018-12-11T12:32:55","date_gmt":"2018-12-11T12:32:55","guid":{"rendered":"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=350"},"modified":"2018-12-12T05:35:31","modified_gmt":"2018-12-12T05:35:31","slug":"scanning-electron-microscopy","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/msp11\/chapter\/scanning-electron-microscopy\/","title":{"rendered":"Scanning Electron Microscopy"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/6DlDq8nce0Q\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>Learning Objectives<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>From this module students may get to know about the following<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><em><strong>i.<\/strong> Surface morphology and topography<\/em><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><em><strong>ii.<\/strong> Secondary and backscattered electrons<\/em><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><em><strong>iii.<\/strong> Electron-beam interactions<\/em><\/p>\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>1. Introduction to surface morphology and topography<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">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,<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 High resolution optical microscopy<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Scanning electron microscope (SEM)<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Fie ld emission scanning electron microscopy (FE-SEM)<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Ultra high resolution-SEM (UHR-SEM)<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Focused ion beam \u2013 scanning electron microscopy (FIB-SEM)<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Scanning transmission e lectron microscopy (STEM)<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Transmission electron microscopy (TEM)<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>1.1 Electron Microscopy<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">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\u00a0 \u00a0and\u00a0 falls\u00a0 \u00a0onto 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\u00a0 charged\u00a0 particle with\u00a0 the\u00a0 electric\u00a0 field\u00a0 near\u00a0 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.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><img class=\"aligncenter size-full wp-image-351\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/01-18.png\" alt=\"\" width=\"936\" height=\"674\" \/><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong> Figure 1.<\/strong><em> Schematic diagram of the optical microscope, TEM, and SEM.<\/em><\/p>\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>1.2 Optical and Electron Microscope<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">The schematic diagram with details of components for the optical and electron microscopies is shown in in Figure 1.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: center\"><strong>The salient features of the optical and electron microscopes are tabulated below<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><img class=\"aligncenter wp-image-352\" style=\"text-align: start;text-indent: 16px\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/02-16.png\" alt=\"\" width=\"791\" height=\"382\" \/>Generally, the objects with dimensions less than half the wavelength of the microscope\u2019s 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.<\/p>\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>2. Origin of Scattering Events<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>2.1 Introduction<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">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.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><img class=\"aligncenter size-full wp-image-353\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/03-14.png\" alt=\"\" width=\"848\" height=\"711\" \/>\r\n<strong>Figure 2. <\/strong><em>Schematics for the electron-matter interactions arising from the impact of an electron beam onto a specimen surface.<\/em><\/p>\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\">The electron-specimen interactions can provide information on:<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Specimen composition<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Topography<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Crystallography<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Electrical Potential<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Local Magnetic Field<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">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.<\/p>\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><em><strong>2.2 Elastic scattering<\/strong><\/em><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">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\u00a0the electron to the sample and the electron leaving the sample (with energy El) is having identica l initial energy E<sub>0,<\/sub> i.e., E<sub>l<\/sub>\u00a0 = E<sub>0<\/sub>.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><img class=\"aligncenter size-full wp-image-354\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/04-16.png\" alt=\"\" width=\"722\" height=\"407\" \/><strong>Figure 3. <\/strong><em>Illustration for the elastic scattering.<\/em><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">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.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">The probability of elastic scattering increases strongly with the square of the atomic number (Z<sup>2<\/sup>), since heavier atoms have much stronger positive charge at nucleus and decreases as square of the energy of the electron (1\/E<sup>2<\/sup>).<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">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).<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><img class=\"aligncenter size-full wp-image-355\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/05-13.png\" alt=\"\" width=\"415\" height=\"524\" \/><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>Figure 4.<\/strong> <em>Scattering of an electron within the electron cloud in an atom.<\/em><\/p>\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>2.3 Inelastic scattering<\/strong><\/p>\r\n<p class=\"no-indent\">Inelastic scattering\u00a0 is a process in which the energy\u00a0 is transferred from incident electrons to sample, resulting a reduction in the electron energy after interaction,<\/p>\r\n<p class=\"no-indent\" style=\"text-align: center\"><strong>EI\u00a0 &lt; E0<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">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).<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><img class=\"aligncenter wp-image-356\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/06-11.png\" alt=\"\" width=\"845\" height=\"292\" \/>\r\n<strong>Figure 5.<\/strong> <em>Illustration for the inelastic scattering.<\/em><\/p>\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\">The inelastic interactions (Figure 5) produce diverse effects including:<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Secondary electrons<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Phonon excitation (heating)<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Cathodoluminescence (visible\u00a0 light fluorescence)<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Continuum radiation (bremsstrahlung or \u201cbraking\u201d radiation)<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Characteristic x-ray radiation<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Plasmon production (secondary electrons)<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Auger electron production (ejection of outer shell electrons)<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">The signals caused by inelastic electron-matter interactions are predominantly utilized in the methods of analytical electron microscopy.<\/p>\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>2.4. Secondary Electrons<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">Several\u00a0 mechanisms\u00a0 of\u00a0 \u00a0inelastic\u00a0 electron-matter\u00a0 can\u00a0 lead\u00a0 to\u00a0 the\u00a0 ejection\u00a0 of\u00a0 secondary\u00a0 electrons, abbreviated as SE:<\/p>\r\n\r\n<ul>\r\n \t<li class=\"no-indent\" style=\"text-align: justify\">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\u00a0 \u00a0 \u00a0in\u00a0 \u00a0 scanning\u00a0 \u00a0 electron\u00a0 \u00a0 microscopy\u00a0 \u00a0 for\u00a0 \u00a0 \u00a0morphology\u00a0 \u00a0 and\u00a0 \u00a0 surface topography.<\/li>\r\n \t<li class=\"no-indent\" style=\"text-align: justify\">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.<\/li>\r\n<\/ul>\r\n<p class=\"no-indent\" style=\"text-align: justify\">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.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">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),<\/p>\r\n<p class=\"no-indent\" style=\"text-align: center\"><strong>\u03b4 = N<sub>SE<\/sub>\u00a0 \/ N<sub>B<\/sub><\/strong><\/p>\r\n<p class=\"no-indent\">When the escape depth of SE is small (a few nanometers), all the SEs created by the beam electrons at greater depths are lost.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">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).<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>SE(I):<\/strong> 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.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>SE(II):<\/strong> 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.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>SE(III):<\/strong> Produced by high energy BSE, which strike the pole pieces and other solid objects within the specimen chamber<\/p>\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-357\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/07-9.png\" alt=\"\" width=\"514\" height=\"545\" \/>\r\n<p class=\"no-indent\"><strong>Figure 6.<\/strong> <em>Different mechanisms for generation of SE<\/em><\/p>\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>2.4.1. Factors effecting SE emission<\/strong><\/p>\r\n\r\n<ul>\r\n \t<li class=\"no-indent\" style=\"text-align: justify\">Work function of the surface.<\/li>\r\n \t<li class=\"no-indent\" style=\"text-align: justify\">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.<\/li>\r\n<\/ul>\r\n<p class=\"no-indent\" style=\"text-align: justify\">Electron yield goes through a maximum at low accelerating voltage\u00a0 and decreases with increasing accelerating voltage shown in Figure 7 below.<\/p>\r\n<img class=\"aligncenter size-full wp-image-358\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/08-6.png\" alt=\"\" width=\"881\" height=\"505\" \/><strong>Figure 7<\/strong>. <em>Electron yield with accelerating voltage<\/em>\r\n\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\">(c) Atomic number (Z)<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 More SE(II) are created with increasing Z<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 The Z-dependence is more pronounced at lower beam energies<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">(d) The effect of surface tilt for SE<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">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).<\/p>\r\n<img class=\"aligncenter size-full wp-image-360\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/09-4.png\" alt=\"\" width=\"623\" height=\"378\" \/>\r\n\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>Figure 8<\/strong>. <em>Effect of tilt on SE<\/em><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">SE can escape from both the sides of ridges and edges. These effects cause tilted surfaces to appear brighter than flat surface.<\/p>\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>2.5. Backscattered\u00a0 Electrons<\/strong><\/p>\r\n<img class=\"aligncenter size-full wp-image-359\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/10-3.png\" alt=\"\" width=\"608\" height=\"353\" \/>\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>Figure 9.<\/strong><em> Backscattered electrons<\/em><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">Elastic scattering\u00a0 of the electron beam produce backscattered and transmitted electrons as the strong electrical field of the specimen\u2019s 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\u00a0 ~50\u00a0 eV up to the accelerating\u00a0 voltage (Eo). The number\u00a0 of\u00a0 backscattered electrons\u00a0 produced\u00a0 from a material may\u00a0 be\u00a0 quantified\u00a0 by\u00a0 its\u00a0 backscattering coefficient, \u03b7b.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>\u03b7b = N<sub>BSE<\/sub> \/ N<sub>B <\/sub><\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">N<sub>SE<\/sub>\u00a0 = number of secondary electrons specimen<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">N<sub>B\u00a0<\/sub> = number of beam electrons incident on the specimen.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">This coefficient depends strongly on a sample's average atomic number, Z. BSE respond to composition allowing for atomic number or compositiona l contrast.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>2.5.1. Factors effecting BSE emission<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>(a) BSE atomic number:<\/strong> The BSE coefficient increases with increasing atomic number.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>(b) BSE beam energy:<\/strong> The BSE coefficient does not depend strongly on beam energy.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>(c) BSE tilt:<\/strong> 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\u00a0 tends toward unity)<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><img class=\"aligncenter size-full wp-image-361\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/11-2.png\" alt=\"\" width=\"804\" height=\"328\" \/>\r\n<strong>Figure 10.<\/strong> <em>Effect of tilt on BSE<\/em><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">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.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>N(\u03c8) \u2248 N<sub>n<\/sub> cos(\u03c8)<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">For small tilt angles (Figure 10b) the distribution of BSE remains roughly symmetrical l around the surface normal.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">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\u00a0 predominance\u00a0 of\u00a0 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.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">(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 (\u03c6) relative to the norma l to the surface.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><img class=\"aligncenter size-full wp-image-362\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/12-2.png\" alt=\"\" width=\"668\" height=\"435\" \/><strong>Figure 11<\/strong>. <em>Effect of angular distribution on BSE<\/em><\/p>\r\n&nbsp;\r\n\r\n<img class=\"aligncenter wp-image-363\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/13-2.png\" alt=\"\" width=\"966\" height=\"332\" \/>\r\n\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>3. Electron Beam \u2013 Specimen Interaction<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>3.1. <em>Interaction cross-section and mean free path<\/em><\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">The probability of a scattering event could be determined by estimating the interaction cross-section (<strong>\u03c3<\/strong>), or by the average distance of an electron trave ls between two interactions i.e. the mean free path \u03bb . Each scattering event might be elastic or inelastic interaction. Hence, the total interaction cross section <strong>\u03c3<sub>T\u00a0<\/sub><\/strong>is the sum of all elastic and inelastic terms which can be estimated by,<\/p>\r\n<p class=\"no-indent\" style=\"text-align: center\"><strong>\u03c3<sub>T\u00a0<\/sub>=\u00a0\u03c3\u00a0<sub>elast +\u00a0\u00a0<\/sub>\u03c3\u00a0<sub>inelast<\/sub><\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">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 (Q<sub>T<\/sub>) is given as,<\/p>\r\n<p class=\"no-indent\" style=\"text-align: center\"><strong>Q<sub>T<\/sub> = N\u03c3= N0\u03c3T \u00fe\/A<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">where, N<sub>0<\/sub>\u00a0 is the Avogadro\u2019s number; A is the atomic mass of the atom of density <strong>\u03c1.<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">The interaction cross-section with the sample thickness (t) is expressed as, <strong>Q<sub>T<\/sub>t = N<sub>0<\/sub>\u03c3T\u03c1t \/ A,<\/strong> and gives the likelihood of a scattering event. The term \u2018<strong>\u03c1t<\/strong>\u2019 is designated as mass-thickness. Doubling the va lue of \u2018\u03c1\u2019 leads to the same QT value, as observed after doubling the \u2018t\u2019 value. The mean free path is related to the scattering cross section by:<\/p>\r\n<p class=\"no-indent\" style=\"text-align: center\"><strong>\u03bb<sub>mfp\u00a0<\/sub> = 1 \/ QT<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">For the probability P of scattering in a specimen of thickness t follows then:<\/p>\r\n<p class=\"no-indent\" style=\"text-align: center\"><strong>P = t \/ \u03bb= Q<sub>T<\/sub>t<\/strong><\/p>\r\n&nbsp;\r\n\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>3.2. Differential cross section<\/strong><\/p>\r\n<img class=\"aligncenter size-full wp-image-367\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/14-1.png\" alt=\"\" width=\"417\" height=\"413\" \/>\r\n\r\n<strong>Figure 12.<\/strong> <em>Annular distribution of the electrons scattered after passing through a thin sample. The scattering semi-angle \u0398 with incremental changes of d\u0398, and the solid angle \u03a9 for their collection (and incremental changes d\u03a9) are used to describe this process quantitatively.<\/em>\r\n<p class=\"no-indent\" style=\"text-align: justify\">The angular distribution of electrons scattered by an atom during the electron-specimen interaction is described by the differential cross section, d<strong>\u03c3<\/strong>\/d<em>\u03a9<\/em>. Electrons are scattered by an angle (<strong>\u03c3<\/strong>) and collected within a solid angle \u03a9 (Figure 12). The cross-section (<strong>\u03c3<\/strong>) decreases with increasing \u0398.\u00a0 Here,\u00a0 the scattering into high angles is rather unlikely.<\/p>\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>3.3. Interaction Volume<\/strong><\/p>\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><span class=\"tight\" style=\"text-align: justify\">The combined effect of the elastic and inelastic interactions is to limit the penetration of the\u00a0 beam into the solid. The\u00a0 region of interaction between the solid and the beam is known\u00a0 as\u00a0 the interaction\u00a0<\/span><span class=\"tight\">volume. Scattering in high angles or\u00a0 even\u00a0 backwards is unlikely in all materials but the likelihood for them increases with increasing Z.<\/span><\/p>\r\n<img class=\"aligncenter size-large wp-image-368\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/15-1-1024x414.png\" alt=\"\" width=\"1024\" height=\"414\" \/><span class=\"tight\"><strong>Figure 13:<\/strong> <em>Interaction of an electron beam with (a) low Z and (b) high Z materials. Most electrons are scattered\u00a0 forward in the same direction undeviatedly. Beam broadening and the likelihood of large angle scattering events or backward scattering increases for higher Z.<\/em><\/span>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><span class=\"tight\">Also, the beam broadening increases with Z (Figure 13). The intensity of the direct beam is weakened by\u00a0<\/span><span class=\"tight\">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.<\/span><span class=\"tight\">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\u00a0 its absorption in the sample\u00a0 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\u00a0 the\u00a0 electrons\u00a0 increase\u00a0 with\u00a0 increasing\u00a0 electron\u00a0energy\u00a0 (voltage),\u00a0 and\u00a0 decrease\u00a0 with\u00a0 increasing\u00a0 the\u00a0 atomic\u00a0 number\u00a0 of\u00a0 the\u00a0 material\u00a0 (high\u00a0 scattering potential).<\/span><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><span class=\"tight\"><img class=\"aligncenter size-full wp-image-369\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/16-1.png\" alt=\"\" width=\"624\" height=\"623\" \/><\/span><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>Figure 14:<\/strong> <em>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.<\/em><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">For example, although secondary and Auger electrons are produced throughout the\u00a0 interaction volume, they have very low energies and can only escape from a thin layer near the sample's surface.<\/p>\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><em><strong>3.3.1. Volume of Excitation<\/strong><\/em><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">The size and shape of the interaction volume is limited by two factors:<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">(1) energy loss through inelastic interactions<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">(2) electron loss or backscattering through elastic interactions.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">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,\u00a0 magnitude of current, the accelerating voltage, and average atomic number (Z) of the sample.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">Generally, the values of \u2018x\u2019 ranges from 1-5 \u00b5m with the beam incidenting perpendicular to the sample. The depth of electron penetration (x) is approximately,<\/p>\r\n<p class=\"no-indent\" style=\"text-align: center\"><strong>x (\u00b5m) = 0.1 Eo<sup>1.5<\/sup> \/ \u03c1<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">where, Eo is the accelerating voltage (in keV) and \u03c1 is the density (in g\/cm3). The width of the excited volume (y) can be approximated by,<\/p>\r\n<p class=\"no-indent\" style=\"text-align: center\"><strong>y (\u00b5m) = 0.077 Eo<sup>1.5<\/sup> \/ \u03c1<\/strong><\/p>\r\n&nbsp;\r\n\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><em><strong>3.3.2. Factors influencing the interaction volume<\/strong><\/em><\/p>\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>(a) Influence of beam energy on the interaction volume:<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">(i) As the beam energy is increased, the electron beam can penetrate to greater depths.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">(ii) There is no significant change in the shape of the interaction volume with beam energy<\/p>\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>(b) Influence of atomic number of the solid in the interaction volume:<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">(i) In specimens of high atomic number the electrons undergo more elastic scattering per unit distance and the average scattering angle is greater.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">(ii) In the high atomic number materials, the electron trajectory tends to deviate from the initial direction of travel more quickly.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">(iii) The shape of the interaction volume is greatly affected by the atomic number of the specimen.<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>(c) Influence of the tilt on the interaction volume:<\/strong><\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify\">As the angle of tilt of the specimen surface increases, the interaction volume becomes smaller and asymmetric.<\/p>\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>SUMMARY<\/strong><\/p>\r\n\r\n<ul>\r\n \t<li class=\"no-indent\" style=\"text-align: justify\">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.<\/li>\r\n \t<li class=\"no-indent\" style=\"text-align: justify\">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.<\/li>\r\n \t<li class=\"no-indent\" style=\"text-align: justify\">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.<\/li>\r\n \t<li class=\"no-indent\" style=\"text-align: justify\">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.<\/li>\r\n \t<li class=\"no-indent\" style=\"text-align: justify\">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.<\/li>\r\n \t<li class=\"no-indent\" style=\"text-align: justify\">Interaction volume increases with increasing acceleration voltage and decreases with increasing the atomic number.<\/li>\r\n<\/ul>\r\n\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Scanning Electron Microscopy<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/6DlDq8nce0Q\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n&nbsp;\r\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>References<\/strong><\/p>\r\n\r\n<ul>\r\n \t<li class=\"no-indent\" style=\"text-align: justify\">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.<\/li>\r\n \t<li class=\"no-indent\" style=\"text-align: justify\">Practical Scanning Electron Microscopy,J.I.Goldstein, pp 49-94,Springer US.<\/li>\r\n \t<li class=\"no-indent\" style=\"text-align: justify\">Goodhew and Humphreys., Electron Microscopy and Analysis, 2nd edition., Taylor &amp; Francis, 1998.<\/li>\r\n \t<li class=\"no-indent\" style=\"text-align: justify\">Fundamentals of Scanning Electron Microscopy (SEM), pp 1-40, Weilie Zhou, Robert Apkarian, Zhong Lin Wang, David Joy, Springer New York.<\/li>\r\n<\/ul>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/6DlDq8nce0Q\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>Learning Objectives<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>From this module students may get to know about the following<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><em><strong>i.<\/strong> Surface morphology and topography<\/em><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><em><strong>ii.<\/strong> Secondary and backscattered electrons<\/em><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><em><strong>iii.<\/strong> Electron-beam interactions<\/em><\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>1. Introduction to surface morphology and topography<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">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,<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 High resolution optical microscopy<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Scanning electron microscope (SEM)<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Fie ld emission scanning electron microscopy (FE-SEM)<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Ultra high resolution-SEM (UHR-SEM)<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Focused ion beam \u2013 scanning electron microscopy (FIB-SEM)<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Scanning transmission e lectron microscopy (STEM)<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Transmission electron microscopy (TEM)<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>1.1 Electron Microscopy<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">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\u00a0 \u00a0and\u00a0 falls\u00a0 \u00a0onto 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\u00a0 charged\u00a0 particle with\u00a0 the\u00a0 electric\u00a0 field\u00a0 near\u00a0 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.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-351\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/01-18.png\" alt=\"\" width=\"936\" height=\"674\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/01-18.png 936w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/01-18-300x216.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/01-18-768x553.png 768w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/01-18-65x47.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/01-18-225x162.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/01-18-350x252.png 350w\" sizes=\"auto, (max-width: 936px) 100vw, 936px\" \/><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong> Figure 1.<\/strong><em> Schematic diagram of the optical microscope, TEM, and SEM.<\/em><\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>1.2 Optical and Electron Microscope<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">The schematic diagram with details of components for the optical and electron microscopies is shown in in Figure 1.<\/p>\n<p class=\"no-indent\" style=\"text-align: center\"><strong>The salient features of the optical and electron microscopes are tabulated below<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-352\" style=\"text-align: start;text-indent: 16px\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/02-16.png\" alt=\"\" width=\"791\" height=\"382\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/02-16.png 764w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/02-16-300x145.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/02-16-65x31.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/02-16-225x109.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/02-16-350x169.png 350w\" sizes=\"auto, (max-width: 791px) 100vw, 791px\" \/>Generally, the objects with dimensions less than half the wavelength of the microscope\u2019s 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.<\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>2. Origin of Scattering Events<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>2.1 Introduction<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">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 &#8211; 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.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-353\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/03-14.png\" alt=\"\" width=\"848\" height=\"711\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/03-14.png 848w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/03-14-300x252.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/03-14-768x644.png 768w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/03-14-65x54.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/03-14-225x189.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/03-14-350x293.png 350w\" sizes=\"auto, (max-width: 848px) 100vw, 848px\" \/><br \/>\n<strong>Figure 2. <\/strong><em>Schematics for the electron-matter interactions arising from the impact of an electron beam onto a specimen surface.<\/em><\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">The electron-specimen interactions can provide information on:<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Specimen composition<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Topography<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Crystallography<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Electrical Potential<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Local Magnetic Field<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">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.<\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><em><strong>2.2 Elastic scattering<\/strong><\/em><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">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\u00a0the electron to the sample and the electron leaving the sample (with energy El) is having identica l initial energy E<sub>0,<\/sub> i.e., E<sub>l<\/sub>\u00a0 = E<sub>0<\/sub>.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-354\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/04-16.png\" alt=\"\" width=\"722\" height=\"407\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/04-16.png 722w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/04-16-300x169.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/04-16-65x37.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/04-16-225x127.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/04-16-350x197.png 350w\" sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><strong>Figure 3. <\/strong><em>Illustration for the elastic scattering.<\/em><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">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.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">The probability of elastic scattering increases strongly with the square of the atomic number (Z<sup>2<\/sup>), since heavier atoms have much stronger positive charge at nucleus and decreases as square of the energy of the electron (1\/E<sup>2<\/sup>).<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">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).<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-355\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/05-13.png\" alt=\"\" width=\"415\" height=\"524\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/05-13.png 415w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/05-13-238x300.png 238w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/05-13-65x82.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/05-13-225x284.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/05-13-350x442.png 350w\" sizes=\"auto, (max-width: 415px) 100vw, 415px\" \/><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>Figure 4.<\/strong> <em>Scattering of an electron within the electron cloud in an atom.<\/em><\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>2.3 Inelastic scattering<\/strong><\/p>\n<p class=\"no-indent\">Inelastic scattering\u00a0 is a process in which the energy\u00a0 is transferred from incident electrons to sample, resulting a reduction in the electron energy after interaction,<\/p>\n<p class=\"no-indent\" style=\"text-align: center\"><strong>EI\u00a0 &lt; E0<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">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).<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-356\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/06-11.png\" alt=\"\" width=\"845\" height=\"292\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/06-11.png 828w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/06-11-300x104.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/06-11-768x265.png 768w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/06-11-65x22.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/06-11-225x78.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/06-11-350x121.png 350w\" sizes=\"auto, (max-width: 845px) 100vw, 845px\" \/><br \/>\n<strong>Figure 5.<\/strong> <em>Illustration for the inelastic scattering.<\/em><\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">The inelastic interactions (Figure 5) produce diverse effects including:<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Secondary electrons<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Phonon excitation (heating)<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Cathodoluminescence (visible\u00a0 light fluorescence)<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Continuum radiation (bremsstrahlung or \u201cbraking\u201d radiation)<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Characteristic x-ray radiation<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Plasmon production (secondary electrons)<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 Auger electron production (ejection of outer shell electrons)<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">The signals caused by inelastic electron-matter interactions are predominantly utilized in the methods of analytical electron microscopy.<\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>2.4. Secondary Electrons<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">Several\u00a0 mechanisms\u00a0 of\u00a0 \u00a0inelastic\u00a0 electron-matter\u00a0 can\u00a0 lead\u00a0 to\u00a0 the\u00a0 ejection\u00a0 of\u00a0 secondary\u00a0 electrons, abbreviated as SE:<\/p>\n<ul>\n<li class=\"no-indent\" style=\"text-align: justify\">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\u00a0 \u00a0 \u00a0in\u00a0 \u00a0 scanning\u00a0 \u00a0 electron\u00a0 \u00a0 microscopy\u00a0 \u00a0 for\u00a0 \u00a0 \u00a0morphology\u00a0 \u00a0 and\u00a0 \u00a0 surface topography.<\/li>\n<li class=\"no-indent\" style=\"text-align: justify\">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.<\/li>\n<\/ul>\n<p class=\"no-indent\" style=\"text-align: justify\">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.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">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),<\/p>\n<p class=\"no-indent\" style=\"text-align: center\"><strong>\u03b4 = N<sub>SE<\/sub>\u00a0 \/ N<sub>B<\/sub><\/strong><\/p>\n<p class=\"no-indent\">When the escape depth of SE is small (a few nanometers), all the SEs created by the beam electrons at greater depths are lost.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">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).<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>SE(I):<\/strong> 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.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>SE(II):<\/strong> 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.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>SE(III):<\/strong> Produced by high energy BSE, which strike the pole pieces and other solid objects within the specimen chamber<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-357\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/07-9.png\" alt=\"\" width=\"514\" height=\"545\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/07-9.png 514w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/07-9-283x300.png 283w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/07-9-65x69.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/07-9-225x239.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/07-9-350x371.png 350w\" sizes=\"auto, (max-width: 514px) 100vw, 514px\" \/><\/p>\n<p class=\"no-indent\"><strong>Figure 6.<\/strong> <em>Different mechanisms for generation of SE<\/em><\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>2.4.1. Factors effecting SE emission<\/strong><\/p>\n<ul>\n<li class=\"no-indent\" style=\"text-align: justify\">Work function of the surface.<\/li>\n<li class=\"no-indent\" style=\"text-align: justify\">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.<\/li>\n<\/ul>\n<p class=\"no-indent\" style=\"text-align: justify\">Electron yield goes through a maximum at low accelerating voltage\u00a0 and decreases with increasing accelerating voltage shown in Figure 7 below.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-358\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/08-6.png\" alt=\"\" width=\"881\" height=\"505\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/08-6.png 881w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/08-6-300x172.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/08-6-768x440.png 768w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/08-6-65x37.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/08-6-225x129.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/08-6-350x201.png 350w\" sizes=\"auto, (max-width: 881px) 100vw, 881px\" \/><strong>Figure 7<\/strong>. <em>Electron yield with accelerating voltage<\/em><\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">(c) Atomic number (Z)<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 More SE(II) are created with increasing Z<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">\u2022 The Z-dependence is more pronounced at lower beam energies<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">(d) The effect of surface tilt for SE<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">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).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-360\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/09-4.png\" alt=\"\" width=\"623\" height=\"378\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/09-4.png 623w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/09-4-300x182.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/09-4-65x39.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/09-4-225x137.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/09-4-350x212.png 350w\" sizes=\"auto, (max-width: 623px) 100vw, 623px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>Figure 8<\/strong>. <em>Effect of tilt on SE<\/em><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">SE can escape from both the sides of ridges and edges. These effects cause tilted surfaces to appear brighter than flat surface.<\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>2.5. Backscattered\u00a0 Electrons<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-359\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/10-3.png\" alt=\"\" width=\"608\" height=\"353\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/10-3.png 608w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/10-3-300x174.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/10-3-65x38.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/10-3-225x131.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/10-3-350x203.png 350w\" sizes=\"auto, (max-width: 608px) 100vw, 608px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>Figure 9.<\/strong><em> Backscattered electrons<\/em><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">Elastic scattering\u00a0 of the electron beam produce backscattered and transmitted electrons as the strong electrical field of the specimen\u2019s 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\u00a0 ~50\u00a0 eV up to the accelerating\u00a0 voltage (Eo). The number\u00a0 of\u00a0 backscattered electrons\u00a0 produced\u00a0 from a material may\u00a0 be\u00a0 quantified\u00a0 by\u00a0 its\u00a0 backscattering coefficient, \u03b7b.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>\u03b7b = N<sub>BSE<\/sub> \/ N<sub>B <\/sub><\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">N<sub>SE<\/sub>\u00a0 = number of secondary electrons specimen<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">N<sub>B\u00a0<\/sub> = number of beam electrons incident on the specimen.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">This coefficient depends strongly on a sample&#8217;s average atomic number, Z. BSE respond to composition allowing for atomic number or compositiona l contrast.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>2.5.1. Factors effecting BSE emission<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>(a) BSE atomic number:<\/strong> The BSE coefficient increases with increasing atomic number.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>(b) BSE beam energy:<\/strong> The BSE coefficient does not depend strongly on beam energy.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>(c) BSE tilt:<\/strong> 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\u00a0 tends toward unity)<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-361\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/11-2.png\" alt=\"\" width=\"804\" height=\"328\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/11-2.png 804w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/11-2-300x122.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/11-2-768x313.png 768w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/11-2-65x27.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/11-2-225x92.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/11-2-350x143.png 350w\" sizes=\"auto, (max-width: 804px) 100vw, 804px\" \/><br \/>\n<strong>Figure 10.<\/strong> <em>Effect of tilt on BSE<\/em><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">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.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>N(\u03c8) \u2248 N<sub>n<\/sub> cos(\u03c8)<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">For small tilt angles (Figure 10b) the distribution of BSE remains roughly symmetrical l around the surface normal.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">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\u00a0 predominance\u00a0 of\u00a0 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.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">(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 (\u03c6) relative to the norma l to the surface.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-362\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/12-2.png\" alt=\"\" width=\"668\" height=\"435\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/12-2.png 668w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/12-2-300x195.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/12-2-65x42.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/12-2-225x147.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/12-2-350x228.png 350w\" sizes=\"auto, (max-width: 668px) 100vw, 668px\" \/><strong>Figure 11<\/strong>. <em>Effect of angular distribution on BSE<\/em><\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-363\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/13-2.png\" alt=\"\" width=\"966\" height=\"332\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/13-2.png 844w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/13-2-300x103.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/13-2-768x264.png 768w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/13-2-65x22.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/13-2-225x77.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/13-2-350x120.png 350w\" sizes=\"auto, (max-width: 966px) 100vw, 966px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>3. Electron Beam \u2013 Specimen Interaction<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>3.1. <em>Interaction cross-section and mean free path<\/em><\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">The probability of a scattering event could be determined by estimating the interaction cross-section (<strong>\u03c3<\/strong>), or by the average distance of an electron trave ls between two interactions i.e. the mean free path \u03bb . Each scattering event might be elastic or inelastic interaction. Hence, the total interaction cross section <strong>\u03c3<sub>T\u00a0<\/sub><\/strong>is the sum of all elastic and inelastic terms which can be estimated by,<\/p>\n<p class=\"no-indent\" style=\"text-align: center\"><strong>\u03c3<sub>T\u00a0<\/sub>=\u00a0\u03c3\u00a0<sub>elast +\u00a0\u00a0<\/sub>\u03c3\u00a0<sub>inelast<\/sub><\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">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 (Q<sub>T<\/sub>) is given as,<\/p>\n<p class=\"no-indent\" style=\"text-align: center\"><strong>Q<sub>T<\/sub> = N\u03c3= N0\u03c3T \u00fe\/A<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">where, N<sub>0<\/sub>\u00a0 is the Avogadro\u2019s number; A is the atomic mass of the atom of density <strong>\u03c1.<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">The interaction cross-section with the sample thickness (t) is expressed as, <strong>Q<sub>T<\/sub>t = N<sub>0<\/sub>\u03c3T\u03c1t \/ A,<\/strong> and gives the likelihood of a scattering event. The term \u2018<strong>\u03c1t<\/strong>\u2019 is designated as mass-thickness. Doubling the va lue of \u2018\u03c1\u2019 leads to the same QT value, as observed after doubling the \u2018t\u2019 value. The mean free path is related to the scattering cross section by:<\/p>\n<p class=\"no-indent\" style=\"text-align: center\"><strong>\u03bb<sub>mfp\u00a0<\/sub> = 1 \/ QT<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">For the probability P of scattering in a specimen of thickness t follows then:<\/p>\n<p class=\"no-indent\" style=\"text-align: center\"><strong>P = t \/ \u03bb= Q<sub>T<\/sub>t<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>3.2. Differential cross section<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-367\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/14-1.png\" alt=\"\" width=\"417\" height=\"413\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/14-1.png 417w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/14-1-150x150.png 150w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/14-1-300x297.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/14-1-65x64.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/14-1-225x223.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/14-1-350x347.png 350w\" sizes=\"auto, (max-width: 417px) 100vw, 417px\" \/><\/p>\n<p><strong>Figure 12.<\/strong> <em>Annular distribution of the electrons scattered after passing through a thin sample. The scattering semi-angle \u0398 with incremental changes of d\u0398, and the solid angle \u03a9 for their collection (and incremental changes d\u03a9) are used to describe this process quantitatively.<\/em><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">The angular distribution of electrons scattered by an atom during the electron-specimen interaction is described by the differential cross section, d<strong>\u03c3<\/strong>\/d<em>\u03a9<\/em>. Electrons are scattered by an angle (<strong>\u03c3<\/strong>) and collected within a solid angle \u03a9 (Figure 12). The cross-section (<strong>\u03c3<\/strong>) decreases with increasing \u0398.\u00a0 Here,\u00a0 the scattering into high angles is rather unlikely.<\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>3.3. Interaction Volume<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><span class=\"tight\" style=\"text-align: justify\">The combined effect of the elastic and inelastic interactions is to limit the penetration of the\u00a0 beam into the solid. The\u00a0 region of interaction between the solid and the beam is known\u00a0 as\u00a0 the interaction\u00a0<\/span><span class=\"tight\">volume. Scattering in high angles or\u00a0 even\u00a0 backwards is unlikely in all materials but the likelihood for them increases with increasing Z.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-368\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/15-1-1024x414.png\" alt=\"\" width=\"1024\" height=\"414\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/15-1-1024x414.png 1024w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/15-1-300x121.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/15-1-768x311.png 768w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/15-1-65x26.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/15-1-225x91.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/15-1-350x142.png 350w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/15-1.png 1270w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><span class=\"tight\"><strong>Figure 13:<\/strong> <em>Interaction of an electron beam with (a) low Z and (b) high Z materials. Most electrons are scattered\u00a0 forward in the same direction undeviatedly. Beam broadening and the likelihood of large angle scattering events or backward scattering increases for higher Z.<\/em><\/span><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><span class=\"tight\">Also, the beam broadening increases with Z (Figure 13). The intensity of the direct beam is weakened by\u00a0<\/span><span class=\"tight\">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.<\/span><span class=\"tight\">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\u00a0 its absorption in the sample\u00a0 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\u00a0 the\u00a0 electrons\u00a0 increase\u00a0 with\u00a0 increasing\u00a0 electron\u00a0energy\u00a0 (voltage),\u00a0 and\u00a0 decrease\u00a0 with\u00a0 increasing\u00a0 the\u00a0 atomic\u00a0 number\u00a0 of\u00a0 the\u00a0 material\u00a0 (high\u00a0 scattering potential).<\/span><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><span class=\"tight\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-369\" src=\"http:\/\/msp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/112\/2018\/12\/16-1.png\" alt=\"\" width=\"624\" height=\"623\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/16-1.png 624w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/16-1-150x150.png 150w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/16-1-300x300.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/16-1-65x65.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/16-1-225x225.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-content\/uploads\/sites\/112\/2018\/12\/16-1-350x349.png 350w\" sizes=\"auto, (max-width: 624px) 100vw, 624px\" \/><\/span><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>Figure 14:<\/strong> <em>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.<\/em><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">For example, although secondary and Auger electrons are produced throughout the\u00a0 interaction volume, they have very low energies and can only escape from a thin layer near the sample&#8217;s surface.<\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><em><strong>3.3.1. Volume of Excitation<\/strong><\/em><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">The size and shape of the interaction volume is limited by two factors:<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">(1) energy loss through inelastic interactions<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">(2) electron loss or backscattering through elastic interactions.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">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,\u00a0 magnitude of current, the accelerating voltage, and average atomic number (Z) of the sample.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">Generally, the values of \u2018x\u2019 ranges from 1-5 \u00b5m with the beam incidenting perpendicular to the sample. The depth of electron penetration (x) is approximately,<\/p>\n<p class=\"no-indent\" style=\"text-align: center\"><strong>x (\u00b5m) = 0.1 Eo<sup>1.5<\/sup> \/ \u03c1<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">where, Eo is the accelerating voltage (in keV) and \u03c1 is the density (in g\/cm3). The width of the excited volume (y) can be approximated by,<\/p>\n<p class=\"no-indent\" style=\"text-align: center\"><strong>y (\u00b5m) = 0.077 Eo<sup>1.5<\/sup> \/ \u03c1<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><em><strong>3.3.2. Factors influencing the interaction volume<\/strong><\/em><\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>(a) Influence of beam energy on the interaction volume:<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">(i) As the beam energy is increased, the electron beam can penetrate to greater depths.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">(ii) There is no significant change in the shape of the interaction volume with beam energy<\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>(b) Influence of atomic number of the solid in the interaction volume:<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">(i) In specimens of high atomic number the electrons undergo more elastic scattering per unit distance and the average scattering angle is greater.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">(ii) In the high atomic number materials, the electron trajectory tends to deviate from the initial direction of travel more quickly.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">(iii) The shape of the interaction volume is greatly affected by the atomic number of the specimen.<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>(c) Influence of the tilt on the interaction volume:<\/strong><\/p>\n<p class=\"no-indent\" style=\"text-align: justify\">As the angle of tilt of the specimen surface increases, the interaction volume becomes smaller and asymmetric.<\/p>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>SUMMARY<\/strong><\/p>\n<ul>\n<li class=\"no-indent\" style=\"text-align: justify\">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.<\/li>\n<li class=\"no-indent\" style=\"text-align: justify\">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.<\/li>\n<li class=\"no-indent\" style=\"text-align: justify\">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.<\/li>\n<li class=\"no-indent\" style=\"text-align: justify\">Secondary electrons (low energy electrons, ~ 10 &#8211; 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.<\/li>\n<li class=\"no-indent\" style=\"text-align: justify\">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.<\/li>\n<li class=\"no-indent\" style=\"text-align: justify\">Interaction volume increases with increasing acceleration voltage and decreases with increasing the atomic number.<\/li>\n<\/ul>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Scanning Electron Microscopy<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/6DlDq8nce0Q\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p class=\"no-indent\" style=\"text-align: justify\"><strong>References<\/strong><\/p>\n<ul>\n<li class=\"no-indent\" style=\"text-align: justify\">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.<\/li>\n<li class=\"no-indent\" style=\"text-align: justify\">Practical Scanning Electron Microscopy,J.I.Goldstein, pp 49-94,Springer US.<\/li>\n<li class=\"no-indent\" style=\"text-align: justify\">Goodhew and Humphreys., Electron Microscopy and Analysis, 2nd edition., Taylor &amp; Francis, 1998.<\/li>\n<li class=\"no-indent\" style=\"text-align: justify\">Fundamentals of Scanning Electron Microscopy (SEM), pp 1-40, Weilie Zhou, Robert Apkarian, Zhong Lin Wang, David Joy, Springer New York.<\/li>\n<\/ul>\n","protected":false},"author":3,"menu_order":18,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["dr-ajit-k-mahapatro"],"pb_section_license":""},"chapter-type":[],"contributor":[58],"license":[],"class_list":["post-350","chapter","type-chapter","status-publish","hentry","contributor-dr-ajit-k-mahapatro"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-json\/pressbooks\/v2\/chapters\/350","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":9,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-json\/pressbooks\/v2\/chapters\/350\/revisions"}],"predecessor-version":[{"id":375,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-json\/pressbooks\/v2\/chapters\/350\/revisions\/375"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-json\/pressbooks\/v2\/chapters\/350\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-json\/wp\/v2\/media?parent=350"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-json\/pressbooks\/v2\/chapter-type?post=350"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-json\/wp\/v2\/contributor?post=350"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp11\/wp-json\/wp\/v2\/license?post=350"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}