# SEM and its mode of operation- continuation

Hello everyone welcome to this material characterization

course in the last class we just looked at the concept of scanning electron microscopy

functions and this basic instrumentation and its controls and operator controls and so

on we will continue this discussion and then we will look at much more details about the

electron beam specimen interactions and what is that going to affect your ultimate resolution

and its effect on main in general imaging. So if you look at the controls which I talked

about yesterday. We will just quickly review this we just started

looking at the operator control in ACM of lenses we have three primary parameters one

of them is the aperture so this schematic clearly shows that if the final aperture which

basically controls the probe diameter which finally impinge on the sample the bite controlling

this objective lens and this is what we just summarized here the optimum aperture angle

that minimizes the abrasion on the final probe size.

The final conversion angle controls the image depth of focus the aperture determines the

current in the final probe because only a fraction of the current spread out to the

angles alpha one passes within the aperture angle alpha a so if you look at this the initial

spread of current this is what you just mentioned here the current sprayed in alpha one eventually

its controls by this upper chair and then it makes alpha e this aperture angle and eventually

it controls the probe size. This is one of the primary parameters which is in control

of the operator and then we can see the next one the working distance. We also define this what is the working distance

it is the distance between the final aperture and the specimen surface and you can clearly

see this effect of working distance from these two schematics which is quite evident that

if you increase the working distance you are increasing the probe sighs you carefully look

at it you can see that the probe size is increase now and obviously it will have some significant

effect on the resolution. So we summarize this increase in working distance

produces a large spot size at the specimen and which will cause degradation of the major

solution and also you see that convergent angle decreases which will result in improved

depth of focus and increasing working distance will also cause weakening the objective to

focus at a long working distance w which eventually increases both the focal length and the aberration

of the lenses. So which is very clearly shown in this schematic

and which also increases the scan length and which will cause reduction in the magnification

as well. So this is again a very important parameter which an operator can have a control

on this and then take a appropriate decision depending upon what we are looking at what

information we are looking at on this specimen surface. The third one is the condenser lens strength

which operator can control which is also is nicely shown in the schematic if you increase

the condenser lens strength which increases the D magnification of each lens which will

cause again the reduction in the probe size so you can see that effect very clearly from

the schematic. So this is the first schematic is for a given field strength if you increase

it further you can see that the final probe size is completely reduced you can see this

is the initial probe size with for a given field strength but if you increase this from

that and you see that there is a control of the probe diameter. So the final probe size can only be reduced

at the expense of decreasing the probe current and a conscious choice between minimizing

the probe size or maximizing the probe current must be made for each imaging situation so

this is exactly I was just mentioning that all these parameter controls has to be done

as per the requirement for the appropriate information we are looking at from the specimen

and it is completely in the user control. So now we will move on to the probe diameter

which we yesterday we quickly reviewed I just want to give an emphasis on the probe diameter

again because whatever we have just seen before ultimately the parameters controls the probe

diameter which results in the complete resolution as well as and its effects on the imaging

process. So to fully understand how the probe size varies with the probe current we need

to calculate the minimum probe size and the maximum probe current say in the idealized

situation the aberration free Gaussian probe diameter d g which is the full width at half

maximum height of the intensity distribution of DG is given by DG is equal to vIP / ß

p a p2. The current in the final probe can be estimated

as I p=v ß p 2 ap2 and DG 2 / 4 if there were no abrasions in the system it would only

be necessary to increase the convergent angle to increase the probe current at constant

probe diameter see why we talked about this Gaussian probe diameter because this is the

one which we will start with to mathematically quantify assuming there is no aberrational

all but eventually that is not going to be the case you are going to have the effect

of each operations which we talked about in an electron optical system and then we can

see how this Gaussian probe diameter is modified because of this aberrations that is what we

are looking at finally is a real probe diameter. So if you look at the minimum probe size involving

all this abrasions calculations of the probe size assume that DP is quadrature some of

the diameters of Gaussian and other aberration you look at this expressions there was a little

bit of typos which was there in the histories presentation I have made the corrections you

see that DP is equal to DG where DG is Gaussian probe diameter and DA2 spherical aberration

diameter + DD2 this is a diffraction disk + DC which is chromatic aberration whole to

the power half at normal voltages sorry I just did a mistake this is not hold the power

of it is square. So DP is equal to dt square plus d square

plus d d square plus DC square voter power square at normal voltage of 10 to 30 kilo

volt the relationship between the probe size and the probe current can be calculated at

a optimum which is d minimum is equal to k CS to the power half d to the power 3 by 4

times IP by ßd2 plus 1 whole to the power 3 by 8 where CS is the spherical aberration

coefficient here only considering this abrasion this expression is valid the it is assumed

that other abrasions do not have a significant influence on that circumstances this expression

is valid maximum probe current at 10 to 30 cloveult you have the I max equal to 3 PI

square x 16 x beta into DP to the power8 by 3 divided by c s to the power 2 by3 so it

is a kind of a maximum resolution one can obtain in the presence of other operation

effects. Now we will look at the plots where the relationship

between the probe current and the probe diameter using a tungsten thermionic source you see

in the beginning we just looked at all the electron gun sources, I just mentioned there

are the two types one is thru bionic source another is field emission source. So this

how this probe current and probe diameter varies with the function thermionic source

versus the field emission sources shown in all these four plots.

You can carefully look at it this the probe diameter which is varying from 1 to 100nanometers

versus probe current it is a normal imaging condition and you can see that you have these

harmonic field I mean thermionic source and as well as you have the field emission source

obviously you can see that field emission source exhibit a superior probe diameter for

at the given 30 kilo volt which is a normal imaging and then you have another low KV imaging

you can see that similar plots are obtained and the nazi shows very low voltage imaging

where you can see that how the probe current varies with the probe diameter.

And this is kind of plot where mostly this kind of situation is used for the chemical

analysis and you can see most of this plot shows that the field emission can source exhibit

superior diameter compared to the thermionic source and then it also varies with the as

a function of operating voltage just to give you an idea how this electron sources controls

the probe diameter as a function of operating voltage we will look at this aspect in the

imaging and it under its resolution and so on in the due course. So now we will look at the much more detail

about this the probing current and so on it is useful to define the primary beam current

I not the backscattered electron current I BSE the AC current is C and the sample current

transmitted through the specimen to the ground is C such that the tech of current law holds

so the primary bream current can be s can be represented as a summation of IBS c plus

I AC plus I s SC. And we are interested in the signals which

is coming out of the samples so basically how they are quantified we know that a secondary

electron signal and the backscattered electron signals are going to come out from the sample

and how they are quantified this is what is about we will see so these signals can be

used to form a complementary images as the beam current is increased each of this currents

will also increase the backscattered electron yield ? and the secondary electron lead d

which refer to the number of back scattered and secondary electrons emitted where incident

electron respectively are defined by the relationship. Where ? is equal to i BAC that is the backscattered

electron current / I not similarly the secondary electron e d is ISE / I0. Both the secondary and backscattered electron

yields increase with decreasing glancing angle of the incidents because more scattering occurs

closer to the surface because more scattering occurs closer to the surface this is one of

the major reasons why the ACM provides an excellent topographical contrast in the SE

mode as the surface changes its slope the number of secondary electrons produced changes

as well this point we just discussed in the introduction of the SEM class as well I just

mentioned why only these two signals be SE and SE for widely used in SEM that is.

Because only these two signals vary as a surface modulation or surface slope changes very sensitive

to the surface unevenness with the backscattered electrons this effect is not as prominent

since. To fully realize it the backscattered electron

detector would have to be repositioned to realize it the backscattered detector would

have to be repositioned to measure the forward scattering this is an operation detail for

detecting this signal we will see how it is being actually done in the lab. The another important aspect of this SEM be

mentioned is a depth of focus and this set of micrograph clearly illustrate that aspect

so what you see here is at his is a machine screw viewed at under the optical microscope

and this is understanding electron microscope you can see that in an optical microscope

you do not see any of this detail when you look at this crew from the top you can see

the all the other the circular details of the screw and C and D are taken with the sides

of the screw you can see that the much more clear details are obtained using scanning

electron microscope this is just to illustrate that effect you have a very high depth of

focus. And you know by now you know that why we get very good depth of focus. The another set of micrographs illustrates

the effect of both secondary electrons as well as backscattered electrons what you are

seeing is it is a legend all I surfaces what we are seeing as bright as a new tactic let

in eutectic people who do not understand this metallurgy of this you can assume that there

are two phases and you can clearly see that this particular micrograph is obtained at

25 kV and this micrograph of the same region is obtained at 5 kV and these two are obtained

using secondary electrons and the same region was imaged using backscattered electron in

this image see. So I would like you to look at this three

images little more carefully and what is the difference you are seeing and if you are able

to figure out the differences then that means you have clearly understood the previous information

what we have discussed and if you are notable to cash that differences I will help you look

at this the scratch here scratch for here and look at this crash mark here.

So you see that these two are up to even though they are obtained using the secondary electron

signals that is a small difference and also you see that this scratch is not at all visible

as clearly as in the micrographs update by secondary electron signals so that clearly

indicates that your secondary electrons are much more sensitive to the surface unevenness

and the difference between this a and B is because of further complications because of

the electron specimen interaction what is that you see that this micrograph is obtained

at lower kv5kv and this is obtained at 25 kv.

So if you recall we just discussed in the beginning of this lecture I probably yesterday

our day for yesterday I had mentioned that the higher the operating voltage the severe

will be the beam specimen interaction and then you also produce a c1 c2 and a c3 and

these signals will get produced more if the electron beam specimen interaction is intense

and when this sc2 and AC three signals they are not going to promote the topological details

in fact when they come out of the specimen they are going to interfere and reduce the

resolution that is what is happening here. You can see that the scratch details are not

as layer as what you see in the image b, so it is not that if you keep on increasing the

operating voltage you are not you are going to obtain much more a clearer image there

is an optimum voltage and other parameters under which circumstances you get the much

more clear picture so this is just to explain that phenomenon and what you see in other

images I mean this figure D is a EDS spectrum and E and F are our maps elemental analysis

maps and this particular about the spectroscopic details we will discuss later in a separate

lecture series right. Now my focus is only on the SEM imaging we

will talk about this elemental analysis and how it is done and what are the limitations

with existing spectrometer and so on we will discuss in a separate lecture series. Now we will just summarize what we have just

looked at in the previous slide the spatial resolution of the SEM due to a c1usually improves

with increasing energy of the primary beam because the beam can be focused into a smaller

spot but at higher energies the increased penetration of the electron beam into the

sample will increase the interaction volume we will quickly see in few minutes what is

this interaction value about which may cause some degradation of the image resolution due

to AC 2 and s III s this is shown in image figure B.

Which is a secondary electron image taken at only 5 kilo electron volt in this case

the reduced electron penetration brings out more surface detailed in the micrograph. And if you look at the method of producing

the backscattered electron image there are two ways to produce v s image one is to put

a grid between the sample and the secondary electron detector with the negative voltage

that is minus 50 volt bias applied to it if you recall when I just introduced the instrumentation

schematic where I said that if you put positive voltage it will collect both BAC and SC if

you put negative voltage it will ripple and then it will correct only one.

So similar thing so that is the bias this will ripple the ACS since only the BSS will

have sufficient energy to penetrate the last electric field of the grid this type of detector

is not very effective for the detection of BSEs because of its small solid angle of the

collection, we will look at the detector system and its details little more as we go along

and this right now we are discussing about how this signals are collected and how what

are the immediate effect of these two individual signals on its image formation.

A much larger solid angle of collection is obtained by placing the detector immediately

above the sample to collect the BAC two types of detectors are commonly used here one type

uses partially depleted n-type silicon diodes coated with a layer of gold which convert

the incident BSEs into electron hole pairs at the rate of one per per3.8 electron volt

using a pair of silicon detectors makes it possible to separate the atomic number contrast

from topographic contrast the other detector type the so-called scintillator photomultiplier

detector uses a material that will fluoresce under the bombardment of the high energy BSEs

to the produce a light signal that can further amplified.

So these are all some of the specific operations of the type of detectors which eventually

give the image in the CRT we will look at this detectors separately and we will talk

about all the functions much more detail in the new course. The photomultiplier detector was used to produce

BAC micrograph in Figure see what we have just seen in two slides before since no second

electrons are present the surface topography of the scratch is no longer evident and only

anatomic number contrast appears atomic number contrast can be used to estimate the concentrations

in binary alloys because the actual BAC signal increases somewhat predictably with the concentration

of the heavier element of the pair. So this point is about the material detail

and what you have to understand this BSE is sensitive to atomic number that we will anyway

we will talk about much more detail when we discuss the image contrast and contrast mechanisms

and so on. Now we will dive at our focus to the very important aspect of imaging that

is electron beam specimen interaction in it involves lot of physics are scattering physics

we need to understand this clearly then only you will be able to interpret all the images

which we are going to see. So I would like to request all of you to pay

much more attention to look at this particular section is more fundamental it may be very

difficult to understand in the beginning but if you look at them again and again and if

you are finding it difficult to follow this I have requested you to go through some of

the basic physics book about the scattering phenomenon and then come back to this section

then things will be alright. So as the beam of electron enter the specimen

they interact as negatively charged particles with the electrical fields of the specimen

atoms the positive charge of the protons is highly concentrated on the nucleus while the

negative charge of electrons is much more dispersed in a shell structure the beam electron

specimen Adam interaction can deflect the beam electrons along the along a new trajectory

which is considered elect elastic scattering causing them to spread out laterally from

the incident footprint. I am going to show you some of the schematic

regarding this to understand the point 13 what we are now talking about so the elastic

scattering after numerous events actually result in beam electrons leaving the specimen

process called backscattering it gives a kind of a definition for the backscattering that

is the elastic scattering after numerous events actually result in a beam electrons leaving

the specimen a mathematical description of elastic scattering process at angle greater

than a specified why not as the form Q which is greater than Phi naught is equal to 1point

6 2 into 10 to the power minus 20 times z square by a square cos square p0/ 2.

So this is events scattering events greater than p0 divided by the electron which is atoms

per centimeter square where Q is called the cross-section which is in centimeter squared

for elastic scattering that is probability of elastic scattering which is given in this

form. The distance between scattering events is

known as the mean free path lambda is calculated from the cross-section and the density of

the atoms along the path when lambda is equal to a divided by n knot ? Q which is in centimeter

a beam electrons loose energy and transfer this energy in various ways to the specimen

atoms which is nothing but inelastic scattering see you see in an SEM we get the characteristic

x-rays for a chemical analysis like be discussed in the beginning the basic.

The basic fundamental physics of that event is what we are now discussing this the beam

of electron lose energy and transfer this energy in various ways so one of the ways

is like know you are getting attacked rustic x-rays and you have seized BSEs and all the

signals solve basically inelastic scattering this transfer takes place gradually. So that

the beam electrons propagate through many Adam layers into the specimen before losing

all their energy. So this the loss of energy of the electron

beam is not going to be instantaneous so it will be more I mean the you can see that how

some of the models are being made for this how the electron beam is losing energy which

I will show you in few minutes we will come that we will get an idea how the electron

beam after impinging on the specimen surface loses energy gradually as a function of interaction

volume inelastic scattering gives rise to useful imaging signals such as second electrons

and analytical signals are just such as x-rays. Method described1930 the rate of energy loss

de with the distance travelled d s as de by D s the energy is given in kilo electron volt

and the distances in centimeter which is equal to 2 pi e square n not into z Ro /AE I l on

1.66 I by j where j is equal to9.76 z+ 58.5 z to the power minus 0point 1 into 9 into

10 to power minus 3where n naught is called Avogadro’s number Rho is the density Z is

the atomic number is the atomic weight I is the electron energy at any point of the specimen

jay is the average loss in energy per event. It is just this expression simply tells you

how this energy loss takes place and how we can visualize quantitatively with all this

variables I just want you to appreciate that point rather than getting into the details

at this mode. So you can see that two plots which are based

on this be that equation how the energy loss due to an elastic scattering is calculated

you can see that plot a is energy loss in rustic scattering calculated with the Betty

equation at intermediate and high beam energies for all this elements

and the plot B is the comparison of energy loss at low energy as calculated for silicon

with methane expression and others. So how this energy loss occurs as the function of

the electron volt. Now what you are going to see is we will look

at what is this interaction volume and the electron beam comes and interacts with the

specimen surface and what you are now seeing is the assimilation is the interaction volume

for a 20 kilo electron volt beam striking the silicon as calculated with a Monte Carlo

electronic eject trajectory simulations and numerical simulation and what you see is you

see that to know there is there are thick black line and then very light black lines

with just getting inside this specimen to the order of what few microns. So this is

happening in a three dimensional. So let us try to understand how this happens

this is you can see that the another schematic showing that this kind of interaction volume

is interpreted through an etching experiment in terms of contours of the energy deposited

in the specimen as calculated with the Monte Carlo simulation. So the left hand side is

how the energy varies as a function of depth using an etching experiment what is this is

etching experiment people have taken some of the low atomic number of materials.

Like poly methyl meth cry late kind of a specimen and then they just do an etching experiment

within a bombardment of electron how it just I mean damage this molecular polymeric molecules

and then how it that the intensity of the damage decreases from the surface to the core

and that is done with that model that is called etching experiment and then the left hand

side is the experimental measurement how the energy varies from the surface to the core

in the three dimension and the right-hand side is the same thing is done numerically

through Monte Carlo simulation and then you get some kind of very close agreement with

this. So the important point to appreciate here

is you get a kind of an idea what is an interaction volume is and how it occurs three-dimensional

you know what are its dimensions, so it gives you a kind of a basic outline about an interaction

volume and please remember whatever we are now just showing is nights only a static images

and actually it is happening dynamically between the interaction between Ron beam and the surface. And I will just show you few more schematic

which you have the just excuse me it mean so I would like to

show this as a function of electron beam energy versus interaction volume you actually what

you will see that the as the electron energy increases the interaction volume also we increase

and somehow this simulation is not working right. Now so you can see that the same effect of

atomic number also you can see influence of atomic number on the interaction volume you

can see it for different material here it is a carbon and this is for a carbon case

shell. And then you have the iron and then you have the iron and case shell you can also

see that as the atomic number increases the linear dimension decreases that is a very

much understandable because the that that is because you are a scattering cross section

varies as the atomic number increases. So you can see that the linear dimension also

decreases in accordance with that number and you can see that a similar systems same effect

for a silver else shell and then you have uranium and uranium m shell and so on so what

I try to tell here is depending upon the atomic number as well as the energy of the electron

beam which is impinging on this sample your interaction volume is going to change and

the scattering physics involved is little more complicated and this has got a significant

influence on your image resolution and the kind of details one can get from the specimen

surface that is all I just want to emphasize here and then we will look at the scanning

action how this the electron beam is scanning the surface and how exactly the image is formed

all those details we will see it in the next class. Thank you.